Citation
Dynamic photosynthetic response of soybeans

Material Information

Title:
Dynamic photosynthetic response of soybeans model development and elevated COâ‚‚ experiments
Creator:
Jones, Pierce, 1946-
Publication Date:
Language:
English
Physical Description:
x, 176 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Biochemistry ( jstor )
Carbon ( jstor )
Carbon dioxide ( jstor )
Chloroplasts ( jstor )
Enzymes ( jstor )
Leaves ( jstor )
Phosphates ( jstor )
Photosynthesis ( jstor )
Starches ( jstor )
Vegetation canopies ( jstor )
Dissertations, Academic -- Mechanical Engineering -- UF
Mechanical Engineering thesis Ph. D
Photosynthesis -- Mathematical models ( lcsh )
Soybean ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1981.
Bibliography:
Bibliography: leaves 170-175.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Pierce Jones.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
028130661 ( ALEPH )
07883258 ( OCLC )
ABS1741 ( NOTIS )
AA00004905_00001 ( sobekcm )

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Full Text


DYNAMIC PHOTOSYNTHETIC RESPONSE OF SOYBEANS:
MODEL DEVELOPMENT AND ELEVATED C02 EXPERIMENTS
By
PIERCE JONES
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981


ACKNOWLEDGEMENTS
I would like to thank everyone who has helped me in my research
program. I have been very fortunate, having been surrounded by com
petent and cooperative people. In particular, I want to thank Dr. Jim
Jones who has been amazingly patient and helpful throughout my Ph.D.
program. Also I want to thank Drs. Hartwell Allen, Ken Boote and
Thomas Humphreys who have all been very generous with their time despite
their busy schedules. In addition, I want to thank Dr. G.L. Zachariah,
chairman of my committee and Drs. D. Buffington, C. Hsieh, and R. Irey
who served as members of my supervisory committee.
I would also like to express my appreciation to Bill Campbell,
Paul Lane and Kelton Johns whose skills were essential to the success
of the experimental phase of my research. Also a special message of
gratitude must go to Klaus Heimburg, Yung Le Morgan and my other friends
who went to such great lengths keeping my spirits elevated yet humble.
Finally, I do want to express my appreciation to Laura, my wife,
and to Ralph and Arlen Jones, my parents, for their excellent support
on every level. I hope that everyone who has been involved with me
during this project will somehow benefit by that association.


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
LIST OF TABLES v
LIST OF FIGURES vii
ABSTRACT ix
INTRODUCTION 1
BIOCHEMICAL PHOTOSYNTHESIS MODEL 11
The Light Reactions 12
Dark Reactions: Calvin Cycle 14
Dark Reactions: Phosphate Translocator System 16
Dark Reactions: Chloroplastic Starch Pathway 19
Dark Reactions: Cytoplasmic Sucrose Pathway 22
Simplifying Assumptions 25
Differential Equation Development 30
Carboxylation, Photorespiration and Enzyme Kinetics 35
CO2 and Op Concentration in the Stroma 40
Membrane transport Considerations 42
Competitive Inhibition of Sucrose Formation 43
Postscript on RuBP Carboxylase-Oxygenase and RuBP
Concentrations 49
Postscript on Photosynthesis-Respiration Roles of
Chloroplastic PGA 52
MODEL RESULTS 56
The Chloroplastic Carbon Dioxide Balance, [CO2] 57
Time Rate of Change of Starch 66
The Chloroplastic Inorganic Phosphate Balance, [PI] 75
The Cytoplasmic Sucrose Balance, [SUCROSE] 86
Real World Scenarios 88
Direct Manipulation; Sucrose Feeding 88
Direct Manipulation; Selective Shading 89
Temperature Manipulation 91
CO2 Concentration Manipulation 92
EXPERIMENTAL METHOD 94
Procedure 94
Physical Characteristics 96
Controlled Environmental Factors 98
Soil Respiration 103
Water 104
i i i


TABLE OF CONTENTS (contd.)
Page
EXPERIMENTAL METHOD (contd.)
Photosynthetically Active Radiation (PAR) 105
Problems 105
EXPERIMENTAL RESULTS 108
Controls 108
Carbon Balance 108
Transpiration 115
Plant Growth Parameters 118
Variations in Photosynthetic Rate 123
Physiological Responses 136
SUMMARY AND CONCLUSIONS 147
APPENDIX 1ABBREVIATIONS LISTING 153
APPENDIX 2--GL0SSARY OF TERMS 157
APPENDIX 3--UNITS LISTING 162
APPENDIX 4SYMBOL LISTING 164
APPENDIX 5PROBABLE ERROR ANALYSIS OF C0~ MASS BALANCE
MEASUREMENTS 165
BIBLIOGRAPHY 170
BIOGRAPHICAL SKETCH 176


LIST OF TABLES
Table Page
1 Calvin cycle reactions ^
2 Chloroplastic starch cycle reactions 20
3 Cytoplasmic sucrose pathway reactions 23
4 Biochemical photosynthesis model equations 44
5 Key assumptions used in model development 48
6 In vivo biochemical parameters used in model evaluation. 59
7 Mesophyll resistance values from the literature 50
8 Comparison of in vivo and in vitro biochemical parameters 64
9 Chloroplastic concentrations of key metabolites in
light and dark 67
10 Measured starch accumulation parameters 69
11 Starch accumulation as a function of inorganic phosphate
concentration 73
12 Measured chioroplastic-cytopiasmic inorganic phosphate
interactions 74
13 Adenosine diphosphate formation as a function of inorganic
phosphate levels 82
14 Final above ground biomass 124
15 Morning-afternoon photosynthetic data 126
16 Regression analysis of photosynthesis data from Chambers
1 (Low-High) and 2 (High-High) 128
17 Regression analysis of photosynthesis data from Chambers
3 (Low-Low) and 4 (High-Low) 130
18 Specific leaf weight measurements 137
19 Comparison of specific leaf weight and soluble carbo
hydrates in Chambers 1 and 4 140
v


LIST OF TABLES (contd.)
Table Page
20 Vertical distribution of leaf nitrogen 142
21 Vertical distribution of leaf chlorophyll 145
22 Vertical distribution of leaf inorganic phosphate. . 146
vi


LIST OF FIGURES
Figure Page
1 Photosynthesis and source-sink balance schematic .... 3
2 Calvin cycle schematic 15
3 Phosphate translocator system schematic 18
4 Chloroplastic starch cycle schematic 21
5 Cytoplasmic sucrose pathway schematic 24
6 PGA-DHAP pathway schematic 28
7 Simplified PGA-DHAP pathway 28
8 DHAP-G6P pathway schematic 29
9 Simplified DHAP-G6P pathway schematic 29
10 Simplified overall photosynthesis schematic 31
11 Carboxylase-oxygenase pathway schematic 38
12 Final photosynthesis schematic 47
13 Modelled [CO^l-photosynthesis-CRuBP] response curves . 62
14 Measured and modelled [^j-photosynthesis response
curves 63
15 Modelled [^l-photosynthesis response curves 65
16 Measured and modelled starch accumulation response ... 70
17 Time courses of modelled inorganic phosphate-starch
response 72
18 Measured and modelled inorganic phosphate-starch response 76
19 Comparison of chloroplastic and external concentrations
of inorganic phosphate 77
20 Comparison of carbon partitioning pathways 79
vi i


Figure Page
21 Measured and modelled inorganic phosphate-transport
response 80
22 Modelled adenosine diphosphate-inorganic phosphate
response 83
23 Measured chloroplastic PGA-inorganic phosphate response. 85
24 Measured and modelled sucrose concentration-[EXPORT]
response 87
25 Control chamber schematic 97
26 Control system schematic 100
27 Diurnal temperature control 109
28 Time courses of PAR, [CO2] and CER on April 21 110
29 Time courses of PAR, and CER on April 22 Ill
30 Photosynthetic light response curves; Chambers 1 (Low-
High) and 2 (High-High) 113
31 Photosynthetic light response curves; Chambers 3 (Low-
Low) and 4 (High-Low) 114
32 Time courses of dark respiration rates 116
33 Time courses of transpiration rates 117
34 Time courses of water use efficiency 119
35 Time courses of individual leaf areas 120
36 Time courses of leaf area index 121
37 Time courses of canopy leaf mass 122
38 Morning and afternoon photosynthetic light response;
Chambers 1 (Low-High) and 4 (High-Low) 125
39 Time courses of morning CER at 500 yE/m**2/sec 134
40 Time courses of afternoon CER at 500 yE/m**2/sec 135
41 Diurnal specific leaf weights; Chambers 1 (Low-High) and
4 (High-Low) 139
42 Comparison of carbohydrate levels and specific leaf
weight 141
43 Vertical nitrogen distribution; Chambers 1 (Low-High)
and 4 (High-Low) 144
vi ii


Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
DYNAMIC PHOTOSYNTHETIC RESPONSE OF SOYBEANS:
MODEL DEVELOPMENT AND ELEVATED C02 EXPERIMENTS
By
Pierce Jones
June 1981
Chairman: Dr. G.L. Zachariah
Major Department: Mechanical Engineering
A biochemical photosynthesis model has been developed and experi
ments at the whole plant level have been conducted in a holistic in
vestigation of photosynthetic rate controls. The model was based on
known biochemical pathways and emphasized the roles of starch, sucrose
and inorganic phosphate in the feedback control of C02 fixation. The
experimental work was designed to investigate short term rate response
to a sudden change in C02 concentration and long term physical adaptation
to distinctive environmental CO^ levels. In the experimental procedure
different source-sink balances were established for each treatment and
plant response was measured. In the model the mechanisms for source-
sink feedback control of the biochemical CC^ fixation process were
developed. The overall purpose of the work has been to demonstrate and
clarify the role played by source-sink relations in the feedback regu
lation of photosynthesis.
Comparison of model predictions with measurements from the litera
ture have shown the model's individual response equations to behave well.
IX


Overall the model demonstrated the central role of inorganic phosphate
as a regulator of the Calvin cycle via its affect on the ATP/ADP ratio
and as a regulator, partitioning CO^ between starch and sucrose syn
thesis. In turn, the concentration of inorganic phosphate was modelled
to depend inversely on cytoplasmic sucrose level which was modelled to
depend on export. By functionally linking the export of sucrose from
the cytoplasm to sink demand, the model qualitatively described the
photosynthetic inhibition and enhancement observed in a variety of
scenarios.
The experimental results showed soybeans (Glycine max c.v. Bragg)
to respond to elevated CC^ levels by increasing net photosynthesis and
respiration in the short term and increasing leaf area and biomass in
the long term. Close analysis of photosynthetic light response found
morning enhancement and/or afternoon inhibition of CC^ fixation in
plants exposed to high [CC^]. In the canopy switched to high CC^, the
magnitude of afternoon inhibition was suppressed by rapidly enhanced
sink strength. Reduced CO2 fixation corresponded to higher levels of
soluble carbohydrates in the leaves. Taken together these results
supported the proposed interdependence between leaf sucrose levels and
photosynthesis.
The experimental work showed the association between source-sink
balancing and photosynthetic rate while the biochemical model demon
strated a linkage mechanism. The differences in detail of the bio
chemical and whole plant levels prevented direct quantitative compari
sons between model and experimental results. Nevertheless the experi
mental and model results were qualitatively consistent and this work
represented a necessary effort at a holistic explanation of photosynthetic
rate regulation.
x


INTRODUCTION
All living systems in the biosphere are based directly or indirectly
on sunlight, carbon dioxide and water. Photosynthesis is the process
common to green plants that combine these elements into energy-rich
carbohydrates. Within plant systems the carbohydrates produced by
photosynthesis have two functions: first, as substrate for plant tissue
synthesis and second, as energy for the synthesis reactions. As some
of the carbohydrate building blocks are combined with nitrogen, sulfur
and other elements into plant tissue, others are respired releasing
required reaction energy.
Photosynthesis occurs in plant leaves while tissue synthesis and
respiration use carbohydrates throughout the plant structure. Carbo
hydrates are translocated from the production source in the leaves to
consumption sinks through the phloem which directly connects the photo
synthetic leaf material to active reaction sites.
More specifically, the chain of events that provides carbohydrates
for plant growth begins in microscopic organelles called chloroplasts
which are suspended in the cytoplasm of photosynthetic cells. Carbon
dioxide diffuses from the atmosphere to the chloroplasts where it is
chemically reduced in a process called the Calvin cycle, driven with
energy supplied by light. The assimilated CO^ is either converted to
sucrose in the cytoplasm, or to starch in the chloroplast, both of which
are carbohydrates. A schematic representation of this system is given
1


2
in Figure (1). The translocation system begins with the export of a
three carbon phosphorylated compound (dihydroxyacetone phosphate, DHAP)
from the chloroplast to the cytoplasm, where it is converted to sucrose,
which moves into the phloem for distribution throughout the plant.
The balance between CO^ fixation in the chloroplast and carbohydrate
export from the cytoplasm is important to photosynthetic feedback control,
but is poorly understood.
The balance between carbohydrate sources and sinks can be disrupted
by changing environmental conditions. When this happens, photosynthesizing
cells must adjust to the new circumstances. If photosynthetic rate is
increased or if transport to the phloem is decreased then excessive
amounts of carbohydrates may accumulate in the photosynthetic cells.
When this occurs starch is reversibly formed in the chloroplasts, storing
fixed carbon until it can be mobilized and shipped to the cytoplasm for
conversion to sucrose and export to the rest of the plant. If starch
accumulation continues past a certain point, cells can be physically
damaged [Noble and Craig, 1973]. It is postulated that before damage
occurs, the plant, under normal conditions, adapts by either decreasing
its rate of photosynthetic supply of carbohydrates, or by increasing
its rate of sucrose translocation and utilization.
Changes in the rate of starch accumulation have been observed in
response to many situations. For instance, when plants have been
switched from atmospheres with ambient levels of CO^ to enriched CC^
conditions, starch accumulation and photosynthesis increased dramati
cally but while starch levels continued to rise after several hours,
photosynthetic rates declined [Mauney et al., 1979]. In another
example, plants acclimated to warm nights were found to have increased


3
PAR
i
Figure 1. Photosynthes
photosynthetically acti
Appendix 1. Terms are
is and source-sink balance schematic,
ve radiation. All abbreviations are
defined in Appendix 2.
PAR is
defined in


4
starch concentrations and decreased photosynthetic rates following
exposure to low night time temperatures.
In the case of high [002] the plants mature leaves exported more
carbohydrates than they had in low [CO,,], but not enough to balance
the increased supply. Consequently, the excess was stored as starch.
In the case of low night temperatures, carbohydrates normally used
in night time growth and maintenance processes were not used due to
temperature dependent reductions in process rates. On the following day
reduced sink demand caused carbohydrate levels in the photosynthetic
cells to increase.
Observations such as these are often explained conceptually in
terms of imbalances in the source-sink relationship. Whether the car
bohydrate levels increase due to high CC^ fixation or reduced sucrose
export, the system balances itself by reducing photosynthesis. On the
other hand, when sink strength is increased and carbohydrate levels in
the photosynthetic cells decline, maximum photosynthetic rates are
observed to increase [Thorne and Koller, 1974]. Source-sink balancing
is superficially a straightforward and satisfying explanation for
alterations in photosynthetic response. Unfortunately, the details of
the proposed source-sink mechanism are not well understood.
The photosynthetic system consists of complex and interrelated
processes all of which serve to control the overall CC^ fixation rate.
In simple terms, every plant's physical and chemical environment is
continuously changing. In turn, compound levels and process rates
which determine photosynthetic rate within the plant are also changing.
In this sense, plant photosynthesis is dynamic.


5
Macroscale variations in photosynthetic capacity are a function of
nutrient availability, water supply, temperature, sunlight, 0^ concen
tration and C0,> concentration. At the cellular level, photosynthetic
capacity is a function of enzyme availability, enzyme activity and
substrate concentrations. All of these factors combine to establish
individual reaction rates, the products of which are substrates for
subsequent reactions. The integrated sum of the various reactions
control particular process rates. Finally, whole plant parameters and
biochemical processes are functionally coupled by transport systems some
of which are passive and some of which are active. In both cases con
centration gradients and transport resistances are determining factors
in the mass transport rates of substances from the environment to the
biochemical reaction sites of photosynthesis. The sum of these inter
actions determines the instantaneous rate of CO^ fixation.
This brief holistic description of photosynthesis emphasizes that
response should be considered at both the whole plant and biochemical
levels of plant organization. Modellers began trying to relate external
environmental conditions to photosynthesis as a biochemical process
thirty years ago [Rabinowitch, 1951]. Since then, a steady stream of
increasingly biochemical models has been developed [Chartier, 1970;
Charies-Edwards and Ludwig, 1974] leading to the biochemical models
proposed by Peisker [1974] and more recently by Farquahr et al. [1980].
One of the main criteria which these modellers have set is the
adequate simulation of various photosynthetic light response curves.
Usually, results from experimental work on photosynthesis are presented
graphically in photosynthetic light response curves which plot carbon
dioxide exchange rate (CER) against light level. Because of the very


6
strong dependence of CO2 assimilation on light level, the graphical
relationship between them has long been considered a fundamental measure
of response, whether research is on whole plant canopies or reconstituted
chloroplasts.
The fundamental importance of the photosynthetic light response
curve (PLRC) is further enhanced by the similar shape of most plots
generated for a wide variety of plants, which implies very similar
underlying mechanisms. Several distinct functional equations have been
proposed which generate curves of the appropriate shape [Thornley, 1976].
However, the most commonly derived equations are variations of the
rectangular hyperbola. This particular equation is scientifically
satisfying because of its theoretical basis in enzyme kinetics, where
it is called a Michaelis-Menten response curve. Because of the cyclical
enzymatic pathways which photosynthesis follows, it seems quite natural
that the rate of CO2 uptake should have a Michaelis-Menten form. The
goal for modellers has been to relate light via an assumed biochemical
pathway to CO2 uptake in such a way that external parameters could be
used to represent the variations in photosynthesis in response to light.
Photosynthesis models such as those described above are currently
used in conjunction with other crop system models to predict growth
rates and yield. These models concentrate on the uptake of CO2 in
response to light level while ignoring how or why fixed carbon is par
titioned between starch and sucrose. As a result, they work well under
normal conditions but are generally inadequate for describing response
to unusual circumstances.
It is hypothesized that partitioning between stored chloroplastic
starch and cytoplasmic sucrose is central to the feedback control of


7
photosynthesis. As noted in the examples of low night temperatures and
increased CO^ levels, starch accumulation is often reported in associa
tion with reduced photosynthetic response. To model this relationship,
starch and sucrose cannot be simply divided into unrelated pools.
Synthesis of starch and sucrose must respond functionally to mechanisms
which prescribe how fixed carbon is to be partitioned. One of the main
goals of this research has been to develop a model based on such mechanisms
To accomplish this goal a detailed photosynthesis model has been
developed, based on five specific biochemical pathways:
1. the light reactions
2. the Calvin cycle,
3. the chloroplastic starch cycle,
4. the cytoplasmic sucrose pathway, and
5. the phosphate translocator system.
The purpose of the developed model is to consider the hypothesized roles
that starch and sucrose play in the feedback control of CO^ fixation.
This is done by identifying the possible interactions among the five
pathways that could limit photosynthesis and control partitioning. From
this perspective it becomes possible to investigate the complex rela
tionship between biochemical dynamics and the ambient environment. Such
a detailed model can also be used to suggest how the photosynthetic
system might respond in the long term to different prevailing environments.
At the whole plant level field experiments were conducted concurrently
with the development of a biochemical photosynthesis model. The experi
mental work was designed to investigate short term response to a
sudden change in (X^ concentration and long term adaptation to distinctive
environmental CO2 levels. All of the treatments were exposed to constant
moderate air temperatures under well-fertilized and well-watered conditions


8
The experiments were conducted under natural sunlight which varied, but
all treatments were exposed equally to these changes.
To assess the plant-environment interactions four general classes
of data are required: (1) external parameters such as temperature,
quantum flux density and CO^ concentration which define the environment;
(2) gas exchange rates such as transpiration, daytime CC^ exchange and
night time CC^ exchange which define water use, photosynthesis and
respiration rates; (3) whole plant parameters such as height, leaf area
and biomass which are indicators of adaptive response; and finally,
(4) physiological parameters such as specific leaf weight, chlorophyll
levels and nitrogen levels which are indicators of biochemical system
response. The short and long-term adaptive response of plants to a
particular sequence of prevailing environments can be characterized in
terms of these four data sets.
At the biochemical level the experimental results can be applied to
questions concerning substrate levels and process rates on the micro
scale. For instance, the data can suggest how CO^ level effects chloro
phyll concentrations and enzyme levels (as a function of nitrogen) as
well as CO2 fixation process rates. On a larger scale the data can
indicate how source-sink balancing is affected by CO2 concentration
through the measurements of diurnal specific leaf weight and by the
instantaneous measurements of photosynthetic light response. Finally,
at the whole plant level, biomass accumulation and leaf area are direct
measures of the integrated adaptive response of whole plants to different
CO2 environments.
The experimental work was designed to provide the data necessary
to answer these questions. With these data, the hypothesis that plants


9
adaptively respond to different prevailing environmental concentrations
of CO^ can be tested. Furthermore, the adjustments that occur at the
whole plant level and the biochemical level can be considered separately,
to determine whether the adaptation of the whole plant is consistent with
biochemical level response.
Combining the experimental results with the biochemical photosynthesis
model, a qualitative explanation of short-term feedback controlled
response and long-term whole plant adaptation to prevailing CO^ concen
trations is proposed. This proposed mathematical-conceptual model pro
vides a framework for both a short-term model to explain inhibition and
enhancement of photosynthetic light response and a long-term model of
adaptation to differing environments.
The overall purpose of this research is based on the concept of
photosynthetic adaptation which has been defined as environmentally
induced adjustments in physiology, anatomy and morphology that allow a
plant to improve photosynthetic efficiency in a new environment [Bjorkman
and Berry, 1973]. Stated another way, adaptation enables whole plants
to maximize photosynthetic productivity under locally prevailing envi
ronmental conditions [Tooming, 1970]. The purpose of this research is
to gain a more complete understanding of photosynthesis as a dynamic
process at both the whole plant and biochemical levels.
It is postulated that plant canopies will adaptively respond to
different prevailing environmental concentrations of carbon dioxide. In
particular, this project has been designed to describe and explain the
responses of soybean canopies grown continuously in different carbon
dioxide concentrations during their vegetative stage of growth and the


10
subsequent short and long-term canopy responses to a step change in CO^
levels. The experimental objective of the research has been to grow
and monitor soybean canopies in four computer controlled, closed environ
mental chambers. A parallel theoretical objective has been to develop a
biochemical level model of photosynthesis. Finally, the third objective
of the research has been to qualitatively relate the whole plant experi
mental observations and the biochemical model within the conceptual
framework of source-sink balancing.
The long range goal of this research is to devise a physically based
dynamic model of photosynthesis complete with feedback controls. Such a
model could be used with other sub-system models to describe any whole
plant system. In turn individual plant models are the basis of crop
models which have increasingly wide application.


BIOCHEMICAL PHOTOSYNTHESIS MODEL
Photosynthesis is commonly modeled [Lehninger, 1970] as a process
in which carbon dioxide (CO2) and water ^0) are chemically combined
in the presence of light quanta (nhv) to form glucose (CgH^Og) and
oxygen (O2). In equation form this is expressed as:
(1)
6 CO2 + 6 H2O + nhv -* CgH^Og + 6 O2 + heat
Note that mass is conserved explicitly in the equation stoichiometry,
whereas energy is implicitly conserved by equating light input (nhv) to
the chemical energy in glucose (CgH^Og) and the energy degraded to
heat. It is useful to rewrite equation (1), replacing the light quanta
term (nhv) with an associated free energy change (aG).
6 C02 + 6 H20 -* C6H-|206 + 602
aG= 686 kcal/mole (2)
This emphasizes that in the formation of glucose, light is not a sub
strate, but rather, indirectly supplies the energy to drive this
"uphill" reaction. Finally, a third equation can be written to make
the obvious point that carbonated water exposed to sunlight will not
produce glucose and oxygen. CO2 and water must pass through an exten
sive series of biochemical cycles and pathways before being transformed
into glucose; therefore, equation (1) might be written once again:
(3)
11


12
In the following sections, some of the details of the photosynthetic
blackbox will be discussed, simplified and condensed into a mathematical
model.
The Light Reactions
When photosynthesis is considered in detail, equation (1) is seen
to incorporate two chemical processes which are coupled into the total
system by which glucose is formed. Light is required in an initial
process in which photosynthetically active radiation (PAR) is converted
into chemical energy via excitation of chlorophyll and accessory pigment
molecules. These initial reactions are called the Light Reactions. PAR
is electromagnetic radiation with wavelength between 400 and 700 nm. It
is usually measured with a quantum sensor and typical units are micro-
Einsteins/m**2/sec. PAR quanta are absorbed by a diverse group of pig
ments located in the chloroplasts of photosynthesizing cells. The most
commonly known and abundant pigment is chlorophyll, of which there are
several kinds that differ slightly in structure and absorption spectrum.
Chlorophyll is the main light absorbing pigment in green plants. When
plants are exposed to PAR, quanta are absorbed, causing high energy
electrons to escape from the excited pigment molecules. Some of these
electrons fall back to ground state and the chlorophyll molecules give
up their captured quanta as fluorescence and heat. Others leave the
chlorophyll completely and enter an electron-carrier pathway, flowing
down an energy gradient from one carrier to the next. When an electron
moves through this transport system, it loses potential energy at each
transfer between carriers. At certain of the transfers in the chain,
the potential drop is partially conserved by driving the energy requiring
phosphorylation of adenosine diphosphate (ADP) to adenosine triphosphate


13
(ATP). Two quanta are absorbed for each electron to move through the
complete pathway. In this manner light-induced electron flow is con
verted to chemical bond energy. The process is called photophosphory
lation and can be represented by the following equation:
ADP + P + nhv -* ATP + heat, (4)
where P is inorganic phosphate.
Only part of the photoinduced potential is used to produce ATP. Most
of the conserved electrochemical energy goes to the last acceptor in the
chain, which is the oxidized form of nicotinamide adenine dinucleotide
phosphate (NADP) which receives the electron as well as a proton and is
accordingly reduced as the final step in the light reactions, This pro
cess of using photoinduced electron flow to yield a reduced product is
called photoreduction. Equation (4) can be expanded to represent the
overall light reaction, including both photophosphorylation and photo
reduction as follows [Lehninger, 1973]:
2 ADP + NADPqx + 2 P + 2 hv + H20
+ NADPre(j + 2 ATP + ^02 + heat. (5)
With this more detailed understanding, equation (1) can be rewritten
again to clarify the relationship between PAR as an energy source and
the glucose formation equation. It is
6 NADPred + 6 H20 + 12 ATP + 6 C02
-* C6H1206 + 6 NADPqx + 12 ADP + 12 P + 6 02 (6)
Equation (6) describes an overall process which has been only briefly
outlined. More complete descriptions of the light reactions are avail
able in articles by Rabinowitch and Godvinjee [1965] and Zelitch [1979].


14
Dark Reactions: Calvin Cycle
The biochemical pathway to sucrose following the light reactions is
referred to as the Dark Reaction. A central portion of this process is
the Calvin Cycle, which occurs in the chloroplast, along with the light
reactions. The first step in the Calvin cycle is the reduction of C02
(the carboxylation reaction). Specifically, the reaction combines C02,
H20 and ribulose-1,5-bisphosphate (RuBP) in the presence of the enzyme
ribulose-1,5-bisphosphate carboxylase (RuBPc) to form 2 molecules of
3-phosphoglyceric acid (PGA). In equation form it is
H20 + C02 + RuBP 2 PGA AG = -8.4 kcal/mole (7)
RuBPc
Equation (7) is an exergonic or downhill reaction having a negative
standard free energy change [Bassham, 1971] and, therefore, requires no
energy or reducing power to proceed. Although not directly required in
equation (7), the light reaction's products (ATP and NADP^ecj) drive the
complex sequence of enzyme catalyzed reactions called the Calvin cycle,
which regenerates RuBP [Bassham, 1971].
In the second reaction of the Calvin cycle, ATP is directly required
for the phosphorylation of PGA, producing the high energy phosphate com
pound 1,3-biphosphoglyceric acid (BPGA):
PGA + ATP -> BPGA + ADP. (8)
The reducing power generated by the light reaction is utilized in the
subsequent step as follows:
BPGA + NADP + GAP + P + NADP (9)
red ox vy
where GAP is glyceraldehyde-3-phosphate. The only other reaction in


15
Figure 2. Calvin cycle schematic. RuBP, ribulose-1,5 -bisphosphate, RuP;
ribulose-5-phosphate; XMP xylulose-5-phosphate; SDMP, sedoheptulose-1-
phosphate; SDBP, sedoheptulose-1,7-bisphosphate; EMP erythrose-4-phosphate;
FMP, fructose-6-phosphate; FBP, fructose-1,6-phosphate; DHAP, dihydrox-
yacetone phosphate; GAP, glyceraldehyde-3-phosphate; BPGA, 1,3-phospho-
glyceric acid; PGA, 3-phosphoglyceric acid. All abbreviations are listed
alphabetically in Appendix 1 (Based on Bassham [1971]).


16
the Calvin cycle directly using the products of the light reaction is
step 13 in Table (1), in which ribulose-5-phosphate (RuP) is phosphory-
lated to RuBP:
RuP + ATP RuBP + ADP. (10)
The preceding three equations summarize the direct interaction
between the Calvin cycle and the light reactions, while equation (7)
represents the all important link between the microscale biochemical
pathways and the macroscale carbon exchange rates.
Dark Reactions: Phosphate Translocator System
Both the light reactions and the Calvin cycle occur in chloroplasts
while the final steps in the dark reactions take place in the cytoplasm,
requiring that the carbon fixed in equation (7) be exported through the
outer chloroplastic membrane. The primary export product is dihydroxy-
acetone phosphate (DHAP) [Heber, 1974], which is produced in reversible
equilibrium with GAP as the fourth step in the Calvin cycle. For this
pathway to function continuously, cytoplasmic phosphate must be imported
to the chloroplast in direct proportion to the exported DHAP. The
exchange is part of the phosphate translocator system. DHAP is a crucial
intermediate which is balanced among three pathways: export for use as
substrate or energy in the cytoplasmic dark reactions, continuation in
the Calvin cycle as substrate for regenerating RuBP, or to storage as
starch in the chloroplast. A schematic is given in Figure (3) to
clarify these relationships. The other portion of the system imports
PGA from the cytoplasm in exchange for chloroplastic inorganic phosphate
[Kelly et al., 1976]. The importance of maintaining phosphate balances
is clear, considering its role in energy transfer and storage. Once


17
Table 1. Calvin cycle reactions (H^O not shown).
Step
Substrate
Enzyme
Product
1
6 C02 + 6 RuBP
RuBP carboxylase
12 PGA
2
12 PGA + 12 ATP
PGA kinase
12 BPGA + 12 ADP
3
12 BPGA + 12 NADP ,
red
GAP dehydrogenase
12 GAP + NADP
ux
4
5 GAP
Trise phosphate isomerase
5 DHAP
5
3 GAP + 3 DHAP
Aldolase
3 FBP
6
3 FBP
FBP dekinase
3 FMP + 3 P
7
2 FMP + 2 GAP
Transketolase
2 XMP + 2 EMP
8
2 EMP + 2 DHAP
Aldolase
2 SBP
9
2 SBP
Phosphatase
2 SMP + 2 P
10
2 SMP + 2 GAP
Transketolase
2 RMP + 2 XMP
11
2 RMP
Isomerase
2 RuP
12
4 XMP
Epimerase
4 RuP
13
6 RuP + 6 ATP
Phosphoribulokinase
6 RuBP + 6 ADP
Note: Reactions are taken from Lenhinger [1970].


18
BPGA
7
GAP
CYTOPLASM
NADPred
NADPox
Figure 3. Phosphate translocator system schematic. Outlines the
membrane exchange mechanism by which fixed carbon is exported from
chloroplasts to cytoplasm for sucrose synthesis. All abbreviations
are identified in Appendix 1 (Based on Heber [1974]).


19
DHAP is in the cytoplasm, it can be utilized as a substrate in the
sucrose pathway or it can be oxidized and dephosphorylated by the
reverse reactions of equations (9) and (10). In this way the energy
equivalents of ATP and NADP^ are transported to the cytoplasm. When
used for energy transfer, the DHAP is converted to PGA, which can be
transported back to the chloroplast [Herold and Walker, 1979].
Dark Reactions: Chloroplastic Starch Pathway
In the chloroplast, the starch pathway is cyclical, moving from
DHAP to starch, and later being reconverted to DHAP. The intermediate
steps have been worked out in detail and are presented in Table (2).
The cycle actually moves through steps (5) and (6) of the Calvin cycle
in which fructose-1,6-bisphosphate (FBP) is irreversibly converted to
fructose-6-phosphate (FMP), which enters the starch pathway, forming
glucose-6-phosphate (G6P). The rate limiting step in starch formation
is the reaction in which ATP combines with glucose-l-phosphate (G1P) to
form ADP-glucose. This reaction is not only promoted by high levels of
ATP, but also by high levels of PGA, and is inhibited by high levels of
inorganic phosphate [Kaiser and Bassham, 1979]. The return starch
mobilization reactions follow the same essential pathway, except that
the rate limiting step is the energy requiring conversion of FMP to
FBP. This reaction obtains energy and a phosphate group from ATP, while
simultaneously being inhibited by high levels of ATP.
The system behavior described acts as a regulator encouraging starch
storage during the day and release at night. Also note that energy units
are required in both the formation and breakdown of starch. A schematic
of this cycle is given in Figure (4).


20
Table 2.
Chloroplastic
starch cycle reactions.
Step
Substrate
Enzyme
Product
1
DHAP + GAP
Aldolase
FBP
2
FBP
Dekinase
FMP + P
3
FMP
Phosphohexoisomerase
G6P
4
G6P
Phosphoglucomutase
G1P
5
G1P + ATP
Pyrophosphorylase
ADP-glucose + P
6
ADP-glucose
Amyl ose synthetase
Starch
7
Starch + P
Glucan phosphorylase
G1P
8
G1P
Phosphoglucomutase
G6P
9
G6P
Phosphohexoisomerase
FMP + ADP
10
FMP + ATP
Phosphofructokinase
FBP
11
FBP
Al dolase
DHAP + GAP
Note: These reactions are based on Lehninger [1970] and Kelly et al.
[1976].


21
ADP
Figure 4. Chloroplastic starch cycle schematic. Outlines the starch
storage and remobilization mechanism by which chloroplast can store fixed
carbon. All abbreviations are listed in Appendix 1 (Based on Kelly et
al. [1976]).


22
Dark Reactions: Cytoplasmic Sucrose Pathway
The other carbon balancing pathway is to the cytoplasm, where DHAP
is the initial substrate leading to sucrose formation. In a series of
steps similar to those in starch formation, DHAP is converted to glucose-
1-phosphate (G1P). At this point, sucrose formation diverges from the
starch pathway. Instead of the common energy compound ATP, G1P combines
with uridine triphosphate (UTP) to form UDP-glucose. This compound
reacts with FMP to form sucrose-6-phosphate (SMP), which directly yields
sucrose. One important aspect of this pathway is that the reaction rate
of the SMP conversion to sucrose may be subject to product inhibition
[Hawker, 1967]. Sucrose is the primary sugar compound exported from
photosynthesizing cells. If the export of sucrose is less than its
synthesis, then cytoplasmic levels will increase. When this happens,
the high concentration of sucrose potentially inhibits the enzyme that
dephosphorylates SMP, causing a buildup of its concentration and a cor
responding decrease in the level of inorganic phosphate. This pathway
is detailed in Table (3), and a schematic is presented in Figure (5).
Another point to consider is that uridine triphosphate (UTP) formation
is driven by ATP, and that the roles of these compounds in carbohydrate
formation are very similar.
In review, equation (1) is seen to represent substrate and energy
fluxes into the photosynthetic blackbox on the left hand side and product
fluxes out of the system on the right hand side. To better understand
this equation, the blackbox has been described in terms of five sub
systems :
1. the 1ight reaction
2. the Calvin cycle
3. the phosphate translocator system
4. the chloroplastic starch cycle
5. the cytoplasmic sucrose pathway


23
Table 3.
Cytoplasmic sucrose
pathway reactions.
Step
Substrate
Enzyme
Product
1
DHAP + GAP
Aldolase
FBP
2
FBP
Dekinase
FMP + P
3
FMP
Phosphohexoisomerase
G6P
4
G6P
Phosphoglucomutase
G1P
5
G1P + UTP
Pyrophosphorylase
UDPG + PP
6
UDPG + FMP
Phosphosynthetase
SMP + UDP
7
SMP
Phosphatase
Sucrose + P
Note: PP
Lehninger
is an abbreviation
[1970] and Kelly et
for pyrophosphate. Reactions
al. [1976].
are based on


24
Figure 5. Cytoplasmic sucrose pathway schematic. Abbreviations are
defined in Appendix 1 (Based on Lehninger [1970] and Kelly et al.
[1976]).


25
From the schematics and equations given to describe these processes,
the fluxes in equation (1) are plainly visible. The light reactions use
captured quanta (nhv) to drive the hydrolysis of water (H^O), which sup
plies electrons for use in the reduction of NADP and simultaneous forma
tion of ATP. Oxygen (0^) is liberated as a by-product of hydrolysis.
These interactions are described in equation (5). Carbon dioxide (CC^)
enters the system reacting with RuBP to form the first products in the
Calvin cycle, according to equation (7). Fixed carbon is transported
from chloroplast to cytoplasm where sucrose is formed and exported from
the cell. Some fixed carbon is temporarily stored in the chloroplast as
starch and later is transported to the cytoplasm, where it also forms
sucrose. The model development emphasizes the feedback regulation of
the carbon flow paths into and out of the photosynthetic cell.
Simplifying Assumptions
As can be seen from the preceding tables and schematics, there are
a large number of intermediates involved in each subsystem. In the model
being developed, the concentration of intermediates fluctuates in response
to net flow. It is assumed that keeping track of each intermediate pool
is not necessary because of the serial nature of the processes. To aid
in determining which intermediates should be retained, mediating enzymes
have been grouped according to their characteristics as given by Kelly
et al. [1976], Heber [1974] and Lehninger [1970]. Essentially, all bio
chemical reactions on the cellular level are catalyzed enzymatically, each
enzyme may or may not be inhibited or promoted by any other compound or ion.
Enzyme, product and substrate groups are also unique in their degree of bio
chemical reversibility, which will vary with pH and other factors. In short,
reactions can range from very simple reversible flow between two proportionate


26
pools to irreversible reactions which are highly sensitive to a range of
inhibitors and promoters. For purposes of modelling, it is essential to
sort out the reactions which may be crucial rate limiting and path
selecting points from those that are not. Four criteria have been
devised to sort out the significant interactions in each subsystem.
The first simplifying criterion is that nonallosteric enzymes can be
ignored and that reversible path reactions between a substrate pool and
a product pool can be condensed into a single representative tank. An
excellent example of this situation is the fourth step in the Calvin
cycle, in which DHAP and GAP quickly reach an equilibrium because of
the continuous availability of active enzyme [Lehninger, 1970].
DHAP t GAP aG=1.0 kcal/mole (11)
In modelling this portion of the Calvin cycle, no distinction needs to
be made between these trise phosphates; the presence of one implies
the presence of the other in some approximately constant ratio. Since
DHAP has a significant role in path selection, the representative
storage pool is referred to as DHAP.
The second criterion extends the conditions of the first to include
nonal!osteric reactions which require energy or reducing units. The
second Calvin cycle reaction fits these requirements.
PGA + ATP t BPGA + ADP aG=4.5 kcal/mole (12)
In the chloroplast exposed to light, ATP levels are high and equation (12)
can be expected to have a net flow to the right, while in the dark, the
flow will reverse direction (see postscript on PGA).
The third Calvin cycle reaction is similar to the second, requiring
reduced NADP to proceed from BPGA to GAP. The reactions described so far


27
under the first and second criteria are modelled schematically in
Figure (6), using "Energy Language Symbols" developed by H.T. Odum [1971]
There are four predominate symbols used: the tank which symbolizes the
concentration of a metabolite in the reaction medium; the interaction
symbol which relates substrates and/or allosteric effectors; the circle
which represents an unlimited flow source, and the interaction arrow,
which shows the explicit path taken (see Appendix IV).
Looking at Figure (6), BPGA and GAP can be consolidated into a flow
path between PGA and DHAP which is moderated by the levels of ATP and
NADPrec|. The process can be further simplified by assuming that reducing
power and energy units come from the same source in a reasonably constant
ratio. Hence, if ATP is available, then NADP^ should also be available
The condensed model is shown schematically in Figure (7).
A third criterion treats the class of nonallosteric reactions which
have products. An example is the dephosphorylation of FBP to form FMP
and inorganic phosphate, P, which occurs in the Calvin cycle as well as
the cytoplasmic sucrose pathway. This process can be modelled schemati
cally as in Figure (8). The assumption is that tanks can be condensed,
but the product P cannot be ignored. FBP can be absorbed into the DHAP
tank and FMP can be absorbed into the G6P tank according to the first
criterion, while P must flow to an inorganic phosphate tank. The simpli-
ifed schematic version is in Figure (9).
The fourth criterion dealswith allosteric rate limited reactions
by controlling flow between pools with elements that sense reaction
inhibitors and/or promoters. In the starch forming reaction, step 6 in
Table (2), the enzyme is inhibited by inorganic phosphate (P) and pro
moted by the intermediate, PGA [Kaiser and Bassham, 1979]. So, even


28
Figure 6. PGA-DHAP pathway schematic. Explicit equations are listed
in Table (1).
Figure 7. Simplified PGA-DHAP pathway. All abbreviations are listed
in Appendix 1. (Symbols are defined in Appendix 4.)


29
Figure 8. DHAP-G6P pathway schematic. Explicit equations are in
Table (2).
Figure 9. Simplified DHAP-G6P pathway schematic. All abbreviations are
defined in Appendix 1. (Symbols are defined in Appendix 4.)


30
though these compounds are not substrates in the reaction, they must be
included in some form to control the reaction.
The application of these criteria to the five subsystems results in
the simplified model shown schematically in Figure (10). As shown below,
the schematic can be used to generate differential equations by doing
simple mass flow balances into and out of each tank.
Differential Equation Development
The interaction symbol between tanks indicates a simple algebraic
process involving the concentrations of reactants and a rate constant.
The level of PGA1 in the chloroplast is expected to vary according to
d^A1-l = 2k [RuBP] [C02] + k2 [PGA2] [PI] k3 [PGA1] [ATP1]. (13)
The first term on the right hand side of equation (13) represents
an addition to the PGA1 pool resulting from the reduction of C02 which
is represented as a function of the concentrations of C02 and RuBP as
moderated by the rate constant k^. The 2 is a numerical constant stoich-
iometrically required to maintain the system's carbon balance. The
second term is the phosphate translocator flow of PGA from the cytoplasm
to chloroplast as a function of [PGA2] and [PI], multiplied by the rate
constant, k^. The third term is the Calvin cycle forward flow to DHAP,
a function of [PGA1] and available energy units, [ATP1]. Notice that
the third term embodies the assumptions outlined in Figures (6) and (7).


31
Figure 10. Simplified overall photosynthesis schematic. In the inter
action symbols the k values are reaction rate constants. The divisor
sign implies inhibition. Numbers following intermediates separate
chloroplastic (1) from cytoplasmic (2) pools. All abbreviations are
defined in Appendix 1. (Symbols are defined in Appendix 4.)


32
Other equations derived from the schematic are
d|~dT~ = k3 [pGA1^ [ATP11 + 2k4 [STARCH3 [pH (14)
- k.n [DHAP1] [ATP1] kc [DHAP1] [P2]
IU o
- kg [DHAP1] [PGA1] [ATP1]/[Pl]
d[sTARCH] = ^ [DHAP]] [PGA1] [ATP1]/[Pl] (15)
- k4 [STARCH] [PI]
= k5 tDHAP13 Cp2l (16)
- k? [DHAP2] [ADP2] kg [DHAP2] [ATP2]/[SUCROSE]
~^P'dt'2^ = k7 ^DHAP2^ EADp2] k2 [PGA2] [PI] (17)
d[SUCR0SE] = ¡-DHAp2j [AjP2]/[SUCR0SE] [EXPORT] (18)
d_[R_uBp] = 3/5kio [DHAP1] [ATP1] [RuBP] [C02]. (19)
In addition to DHAP and PGA, separate tanks in chloroplast and
cytoplasm are maintained for ATP, ADP, and P. Their differential
equations are


33
d[ATPll = k [LIGHT] [ADP] [PI] (20)
at y
- k3 [PGA1] [ATP1] k4 [STARCH] [PI]
- k. [DHAP1] [PGA1] [ATP1]/[P1]
o
- k1Q [DHAP1] [ATP1]
d[ADPl ] d[ATPl ]
dt dt K
= k5 [DHAPI] [P2] + 2k6 [DHAP1 ] [PGA1] [ATP1]/[P1] (22)
- k4 [STARCH] [PI] k2 [PGA2] [PI]
- kg [LIGHT] [ADP] [PI]
d-^P2-l = k? [DHAP2] [ADP2] (23)
- kg [DHAP2] [ATP2]/[SUCROSE]
d[ADP2] ^ -d[ATP2] (24)
dt dt
= k2 [PGA2] [PI] + 2kg [DHAP2] [ATP2]/[SUCR0SE] (25)
- kg [DHAPI] [P2].
Some terms require numerical constants in order to maintain the system's
carbon and phosphate balances.


34
Most of the terms in these equations are concentration driven in
the sense that higher substrate or cofactor levels increase the proba
bility of a reaction. Allosteric effects should be distinguished; in
equation (14), the last term, PGA1, behaves like the substrate DHAPl, but
its effect is to promote the enzyme which catalyzes the reaction. In the
same term, PI acts to allosterically inhibit the process rate. The
algebraic form of the inhibitory effect is arbitrary in this equation.
Different responses could be obtained with different algebraic arrange
ments. Without in vivo response curves, a very simple feedback response
has been chosen.
In the schematic given in Figure (10), the components of equation (1),
which flow into and out of the blackbox, are each treated differently.
This reflects certain assumptions about the paths which each input and
output to the photosynthesizing system must follow. The source of the
PAR is represented schematically as a circle rather than a tank, since
the absorption of quanta has no effect on the rate of quanta arriving at
the active site. In contrast, C02 is a tank placed inside the chloroplast,
implying that concentration of available CC^ is affected by the rates of
CO^ arrival and exit at the active site. Water is ignored, since it is
always present in abundance for chemical reaction, even when the plant is
under water stress. Oxygen which is liberated in the chloroplast is also
ignored because it has only a minor impact on the high levels of 0^
already present due to diffusion from the atmosphere. Finally, sucrose
(carbohydrate) is exported according to some arbitrary function with a
dependence on sucrose concentration.
The most glaring shortcoming of the model developed so far involves
the first step in the Calvin cycle. This is the rate limiting reaction
for the entire system. As such, it must be considered in more detail.


35
A second major omission from the model is the competitive oxy
genase reaction, photorespiration, which is closely related to the first
Calvin cycle step, the carboxylase reaction.
Carboxylation, Photorespiration and Enzyme Kinetics
As described in equation (1), the first reaction in the Calvin cycle
is the fixation of CC>2, which can be abbreviated for purposes of a
Michaelis-Menten style analysis to the following
C02 + RuBP 2 PGA. (26)
RuBPc
Water has been eliminated since it is always at saturation levels
and does not affect the reactions rate. In competition with this reac
tion is photorespiration, which can be written as
02 + RuBP 3/2 PGA + 1/2 C02. (27)
RuBPo
Equation (27) is not strictly chemically correct as written. Actually,
phosphoglycolate is a product of this reaction that goes on to produce
C02 and PGA, which are products of interest in this model. Both of
these reactions utilize the same enzyme, called ribulose bisphosphate
carboxylase (RuBPc) in equation (26) and ribulose bisphosphate oxygenase
(RuBPo) in equation (27). In addition, both reactions require the same
second substance, RuBP, which is often assumed to be at saturating con
centrations [Jensen et al., 1978], allowing it to be ignored, like water.
With this assumption, both reactions above can be approximated by first
order processes which can be analyzed with enzyme kinetic theory.
Consider the reactions to be occurring in a well mixed medium, with
concentrations of carbon dioxide substrate, [C02] oxygen substrate,


36
[02] ribulose bisphosphate substrate [RuBP] and activated ribulose
bisphosphate carboxylase-oxygenase enzyme (E). Assume that the enzyme
reacts with either CO^ or O2 as a function of the activated enzyme's
relative affinity for the two substrates and the temperature adjusted
relative concentrations of the two substrates. Under the assumption that
RuBP can be ignored because it is at saturation levels, the carboxylation
reaction equations are
C1
E + C09^= EC09 (28)
C2
C5
EC02 * PGA,
where C2 and are reaction rate constants, and EC02 is the enzyme
substrate complex. These equations can be manipulated to yield a
Michaelis-Menten equation of the following form:
V c =
Vcmax [C02]
[C02] + Kc
(29)
where Vc is the rate of substrate C02 utilization, Vcmax is the maximum
rate of substrate C0o utilization and K is the concentration of sub-
2 c
strate C02 that will sustain the reaction at 1/2 the maximum rate. The
corresponding equation for the oxygenase reaction is
Vomax [0?]
V0= t-02J +K (30>
where the variables are analogous to those in the preceding equation.
Given that both of these "first order" reactions use the same enzyme and
assuming that neither substrate affects the affinity of the enzyme for


37
the other, they can be treated as a classic case of competitive inhi
bition. The resulting equation for carboxylation which includes this
competitive effect is
Vco
Vcomax [C02]
rc02j + Kc (1 + L02J/Kq)
(31)
If RuBP is not assumed to be at saturating levels and is included in
the analysis, the carboxylation equations must be expanded to include
an intermediate reaction as follows:
E + C02 ^ ECO,
c3
EC02 + RuBP £ EC02RuBP
EC02RuBP C5 E + PGA ,
(32)
where C2 and are reaction rate constants and EC02RuBP is a second
stage substrate-enzyme complex. Assuming that each substrate combines
with its specific site without either substrate affecting the enzyme's
affinity for the other, then the carboxylation equation is
Vcr = Vcrmax
[co2]
V.
[RuBP]
[C02] + Kc y^LRuBPJ + K,
(33)
As before, parallel development yields the following oxygenase equation
Vor = Vormax
[o2]
[02] + Ko
(.. ..LRuBPJ )
^[RuBP] + Kr y
(34)
These relationships describe the flow rates among the reactant and
product pools as shown in Figure (11).


38
Figure 11. Carboxylase-oxygenase pathway schematic. This schematic
models the competition by 0^ and CC^ for RuBP. The numbers represent
stoichiometric balances for each path and the new interaction
symbol represents a Michaelis-Menten function.


39
From the equations developed, it is postulated that the rate of
photosynthesis is a function of the substrate concentrations within the
stroma. The carboxylase reaction is regulated by the concentration of
CC>2 at the reaction site, while the oxygenase reaction is a function of
C>2 concentration and both processes depend on the RuBP level. Since both
pathways draw on the available supply of RuBP, the steady state level is
lowered, which effectively depresses both reaction rates [Canvin, 1978],
The effect of this analysis on the model is to change the functional
form of the flows among the tanks involved in the first Calvin cycle
reaction. This involves the differential equations for PGA1 and RuBP,
which are numbers (13) and (19), respectively. Instead of the simple
algebraic product of concentrations, equations (33) and (34) are used
to model flows from the RuBP tank and to the PGA tank. The new balance
equations are
d[PGAl]
dt
2 Vcrmax
+ k2 [PGA2] [PI]- k3 [PGA1] [ATP1]
(35)
d[RuBP]
dt
= k]0 [DHAP1] [ATP1]
(36)


40
Note that in equation (35), the first term on the left hand side is
multiplied by a factor of two. This is consistent with the stoichiometry
of equation (7), in which one mole of RuBP is oxidized by one mole of
C02 to yield 2 moles of PGA. In the oxygenase reaction, the factor is
3/2. It remains to consider the pools of C02 and 02 in the stromal
compartment [Hall and Bjorkman, 1975; Bruin et al., 1970].
COq and 02 Concentration in the Stroma
Ambient levels of C02 are unaffected by the flux to an individual
leaf and can be treated as an unlimited source, while the carboxylation
reaction in the leaf's chloroplast acts as a sink. The effect is to
create a concentration gradient between the ambient source and each
chloroplastic tank. Between source and sink, there are resistances,
some of which are more constant than others. The primary resistance
to C02 flux in terrestrial plants such as soybeans, is caused by the
stomates, which respond to a variety of factors, such as light, leaf
water potential and C02 concentration. For stomatal response in this
model, water stress is ignored, light level is treated as an "opening"
switch, and C02 concentration does not affect resistance. Under these
assumptions, the daytime cellular C02 concentration, [C02J^, is treated
as a constant for any given ambient CC>2 level [Wong et al., 1979]. The
diffusion of C02 from the intercellular space, through the cell wall,
through the cytoplasm, through the chloroplastic membrane and into the
stroma, is the process of interest. In some previous models, this
process has been approximated by assuming a C02 concentration of zero
at the active site [Chartier and Prioul, 1976], and solving for a
"mesophyll resistance," which is a conglomerate of various membrane,
photorespiration and carboxylation effects. In this model, the reduction


41
of C02 is assumed to take place in the well mixed fluid compartment
of the chloroplast, the stroma, which has an average CO^ concentration
[C02] The resistance to diffusive transport between the intercellular
space and the stroma is the sum of the two membranes and the intervening
cytoplasmic fluid, which is defined as membrane resistance, Rm. This
process is modelled as simple diffusion transport, using the equation
CER
[co2]. [co2]
Rm
(37)
Using estimated values for Rm [Charies-Edwards and Ludwig, 1974],[CO2]
can be defined in terms of CER, which is the carbon dioxide exchange rate.
A second source of stromal C02 is the oxidation of phosphoglycolate
(PGly) shown in Figure (11). According to work done by Bruin et al. [1970],
one mole of oxygenated RuBP produces 3/2 moles of PGA and 1/2 mole of C02.
The input to the stromal C02 tank due to photorespiration can be written
as a fraction of equation (34). The rate of export from the C02 tank is
equal to the carboxylation rate in equation (33). Using these equations
as well as equation (37), a differential balance for the stromal CO^
concentration can be written as follows:
d[C02] [C02]. [C02]
dt Rm
+ 2 Vormax
[09]
[RuBP]
1 Vcrroax
\L02J + K0^LRuBPJ + Kr<
/ [C02] W [RuBp] ^
^i.C02J + Kc J I L'RuBPJ + Kr J
(38)
The oxygen concentration at the reaction site within the chloroplast
is a function of diffusion from an unlimited ambient reservoir where


42
its absolute concentration is 700 times greater than [CO^]. In addition,
0^ is being supplied in the thylakoids, where the light reaction is
splitting water faster than the oxygenase reaction can remove it.
Deviations from equilibrium with air levels of oxygen caused by the last
two processes are assumed to be damped out by the diffusion process.
Oxygen concentration is assumed to be in constant equilibrium with ambient
levels (21% at 1 atmosphere) [Sinclair et al., 1977].
Membrane Transport Considerations
During analysis of model results, a two-substrate Michaelis-Menten
function describing the exchange of DHAP1 for P2 was found to correspond
to empirical results much better than a first order function (see Figure
21 ). Therefore, the term
k5 [DHAP1] [P2]
used in equations (14) and (16) has been replaced by the following:
There is ample theoretical basis for modelling membrane transport with a
Michaelis-Menten function [Epstein and Hagen, 1952].
A second assumption has been made simply for the sake of convenience.
The modelled exchange of PI for PGA2 has been found to be a relatively
small term on a functional basis. Further, direct measurements of this
particular process have not been made. Thus, with no direct data on
process rate or how it may be altered by chloroplastic or cytoplasmic
conditions, the term is too arbitrary to remain in the model. The term
k2 [PGA2] [PI]


43
is assumed to be small and without recognized control significance;
therefore it has been dropped from equations (13), (17), (22), and (25).
Competitive Inhibition of Sucrose Formation
As with membrane transport, the formation of sucrose was not well
modelled as a first order reaction. During model analysis it was found
that sucrose formation could be realistically modelled as a Michaelis-
Menten function of [DHAP2] competitively inhibited by [SUCROSE]. There
fore, the term
kg [DHAP2] [ATP2]/[SUCR0SE]
used in equations (16) and (18) has been replaced by the following:
Vdsmax [DHAP2]
[DHAP2J + Kd2 (1 + [SUCROSE]/Ks) *
The basis for modelling sucrose formation this way is provided by the
results obtained by Hawker [1967]. Those results indicated that the
conversion of sucrose phosphate to sucrose is regulated by competitive
inhibition of the mediating enzyme by sucrose itself. Since information
on [ATP2] is so limited, it has not been included in the new term.
The modelled system of equations as altered by the assumptions in
the preceding three sections is listed in Table (4). A final schematic
representation of the model as described by the system of equations is
given in Figure (12). In addition, a listing of major assumptions
involved in the model's development are listed in Table (5).
During model development many explicit and implicit assumptions
were made. In the following postscripts two important central assumptions
are considered in detail. The first is an explicit assumption about


44
Table 4. Biochemical photosynthesis model equations.
d[PGA1] o Vcrma ( [C2] \( [RuBP] ^ (391
dt \rc02J + Kc J l FRuBFJ + Kr J {^}
3 f ^2^
+ 2 Vormax
- k3 [PGA1] [ATP1]
d[DHAPl]_ = [PGA1] [ATPl] + 2k4 [STARCH] [PI] (40)
- k1Q [DHAP1] [ATP1] kg [DHAP1] [PGA1] [ATP1]/[PI]
- Vtemax ( [dhaptT+V) ([P2]2i kp)
dlSTARCI = [-DHAplj [PGA1] [ATP1 ]/[PI ] (15)
at o
- k4 [STARCH] [PI]
d[DHAP2] 1(J l [DHAP1 ] \ { [P2] \
dt = Vdpni3X ^[DHAPl] V Kd~) [ [P2] + Kp j (41}
- k? [DHAP2] [ADP2]
Vdsmax [DHAP2]
" [DHAP2J + Kd2 (1 + LSUCROSEJ/Ks)
_d_[PGA2] = k [DHAP2] [ADP2] (42)
[RuBP]
[RuBPJ + Kr
d[SUCR0SE] is Vdsmax [DHAP2]
dt LDHAP2J + Kd2 (1 + LSUCR'OSE J/Ks)
(43)
- [EXPORT]


45
Table 4. (contd.)
d[.R.u|P] = |k^Q j-DHAplj [ATP1]
- Vcrmax
[co2]
[RuBP]
LCOJ + Kc / l[RuBPJ + Kr
[o2]
- Vormax ^ ^j"+ Ko j ^RuBPJP+ Kr^
d^Yt^ = kQ ^LIGHT^ [ADP11 [pil
k3 [PGA1] [ATP 1] k4 [STARCH] [PI]
kc [DHAP1] [PGA1] [ATP1]/[PI]
0
k]Q [DHAP1] [ATP1]
d[ADPl] = d[ATPl]
dt dt
d[pl] = VdDmax ( [DHAP1] \ I [P2]
dt Vdpmax ^DHApj + Kdy^LP2j + Kp
+ 2kg [DHAP1] [PGA1] [ATP1]/[P1]
kg [LIGHT] [ADP1] [PI] k4 [STARCH] [PI]
d[ATP2]
dt
= k7 [DHAP2] [ADP2]
Vdsmax [DHAP2]
LDHAP2J + Kd2 (1 + [SUCROSEJ/Ks)
d[ADP2]
dt
d[ATP2]
dt
(36)
(20)
(21)
(44)
(45)
(24)


46
Table
d[P2]
dt
d[C02]
dt
(contd.)
2 Vdsmax [DHAP2]
[DHAP2] + Kd2 (1 + [SUCROSE]/Ks)
Vdomax (. tDHAP1J ^ (. ^P2] \
- Vdpmax ^|_DHAP1j + Kd I ^LP2J + Kp )
(46)
= ([C02]i [C02])/Rm
1
Vormax
[o2]
[RuBP]
L09J + Ko j \[RuBPJ + Kr,
- Vcrmax
[co2]
[RuBP]
LC02] + KcJ V L RuBP J +
Kr
(38)


47
CHLOROPLAST
[EXPORT]
Figure 12. Final photosynthesis schematic. This is a schematic repre
sentation of the equations in Table (4) and the assumptions in Table (5).
The new rounded interaction symbol indicates a Michaelis-Menten response.
All abbreviations are defined in Appendix 1.


48
Table 5. Key assumptions used in model development.
1. Intermediate biochemical compounds that are not at path selecting
points and do not allosterically affect enzyme activity levels can
be ignored.
2. RuBP carboxylase-oxygenase is assumed to have a constant activity
level which can limit overall CO^ fixation rate.
3. Starch and sucrose formation pathways are regulated by allosteric
control of enzyme activity levels which can be functionally expressed
as concentrations of inhibitors and enhancers.
4. Concentration of CO^ in the intercellular space is a constant
function of external CO^ concentration.
5. Concentration of in the chloroplast is assumed to be in equilibrium
with ambient 0^ level which is constant at a partial pressure of
210 mbar.
6. The dark reactions all take place in the stroma of the chloroplast
which is treated as a well-mixed reaction tank with uniform
concentrations throughout.


49
the enzyme kinetics of RuBPc-o and the second is an implicit assumption
about the thermodynamically uphill nature of the Calvin cycle. These
discussions help to demonstrate the ever-present perils of modelling
as well as the insights to be gained from modelling.
Postscript on RuBP Carboxylase-Oxygenase and RuBP Concentrations
Enzyme kinetic theory which was used in the last section to derive
the Michaelis-Menten style relationships for photosynthesis and photo
respiration relies implicitly on certain assumptions about the behavior
of an enzyme.
In the carboxylase reaction described in equation (32), it was
assumed that RuBPc had a constant activity level over the range of cir
cumstances for which the analysis applies. More precisely, the well-
stirred reaction tank (stroma) is assumed to have a fixed quantity of
enzyme, which is either tied up as an enzyme-substrate complex, or is
available for reaction. The available portion is expected to have a
certain affinity for the various substrates which is unaffected by
conditions inside the reaction medium. Recent work suggests that these
assumptions may not be applicable to RuBPc-o.
It is well established that the activity level of RuBPc-o, measured
in vitro, is highly variable [Bassham et al., 1978]. Until recently,
these measurements gave Michaelis-Menten constants which were consistently
too high to account for associated photosynthetic rates. It has now been
established that, if the enzyme is preincubated in the presence of CO^
and Mg++, then the activity levels in vivo reaction rates can be obtained


50
[Bahr and Jensen, 1978]. Even under these circumstances, the high
activity rate can only be maintained for a short period of time.
Based on their work, Jensen et al. [1978], have suggested that the
enzyme exists within the intact chloroplasts in a range of active states
which are regulated by the pH and Mg++ ion concentration. The chloro-
plast can be divided into two compartments, the stroma and thylokoid.
When exposed to light, a proton gradient is established between these
compartments which raises the pH in the stroma. In counter flow to the
hydrogen ions moving out, Mg++ ions move from the thylakoid to the
stroma. Thus, during the day, the enzyme's activity is enhanced and in
the dark it is deactivated. In support of this hypothesis, Bassham
et al. [1978] found that a stable pool of RuBP is maintained by chloro-
plast in the dark. This is surprising in view of the extremely negative
standard free energy change associated with the carboxylation reaction
(aG -8.4 kcal/mole). If the enzyme were active, the reaction would
certainly proceed rapidly and irreversibly. Although this evidence
seems compelling, very recent work by Robinson et al. [1979] indicates
that, in vivo, the activity level changes only slightly. Clearly, the
issue is controversial.
This raises the question of whether or not the postulated dependence
of photosynthesis on the concentrations of CC^, RuBP and is only
partially true. Does the changing pH of the reaction medium alter the
enzyme's turnover rate enough to affect the photosynthetic light response
curve? Do the assumptions put forth in the various biochemical-empirical
models actually predict biochemical observations? An example may clarify
the situation.


51
For a Cg plant under ambient levels of C02 320 vpm), Wong et al.
[1979] have found that, regardless of light level, the intercellular
level of CO2 is constant 250 vpm). Also, assume that Rm which is
the CO2 diffusion resistance associated with cell walls, membranes,
cytoplasm and chloroplast stroma, is between 1 and 5 sec/cm [Tenhunen
et al., 1977]. Then, rewriting equation (37), the stromal concentration
of C02 can be solved for any given carbon dioxide exchange rate, CER.
[C02] = [C02]i CER Rm (44)
Let CER1 = 1 g/m**2/hr,
CER2 = 5 g/m**2/hr and
Rm =2 sec/cm.
Then [C02] 1 = .28 gC02/m**3^192 vpm
[C02] 2 = .06 gC02/m**3^41 vpm.
The estimated stromal C02 concentration decreases by a factor of
4.67 for a five fold increase in the carbon exchange rate (CER). Assume
that the carboxylation reaction rate, Vcr, changes in the same proportion
as CER, then using standard chemical kinetics to estimate the relative
concentrations of RuBP
[RuBP]l Vcrl [C02] 2
[RuBP]2 Vcr2 "[C02]1 '
The calculation yields 47.9 times more RuBP in case 2 than in case 1.
Using enzyme kinetics as in equation (33) would yield an even larger
ratio.
This analysis seems reasonable, at saturating light levels C02
becomes limiting while ATP and NADPrecj levels are high, allowing for


52
very rapid replacement of RuBP used, thus RuBP 1evels are high while
CO^ levels are low and vice versa. This conclusion is completely incon
sistent with the biochemical literature. Jensen et al. [1978] found that
the RuBP pool sizes in isolated chloroplasts were approximately the same
under 25 microEinsteins/m**2/sec and 800 microEinsteins/m**2/sec, even
though the carbon exchange rate was 5 times higher under high light.
Bassham et al. [1978] found that the RuBP pool size did increase with
decreasing [CO2] in reconstituted spinach chloroplasts. [RuBP] concen
tration increased by 1/3 when CO2 was decreased from 202 vpm to 116 vpm.
Neither of these experiments were done on whole leaves, but the dif
ference in results observed and predicted with the equations above is
striking.
At present, the mechanistic nature of the enzyme RuBPc-o is not
well enough understood to be included in the model. When sufficient
data are available,it can be included by functionally adjusting Kc, Kr,
Ko, Vermax and Vormax to light level, or any other relevant parameter.
In the meantime, this exercise will illustrate the potential of modelling
biochemical pathways of photosynthesis, but unresolved complexities
should serve as a reminder of the limitations of this model.
Postscript on Photosynthesis-Respiration Roles of Chloroplastic PGA
Control over the photosynthetic rate may be directly related to the
dual purposes served by the first few reactions of the Calvin cycle. The
reversible nature of these reactions was briefly discussed in applying
simplifying assumptions to equations (16). The direction of these
processes is a function of straight forward thermodynamic considerations.
In this model, the direction of this sequence of chemical reactions is
not in question, since "forward" reactions predominate during photosynthesis.


53
However, the thermodynamic requirements that determine the net direction
of a reaction are manifested in the concentrations of the reactants. The
resulting dynamic balance among the various biochemical intermediates
has been postulated to be a central control mechanism regulating photo
synthetic rate [Walker and Robinson, 1978]. The following discussion
describes the thermodynamics involved and demonstrates how equation (8)
is affected.
The first product of photosynthetic CO^ reduction is 3-phosphoglyceric
acid (PGA), which, through three subsequent steps yields DHAP at the
expense of one unit each of ATP and NADPrec|- This process is shown
schematically in Figure (5) and the specific equations are numbers 1
through 4 in Table (1). The requirement for light generated energy
units in this sequence implies that the pathway is "uphill." Recog
nizing that the reactions are reversible and that the reverse "downhill"
reactions form part of the oxidative glycolytic pathway [Kelly et al.,
1976], the situation becomes even more intriguing.
During the daytime, when absorbed light energy is abundant, the
chloroplasts are autotropic, photosynthetically forming energy rich
carbohydrates, some of which are exported to the heterotrophic cytoplasm
and some of which are stored in the chloroplasts as starch. In the
dark, the chloroplasts, like the rest of the cell, are heterotrophic
and must obtain energy by breaking down carbohydrates. Thus, in the
light the "uphill" energy pathways predominate, while at night, the
"downhill" energy releasing paths are activated. PGA and DHAP are both
intermediates in both the "uphill" Calvin cycle and the "downhill"
glycolytic pathway.
The choice of which pathway is active can be shown by rewriting
equation (8):


54
PGA + ATP BPGA + ADP aG = +4.5 Kcal
(8)
For a reaction to occur, the free energy change (aG) must be negative.
Such reactions are termed exergonic. Chemical reactions with a positive
free energy change are termed endergonic and will not occur without
energy input. Qualitatively, the free energy change is the fraction of
total energy change which is available to do work as the system proceeds
toward equilibrium, in accord with the second law of thermodynamics. For
this reaction, the free energy change (aG) is a function of the law of
chemical equilibrium (or the mass action law) which simply states that
in a system at chemical equilibrium, the concentrations of reactants
and products will be such that the following expression holds:
[BPGA]
[ADP]
LPGA]
LATP'J
where Keq is the equilibrium constant.
Free energy change is related to the above relationship as follows:
aG + aG + RT 1 n
[BPGA] [ADP]
[PGAJ [ATP] 5
where R is the universal gas constant, T is absolute temperature and aG
is the standard free energy change. At equilibrium conditions for a
given temperature, free energy is minimized (entropy is maximized),
allowing for no further change in free energy (aG = 0). Therefore, the
standard free energy is expressed as
AG = -RT In (Keq).
The net reaction direction, therefore, depends on the concentrations
of products and reactants at a particular time. Since the standard free


55
energy for this reactionis a positive 4.5 Kcal, the balance of concen
trations must be such that
Kcal/mole
if the forward reaction is to proceed. At 25 C the required concen
tration balance can be calculated for the Calvin cycle to predominate;
the ratio of reactants to products must be
The ratio ATP/ADP is reported to be in the range of 1 to 10 [Heber, 1974];
therefore, the ratio of PGA to BPGA is expected to range between 2000
and 200. Thus, the chloroplastic levels of BPGA under lighted conditions
are expected to be very low [Walker and Robinson, 1978]. This conclusion
is consistent with the relative abundance of data on the PGA concentra
tion and the almost total lack of data on BPGA levels.
In summary, when chloroplasts are exposed to light, the Calvin cycle
pathway providing RuBP for C0^ reduction is enzymatically activated,
rapidly leading to production of PGA. As the concentration of PGA
rapidly increases and the balance of ATP to ADP responds to the balance
of light levels and bioenergetic requirements, the "forward reaction" is
quickly established and photosynthesis proceeds. Concentrations and
flow between tanks quickly reaches a quasi-steady state which is a func
tion of all the factors affecting the balance of intermediates such as
light driven regeneration of ATP. These various factors have been
incorporated into the model and are analyzed in the following results
section.


MODEL RESULTS
The biochemical photosynthesis model outlined in Figure (12) and
Table (4) is functionally complete. Given a complete set of data, it
would be possible to do computer simulations without further assumptions.
However, the data set required would be extensive, precise and subject
to wide variations from one set of conditions to another. In an effort
to circumvent this problem and to evaluate the model's behavior, a
series of simple flow situations have been posed, based on partial data
sets and supplemental assumptions. Measured substrate and product
fluxes and concentrations of intermediates given in the literature have
been used to analyze specific tanks within the model for consistency
with the real world.
This section emphasizes the feedback interdependence of the entire
system, which expresses itself in control of the photosynthetic rate.
At the biochemical level a steady flow system is established in response
to external conditions, such that intermediate concentrations are adjusted,
partitioning between starch storage and sucrose is delineated and net
carbon uptake is fixed. The analysis centers on the flows of CO^ into
and out of the modelled system. The analysis begins with the modelled
CO^ balance, followed by the starch balance, the partition regulating
phosphate balances and,finally, the sucrose balance. Working forward
along the photosynthetic carbon pathway through each of these key tanks,
the response of each balance equation is evaluated. By considering how
56


57
the modelled tank balances compare to measured concentrations under
differeing steady flow situations, the model's usefulness can be tested.
The Chloroplastic Carbon Dioxide Balance, [CO,-,]
The CO^ concentration balance in the stroma of the chloroplast is
described in the model by equation (38):
- Vcrmax
[RuBP]
L RuBP J + K
5
where the right hand terms represent fluxes due to diffusion, photo
respiration and photosynthesis, respectively. Under steady flow condi
tions, the chloroplastic CO^ concentration is in steady state and
equation (38) can be written as follows:
[C02]i [C02]
Rm
[RuBP] \
[RuBP J + Krj
Vcrmax [CO^]\
W+nW
-| / Vormax [02]\
2("[op-nr-j
(47)
The equation has been rearranged so that each side equals the net flux
of ambient CO^ into the chloroplasts, referred to as net photosynthesis
or the carbon dioxide exchange rate (CER). Thus the following two equa
tions can be written as:
CER
CER
[co2]. [co2]
Rm
[RuBP] \r/Vcrmax [C02])
LRubpj + k(,j Ihcty + \'c j
1 f Vormax [0o] \
2VL02J + Ko /
(37)
(48)


58
Equation (48) involves eight biochemical parameters on the right hand
side, all of which have been measured and reported under a variety of
circumstances with variable credibility. The parameter values to be used
in the following analysis are listed in Table (6). It is useful to
recognize parameters in Table (6) as two separate groups. The first
group includes Kq, Vormax, Kc, Vcrmax and Kr, which are assumed constant,
although that depends entirely on the constancy of the activity of the
enzyme, RuBPc-o. The second group, [02] [CO^] and [RuBP], is assumed
to vary, although under real world conditions, [C^] is approximately
constant.
By rearranging equation (48), the values in Table (6) can be used
to solve for [CC^] as follows:
[co2] =
= 128 vpm .
For the specific experimental treatment presented by Heldt et al. [1977],
the [CO^H is 128 vpm or 4.3 pM dissolved CC^. As a check on the value,
equation (47) can be rearranged to solve for Rm.
Rm = ([C02]. [C02]) / CER = 1.84 sec/cm
The value obtained compares well with Rm values found by various inde
pendent researchers. Several values are presented in Table (7) for
comparison.


59
Table 6. In vivo biochemical parameters used in model evaluation.
Biochemical
Parameter
In Vivo Value
Reference
[CO2]a
320 vpm
Wong et al. [1979]
[CO2]i
230 vpm
Wong et al. [1979]
Kc
230 vpm
Bahr and Jensen [1978]
Vcrmax
300 pmol C^/mg chl/hr
Farquahr et al. [1980]
[o2]
210 mbar
Sinclair et al. [197 ]
Ko
330 mbar
Farquahr et al. [1980]
Vormax
80 pmol 02/mg chl/hr
Kent and Young [1980]
[RuBP]
280 pM
Heldt et al. [1978]
Kr
30 pM
Bassham et al. [1978]
Note: This table contains recent approximation-measurements of the
various parameters in equations (47) and (48). The term in vivo
refers to the functioning living plant; such values are not necessarily
constant when biochemical systems are reproduced outside the functioning
plant, in vitro. Abbreviations are in Appendix 1.


60
Table 7. Mesophyll
resistance values
from the literature.
Mesophyl1
Resistance
Crop
Reference
6.8 sec/cm
Bean
Chartier et al. [1970]
2.3 sec/cm
Wheat
Ku and Edwards [1977]
2.9 sec/cm
Cotton
Jones and Slayter [1972]
Note: This table contains suggested Rm values for Cg plants as
determined by independent researchers. These values^compare favorably
with the value obtained using Table (6) in vivo parameters.


61
As a first analysis of the model sensitivity, a series of CER vs
[CO^] response curves at various constant RuBP concentrations have been
generated while [0^] is constant at 210 mbars. Since both RuBP and CO^
are substrates in the carboxylation reaction, it is expected that to
increase either one will increase photosynthetic rate. As shown in
Figure (13), the modelled responses are consistent with reported CER
responses to CO^ concentrations.
In a more specific test of the model's sensitivity, equation (48)
is used to generate CER from 6 pairs of RuBP and CC^ concentrations for
comparison with data obtained by Bassham et al. [1978] in experimental
work with reconstituted spinach chloroplasts. When the values in Table
(6) are used, the results are greatly shifted. Recognizing that RuBP
c-o activity is certainly reduced in vitro, values for Vcrmax and Vormax
were lowered to 140 pmol CC^/mg chl/hr and 28 umol 02/mg chl/hr, and K£
increased to 400 vpm. With the modified biochemical constants, the
comparison between modelled and measured values is quite good.
The characteristic behavior of the simulated CER response to [CC^]
is consistent with the in vitro data of Bassham et al. [1978]. In addi
tion, the magnitude of the simulated response was similar to those results.
Simulated and measured values are compared in Figure (14).
The effect of photorespiration can be examined by varying the level
of 02 for different fixed values of [CC^] and [RuBP]. Results are
graphically presented in Figure (15). The trends predicted for changing
O2 values are consistent with general observations. Higher levels of
oxygen increase the rate of photorespiration and decrease the carbon
dioxide exchange rate.
The results of the modelled initial fixation of carbon are generally
consistent with empirically observed behavior. Moving forward through


CER, mg/dm**2/hr
62
Figure 13. Modelled [CO]-photosynthesis-[RuBP] response curves. CER
is modelled in units of mg CC^ fixed/dm**2 leaf area/hour at four
different fixed concentrations of RuBP. [C^] is assumed to be in
equilibrium with an atmospheric partial pressure of 210 mbar.


CER, ymol C0?/mg chl/hr
63
Figure 14. Measured and modelled [C0?]-photosynthesis response curves.
Graphs compare measured values from Bassham et al. [1978] with values
from the model. The measured values were obtained in vitro. Therefore,
in vitro rate constants listed in Table (8) were used to obtain the model
values. The difference between the curves is in the K values. For the
dashed curve Kc equals 400 vpm. The other curve has a Kc value of 230 vpm.


64
Table 8. Comparison of in vivo and in vitro biochemical parameters.
Biochemical
Parameters
In Vivo Values
In Vitro Values
Kc
230 vpm
400 vpm
Vcrmax
300 pmol CO^/mg chl/hr
140 ymol ^/mg chl/hr
Ko
330 mbar
330 mbar
Vormax
80 ymol 02/mg chl/hr
37 ymol 02/mg chl/hr
Kr
30
30
Note: In vitro values are primarily from Bassham et al. [1978] and
in vivo values are from Table (6). All abbreviations are defined in
Appendix 1.


CER, ymol COp/mg chl/hr
65
Figure 15. Modelled [CL]-photosynthesis response curves. For the solid
lines [RuBP] is constant at 280 yM. For the dashed line [RuBP] is
280 yM for the left most value and 50 yM for the right most value. Since
increased [O2] increases the competition for RuBP its level is expected
to decline as in the dashed lines.


66
the model, fixed carbon is partitioned between paths leading to export and
to storage in the starch tank. Although it represents a relatively
small fraction of carbon fixed, starch formation rate and concentration
are highly visible barometers of shifting biochemical balances within
photosynthetic cells. As such, it is the next model compartment for
consideration.
Time Rate of Change of Starch
As an initial test of the starch balance predicted by the model in
equation (15), fluxes to the starch tank under light and dark conditions
have been considered. Since starch has been widely observed to accumu
late during the day and to be remobilized in the dark [Heldt et al.,
[1977], equation (15) should show a net flux into the starch tank under
lighted conditions and net export in the dark. Rewriting equation (15)
d[STARCH] = [DHAP1] [ATP1] [PGA1 ] / [PI]
- k4 [PI] [STARCH] (15)
the first term on the right hand side is the functional rate of starch
formation and the second term is the rate of mobilization and export of
starch. There are five variables and two constants to be considered in
solving for the starch flux, d[STARCH]/dt. Although these variables
are dynamic, changing rapidly in response to external conditions, they
tend to have fundamentally different values under light and dark condi
tions. Table (9) lists relative values suggested from the literature
for some of the variables.
With these values, the rate of starch formation term would be a
factor of 20 lower in the dark than in the light, while the starch


67
Table 9. Chloroplastic concentration of key metabolites in light and
dark.
Metabolite
Light
Dark
Reference
[PGA1]
4.0 mM
1.6 mM
Kaiser and Bassham [1979]
[DHAP1]
.4 mM
.4 mM
Kaiser and Urbach [1977]
[PI]
3.0 mM
12.0 mM
Kaiser and Bassham [1979]
[ATP 1 ]
2.0
1.0
Heber [1974
Note: Recently measured-approximated concentrations of metabolites
important to starch formation and remobilization. The values for
ATP1 are relative numbers only.


68
mobilization term would be 4 times higher in the dark than in the light.
Equation (15) predicts that, in the light, starch formation will predomi
nate, while in the dark, starch will be exported. This result is con
sistent with observed empirical behavior.
If the variables [DHAP1], [ATP1], [PGA1] and [PI] are assumed to be
constant, the starch balance can be written as
d[STARCH] = A B [STARCH] (49)
where A = %kg [ATP1] [DHAP1] [PGA1] / [PI] and B = k^ [PI]. This equation
can be integrated to yield
[STARCH] = A (l-e-Bt)/B (50)
which is valid as long as A and B are constant. Linder steady flow con
ditions, intermediates are at least roughly in steady state. In experi
mental work done by Upmeyer and Roller [1973], soybean seedlings were
grown under constant conditions: saturating light, 300 vpm CO^, 25 C
and 60% relative humidity. Artificial lighting was switched on for 16
hours and off for 8 hours every day. Their data indicated that, from four
hours after the lights were switched on until twelve hours later, the CO^
2
exchange rate (CER) was constant at 34 mg/dm /hr. These conditions
approximate a steady flow state; therefore, the variables A and B can
be assumed constant.
Measurements of starch flux and concentration taken directly from
Upmeyer and Roller's data can be plugged into equations (49) and (50)
to solve for A and B. Values are given in Table (10).
The predicted values of [STARCH] based on Table (10) values of A and
B are plotted graphically with the experimentally measured values in
Figure (16).


69
Table 10. Measured starch accumulation parameters.
Hours Under
Constant Light
d[STARCH]
dt
[STARCH]
4
4.25 mg/dm**2/hr
25.5 mg/dm**2
12
.87 mg/dm**2/hr
46.0 mg/dm**2
A = 8.45 mg/dm**2/hr
B = .16 hr-1
Note: Values are from graphical data presented by Upmeyer and Koller
[1973]. These values are used to calculate parameters A and B from
equation (49).


70
O
25
H 1 H 1 1 1
2 4 6 8 10 12
Hours at Constant Light
Figure 16. Measured and modelled starch accumulation response. Measured
values are from Upmeyer and Koller [1973].


71
Since the level of chloroplastic inorganic phosphate [PI] is
proportional to starch mobilization and inversely proportional to
starch formation, it is the primary functional mechanism affecting the
starch accumulation rate. To determine how changes in [PI] affect
[STARCH] a proportionate family of constants was calculated.
The ratio A/B is numerically equivalent to the maximum predicted
concentration of starch. The curves resulting from the five sets of
constants are given in Figure (17).
The general trend predicted by the set of curves in Figure (17) is
consistent with observations that starch accumulation is increased as
inorganic phosphate levels are decreased. In experimental work com
paring starch levels in phosphate deficient plants and phosphate rich
plants, starch concentrations were as much as 10 times higher in the
plants deprived of phosphate [Herold et al., 1976]. The starch levels
predicted and graphed in Figure (17) mimic these observations, ranging
over a factor of approximately 10.
A more realistic analysis of the model's starch balance must con
sider the other variables [DHAP1], [PGA1] and [ATP1] in addition to
inorganic phosphate [PI]. The regulatory role played by the precise
mix of these variables can be explored in more detail by using a set of
data in which the chloroplastic level of [PI] was held at four differing
quasi-steady state levels. Heldt et al. [1977] manipulated [PI] levels
in a suspension of chloroplasts by controlling the level of inorganic
phosphate in the medium external to the chloroplasts. This is equiva
lent to controlling [P2] in the model. Experiments were short term, 10
minutes and all external variables such as light, temperature and pre
treatment of chloroplasts were the same for each [P2]. Pertinent data
from the experiments are listed in Table (12).


[STARCH], mg/dm**2
72
Figure 17. Time courses of modelled inorganic phosphate-starch response.
[P1]r is the relative concentration of chloroplastic inorganic phos
phate. It is equal to the normalizing ratio [Pl]n/[P1]3 given in Table 11.


73
Table 11.
Starch accumulation as a function
concentration.
of inorganic
phosphate
n
[PI ]n/[P1]3
An
mg/dm**2/hr
Bn
hr"
An/Bn
mg/dm**2
1
2.00
4.22
.33
12.8
2
1.33
6.34
.22
28.9
3
1.00
8.45
.16
51.3
4
.80
10.56
.13
80.2
5
.67
12.67
.11
115.5
Note: This table demonstrates how changes in the relative value of [PI]
effect the starch formation parameters A and B. Relative values of [PI]
are obtained by normalizing [Pl]n by [PI]^
i


74
Table 12. Measured chloroplastic-cytoplasmic inorganic phosphate
interactions.
Metaboli tes
Mm
1
2
Treatment
3
4
[P2]
.96
.43
.19
.08
[PI]
9.60
7.00
4.00
2.20
[PGA2]
.004
.009
.016
.024
[PGA1]
2.90
6.00
6.90
8.90
[DHAP1]
.17
.33
.40
.25
[RuBP]
3.20
3.70
4.10
4.90
Rates
umol CC^/mg chl/hr
[STARCH]
.30
1.40
7.90
7.70
CER
91.3
108.40
113.90
59.70
Note: Metabolite and rate responses to changes in the cytoplasmic level
of inorganic phosphate. Values are from Heldt et al. [1977]. No data on
ATP levels were given. Abbreviations are in Appendix 1.


75
Assuming that in this short experiment starch levels are very low,
the mobilization term can be neglected. Therefore, starch accumulation
is a function only of the starch formation rate:
d [ST/^cHl sjjk [ATP1 ] [DHAP1 ] [PGA1 ] / [PI] (51)
dt o
Values predicted by this equation are compared with measured values in
Figure (18). (No values for [ATP1] were given, so for convenience of
scale, assume that kg* [ATP1] is constant and equals 7.7.)
For the various steady flow situations outlined, the model correctly
mimics qualitative behavior and corresponds reasonably well with absolute
values. From this analysis, the most obvious feature of the modelled
starch tank to emerge is the central regulating role played by chloro-
plastic levels of inorganic phosphate. To further explore the inorganic
phosphate control mechanism as it affects starch accumulation as well as
carbon export, the [PI] tank is treated in the following section.
The Chloroplastic Inorganic Phosphate Balance, [PI]
In the experimental work summarized by the data in Table (12), dif
ferent levels of PI were maintained by manipulating the inorganic phosphate
concentrations in the medium, external to the chloroplasts. This was
equivalent to adjusting the cytoplasmic inorganic phosphate concentra
tion, [P2]. The correspondence between [PI] and [P2] is quite strong,
as can be seen in Table (12), and graphically in Figure (19).
This strong proportional dependence should be reflected in equation
(44), which is the chloroplastic inorganic phosphate balance equation:
d[P1] =
dt
Vdpmax [DHAP1] [P2]
([DHAP1] + Kd)([P2] + Kp2) + k6
[DHAP1] [PGA1] [ATP1] / [PI]
- kg [LIGHT] [ADP1] [PI] k4 [STARCH] [PI] .
(44)


[STARCH], umol C09/mg chl/hr
76
Figure 18. Measured and modelled inorganic phosphate-starch response.
Graph compares measured and modelled rates of starch formation as a
function of chloroplastic levels of inorganic phosphate, [PI]. Starch
accumulation rates are in units of ymol CC^ fixed as starch/mg
chiorophyll/hour.


W [2d]
77
[PI], mM
Figure 19. Comparison of chloroplastic and external concentrations of
inorganic phosphate. Based on data from Heldt et al. [1977].


78
In equation (44), the modelled dependence of [PI] for [P2] is in the
first term on the right hand side. This term represents the export of
DHAP1 from the chloroplast in strict counter exchange for inorganic
phosphate from the cytoplasm, P2. The second term on the right hand
side is the flux to the PI pool, resulting from the net dephosphorylation
of glucose phosphate in the accumulation of starch. Comparing the rates
of starch accumulation with C02 assimilation rates in Table (12), it is
clear that much more fixed carbon was being exported (term 1) than was
being stored as starch (term 2). This relationship is illustrated
graphically in Figure (20). Numerically, in the most extreme case with
[PI] equal to 2.2 mM in treatment 4, starch accumulation was approxi
mately 13% of the total carbon dioxide fixed and sucrose export was 87%
of CO^ fixed.
In other experimental work, the maximum rates of starch buildup are
cited as being from 10% to 20% under normal conditions [Herold and
Walker, 1979]. Based on these data, the first term on the right hand
side of equation (44) is the primary process supplying inorganic phosphate
to the chloroplast. Therefore, the strong measured functional dependence
of [PI] on [P2] is also a predominant feature of the modelled [PI] balance.
In the discussion above, the modelled correspondence between the first
term on the right hand side and export of DHAP1 to the sucrose tank are
equated. This can be expressed as
[TRANSPORT]
(52)
where [TRANSPORT] equals the time rate of DHAP1 transport to the cytoplasm.
Equation (52) can be tested directly, using the data in Table (12), along
with assumed values for K
jl, Kp and Vdpmax. Results are shown in Figure (21).


CER, Mmol C02/mg chl/hr
79
120-r
100--
80..
60-
40..
20- -
A
+
2
Starch accumulation
4 6 8 10
[PI], mM
Figure 20. Comparison of carbon partitioning pathways. Compares total
C02 fixation rate with the rates of sucrose export and starch accumula
tion at various measured levels of chloroplastic inorganic phosphate,
[PI]. Based on data from Heldt et al. [1977]. CER is given in units
of micromoles CO2 fixed/mg chlorophyll/hr.


[TRANSPORT], ymol (XL/mg chl/hr
80
Figure 21. Measured and modelled inorganic phosphate-transport response.
Graphs compare the amount of fixed carbon transported from chloroplast
to cytoplasm as a function of [P2]. Modelled curve constants were
adjusted to intersect at the right most point. Measured values are
from Heldt et al. [1977].


81
For a comparison, a first order relationship is also tested and illus
trated in Figure (21). The first order function has the following form:
(53)
[TRANSPORT] = Kg [DHAP1] [P2] .
The modelled term based on two substrate Michaelis-Menten kinetics
clearly fits the observed data better than the first order relationship.
Under steady flow conditions, such that CC^ uptake (CER) equals carbo
hydrate production over a given period of time, concentrations of the
various cyclical intermediates are very nearly in steady state. With
this assumption, the [PI] balance can be analyzed in steady state, which
can be written as follows:
[DHAP1] [PGA1] [ATP1] / [PI]
- k4 [STARCH] [PI]) = kg [LIGHT] [ADP1] [PI] (54)
In equation (54), the first term equals export from the chloroplast to
the sucrose tank, the second term is the net accumulation of starch
within the chloroplast. Taken together, the terms on the left hand
side represent total carbohydrate formation rate which, in steady flow,
must equal the carbon dioxide exchange rate. The right hand side of the
equation is simply the rate of [ATP 1] formation.
Using data from Table (12), equation (54) can be solved for the term
kg [LIGHT] [ADP1] at different values of [PI]. Since [LIGHT] is constant
in all four treatments, differences in the term reflect changing values
of [ADP1]. Results for the four treatments described in Table (12) are
listed in Table (13) and graphed in Figure (22).
The results show an increase in [ADP1]as [PI] decreases. If the sum
of [ADP1] and [ATP1] is assumed constant, then [ATP1] levels must decline


82
Table 13. Adenosine diphosphate formation as a function of inorganic
phosphate levels.
Val ue
1
Treatment
2 3
4
[PI] mM
9.6
7.0
4.0
2.2
CER mol C2/mg chl/hr
91.3
108.4
113.9
59.7
kg [LIGHT] [ADP1]
9.5
15.5
28.5
27.2
Note: This table uses values from Table (12) to evaluate the relative
levels of ADP1 that result from changing PI levels. [LIGHT] and k are
constant in each treatment.


[LIGHT] [ADP1]
83
1 1 1 1 1 I
2 4 6 8 10 12
[PI], mM
Figure 22. Modelled adenosine diphosphate-inorganic phosphate response.
Based on data from Heldt et al. [1977]. [PI] is the chloroplastic con
centration of inorganic phosphate. Adenosine diphosphate is a function
of [LIGHT] which was constant in the experimental work and the rate
constant, kg. Therefore, changes in the kg [LIGHT] [ADP1] term reflect
changes in the modelled concentration of AUPl.


84
as [ADP1] increases and the [ATP1] / [ADP1] ratio must therefore decrease
as [PI] decreases.
In general terms, the relationship found in Figure (22) is consis
tent with data presented by Kaiser and Urbach [1977], which detail the
interactions between [PI], [ATP1] and [ADP1]. In essence, they showed
that when internal levels of PI were reduced, the [ATP1] / [ADP1] ratio
responded immediately by decreasing dramatically. They further found
that the decline in [ATP1] / [ADP1] could be quickly reversed by
increasing the external supplies of inorganic phosphate, equivalent to
increasing [P2] in the model.
Further indirect evidence for the [ATP1] / [ADP1] ratios dependence
on [PI] and [PGA1] is shown in Figure (23).
From Figures (22) and (23), the overall relationship that emerges
is a direct correspondence between [PI] and [ATP1] and an inverse pro
portionality between [PI] and [PGA1]. As explained in the model develop
ment section, the concentration of PGA1 is thermodynamically regulated.
For the forward cyclic PGA1 reaction to proceed against a relatively
large positive standard Gibbs' free energy change, the ratio in the
following function
must be very large. This constraint couples [PI] levels directly to
[PGA1] through its effect on the [ATP1] / [ADP1] ratio.
This explains the control path between chloroplasts and cytoplasm.
[PI] is closely dependent on [P2] and by regulating the level of ATP1,
[PI] can affect both the concentrations of intermediates and individual
reaction rates as was shown in Figure (19).


[PI], mM
85
10,
8
6
4
2
o
N
\
\
\
S
\
\
o
o
o
[PGA1], mM
Figure 23. Measured chloroplastic PGA-inorganic phosphate response.
Based on data from Heldt et al. [1977],


86
The following section considers how the cytoplasmic inorganic
phosphate levels are regulated within the sucrose export system.
The Cytoplasmic Sucrose Balance, [SUCROSE]
Photosynthate that does not go to the starch tank flows to the cyto
plasmic sucrose tank, from which it is exported to the rest of the
plant. This balance is modelled by equation (43):
d[SUCR0SE] h Vdsmax [DHAP2]
dt [DHAP2] + Kd2(l + [SUCROSE] / K )
- [EXPORT] ,
(43)
where [EXPORT] equals the time rate of sucrose export from the cytoplasm.
Under steady flow conditions, the sucrose tank is in steady state with
imports from the chloroplasts just offsetting exports to the rest of
the plant. In steady state, equation (18) can be simplified to the
following:
[EXPORT] =
h Vdsmax [DHAP2]
[DHAP2J + Kd2 (1 + LSUCROSEJ / K )
(55)
Equation (55) has two variables and three constants on the right hand
side. For purposes of analysis, assume that [DHAP2] is normalized by
some average concentration such that, at an average concentration
[DHAP2]n equals 1. Further assume that Vexmax is approximately equal
to the maximum rate of CO^ fixation, Vcrmax, which has been approximated
in Table (6) to equal 300 ymol CO^/mg chl/hr. and have been
assumed to equal 1.5 and 100 mM respectively, based partially on Hawker
[1967]. The responsiveness of equation (55) can be tested with these
values. Figure (24) illustrates the effect on [EXPORT] of varying


[EXPORT], ymol C0?/mg chl/hr
87
Figure 24. Measured and modelled sucrose concentration--[EXPORT] response.
Measured values (0) are from Hawker [1967]. Modelled values () are
modelled for different normalized DHAP2 concentrations. [EXPORT] is
given in units of ymol CO^ fixed and exported/mg chlorophyll/hour.


88
[SUCROSE] while [DHAP2]n is held constant, the dashed line is from data
taken by Hawker [1967], who did pioneering work on feedback inhibition
of sucrose formation.
Real World Scenarios
Much experimental work has been done on the relationships between
photosynthesis, starch and sucrose. A question of particular interest
is how partitioning between these photosynthetic end products and their
respective concentrations might functionally affect photosynthetic
rate. In researching this question, experimentalists have caused many
different techniques to alter levels of starch and sucrose in a wide
variety of plant materials and in settings ranging from laboratory to
field conditions.
Some of the more common methods of changing leaf carbohydrate levels
are manipulations of diurnal temperature regimes, ambient CO^ concentra
tions and by manipulating the source-sink balance of carbohydrates. In
each of these methods, enough work has been done to suggest certain
general response patterns, although there are numerous exceptions which
appear irreconcilable with the general trend. Direct manipulation of
source-sink balance fits into the model more simply than temperature
or CO2 manipulation and will be considered first.
Direct Manipulation; Sucrose Feeding
In two specific experiments [Moore et al., 1974; Habeshaw, 1973],
sucrose was directly applied to photosynthetic plant material. In both
cases, increased levels of external sucrose depressed photosynthetic
rate and increased carbohydrate concentrations in leaves. A large
fraction of the increased carbohydrate was in the form of starch. A
typical scenario can be applied to the model as follows.


89
The experimental plants are grown in some consistent environment,
resulting in a particular balance between the sucrose exported from
photosynthetic cells and the substrate and energy requirements of
plant's growing points. By direct external application of sucrose,
the concentration in the region around photosynthetic cells increases
and apparent demand for sucrose decreases (perhaps by disrupting a dif
fusion gradient). This results in decreased export and cytoplasmic
sucrose levels rise. High concentrations of sucrose cause [P2] to
decrease, which can subsequently decrease [PI] enough to reduce photo
synthesis. Low levels of PI are also directly linked to increased
levels of PGA1, which promote the accumulation of starch.
Direct Manipulation; Selective Shading
Another type of direct source-sink manipulation is the experimental
work done by Thorne and Koller [1974], in which experimental plants grown
in full light were completely shaded except for one leaf (the "source
leaf"). Control plants remained unshaded. The "source leaf" on the
experimental plant and a comparable leaf on a control plant were moni
tored for starch level, sucrose level, photosynthetic rate and inorganic
phosphate level.
After eight days, the source leaves from the shaded plants had much
lower levels of starch, higher levels of sucrose, higher levels of
inorganic phosphate, and higher photosynthetic rates than did the source
leaves from the unshaded control plants.
In terms of the model, this experiment poses an interesting problem.
The sink demand was much higher for the source leaves on shaded plants
than on the unshaded plants. According to the model, this should have
decreased the cytoplasmic SUCROSE levels, increasing [P2] and [PI],


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DYNAMIC PHOTOSYNTHETIC RESPONSE OF SOYBEANS:
MODEL DEVELOPMENT AND ELEVATED C02 EXPERIMENTS
By
PIERCE JONES
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981

ACKNOWLEDGEMENTS
I would like to thank everyone who has helped me in my research
program. I have been very fortunate, having been surrounded by com¬
petent and cooperative people. In particular, I want to thank Dr. Jim
Jones who has been amazingly patient and helpful throughout my Ph.D.
program. Also I want to thank Drs. Hartwell Allen, Ken Boote and
Thomas Humphreys who have all been very generous with their time despite
their busy schedules. In addition, I want to thank Dr. G.L. Zachariah,
chairman of my committee and Drs. D. Buffington, C. Hsieh, and R. Irey
who served as members of my supervisory committee.
I would also like to express my appreciation to Bill Campbell,
Paul Lane and Kelton Johns whose skills were essential to the success
of the experimental phase of my research. Also a special message of
gratitude must go to Klaus Heimburg, Yung Le Morgan and my other friends
who went to such great lengths keeping my spirits elevated yet humble.
Finally, I do want to express my appreciation to Laura, my wife,
and to Ralph and Arlen Jones, my parents, for their excellent support
on every level. I hope that everyone who has been involved with me
during this project will somehow benefit by that association.

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
LIST OF TABLES v
LIST OF FIGURES vii
ABSTRACT ix
INTRODUCTION 1
BIOCHEMICAL PHOTOSYNTHESIS MODEL 11
The Light Reactions 12
Dark Reactions: Calvin Cycle 14
Dark Reactions: Phosphate Translocator System 16
Dark Reactions: Chloroplastic Starch Pathway 19
Dark Reactions: Cytoplasmic Sucrose Pathway 22
Simplifying Assumptions 25
Differential Equation Development 30
Carboxylation, Photorespiration and Enzyme Kinetics 35
CO2 and Op Concentration in the Stroma 40
Membrane transport Considerations 42
Competitive Inhibition of Sucrose Formation 43
Postscript on RuBP Carboxylase-Oxygenase and RuBP
Concentrations 49
Postscript on Photosynthesis-Respiration Roles of
Chloroplastic PGA 52
MODEL RESULTS 56
The Chloroplastic Carbon Dioxide Balance, [CO2] 57
Time Rate of Change of Starch 66
The Chloroplastic Inorganic Phosphate Balance, [PI] 75
The Cytoplasmic Sucrose Balance, [SUCROSE] 86
Real World Scenarios 88
Direct Manipulation; Sucrose Feeding 88
Direct Manipulation; Selective Shading 89
Temperature Manipulation 91
CO2 Concentration Manipulation 92
EXPERIMENTAL METHOD 94
Procedure 94
Physical Characteristics 96
Controlled Environmental Factors 98
Soil Respiration 103
Water 104
i i i

TABLE OF CONTENTS (contd.)
Page
EXPERIMENTAL METHOD (contd.)
Photosynthetically Active Radiation (PAR) 105
Problems 105
EXPERIMENTAL RESULTS 108
Controls 108
Carbon Balance 108
Transpiration 115
Plant Growth Parameters 118
Variations in Photosynthetic Rate 123
Physiological Responses 136
SUMMARY AND CONCLUSIONS 147
APPENDIX 1— ABBREVIATIONS LISTING 153
APPENDIX 2--GL0SSARY OF TERMS 157
APPENDIX 3--UNITS LISTING 162
APPENDIX 4—SYMBOL LISTING 164
APPENDIX 5—PROBABLE ERROR ANALYSIS OF C0~ MASS BALANCE
MEASUREMENTS . 165
BIBLIOGRAPHY 170
BIOGRAPHICAL SKETCH 176

LIST OF TABLES
Table Page
1 Calvin cycle reactions 1'
2 Chloroplastic starch cycle reactions 20
3 Cytoplasmic sucrose pathway reactions 23
4 Biochemical photosynthesis model equations 44
5 Key assumptions used in model development 48
6 In vivo biochemical parameters used in model evaluation. 59
7 Mesophyll resistance values from the literature 50
8 Comparison of in vivo and in vitro biochemical parameters 64
9 Chloroplastic concentrations of key metabolites in
light and dark 67
10 Measured starch accumulation parameters 69
11 Starch accumulation as a function of inorganic phosphate
concentration 73
12 Measured chloroplastic-cytoplasmic inorganic phosphate
interactions 74
13 Adenosine diphosphate formation as a function of inorganic
phosphate levels 82
14 Final above ground biomass 124
15 Morning-afternoon photosynthetic data 126
16 Regression analysis of photosynthesis data from Chambers
1 (Low-High) and 2 (High-High) 128
17 Regression analysis of photosynthesis data from Chambers
3 (Low-Low) and 4 (High-Low) 130
18 Specific leaf weight measurements 137
19 Comparison of specific leaf weight and soluble carbo¬
hydrates in Chambers 1 and 4 140
v

LIST OF TABLES (contd.)
Table Page
20 Vertical distribution of leaf nitrogen 142
21 Vertical distribution of leaf chlorophyll 145
22 Vertical distribution of leaf inorganic phosphate. . . . 146
vi

LIST OF FIGURES
Figure Page
1 Photosynthesis and source-sink balance schematic .... 3
2 Calvin cycle schematic 15
3 Phosphate translocator system schematic 18
4 Chloroplastic starch cycle schematic 21
5 Cytoplasmic sucrose pathway schematic 24
6 PGA-DHAP pathway schematic 28
7 Simplified PGA-DHAP pathway 28
8 DHAP-G6P pathway schematic 29
9 Simplified DHAP-G6P pathway schematic 29
10 Simplified overall photosynthesis schematic 31
11 Carboxylase-oxygenase pathway schematic 38
12 Final photosynthesis schematic 47
13 Modelled [CO^l-photosynthesis-CRuBP] response curves . . 62
14 Measured and modelled [^j-photosynthesis response
curves 63
15 Modelled [^J-photosynthesis response curves 65
16 Measured and modelled starch accumulation response ... 70
17 Time courses of modelled inorganic phosphate-starch
response 72
18 Measured and modelled inorganic phosphate-starch response 76
19 Comparison of chloroplastic and external concentrations
of inorganic phosphate 77
20 Comparison of carbon partitioning pathways 79
vi i

Figure Page
21 Measured and modelled inorganic phosphate-transport
response 80
22 Modelled adenosine diphosphate-inorganic phosphate
response 83
23 Measured chloroplastic PGA-inorganic phosphate response. . 85
24 Measured and modelled sucrose concentration-[EXPORT]
response 87
25 Control chamber schematic 97
26 Control system schematic 100
27 Diurnal temperature control 109
28 Time courses of PAR, [CO2] and CER on April 21 110
29 Time courses of PAR, and CER on April 22 Ill
30 Photosynthetic light response curves; Chambers 1 (Low-
High) and 2 (High-High) 113
31 Photosynthetic light response curves; Chambers 3 (Low-
Low) and 4 (High-Low) 114
32 Time courses of dark respiration rates 116
33 Time courses of transpiration rates 117
34 Time courses of water use efficiency 119
35 Time courses of individual leaf areas 120
36 Time courses of leaf area index 121
37 Time courses of canopy leaf mass 122
38 Morning and afternoon photosynthetic light response;
Chambers 1 (Low-High) and 4 (High-Low) 125
39 Time courses of morning CER at 500 ;iE/m**2/sec 134
40 Time courses of afternoon CER at 500 yE/m**2/sec 135
41 Diurnal specific leaf weights; Chambers 1 (Low-High) and
4 (High-Low) 139
42 Comparison of carbohydrate levels and specific leaf
weight 141
43 Vertical nitrogen distribution; Chambers 1 (Low-High)
and 4 (High-Low) 144
vi ii

Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
DYNAMIC PHOTOSYNTHETIC RESPONSE OF SOYBEANS:
MODEL DEVELOPMENT AND ELEVATED C02 EXPERIMENTS
By
Pierce Jones
June 1981
Chairman: Dr. G.L. Zachariah
Major Department: Mechanical Engineering
A biochemical photosynthesis model has been developed and experi¬
ments at the whole plant level have been conducted in a holistic in¬
vestigation of photosynthetic rate controls. The model was based on
known biochemical pathways and emphasized the roles of starch, sucrose
and inorganic phosphate in the feedback control of C02 fixation. The
experimental work was designed to investigate short term rate response
to a sudden change in C02 concentration and long term physical adaptation
to distinctive environmental CO^ levels. In the experimental procedure
different source-sink balances were established for each treatment and
plant response was measured. In the model the mechanisms for source-
sink feedback control of the biochemical CC^ fixation process were
developed. The overall purpose of the work has been to demonstrate and
clarify the role played by source-sink relations in the feedback regu¬
lation of photosynthesis.
Comparison of model predictions with measurements from the litera¬
ture have shown the model's individual response equations to behave well.
IX

Overall the model demonstrated the central role of inorganic phosphate
as a regulator of the Calvin cycle via its affect on the ATP/ADP ratio
and as a regulator, partitioning CO^ between starch and sucrose syn¬
thesis. In turn, the concentration of inorganic phosphate was modelled
to depend inversely on cytoplasmic sucrose level which was modelled to
depend on export. By functionally linking the export of sucrose from
the cytoplasm to sink demand, the model qualitatively described the
photosynthetic inhibition and enhancement observed in a variety of
scenarios.
The experimental results showed soybeans (Glycine max c.v. Bragg)
to respond to elevated CC^ levels by increasing net photosynthesis and
respiration in the short term and increasing leaf area and biomass in
the long term. Close analysis of photosynthetic light response found
morning enhancement and/or afternoon inhibition of CC^ fixation in
plants exposed to high [CC^]. In the canopy switched to high CC^, the
magnitude of afternoon inhibition was suppressed by rapidly enhanced
sink strength. Reduced CO2 fixation corresponded to higher levels of
soluble carbohydrates in the leaves. Taken together these results
supported the proposed interdependence between leaf sucrose levels and
photosynthesis.
The experimental work showed the association between source-sink
balancing and photosynthetic rate while the biochemical model demon¬
strated a linkage mechanism. The differences in detail of the bio¬
chemical and whole plant levels prevented direct quantitative compari¬
sons between model and experimental results. Nevertheless the experi¬
mental and model results were qualitatively consistent and this work
represented a necessary effort at a holistic explanation of photosynthetic
rate regulation.
x

INTRODUCTION
All living systems in the biosphere are based directly or indirectly
on sunlight, carbon dioxide and water. Photosynthesis is the process
common to green plants that combine these elements into energy-rich
carbohydrates. Within plant systems the carbohydrates produced by
photosynthesis have two functions: first, as substrate for plant tissue
synthesis and second, as energy for the synthesis reactions. As some
of the carbohydrate building blocks are combined with nitrogen, sulfur
and other elements into plant tissue, others are respired releasing
required reaction energy.
Photosynthesis occurs in plant leaves while tissue synthesis and
respiration use carbohydrates throughout the plant structure. Carbo¬
hydrates are translocated from the production source in the leaves to
consumption sinks through the phloem which directly connects the photo¬
synthetic leaf material to active reaction sites.
More specifically, the chain of events that provides carbohydrates
for plant growth begins in microscopic organelles called chloroplasts
which are suspended in the cytoplasm of photosynthetic cells. Carbon
dioxide diffuses from the atmosphere to the chloroplasts where it is
chemically reduced in a process called the Calvin cycle, driven with
energy supplied by light. The assimilated CO^ is either converted to
sucrose in the cytoplasm, or to starch in the chloroplast, both of which
are carbohydrates. A schematic representation of this system is given
1

2
in Figure (1). The translocation system begins with the export of a
three carbon phosphorylated compound (dihydroxyacetone phosphate, DHAP)
from the chloroplast to the cytoplasm, where it is converted to sucrose,
which moves into the phloem for distribution throughout the plant.
The balance between CO^ fixation in the chloroplast and carbohydrate
export from the cytoplasm is important to photosynthetic feedback control,
but is poorly understood.
The balance between carbohydrate sources and sinks can be disrupted
by changing environmental conditions. When this happens, photosynthesizing
cells must adjust to the new circumstances. If photosynthetic rate is
increased or if transport to the phloem is decreased then excessive
amounts of carbohydrates may accumulate in the photosynthetic cells.
When this occurs starch is reversibly formed in the chloroplasts, storing
fixed carbon until it can be mobilized and shipped to the cytoplasm for
conversion to sucrose and export to the rest of the plant. If starch
accumulation continues past a certain point, cells can be physically
damaged [Noble and Craig, 1973]. It is postulated that before damage
occurs, the plant, under normal conditions, adapts by either decreasing
its rate of photosynthetic supply of carbohydrates, or by increasing
its rate of sucrose translocation and utilization.
Changes in the rate of starch accumulation have been observed in
response to many situations. For instance, when plants have been
switched from atmospheres with ambient levels of CO^ to enriched CC^
conditions, starch accumulation and photosynthesis increased dramati¬
cally but while starch levels continued to rise after several hours,
photosynthetic rates declined [Mauney et al., 1979]. In another
example, plants acclimated to warm nights were found to have increased

3
PAR
i
Figure 1. Photosynthesis and source-sink balance schematic. PAR is
photosynthetically active radiation. All abbreviations are defined in
Appendix 1. Terms are defined in Appendix 2.

4
starch concentrations and decreased photosynthetic rates following
exposure to low night time temperatures.
In the case of high [CC^], the plants mature leaves exported more
carbohydrates than they had in low [CO,,], but not enough to balance
the increased supply. Consequently, the excess was stored as starch.
In the case of low night temperatures, carbohydrates normally used
in night time growth and maintenance processes were not used due to
temperature dependent reductions in process rates. On the following day
reduced sink demand caused carbohydrate levels in the photosynthetic
cells to increase.
Observations such as these are often explained conceptually in
terms of imbalances in the source-sink relationship. Whether the car¬
bohydrate levels increase due to high CO^ fixation or reduced sucrose
export, the system balances itself by reducing photosynthesis. On the
other hand, when sink strength is increased and carbohydrate levels in
the photosynthetic cells decline, maximum photosynthetic rates are
observed to increase [Thorne and Koller, 1974]. Source-sink balancing
is superficially a straightforward and satisfying explanation for
alterations in photosynthetic response. Unfortunately, the details of
the proposed source-sink mechanism are not well understood.
The photosynthetic system consists of complex and interrelated
processes all of which serve to control the overall CC^ fixation rate.
In simple terms, every plant's physical and chemical environment is
continuously changing. In turn, compound levels and process rates
which determine photosynthetic rate within the plant are also changing.
In this sense, plant photosynthesis is dynamic.

5
Macroscale variations in photosynthetic capacity are a function of
nutrient availability, water supply, temperature, sunlight, 0^ concen¬
tration and C0,> concentration. At the cellular level, photosynthetic
capacity is a function of enzyme availability, enzyme activity and
substrate concentrations. All of these factors combine to establish
individual reaction rates, the products of which are substrates for
subsequent reactions. The integrated sum of the various reactions
control particular process rates. Finally, whole plant parameters and
biochemical processes are functionally coupled by transport systems some
of which are passive and some of which are active. In both cases con¬
centration gradients and transport resistances are determining factors
in the mass transport rates of substances from the environment to the
biochemical reaction sites of photosynthesis. The sum of these inter¬
actions determines the instantaneous rate of CO^ fixation.
This brief holistic description of photosynthesis emphasizes that
response should be considered at both the whole plant and biochemical
levels of plant organization. Modellers began trying to relate external
environmental conditions to photosynthesis as a biochemical process
thirty years ago [Rabinowitch, 1951]. Since then, a steady stream of
increasingly biochemical models has been developed [Chartier, 1970;
Charies-Edwards and Ludwig, 1974] leading to the biochemical models
proposed by Peisker [1974] and more recently by Farquahr et al. [1980].
One of the main criteria which these modellers have set is the
adequate simulation of various photosynthetic light response curves.
Usually, results from experimental work on photosynthesis are presented
graphically in photosynthetic light response curves which plot carbon
dioxide exchange rate (CER) against light level. Because of the very

6
strong dependence of CO2 assimilation on light level, the graphical
relationship between them has long been considered a fundamental measure
of response, whether research is on whole plant canopies or reconstituted
chloroplasts.
The fundamental importance of the photosynthetic light response
curve (PLRC) is further enhanced by the similar shape of most plots
generated for a wide variety of plants, which implies very similar
underlying mechanisms. Several distinct functional equations have been
proposed which generate curves of the appropriate shape [Thornley, 1976].
However, the most commonly derived equations are variations of the
rectangular hyperbola. This particular equation is scientifically
satisfying because of its theoretical basis in enzyme kinetics, where
it is called a Michaelis-Menten response curve. Because of the cyclical
enzymatic pathways which photosynthesis follows, it seems quite natural
that the rate of CO2 uptake should have a Michaelis-Menten form. The
goal for modellers has been to relate light via an assumed biochemical
pathway to CO2 uptake in such a way that external parameters could be
used to represent the variations in photosynthesis in response to light.
Photosynthesis models such as those described above are currently
used in conjunction with other crop system models to predict growth
rates and yield. These models concentrate on the uptake of CO2 in
response to light level while ignoring how or why fixed carbon is par¬
titioned between starch and sucrose. As a result, they work well under
normal conditions but are generally inadequate for describing response
to unusual circumstances.
It is hypothesized that partitioning between stored chloroplastic
starch and cytoplasmic sucrose is central to the feedback control of

7
photosynthesis. As noted in the examples of low night temperatures and
increased CO^ levels, starch accumulation is often reported in associa¬
tion with reduced photosynthetic response. To model this relationship,
starch and sucrose cannot be simply divided into unrelated pools.
Synthesis of starch and sucrose must respond functionally to mechanisms
which prescribe how fixed carbon is to be partitioned. One of the main
goals of this research has been to develop a model based on such mechanisms
To accomplish this goal a detailed photosynthesis model has been
developed, based on five specific biochemical pathways:
1. the light reactions
2. the Calvin cycle,
3. the chloroplastic starch cycle,
4. the cytoplasmic sucrose pathway, and
5. the phosphate translocator system.
The purpose of the developed model is to consider the hypothesized roles
that starch and sucrose play in the feedback control of CO^ fixation.
This is done by identifying the possible interactions among the five
pathways that could limit photosynthesis and control partitioning. From
this perspective it becomes possible to investigate the complex rela¬
tionship between biochemical dynamics and the ambient environment. Such
a detailed model can also be used to suggest how the photosynthetic
system might respond in the long term to different prevailing environments.
At the whole plant level field experiments were conducted concurrently
with the development of a biochemical photosynthesis model. The experi¬
mental work was designed to investigate short term response to a
sudden change in (X^ concentration and long term adaptation to distinctive
environmental CO^ levels. All of the treatments were exposed to constant
moderate air temperatures under well-fertilized and well-watered conditions

8
The experiments were conducted under natural sunlight which varied, but
all treatments were exposed equally to these changes.
To assess the plant-environment interactions four general classes
of data are required: (1) external parameters such as temperature,
quantum flux density and CC^ concentration which define the environment;
(2) gas exchange rates such as transpiration, daytime CC^ exchange and
night time CC^ exchange which define water use, photosynthesis and
respiration rates; (3) whole plant parameters such as height, leaf area
and biomass which are indicators of adaptive response; and finally,
(4) physiological parameters such as specific leaf weight, chlorophyll
levels and nitrogen levels which are indicators of biochemical system
response. The short and long-term adaptive response of plants to a
particular sequence of prevailing environments can be characterized in
terms of these four data sets.
At the biochemical level the experimental results can be applied to
questions concerning substrate levels and process rates on the micro¬
scale. For instance, the data can suggest how CO^ level effects chloro¬
phyll concentrations and enzyme levels (as a function of nitrogen) as
well as CO2 fixation process rates. On a larger scale the data can
indicate how source-sink balancing is affected by CO2 concentration
through the measurements of diurnal specific leaf weight and by the
instantaneous measurements of photosynthetic light response. Finally,
at the whole plant level, biomass accumulation and leaf area are direct
measures of the integrated adaptive response of whole plants to different
CO2 environments.
The experimental work was designed to provide the data necessary
to answer these questions. With these data, the hypothesis that plants

9
adaptively respond to different prevailing environmental concentrations
of CO^ can be tested. Furthermore, the adjustments that occur at the
whole plant level and the biochemical level can be considered separately,
to determine whether the adaptation of the whole plant is consistent with
biochemical level response.
Combining the experimental results with the biochemical photosynthesis
model, a qualitative explanation of short-term feedback controlled
response and long-term whole plant adaptation to prevailing CO^ concen¬
trations is proposed. This proposed mathematical-conceptual model pro¬
vides a framework for both a short-term model to explain inhibition and
enhancement of photosynthetic light response and a long-term model of
adaptation to differing environments.
The overall purpose of this research is based on the concept of
photosynthetic adaptation which has been defined as environmentally
induced adjustments in physiology, anatomy and morphology that allow a
plant to improve photosynthetic efficiency in a new environment [Bjorkman
and Berry, 1973]. Stated another way, adaptation enables whole plants
to maximize photosynthetic productivity under locally prevailing envi¬
ronmental conditions [Tooming, 1970]. The purpose of this research is
to gain a more complete understanding of photosynthesis as a dynamic
process at both the whole plant and biochemical levels.
It is postulated that plant canopies will adaptively respond to
different prevailing environmental concentrations of carbon dioxide. In
particular, this project has been designed to describe and explain the
responses of soybean canopies grown continuously in different carbon
dioxide concentrations during their vegetative stage of growth and the

10
subsequent short and long-term canopy responses to a step change in CO^
levels. The experimental objective of the research has been to grow
and monitor soybean canopies in four computer controlled, closed environ¬
mental chambers. A parallel theoretical objective has been to develop a
biochemical level model of photosynthesis. Finally, the third objective
of the research has been to qualitatively relate the whole plant experi¬
mental observations and the biochemical model within the conceptual
framework of source-sink balancing.
The long range goal of this research is to devise a physically based
dynamic model of photosynthesis complete with feedback controls. Such a
model could be used with other sub-system models to describe any whole
plant system. In turn individual plant models are the basis of crop
models which have increasingly wide application.

BIOCHEMICAL PHOTOSYNTHESIS MODEL
Photosynthesis is commonly modeled [Lehninger, 197C] as a process
in which carbon dioxide (CO2) and water ^0) are chemically combined
in the presence of light quanta (nhv) to form glucose (CgH^Og) and
oxygen (O2). In equation form this is expressed as:
(1)
6 CO2 + 6 H2O + nhv -* CgH^Og + 6 O2 + heat
Note that mass is conserved explicitly in the equation stoichiometry,
whereas energy is implicitly conserved by equating light input (nhv) to
the chemical energy in glucose (CgH^Og) and the energy degraded to
heat. It is useful to rewrite equation (1), replacing the light quanta
term (nhv) with an associated free energy change (aG).
6 C02 + 6 H20 -* C6H1206 + 602
aG°= 686 kcal/mole (2)
This emphasizes that in the formation of glucose, light is not a sub¬
strate, but rather, indirectly supplies the energy to drive this
"uphill" reaction. Finally, a third equation can be written to make
the obvious point that carbonated water exposed to sunlight will not
produce glucose and oxygen. CO2 and water must pass through an exten¬
sive series of biochemical cycles and pathways before being transformed
into glucose; therefore, equation (1) might be written once again:
(3)
11

12
In the following sections, some of the details of the photosynthetic
blackbox will be discussed, simplified and condensed into a mathematical
model.
The Light Reactions
When photosynthesis is considered in detail, equation (1) is seen
to incorporate two chemical processes which are coupled into the total
system by which glucose is formed. Light is required in an initial
process in which photosynthetically active radiation (PAR) is converted
into chemical energy via excitation of chlorophyll and accessory pigment
molecules. These initial reactions are called the Light Reactions. PAR
is electromagnetic radiation with wavelength between 400 and 700 nm. It
is usually measured with a quantum sensor and typical units are micro-
Einsteins/m**2/sec. PAR quanta are absorbed by a diverse group of pig¬
ments located in the chloroplasts of photosynthesizing cells. The most
commonly known and abundant pigment is chlorophyll, of which there are
several kinds that differ slightly in structure and absorption spectrum.
Chlorophyll is the main light absorbing pigment in green plants. When
plants are exposed to PAR, quanta are absorbed, causing high energy
electrons to escape from the excited pigment molecules. Some of these
electrons fall back to ground state and the chlorophyll molecules give
up their captured quanta as fluorescence and heat. Others leave the
chlorophyll completely and enter an electron-carrier pathway, flowing
down an energy gradient from one carrier to the next. When an electron
moves through this transport system, it loses potential energy at each
transfer between carriers. At certain of the transfers in the chain,
the potential drop is partially conserved by driving the energy requiring
phosphorylation of adenosine diphosphate (ADP) to adenosine triphosphate

13
(ATP). Two quanta are absorbed for each electron to move through the
complete pathway. In this manner light-induced electron flow is con¬
verted to chemical bond energy. The process is called photophosphory¬
lation and can be represented by the following equation:
ADP + P + nhv -* ATP + heat, (4)
where P is inorganic phosphate.
Only part of the photoinduced potential is used to produce ATP. Most
of the conserved electrochemical energy goes to the last acceptor in the
chain, which is the oxidized form of nicotinamide adenine dinucleotide
phosphate (NADP) which receives the electron as well as a proton and is
accordingly reduced as the final step in the light reactions, This pro¬
cess of using photoinduced electron flow to yield a reduced product is
called photoreduction. Equation (4) can be expanded to represent the
overall light reaction, including both photophosphorylation and photo¬
reduction as follows [Lehninger, 1973]:
2 ADP + NADPqx + 2 P + 2 hv + H20
+ NADPre(j + 2 ATP + ^02 + heat. (5)
With this more detailed understanding, equation (1) can be rewritten
again to clarify the relationship between PAR as an energy source and
the glucose formation equation. It is
6 NADPred + 6 H20 + 12 ATP + 6 C02
-* C6H1206 + 6 NADPqx + 12 ADP + 12 P + 6 02 (6)
Equation (6) describes an overall process which has been only briefly
outlined. More complete descriptions of the light reactions are avail¬
able in articles by Rabinowitch and Godvinjee [1965] and Zelitch [1979].

14
Dark Reactions: Calvin Cycle
The biochemical pathway to sucrose following the light reactions is
referred to as the Dark Reaction. A central portion of this process is
the Calvin Cycle, which occurs in the chloroplast, along with the light
reactions. The first step in the Calvin cycle is the reduction of C02
(the carboxylation reaction). Specifically, the reaction combines C02,
H20 and ribulose-1,5-bisphosphate (RuBP) in the presence of the enzyme
ribulose-1,5-bisphosphate carboxylase (RuBPc) to form 2 molecules of
3-phosphoglyceric acid (PGA). In equation form it is
H20 + C02 + RuBP 2 PGA AG° = -8.4 kcal/mole (7)
RuBPc
Equation (7) is an exergonic or downhill reaction having a negative
standard free energy change [Bassham, 1971] and, therefore, requires no
energy or reducing power to proceed. Although not directly required in
equation (7), the light reaction's products (ATP and NADP^ecj) drive the
complex sequence of enzyme catalyzed reactions called the Calvin cycle,
which regenerates RuBP [Bassham, 1971].
In the second reaction of the Calvin cycle, ATP is directly required
for the phosphorylation of PGA, producing the high energy phosphate com¬
pound 1,3-biphosphoglyceric acid (BPGA):
PGA + ATP -> BPGA + ADP. (8)
The reducing power generated by the light reaction is utilized in the
subsequent step as follows:
BPGA + NADP , + GAP + P + NADP , (9)
red ox vy
where GAP is glyceraldehyde-3-phosphate. The only other reaction in

15
Figure 2. Calvin cycle schematic. RuBP, ribulose-1,5 -bisphosphate, RuP;
ribulose-5-phosphate; XMP xylulose-5-phosphate; SDMP, sedoheptulose-1-
phosphate; SDBP, sedoheptulose-1,7-bisphosphate; EMP erythrose-4-phosphate;
FMP, fructose-6-phosphate; FBP, fructose-1,6-phosphate; DHAP, dihydrox-
yacetone phosphate; GAP, glyceraldehyde-3-phosphate; BPGA, 1,3-phospho-
glyceric acid; PGA, 3-phosphoglyceric acid. All abbreviations are listed
alphabetically in Appendix 1 (Based on Bassham [1971]).

16
the Calvin cycle directly using the products of the light reaction is
step 13 in Table (1), in which ribulose-5-phosphate (RuP) is phosphory-
lated to RuBP:
RuP + ATP RuBP + ADP. (10)
The preceding three equations summarize the direct interaction
between the Calvin cycle and the light reactions, while equation (7)
represents the all important link between the microscale biochemical
pathways and the macroscale carbon exchange rates.
Dark Reactions: Phosphate Translocator System
Both the light reactions and the Calvin cycle occur in chloroplasts
while the final steps in the dark reactions take place in the cytoplasm,
requiring that the carbon fixed in equation (7) be exported through the
outer chloroplastic membrane. The primary export product is dihydroxy-
acetone phosphate (DHAP) [Heber, 1974], which is produced in reversible
equilibrium with GAP as the fourth step in the Calvin cycle. For this
pathway to function continuously, cytoplasmic phosphate must be imported
to the chloroplast in direct proportion to the exported DHAP. The
exchange is part of the phosphate translocator system. DHAP is a crucial
intermediate which is balanced among three pathways: export for use as
substrate or energy in the cytoplasmic dark reactions, continuation in
the Calvin cycle as substrate for regenerating RuBP, or to storage as
starch in the chloroplast. A schematic is given in Figure (3) to
clarify these relationships. The other portion of the system imports
PGA from the cytoplasm in exchange for chloroplastic inorganic phosphate
[Kelly et al., 1976]. The importance of maintaining phosphate balances
is clear, considering its role in energy transfer and storage. Once

17
Table 1. Calvin cycle reactions (H^O not shown).
Step
Substrate
Enzyme
Product
1
6 C02 + 6 RuBP
RuBP carboxylase
12 PGA
2
12 PGA + 12 ATP
PGA kinase
12 BPGA + 12 ADP
3
12 BPGA + 12 NADP ,
red
GAP dehydrogenase
12 GAP + NADP
ux
4
5 GAP
Trióse phosphate isomerase
5 DHAP
5
3 GAP + 3 DHAP
Aldolase
3 FBP
6
3 FBP
FBP dekinase
3 FMP + 3 P
7
2 FMP + 2 GAP
Transketolase
2 XMP + 2 EMP
8
2 EMP + 2 DHAP
Aldolase
2 SBP
9
2 SBP
Phosphatase
2 SMP + 2 P
10
2 SMP + 2 GAP
Transketolase
2 RMP + 2 XMP
11
2 RMP
Isomerase
2 RuP
12
4 XMP
Epimerase
4 RuP
13
6 RuP + 6 ATP
Phosphoribulokinase
6 RuBP + 6 ADP
Note: Reactions are taken from Lenhinger [1970].

18
NADPred
NADPox
BPGA
CYTOPLASM
Figure 3. Phosphate translocator system schematic. Outlines the
membrane exchange mechanism by which fixed carbon is exported from
chloroplasts to cytoplasm for sucrose synthesis. All abbreviations
are identified in Appendix 1 (Based on Heber [1974]).

19
DHAP is in the cytoplasm, it can be utilized as a substrate in the
sucrose pathway or it can be oxidized and dephosphorylated by the
reverse reactions of equations (9) and (10). In this way the energy
equivalents of ATP and NADP^ are transported to the cytoplasm. When
used for energy transfer, the DHAP is converted to PGA, which can be
transported back to the chloroplast [Herold and Walker, 1979].
Dark Reactions: Chloroplastic Starch Pathway
In the chloroplast, the starch pathway is cyclical, moving from
DHAP to starch, and later being reconverted to DHAP. The intermediate
steps have been worked out in detail and are presented in Table (2).
The cycle actually moves through steps (5) and (6) of the Calvin cycle
in which fructose-1,6-bisphosphate (FBP) is irreversibly converted to
fructose-6-phosphate (FMP), which enters the starch pathway, forming
glucose-6-phosphate (G6P). The rate limiting step in starch formation
is the reaction in which ATP combines with glucose-l-phosphate (G1P) to
form ADP-glucose. This reaction is not only promoted by high levels of
ATP, but also by high levels of PGA, and is inhibited by high levels of
inorganic phosphate [Kaiser and Bassham, 1979]. The return starch
mobilization reactions follow the same essential pathway, except that
the rate limiting step is the energy requiring conversion of FMP to
FBP. This reaction obtains energy and a phosphate group from ATP, while
simultaneously being inhibited by high levels of ATP.
The system behavior described acts as a regulator encouraging starch
storage during the day and release at night. Also note that energy units
are required in both the formation and breakdown of starch. A schematic
of this cycle is given in Figure (4).

20
Table 2.
Chloroplastic
starch cycle reactions.
Step
Substrate
Enzyme
Product
1
DHAP + GAP
Aldolase
FBP
2
FBP
Dekinase
FMP + P
3
FMP
Phosphohexoisomerase
G6P
4
G6P
Phosphoglucomutase
G1P
5
G1P + ATP
Pyrophosphorylase
ADP-glucose + P
6
ADP-glucose
Amyl ose synthetase
Starch
7
Starch + P
Glucan phosphorylase
G1P
8
G1P
Phosphoglucomutase
G6P
9
G6P
Phosphohexoisomerase
FMP + ADP
10
FMP + ATP
Phosphofructokinase
FBP
11
FBP
Al dolase
DHAP + GAP
Note: These reactions are based on Lehninger [1970] and Kelly et al.
[1976].

21
ADP
Figure 4. Chloroplastic starch cycle schematic. Outlines the starch
storage and remobilization mechanism by which chloroplast can store fixed
carbon. All abbreviations are listed in Appendix 1 (Based on Kelly et
al. [1976]).

22
Dark Reactions: Cytoplasmic Sucrose Pathway
The other carbon balancing pathway is to the cytoplasm, where DHAP
is the initial substrate leading to sucrose formation. In a series of
steps similar to those in starch formation, DHAP is converted to glucose-
1-phosphate (G1P). At this point, sucrose formation diverges from the
starch pathway. Instead of the common energy compound ATP, G1P combines
with uridine triphosphate (UTP) to form UDP-glucose. This compound
reacts with FMP to form sucrose-6-phosphate (SMP), which directly yields
sucrose. One important aspect of this pathway is that the reaction rate
of the SMP conversion to sucrose may be subject to product inhibition
[Hawker, 1967]. Sucrose is the primary sugar compound exported from
photosynthesizing cells. If the export of sucrose is less than its
synthesis, then cytoplasmic levels will increase. When this happens,
the high concentration of sucrose potentially inhibits the enzyme that
dephosphorylates SMP, causing a buildup of its concentration and a cor¬
responding decrease in the level of inorganic phosphate. This pathway
is detailed in Table (3), and a schematic is presented in Figure (5).
Another point to consider is that uridine triphosphate (UTP) formation
is driven by ATP, and that the roles of these compounds in carbohydrate
formation are very similar.
In review, equation (1) is seen to represent substrate and energy
fluxes into the photosynthetic blackbox on the left hand side and product
fluxes out of the system on the right hand side. To better understand
this equation, the blackbox has been described in terms of five sub¬
systems :
1. the 1ight reaction
2. the Calvin cycle
3. the phosphate translocator system
4. the chloroplastic starch cycle
5. the cytoplasmic sucrose pathway

23
Table 3.
Cytoplasmic sucrose
pathway reactions.
Step
Substrate
Enzyme
Product
1
DHAP + GAP
Aldolase
FBP
2
FBP
Dekinase
FMP + P
3
FMP
Phosphohexoisomerase
G6P
4
G6P
Phosphoglucomutase
G1P
5
G1P + UTP
Pyrophosphorylase
UDPG + PP
6
UDPG + FMP
Phosphosynthetase
SMP + UDP
7
SMP
Phosphatase
Sucrose + P
Note: PP
Lehninger
is an abbreviation
[1970] and Kelly et
for pyrophosphate. Reactions
al. [1976].
are based on

24
Figure 5. Cytoplasmic sucrose pathway schematic. Abbreviations are
defined in Appendix 1 (Based on Lehninger [1970] and Kelly et al.
[1976]).

25
From the schematics and equations given to describe these processes,
the fluxes in equation (1) are plainly visible. The light reactions use
captured quanta (nhv) to drive the hydrolysis of water (H^O), which sup¬
plies electrons for use in the reduction of NADP and simultaneous forma¬
tion of ATP. Oxygen (0^) is liberated as a by-product of hydrolysis.
These interactions are described in equation (5). Carbon dioxide (CC^)
enters the system reacting with RuBP to form the first products in the
Calvin cycle, according to equation (7). Fixed carbon is transported
from chloroplast to cytoplasm where sucrose is formed and exported from
the cell. Some fixed carbon is temporarily stored in the chloroplast as
starch and later is transported to the cytoplasm, where it also forms
sucrose. The model development emphasizes the feedback regulation of
the carbon flow paths into and out of the photosynthetic cell.
Simplifying Assumptions
As can be seen from the preceding tables and schematics, there are
a large number of intermediates involved in each subsystem. In the model
being developed, the concentration of intermediates fluctuates in response
to net flow. It is assumed that keeping track of each intermediate pool
is not necessary because of the serial nature of the processes. To aid
in determining which intermediates should be retained, mediating enzymes
have been grouped according to their characteristics as given by Kelly
et al. [1976], Heber [1974] and Lehninger [1970]. Essentially, all bio¬
chemical reactions on the cellular level are catalyzed enzymatically, each
enzyme may or may not be inhibited or promoted by any other compound or ion.
Enzyme, product and substrate groups are also unique in their degree of bio¬
chemical reversibility, which will vary with pH and other factors. In short,
reactions can range from very simple reversible flow between two proportionate

26
pools to irreversible reactions which are highly sensitive to a range of
inhibitors and promoters. For purposes of modelling, it is essential to
sort out the reactions which may be crucial rate limiting and path
selecting points from those that are not. Four criteria have been
devised to sort out the significant interactions in each subsystem.
The first simplifying criterion is that nonallosteric enzymes can be
ignored and that reversible path reactions between a substrate pool and
a product pool can be condensed into a single representative tank. An
excellent example of this situation is the fourth step in the Calvin
cycle, in which DHAP and GAP quickly reach an equilibrium because of
the continuous availability of active enzyme [Lehninger, 1970].
DHAP t GAP aG°=1.0 kcal/mole (11)
In modelling this portion of the Calvin cycle, no distinction needs to
be made between these trióse phosphates; the presence of one implies
the presence of the other in some approximately constant ratio. Since
DHAP has a significant role in path selection, the representative
storage pool is referred to as DHAP.
The second criterion extends the conditions of the first to include
nonallosteric reactions which require energy or reducing units. The
second Calvin cycle reaction fits these requirements.
PGA + ATP t BPGA + ADP aG°=4.5 kcal/mole (12)
In the chloroplast exposed to light, ATP levels are high and equation (12)
can be expected to have a net flow to the right, while in the dark, the
flow will reverse direction (see postscript on PGA).
The third Calvin cycle reaction is similar to the second, requiring
reduced NADP to proceed from BPGA to GAP. The reactions described so far

27
under the first and second criteria are modelled schematically in
Figure (6), using "Energy Language Symbols" developed by H.T. Odum [1971]
There are four predominate symbols used: the tank which symbolizes the
concentration of a metabolite in the reaction medium; the interaction
symbol which relates substrates and/or allosteric effectors; the circle
which represents an unlimited flow source, and the interaction arrow,
which shows the explicit path taken (see Appendix IV).
Looking at Figure (6), BPGA and GAP can be consolidated into a flow
path between PGA and DHAP which is moderated by the levels of ATP and
NADPrec|. The process can be further simplified by assuming that reducing
power and energy units come from the same source in a reasonably constant
ratio. Hence, if ATP is available, then NADPred should also be available
The condensed model is shown schematically in Figure (7).
A third criterion treats the class of nonallosteric reactions which
have products. An example is the dephosphorylation of FBP to form FMP
and inorganic phosphate, P, which occurs in the Calvin cycle as well as
the cytoplasmic sucrose pathway. This process can be modelled schemati¬
cally as in Figure (8). The assumption is that tanks can be condensed,
but the product P cannot be ignored. FBP can be absorbed into the DHAP
tank and FMP can be absorbed into the G6P tank according to the first
criterion, while P must flow to an inorganic phosphate tank. The simpli-
ifed schematic version is in Figure (9).
The fourth criterion dealswith allosteric rate limited reactions
by controlling flow between pools with elements that sense reaction
inhibitors and/or promoters. In the starch forming reaction, step 6 in
Table (2), the enzyme is inhibited by inorganic phosphate (P) and pro¬
moted by the intermediate, PGA [Kaiser and Bassham, 1979]. So, even

28
Figure 6. PGA-DHAP pathway schematic. Explicit equations are listed
in Table (1).
Figure 7. Simplified PGA-DHAP pathway. All abbreviations are listed
in Appendix 1. (Symbols are defined in Appendix 4.)

29
Figure 8. DHAP-G6P pathway schematic. Explicit equations are in
Table (2).
Figure 9. Simplified DHAP-G6P pathway schematic. All abbreviations are
defined in Appendix 1. (Symbols are defined in Appendix 4.)

30
though these compounds are not substrates in the reaction, they must be
included in some form to control the reaction.
The application of these criteria to the five subsystems results in
the simplified model shown schematically in Figure (10). As shown below,
the schematic can be used to generate differential equations by doing
simple mass flow balances into and out of each tank.
Differential Equation Development
The interaction symbol between tanks indicates a simple algebraic
process involving the concentrations of reactants and a rate constant.
The level of PGA1 in the chloroplast is expected to vary according to
d^A1J- = 2k [RuBP] [C02] + k2 [PGA2] [PI] - k3 [PGA1] [ATP1]. (13)
The first term on the right hand side of equation (13) represents
an addition to the PGA1 pool resulting from the reduction of C02 which
is represented as a function of the concentrations of CO^ and RuBP as
moderated by the rate constant k^. The 2 is a numerical constant stoich-
iometrically required to maintain the system's carbon balance. The
second term is the phosphate translocator flow of PGA from the cytoplasm
to chloroplast as a function of [PGA2] and [PI], multiplied by the rate
constant, k^. The third term is the Calvin cycle forward flow to DHAP,
a function of [PGA1] and available energy units, [ATP1]. Notice that
the third term embodies the assumptions outlined in Figures (6) and (7).

31
Figure 10. Simplified overall photosynthesis schematic. In the inter¬
action symbols the k values are reaction rate constants. The divisor
sign implies inhibition. Numbers following intermediates separate
chloroplastic (1) from cytoplasmic (2) pools. All abbreviations are
defined in Appendix 1. (Symbols are defined in Appendix 4.)

32
Other equations derived from the schematic are
d|^dT~ = k3 tPGA1^ [ATP11 + 2k4 [STARCH3 [pH (14)
- k.n [DHAP1] [ATP1] - kc [DHAP1] [P2]
IU o
- kg [DHAP1] [PGA1] [ATP1]/[Pl]
d[sTARCH] = ^ [DHAP]] [PGA1] [ATP1]/[Pl] (15)
- k4 [STARCH] [PI]
~'^'t'P~~ = k5 tDHAP13 Cp2l (16)
- k? [DHAP2] [ADP2] - kg [DHAP2] [ATP2]/[SUCR0SE]
~^P'dt'2^ = k7 ^DHAP2^ EADp2] - k2 [PGA2] [PI] (17)
d[SUCR0SE] = ¡-DHAp2j [AjP2]/[SUCR0SE] - [EXPORT] (18)
d_[R_uBp] = 3/5k [DHAP1] [ATP1] - [RuBP] [COg]. (19)
In addition to DHAP and PGA, separate tanks in chloroplast and
cytoplasm are maintained for ATP, ADP, and P. Their differential
equations are

33
d[ATPll = k [|_IGHT] [ADP] [PI] (20)
at y
- k3 [PGA1] [ATP1] - k4 [STARCH] [PI]
- k. [DHAP1] [PGA1] [ATP1]/[P1]
o
- k1Q [DHAP1] [ATP1]
d[ADPl] = _ d[ATPl] /21\
dt dt
= k5 [DHAP1] [P2] + 2k6 [DHAP1 ] [PGA1 ] [ATP1]/[P1] (22)
- k4 [STARCH] [PI] - k2 [PGA2] [PI]
- kg [LIGHT] [ADP] [PI]
d-^P2-l = k? [DHAP2] [ADP2] (23)
- kg [DHAP2] [ATP2]/[SUCROSE]
d[ADP2] ^ -d[ATP2] (24)
dt dt
= k2 [PGA2] [PI] + 2kg [DHAP2] [ATP2]/[SUCR0SE] (25)
- kg [DHAP1] [P2].
Some terms require numerical constants in order to maintain the system's
carbon and phosphate balances.

34
Most of the terms in these equations are concentration driven in
the sense that higher substrate or cofactor levels increase the proba¬
bility of a reaction. Allosteric effects should be distinguished; in
equation (14), the last term, PGA1, behaves like the substrate DHAPl, but
its effect is to promote the enzyme which catalyzes the reaction. In the
same term, PI acts to allosterically inhibit the process rate. The
algebraic form of the inhibitory effect is arbitrary in this equation.
Different responses could be obtained with different algebraic arrange¬
ments. Without in vivo response curves, a very simple feedback response
has been chosen.
In the schematic given in Figure (10), the components of equation (1),
which flow into and out of the blackbox, are each treated differently.
This reflects certain assumptions about the paths which each input and
output to the photosynthesizing system must follow. The source of the
PAR is represented schematically as a circle rather than a tank, since
the absorption of quanta has no effect on the rate of quanta arriving at
the active site. In contrast, C02 is a tank placed inside the chloroplast,
implying that concentration of available CC^ is affected by the rates of
CO^ arrival and exit at the active site. Water is ignored, since it is
always present in abundance for chemical reaction, even when the plant is
under water stress. Oxygen which is liberated in the chloroplast is also
ignored because it has only a minor impact on the high levels of 0^
already present due to diffusion from the atmosphere. Finally, sucrose
(carbohydrate) is exported according to some arbitrary function with a
dependence on sucrose concentration.
The most glaring shortcoming of the model developed so far involves
the first step in the Calvin cycle. This is the rate limiting reaction
for the entire system. As such, it must be considered in more detail.

35
A second major omission from the model is the competitive oxy¬
genase reaction, photorespiration, which is closely related to the first
Calvin cycle step, the carboxylase reaction.
Carboxylation, Photorespiration and Enzyme Kinetics
As described in equation (1), the first reaction in the Calvin cycle
is the fixation of CC>2, which can be abbreviated for purposes of a
Michaelis-Menten style analysis to the following
C02 + RuBP 2 PGA. (26)
RuBPc
Water has been eliminated since it is always at saturation levels
and does not affect the reactions rate. In competition with this reac¬
tion is photorespiration, which can be written as
02 + RuBP 3/2 PGA + 1/2 C02. (27)
RuBPo
Equation (27) is not strictly chemically correct as written. Actually,
phosphoglycolate is a product of this reaction that goes on to produce
C02 and PGA, which are products of interest in this model. Both of
these reactions utilize the same enzyme, called ribulose bisphosphate
carboxylase (RuBPc) in equation (26) and ribulose bisphosphate oxygenase
(RuBPo) in equation (27). In addition, both reactions require the same
second substance, RuBP, which is often assumed to be at saturating con¬
centrations [Jensen et al., 1978], allowing it to be ignored, like water.
With this assumption, both reactions above can be approximated by first
order processes which can be analyzed with enzyme kinetic theory.
Consider the reactions to be occurring in a well mixed medium, with
concentrations of carbon dioxide substrate, [C02] , oxygen substrate,

36
[02] , ribulose bisphosphate substrate [RuBP] and activated ribulose
bisphosphate carboxylase-oxygenase enzyme (E). Assume that the enzyme
reacts with either CO^ or O2 as a function of the activated enzyme's
relative affinity for the two substrates and the temperature adjusted
relative concentrations of the two substrates. Under the assumption that
RuBP can be ignored because it is at saturation levels, the carboxylation
reaction equations are
C1
E + C09^=± ECCL (28)
C2
C5
EC02 »■ PGA,
where , C2 and are reaction rate constants, and EC02 is the enzyme
substrate complex. These equations can be manipulated to yield a
Michaelis-Menten equation of the following form:
V c =
Vcmax [C02]
[C02] + Kc
(29)
where Vc is the rate of substrate C02 utilization, Vcmax is the maximum
rate of substrate C0o utilization and K is the concentration of sub-
2 c
strate C02 that will sustain the reaction at 1/2 the maximum rate. The
corresponding equation for the oxygenase reaction is
Vomax [0?]
Vo= ro2j +k0 - (30>
where the variables are analogous to those in the preceding equation.
Given that both of these "first order" reactions use the same enzyme and
assuming that neither substrate affects the affinity of the enzyme for

37
the other, they can be treated as a classic case of competitive inhi¬
bition. The resulting equation for carboxylation which includes this
competitive effect is
Vco
Vcomax [C02]
rc02j + Kc (1 + L02J/Kq)
(31)
If RuBP is not assumed to be at saturating levels and is included in
the analysis, the carboxylation equations must be expanded to include
an intermediate reaction as follows:
E + C02 ^ ECO,
c3
EC02 + RuBP £ EC02RuBP
EC02RuBP C5 E + PGA ,
(32)
where C2 and are reaction rate constants and EC02RuBP is a second
stage substrate-enzyme complex. Assuming that each substrate combines
with its specific site without either substrate affecting the enzyme's
affinity for the other, then the carboxylation equation is
Vcr = Vcrmax
[co2]
V.
[RuBP]
[C02] + Kc y^LRuBPJ + K,
(33)
As before, parallel development yields the following oxygenase equation
Vor = Vormax
[02]
[02] + Ko
(.. ..LRuBPJ )
^[RuBP] + Kr y
(34)
These relationships describe the flow rates among the reactant and
product pools as shown in Figure (11).

38
Figure 11. Carboxylase-oxygenase pathway schematic. This schematic
models the competition by 0^ and CC^ for RuBP. The numbers represent
stoichiometric balances for each path and the new interaction
symbol represents a Michaelis-Menten function.

39
From the equations developed, it is postulated that the rate of
photosynthesis is a function of the substrate concentrations within the
stroma. The carboxylase reaction is regulated by the concentration of
CC>2 at the reaction site, while the oxygenase reaction is a function of
C>2 concentration and both processes depend on the RuBP level. Since both
pathways draw on the available supply of RuBP, the steady state level is
lowered, which effectively depresses both reaction rates [Canvin, 1978],
The effect of this analysis on the model is to change the functional
form of the flows among the tanks involved in the first Calvin cycle
reaction. This involves the differential equations for PGA1 and RuBP,
which are numbers (13) and (19), respectively. Instead of the simple
algebraic product of concentrations, equations (33) and (34) are used
to model flows from the RuBP tank and to the PGA tank. The new balance
equations are
d[PGAl]
dt
2 Vcrmax
+ k2 [PGA2] [PI]- k3 [PGA1] [ATP1]
(35)
d[RuBP]
dt
= k1Q [DHAP1] [ATP1]
(36)

40
Note that in equation (35), the first term on the left hand side is
multiplied by a factor of two. This is consistent with the stoichiometry
of equation (7), in which one mole of RuBP is oxidized by one mole of
C02 to yield 2 moles of PGA. In the oxygenase reaction, the factor is
3/2. It remains to consider the pools of C02 and 02 in the stromal
compartment [Hall and Bjorkman, 1975; Bruin et al., 1970].
COq and 02 Concentration in the Stroma
Ambient levels of C02 are unaffected by the flux to an individual
leaf and can be treated as an unlimited source, while the carboxylation
reaction in the leaf's chloroplast acts as a sink. The effect is to
create a concentration gradient between the ambient source and each
chloroplastic tank. Between source and sink, there are resistances,
some of which are more constant than others. The primary resistance
to C02 flux in terrestrial plants such as soybeans, is caused by the
stomates, which respond to a variety of factors, such as light, leaf
water potential and C02 concentration. For stomatal response in this
model, water stress is ignored, light level is treated as an "opening"
switch, and C02 concentration does not affect resistance. Under these
assumptions, the daytime cellular C02 concentration, [C02]^, is treated
as a constant for any given ambient CC>2 level [Wong et al., 1979]. The
diffusion of C02 from the intercellular space, through the cell wall,
through the cytoplasm, through the chloroplastic membrane and into the
stroma, is the process of interest. In some previous models, this
process has been approximated by assuming a C02 concentration of zero
at the active site [Chartier and Prioul, 1976], and solving for a
"mesophyll resistance," which is a conglomerate of various membrane,
photorespiration and carboxylation effects. In this model, the reduction

41
of C02 is assumed to take place in the well mixed fluid compartment
of the chloroplast, the stroma, which has an average CO^ concentration
[C02] . The resistance to diffusive transport between the intercellular
space and the stroma is the sum of the two membranes and the intervening
cytoplasmic fluid, which is defined as membrane resistance, Rm. This
process is modelled as simple diffusion transport, using the equation
CER
[co2]. - [co2]
Rm
(37)
Using estimated values for Rm [Charles-Edwards and Ludwig, 1974],[CO2]
can be defined in terms of CER, which is the carbon dioxide exchange rate.
A second source of stromal C02 is the oxidation of phosphoglycolate
(PGly) shown in Figure (11). According to work done by Bruin et al. [1970],
one mole of oxygenated RuBP produces 3/2 moles of PGA and 1/2 mole of C02.
The input to the stromal CC>2 tank due to photorespiration can be written
as a fraction of equation (34). The rate of export from the C02 tank is
equal to the carboxylation rate in equation (33). Using these equations
as well as equation (37), a differential balance for the stromal CO^
concentration can be written as follows:
d[C02] [C02]. - [C02]
dt - Rm
+ ^ Vormax
[09]
[RuBP]
1 Merma x
\L02J + K0^LRuBPJ + Kr<
/ [C02] W [RuBp] ^
^i.C02J + Kc J I L'RuBPJ + Kr J ‘
(38)
The oxygen concentration at the reaction site within the chloroplast
is a function of diffusion from an unlimited ambient reservoir where

42
its absolute concentration is 700 times greater than [CO^]. In addition,
is being supplied in the thylakoids, where the light reaction is
splitting water faster than the oxygenase reaction can remove it.
Deviations from equilibrium with air levels of oxygen caused by the last
two processes are assumed to be damped out by the diffusion process.
Oxygen concentration is assumed to be in constant equilibrium with ambient
levels (21% at 1 atmosphere) [Sinclair et al., 1977].
Membrane Transport Considerations
During analysis of model results, a two-substrate Michaelis-Menten
function describing the exchange of DHAP1 for P2 was found to correspond
to empirical results much better than a first order function (see Figure
21 ). Therefore, the term
k5 [DHAP1] [P2]
used in equations (14) and (16) has been replaced by the following:
There is ample theoretical basis for modelling membrane transport with a
Michaelis-Menten function [Epstein and Hagen, 1952].
A second assumption has been made simply for the sake of convenience.
The modelled exchange of PI for PGA2 has been found to be a relatively
small term on a functional basis. Further, direct measurements of this
particular process have not been made. Thus, with no direct data on
process rate or how it may be altered by chloroplastic or cytoplasmic
conditions, the term is too arbitrary to remain in the model. The term
k2 [PGA2] [PI]

43
is assumed to be small and without recognized control significance;
therefore it has been dropped from equations (13), (17), (22), and (25).
Competitive Inhibition of Sucrose Formation
As with membrane transport, the formation of sucrose was not well
modelled as a first order reaction. During model analysis it was found
that sucrose formation could be realistically modelled as a Michaelis-
Menten function of [DHAP2] competitively inhibited by [SUCROSE]. There¬
fore, the term
kg [DHAP2] [ATP2]/[SUCR0SE]
used in equations (16) and (18) has been replaced by the following:
Vdsmax [DHAP2]
[DHAP2J + Kd2 (1 + [SUCROSE]/Ks) *
The basis for modelling sucrose formation this way is provided by the
results obtained by Hawker [1967]. Those results indicated that the
conversion of sucrose phosphate to sucrose is regulated by competitive
inhibition of the mediating enzyme by sucrose itself. Since information
on [ATP2] is so limited, it has not been included in the new term.
The modelled system of equations as altered by the assumptions in
the preceding three sections is listed in Table (4). A final schematic
representation of the model as described by the system of equations is
given in Figure (12). In addition, a listing of major assumptions
involved in the model's development are listed in Table (5).
During model development many explicit and implicit assumptions
were made. In the following postscripts two important central assumptions
are considered in detail. The first is an explicit assumption about

44
Table 4. Biochemical photosynthesis model equations.
d[PGAl] _ 0 v ( [C02] \f [RuBP] \ (3!))
~dt VC 9 \rC02J + Kc ) 1 rRVBTJT IFJ
3 f ^2^
+ 2 Vormax
- k3 [PGA1] [ATP1]
d[DHAPl2 = [PGA1] [ATPl] + 2k4 [STARCH] [PI] (40)
- k1Q [DHAP1] [ATP1] - kg [DHAP1] [PGA1] [ATP1]/[P1]
- Vt|Pmax ( [dhaptT+V) ([P2]2i kp)
d.[.sTARCül = [DHAP1j [PGA1] [ATP1 ]/[PI ] (15)
at o
- k4 [STARCH] [PI]
d[DHAP2] WJ l [DHAP1 ] \ { [P2] \ //llX
dt = Vdpni3X ^[DHAPl] V KTJ [ [P2] + Kp j (41}
- k? [DHAP2] [ADP2]
Vdsmax [DHAP2]
" "[DHAP2J + Kd2 (1 + LSUCROSE J/Ks)
_d_[PGA2] = k [DHAP2] [ADP2] (42)
[RuBP]
[RuBPJ + Kr
d[SUCR0SE] _ *a Vdsmax [DHAP2]
dt LDHAP2J + Kd2 (1 + LSUCR'OSE J/Ks)
(43)
- [EXPORT]

45
Table 4. (contd.)
d[Ru|P] = |k^Q j-DHAplj [ATP] ]
- Vcrmax
[co2]
[RuBP]
LCOJ + Kc / l[RuBPJ + Kr
[o2]
- Vormax ^ ^j"+ Ko j ^RuBPJP+ Kr^
d^Yt^ = kQ ^LIGHT^ [ADP11 [pil
k3 [PGA1] [ATP 1] - k4 [STARCH] [PI]
kc [DHAP1] [PGA1] [ATP1]/[PI]
0
k]Q [DHAP1] [ATP1]
d[ADPl] = _ d[ATP1]
dt dt
d[pl] = VdDmax ( [DHAP1] \ ( [P2]
dt Vdpmax ^DHAp”j + Kdy^LP2j + Kp
+ 2kg [DHAP1] [PGA1] [ATP1]/[P1]
kg [LIGHT] [ADP1] [PI] - k4 [STARCH] [PI]
d[ATP2]
dt
= k7 [DHAP2] [ADP2]
Vdsmax [DHAP2]
LDHAP2J + Kd2 (1 + [SUCROSEJ/Ks)
d[ADP2]
dt
d[ATP2]
dt
(36)
(20)
(21)
(44)
(45)
(24)

46
Table
d[P2]
dt
d[C02]
dt
(contd.)
2 Vdsmax [DHAP2]
[DHAP2] + Kd2 (1 + [SUCROSE]/Ks)
Vdomax (. tDHAP1J ^ (. ^P2] \
- Vdpmax ^|_DHAP1j + Kd I ^LP2J + Kp )
(46)
= ([C02]i - [C02])/Rm
1
Vormax
[o2]
[RuBP]
L09J + Ko j l[RuBPJ + Kr,
- Vcrmax
[co2]
[RuBP]
LC02] + KcJ V L RuBP J +
Kr
(38)

47
CHLOROPLAST
[EXPORT]
Figure 12. Final photosynthesis schematic. This is a schematic repre¬
sentation of the equations in Table (4) and the assumptions in Table (5).
The new rounded interaction symbol indicates a Michaelis-Menten response.
All abbreviations are defined in Appendix 1.

48
Table 5. Key assumptions used in model development.
1. Intermediate biochemical compounds that are not at path selecting
points and do not allosterically affect enzyme activity levels can
be ignored.
2. RuBP carboxylase-oxygenase is assumed to have a constant activity
level which can limit overall CO^ fixation rate.
3. Starch and sucrose formation pathways are regulated by allosteric
control of enzyme activity levels which can be functionally expressed
as concentrations of inhibitors and enhancers.
4. Concentration of CO^ in the intercellular space is a constant
function of external CO^ concentration.
5. Concentration of in the chloroplast is assumed to be in equilibrium
with ambient 0^ level which is constant at a partial pressure of
210 mbar.
6. The dark reactions all take place in the stroma of the chloroplast
which is treated as a well-mixed reaction tank with uniform
concentrations throughout.

49
the enzyme kinetics of RuBPc-o and the second is an implicit assumption
about the thermodynamically uphill nature of the Calvin cycle. These
discussions help to demonstrate the ever-present perils of modelling
as well as the insights to be gained from modelling.
Postscript on RuBP Carboxylase-Oxygenase and RuBP Concentrations
Enzyme kinetic theory which was used in the last section to derive
the Michaelis-Menten style relationships for photosynthesis and photo¬
respiration relies implicitly on certain assumptions about the behavior
of an enzyme.
In the carboxylase reaction described in equation (32), it was
assumed that RuBPc had a constant activity level over the range of cir¬
cumstances for which the analysis applies. More precisely, the well-
stirred reaction tank (stroma) is assumed to have a fixed quantity of
enzyme, which is either tied up as an enzyme-substrate complex, or is
available for reaction. The available portion is expected to have a
certain affinity for the various substrates which is unaffected by
conditions inside the reaction medium. Recent work suggests that these
assumptions may not be applicable to RuBPc-o.
It is well established that the activity level of RuBPc-o, measured
in vitro, is highly variable [Bassham et al., 1978]. Until recently,
these measurements gave Michaelis-Menten constants which were consistently
too high to account for associated photosynthetic rates. It has now been
established that, if the enzyme is preincubated in the presence of CO^
and Mg++, then the activity levels in vivo reaction rates can be obtained

50
[Bahr and Jensen, 1978]. Even under these circumstances, the high
activity rate can only be maintained for a short period of time.
Based on their work, Jensen et al. [1978], have suggested that the
enzyme exists within the intact chloroplasts in a range of active states
which are regulated by the pH and Mg++ ion concentration. The chloro-
plast can be divided into two compartments, the stroma and thylokoid.
When exposed to light, a proton gradient is established between these
compartments which raises the pH in the stroma. In counter flow to the
hydrogen ions moving out, Mg++ ions move from the thylakoid to the
stroma. Thus, during the day, the enzyme's activity is enhanced and in
the dark it is deactivated. In support of this hypothesis, Bassham
et al. [1978] found that a stable pool of RuBP is maintained by chloro-
plast in the dark. This is surprising in view of the extremely negative
standard free energy change associated with the carboxylation reaction
(aG° - -8.4 kcal/mole). If the enzyme were active, the reaction would
certainly proceed rapidly and irreversibly. Although this evidence
seems compelling, very recent work by Robinson et al. [1979] indicates
that, in vivo, the activity level changes only slightly. Clearly, the
issue is controversial.
This raises the question of whether or not the postulated dependence
of photosynthesis on the concentrations of CC^, RuBP and is only
partially true. Does the changing pH of the reaction medium alter the
enzyme's turnover rate enough to affect the photosynthetic light response
curve? Do the assumptions put forth in the various biochemical-empirical
models actually predict biochemical observations? An example may clarify
the situation.

51
For a Cg plant under ambient levels of C02 320 vpm), Wong et al.
[1979] have found that, regardless of light level, the intercellular
level of CO2 is constant 250 vpm). Also, assume that Rm which is
the CO2 diffusion resistance associated with cell walls, membranes,
cytoplasm and chloroplast stroma, is between 1 and 5 sec/cm [Tenhunen
et al., 1977]. Then, rewriting equation (37), the stromal concentration
of C02 can be solved for any given carbon dioxide exchange rate, CER.
[C02] = [C02]i - CER * Rm (44)
Let CER1 = 1 g/m**2/hr,
CER2 = 5 g/m**2/hr and
Rm =2 sec/cm.
Then [C02] 1 = .28 gC02/m**3^192 vpm
[C02] 2 = .06 gC02/m**3^41 vpm.
The estimated stromal C02 concentration decreases by a factor of
4.67 for a five fold increase in the carbon exchange rate (CER). Assume
that the carboxylation reaction rate, Vcr, changes in the same proportion
as CER, then using standard chemical kinetics to estimate the relative
concentrations of RuBP
[RuBP]l Vcrl [C02] 2
[RuBP]2 " Vcr2 '"[C02]1 *
The calculation yields 47.9 times more RuBP in case 2 than in case 1.
Using enzyme kinetics as in equation (33) would yield an even larger
ratio.
This analysis seems reasonable, at saturating light levels C02
becomes limiting while ATP and NADPred levels are high, allowing for

52
very rapid replacement of RuBP used, thus RuBP 1evels are high while
CO^ levels are low and vice versa. This conclusion is completely incon¬
sistent with the biochemical literature. Jensen et al. [1978] found that
the RuBP pool sizes in isolated chloroplasts were approximately the same
under 25 microEinsteins/m**2/sec and 800 microEinsteins/m**2/sec, even
though the carbon exchange rate was 5 times higher under high light.
Bassham et al. [1978] found that the RuBP pool size did increase with
decreasing [CO2] in reconstituted spinach chloroplasts. [RuBP] concen¬
tration increased by 1/3 when CO2 was decreased from 202 vpm to 116 vpm.
Neither of these experiments were done on whole leaves, but the dif¬
ference in results observed and predicted with the equations above is
striking.
At present, the mechanistic nature of the enzyme RuBPc-o is not
well enough understood to be included in the model. When sufficient
data are available,it can be included by functionally adjusting Kc, Kr,
Ko, Vermax and Vormax to light level, or any other relevant parameter.
In the meantime, this exercise will illustrate the potential of modelling
biochemical pathways of photosynthesis, but unresolved complexities
should serve as a reminder of the limitations of this model.
Postscript on Photosynthesis-Respiration Roles of Chloroplastic PGA
Control over the photosynthetic rate may be directly related to the
dual purposes served by the first few reactions of the Calvin cycle. The
reversible nature of these reactions was briefly discussed in applying
simplifying assumptions to equations (16). The direction of these
processes is a function of straight forward thermodynamic considerations.
In this model, the direction of this sequence of chemical reactions is
not in question, since "forward" reactions predominate during photosynthesis.

53
However, the thermodynamic requirements that determine the net direction
of a reaction are manifested in the concentrations of the reactants. The
resulting dynamic balance among the various biochemical intermediates
has been postulated to be a central control mechanism regulating photo¬
synthetic rate [Walker and Robinson, 1978]. The following discussion
describes the thermodynamics involved and demonstrates how equation (8)
is affected.
The first product of photosynthetic CO^ reduction is 3-phosphoglyceric
acid (PGA), which, through three subsequent steps yields DHAP at the
expense of one unit each of ATP and NADPrec|- This process is shown
schematically in Figure (5) and the specific equations are numbers 1
through 4 in Table (1). The requirement for light generated energy
units in this sequence implies that the pathway is "uphill." Recog¬
nizing that the reactions are reversible and that the reverse "downhill"
reactions form part of the oxidative glycolytic pathway [Kelly et al.,
1976], the situation becomes even more intriguing.
During the daytime, when absorbed light energy is abundant, the
chloroplasts are autotropic, photosynthetically forming energy rich
carbohydrates, some of which are exported to the heterotrophic cytoplasm
and some of which are stored in the chloroplasts as starch. In the
dark, the chloroplasts, like the rest of the cell, are heterotrophic
and must obtain energy by breaking down carbohydrates. Thus, in the
light the "uphill" energy pathways predominate, while at night, the
"downhill" energy releasing paths are activated. PGA and DHAP are both
intermediates in both the "uphill" Calvin cycle and the "downhill"
glycolytic pathway.
The choice of which pathway is active can be shown by rewriting
equation (8):

54
PGA + ATP íBPGA + ADP aG° = +4.5 Kcal
(8)
For a reaction to occur, the free energy change (aG) must be negative.
Such reactions are termed exergonic. Chemical reactions with a positive
free energy change are termed endergonic and will not occur without
energy input. Qualitatively, the free energy change is the fraction of
total energy change which is available to do work as the system proceeds
toward equilibrium, in accord with the second law of thermodynamics. For
this reaction, the free energy change (aG) is a function of the law of
chemical equilibrium (or the mass action law) which simply states that
in a system at chemical equilibrium, the concentrations of reactants
and products will be such that the following expression holds:
[BPGA]
[ADP]
LPGA]
LATP'J
where Keq is the equilibrium constant.
Free energy change is related to the above relationship as follows:
aG + aG° + RT 1 n
[BPGA] [ADP]
[PGAJ [ATP] 5
where R is the universal gas constant, T is absolute temperature and aG
is the standard free energy change. At equilibrium conditions for a
given temperature, free energy is minimized (entropy is maximized),
allowing for no further change in free energy (aG = 0). Therefore, the
standard free energy is expressed as
AG° = -RT In (Keq).
The net reaction direction, therefore, depends on the concentrations
of products and reactants at a particular time. Since the standard free

55
energy for this reactionis a positive 4.5 Kcal, the balance of concen¬
trations must be such that
Kcal/mole
if the forward reaction is to proceed. At 25° C the required concen¬
tration balance can be calculated for the Calvin cycle to predominate;
the ratio of reactants to products must be
The ratio ATP/ADP is reported to be in the range of 1 to 10 [Heber, 1974];
therefore, the ratio of PGA to BPGA is expected to range between 2000
and 200. Thus, the chloroplastic levels of BPGA under lighted conditions
are expected to be very low [Walker and Robinson, 1978]. This conclusion
is consistent with the relative abundance of data on the PGA concentra¬
tion and the almost total lack of data on BPGA levels.
In summary, when chloroplasts are exposed to light, the Calvin cycle
pathway providing RuBP for C0^ reduction is enzymatically activated,
rapidly leading to production of PGA. As the concentration of PGA
rapidly increases and the balance of ATP to ADP responds to the balance
of light levels and bioenergetic requirements, the "forward reaction" is
quickly established and photosynthesis proceeds. Concentrations and
flow between tanks quickly reaches a quasi-steady state which is a func¬
tion of all the factors affecting the balance of intermediates such as
light driven regeneration of ATP. These various factors have been
incorporated into the model and are analyzed in the following results
section.

MODEL RESULTS
The biochemical photosynthesis model outlined in Figure (12) and
Table (4) is functionally complete. Given a complete set of data, it
would be possible to do computer simulations without further assumptions.
However, the data set required would be extensive, precise and subject
to wide variations from one set of conditions to another. In an effort
to circumvent this problem and to evaluate the model's behavior, a
series of simple flow situations have been posed, based on partial data
sets and supplemental assumptions. Measured substrate and product
fluxes and concentrations of intermediates given in the literature have
been used to analyze specific tanks within the model for consistency
with the real world.
This section emphasizes the feedback interdependence of the entire
system, which expresses itself in control of the photosynthetic rate.
At the biochemical level a steady flow system is established in response
to external conditions, such that intermediate concentrations are adjusted,
partitioning between starch storage and sucrose is delineated and net
carbon uptake is fixed. The analysis centers on the flows of CO^ into
and out of the modelled system. The analysis begins with the modelled
CO^ balance, followed by the starch balance, the partition regulating
phosphate balances and,finally, the sucrose balance. Working forward
along the photosynthetic carbon pathway through each of these key tanks,
the response of each balance equation is evaluated. By considering how
56

57
the modelled tank balances compare to measured concentrations under
differeing steady flow situations, the model's usefulness can be tested.
The Chloroplastic Carbon Dioxide Balance, [CO,-,]
The CO^ concentration balance in the stroma of the chloroplast is
described in the model by equation (38):
- Vcrmax
[RuBP]
L RuBP J + K
9
where the right hand terms represent fluxes due to diffusion, photo¬
respiration and photosynthesis, respectively. Under steady flow condi¬
tions, the chloroplastic CO^ concentration is in steady state and
equation (38) can be written as follows:
[C02]i - [C02]
Rm
[RuBP] \
[RuBP J + Krj
Vcrmax [CO^]\
W+nW
Vormax [O^lV
"L¥ VVÍ
(47)
The equation has been rearranged so that each side equals the net flux
of ambient CO^ into the chloroplasts, referred to as net photosynthesis
or the carbon dioxide exchange rate (CER). Thus the following two equa¬
tions can be written as:
CER
CER
[co2]. - [co2]
Rm
’ [RuBP] \r/Vcrmax [C02])
I RuBP J + KLCOgJ + Kc j
1 ( Vormax [0o] \
2VL02J + Ko /
(37)
(48)

58
Equation (48) involves eight biochemical parameters on the right hand
side, all of which have been measured and reported under a variety of
circumstances with variable credibility. The parameter values to be used
in the following analysis are listed in Table (6). It is useful to
recognize parameters in Table (6) as two separate groups. The first
group includes Kq, Vormax, Kc, Vcrmax and Kr, which are assumed constant,
although that depends entirely on the constancy of the activity of the
enzyme, RuBPc-o. The second group, [02]» [CO^] and [RuBP], is assumed
to vary, although under real world conditions, [C^] is approximately
constant.
By rearranging equation (48), the values in Table (6) can be used
to solve for [CC^] as follows:
[co2] =
= 128 vpm .
For the specific experimental treatment presented by Heldt et al. [1977],
the [CO^H is 128 vpm or 4.3 pM dissolved CC^. As a check on the value,
equation (47) can be rearranged to solve for Rm.
Rm = ([C02]. - [C02]) / CER = 1.84 sec/cm
The value obtained compares well with Rm values found by various inde¬
pendent researchers. Several values are presented in Table (7) for
comparison.

59
Table 6. In vivo biochemical parameters used in model evaluation.
Biochemical
Parameter
In Vivo Value
Reference
[CO2]a
320 vpm
Wong et al. [1979]
[CO2]i
230 vpm
Wong et al. [1979]
Kc
230 vpm
Bahr and Jensen [1978]
Vcrmax
300 pmol C^/mg chl/hr
Farquahr et al. [1980]
[o2]
210 mbar
Sinclair et al. [197 ]
Ko
330 mbar
Farquahr et al. [1980]
Vormax
80 pmol 02/mg chl/hr
Kent and Young [1980]
[RuBP]
280 pM
Heldt et al. [1978]
Kr
30 pM
Bassham et al. [1978]
Note: This table contains recent approximation-measurements of the
various parameters in equations (47) and (48). The term in vivo
refers to the functioning living plant; such values are not necessarily
constant when biochemical systems are reproduced outside the functioning
plant, in vitro. Abbreviations are in Appendix 1.

60
Table 7. Mesophyll
resistance values
from the literature.
Mesophyl1
Resistance
Crop
Reference
6.8 sec/cm
Bean
Chartier et al. [1970]
2.3 sec/cm
Wheat
Ku and Edwards [1977]
2.9 sec/cm
Cotton
Jones and Slayter [1972]
Note: This table contains suggested Rm values for Cg plants as
determined by independent researchers. These values^compare favorably
with the value obtained using Table (6) in vivo parameters.

61
As a first analysis of the model sensitivity, a series of CER vs
[CO^] response curves at various constant RuBP concentrations have been
generated while [0^] is constant at 210 mbars. Since both RuBP and CO^
are substrates in the carboxylation reaction, it is expected that to
increase either one will increase photosynthetic rate. As shown in
Figure (13), the modelled responses are consistent with reported CER
responses to CO^ concentrations.
In a more specific test of the model's sensitivity, equation (48)
is used to generate CER from 6 pairs of RuBP and CC^ concentrations for
comparison with data obtained by Bassham et al. [1978] in experimental
work with reconstituted spinach chloroplasts. When the values in Table
(6) are used, the results are greatly shifted. Recognizing that RuBP
c-o activity is certainly reduced in vitro, values for Vcrmax and Vormax
were lowered to 140 pmol CC^/mg chl/hr and 28 umol 02/mg chl/hr, and K£
increased to 400 vpm. With the modified biochemical constants, the
comparison between modelled and measured values is quite good.
The characteristic behavior of the simulated CER response to [CC^]
is consistent with the in vitro data of Bassham et al. [1978]. In addi¬
tion, the magnitude of the simulated response was similar to those results.
Simulated and measured values are compared in Figure (14).
The effect of photorespiration can be examined by varying the level
of 02 for different fixed values of [C02] and [RuBP]. Results are
graphically presented in Figure (15). The trends predicted for changing
O2 values are consistent with general observations. Higher levels of
oxygen increase the rate of photorespiration and decrease the carbon
dioxide exchange rate.
The results of the modelled initial fixation of carbon are generally
consistent with empirically observed behavior. Moving forward through

CER, mg/dm**2/hr
62
Figure 13. Modelled [CO„]-photosynthesis-[RuBP] response curves. CER
is modelled in units of mg CC^ fixed/dm**2 leaf area/hour at four
different fixed concentrations of RuBP. [0^] is assumed to be in
equilibrium with an atmospheric partial pressure of 210 mbar.

CER, ymol C0?/mg chl/hr
63
Figure 14. Measured and modelled [C0?]-photosynthesis response curves.
Graphs compare measured values from Bassham et al. [1978] with values
from the model. The measured values were obtained in vitro. Therefore,
in vitro rate constants listed in Table (8) were used to obtain the model
values. The difference between the curves is in the Kc values. For the
dashed curve Kc equals 400 vpm. The other curve has aLKc value of 230 vpm.

64
Table 8. Comparison of in vivo and in vitro biochemical parameters.
Biochemical
Parameters
In Vivo Values
In Vitro Values
Kc
230 vpm
400 vpm
Vcrmax
300 pmol CO^/mg chl/hr
140 ymol ^/mg chl/hr
Ko
330 mbar
330 mbar
Vormax
80 ymol 02/mg chl/hr
37 ymol 02/mg chl/hr
Kr
30
30
Note: In vitro values are primarily from Bassham et al. [1978] and
in vivo values are from Table (6). All abbreviations are defined in
Appendix 1.

CER, ymol COp/mg chl/hr
65
Figure 15. Modelled [CL]-photosynthesis response curves. For the solid
lines [RuBP] is constant at 280 yM. For the dashed line [RuBP] is
280 yM for the left most value and 50 yM for the right most value. Since
increased [O2] increases the competition for RuBP its level is expected
to decline as in the dashed lines.

66
the model, fixed carbon is partitioned between paths leading to export and
to storage in the starch tank. Although it represents a relatively
small fraction of carbon fixed, starch formation rate and concentration
are highly visible barometers of shifting biochemical balances within
photosynthetic cells. As such, it is the next model compartment for
consideration.
Time Rate of Change of Starch
As an initial test of the starch balance predicted by the model in
equation (15), fluxes to the starch tank under light and dark conditions
have been considered. Since starch has been widely observed to accumu¬
late during the day and to be remobilized in the dark [Heldt et al.,
[1977], equation (15) should show a net flux into the starch tank under
lighted conditions and net export in the dark. Rewriting equation (15)
d[STARCH] = [DHAP1] [ATP1] [PGA1 ] / [PI]
- k4 [PI] [STARCH] , (15)
the first term on the right hand side is the functional rate of starch
formation and the second term is the rate of mobilization and export of
starch. There are five variables and two constants to be considered in
solving for the starch flux, d[STARCH]/dt. Although these variables
are dynamic, changing rapidly in response to external conditions, they
tend to have fundamentally different values under light and dark condi¬
tions. Table (9) lists relative values suggested from the literature
for some of the variables.
With these values, the rate of starch formation term would be a
factor of 20 lower in the dark than in the light, while the starch

67
Table 9. Chloroplastic concentration of key metabolites in light and
dark.
Metabolite
Light
Dark
Reference
[PGA1]
4.0 mM
1.6 mM
Kaiser and Bassham [1979]
[DHAP1]
.4 mM
.4 mM
Kaiser and Urbach [1977]
[PI]
3.0 mM
12.0 mM
Kaiser and Bassham [1979]
[ATP 1 ]
2.0
1.0
Heber [1974
Note: Recently measured-approximated concentrations of metabolites
important to starch formation and remobilization. The values for
ATP1 are relative numbers only.

68
mobilization term would be 4 times higher in the dark than in the light.
Equation (15) predicts that, in the light, starch formation will predomi¬
nate, while in the dark, starch will be exported. This result is con¬
sistent with observed empirical behavior.
If the variables [DHAP1], [ATP1], [PGA1] and [PI] are assumed to be
constant, the starch balance can be written as
d[STARCH] = A _ B [STARCH] , (49)
where A= [ATP1] [DHAP1] [PGA1] / [PI] and B = k^ [PI]. This equation
can be integrated to yield
[STARCH] = A (l-e-Bt)/B , (50)
which is valid as long as A and B are constant. Linder steady flow con¬
ditions, intermediates are at least roughly in steady state. In experi¬
mental work done by Upmeyer and Roller [1973], soybean seedlings were
grown under constant conditions: saturating light, 300 vpm CO^, 25° C
and 60% relative humidity. Artificial lighting was switched on for 16
hours and off for 8 hours every day. Their data indicated that, from four
hours after the lights were switched on until twelve hours later, the CO^
2
exchange rate (CER) was constant at 34 mg/dm /hr. These conditions
approximate a steady flow state; therefore, the variables A and B can
be assumed constant.
Measurements of starch flux and concentration taken directly from
Upmeyer and Roller's data can be plugged into equations (49) and (50)
to solve for A and B. Values are given in Table (10).
The predicted values of [STARCH] based on Table (10) values of A and
B are plotted graphically with the experimentally measured values in
Figure (16).

69
Table 10. Measured starch accumulation parameters.
Hours Under
Constant Light
d[STARCH]
dt
[STARCH]
4
4.25 mg/dm**2/hr
25.5 mg/dm**2
12
.87 mg/dm**2/hr
46.0 mg/dm**2
A = 8.45 mg/dm**2/hr
B = .16 hr-1
Note: Values are from graphical data presented by Upmeyer and Koller
[1973]. These values are used to calculate parameters A and B from
equation (49).

70
O
25
H 1 —H — 1 1 1
2 4 6 8 10 12
Hours at Constant Light
Figure 16. Measured and modelled starch accumulation response. Measured
values are from Upmeyer and Koller [1973].

71
Since the level of chloroplastic inorganic phosphate [PI] is
proportional to starch mobilization and inversely proportional to
starch formation, it is the primary functional mechanism affecting the
starch accumulation rate. To determine how changes in [PI] affect
[STARCH] a proportionate family of constants was calculated.
The ratio A/B is numerically equivalent to the maximum predicted
concentration of starch. The curves resulting from the five sets of
constants are given in Figure (17).
The general trend predicted by the set of curves in Figure (17) is
consistent with observations that starch accumulation is increased as
inorganic phosphate levels are decreased. In experimental work com¬
paring starch levels in phosphate deficient plants and phosphate rich
plants, starch concentrations were as much as 10 times higher in the
plants deprived of phosphate [Herold et al., 1976]. The starch levels
predicted and graphed in Figure (17) mimic these observations, ranging
over a factor of approximately 10.
A more realistic analysis of the model's starch balance must con¬
sider the other variables [DHAP1], [PGA1] and [ATP1] in addition to
inorganic phosphate [PI]. The regulatory role played by the precise
mix of these variables can be explored in more detail by using a set of
data in which the chloroplastic level of [PI] was held at four differing
quasi-steady state levels. Heldt et al. [1977] manipulated [PI] levels
in a suspension of chloroplasts by controlling the level of inorganic
phosphate in the medium external to the chloroplasts. This is equiva¬
lent to controlling [P2] in the model. Experiments were short term, 10
minutes and all external variables such as light, temperature and pre¬
treatment of chloroplasts were the same for each [P2]. Pertinent data
from the experiments are listed in Table (12).

[STARCH], mg/dm**2
72
Figure 17. Time courses of modelled inorganic phosphate-starch response.
[P1]r is the relative concentration of chloroplastic inorganic phos¬
phate. It is equal to the normalizing ratio [Pl]n/[P1]3 given in Table 11.

73
Table 11.
Starch accumulation as a function
concentration.
of inorganic
phosphate
n
[PI ]n/[P1]3
An
mg/dm**2/hr
Bn
hr"
An/Bn
mg/dm**2
1
2.00
4.22
.33
12.8
2
1.33
6.34
.22
28.9
3
1.00
8.45
.16
51.3
4
.80
10.56
.13
80.2
5
.67
12.67
.11
115.5
Note: This table demonstrates how changes in the relative value of [PI]
effect the starch formation parameters A and B. Relative values of [PI]
are obtained by normalizing [Pl]n by [PI]^*
i

74
Table 12. Measured chloroplastic-cytoplasmic inorganic phosphate
interactions.
Metaboli tes
Mm
1
2
Treatment
3
4
[P2]
.96
.43
.19
.08
[PI]
9.60
7.00
4.00
2.20
[PGA2]
.004
.009
.016
.024
[PGA1]
2.90
6.00
6.90
8.90
[DHAP1]
.17
.33
.40
.25
[RuBP]
3.20
3.70
4.10
4.90
Rates
umol CC^/mg chl/hr
[STARCH]
.30
1.40
7.90
7.70
CER
91.3
108.40
113.90
59.70
Note: Metabolite and rate responses to changes in the cytoplasmic level
of inorganic phosphate. Values are from Heldt et al. [1977]. No data on
ATP levels were given. Abbreviations are in Appendix 1.

75
Assuming that in this short experiment starch levels are very low,
the mobilization term can be neglected. Therefore, starch accumulation
is a function only of the starch formation rate:
d [ST/^cHl =jjk [ATP1 ] [DHAP1 ] [PGA1 ] / [PI] . (51)
dt o
Values predicted by this equation are compared with measured values in
Figure (18). (No values for [ATP1] were given, so for convenience of
scale, assume that kg* [ATP1] is constant and equals 7.7.)
For the various steady flow situations outlined, the model correctly
mimics qualitative behavior and corresponds reasonably well with absolute
values. From this analysis, the most obvious feature of the modelled
starch tank to emerge is the central regulating role played by chloro-
plastic levels of inorganic phosphate. To further explore the inorganic
phosphate control mechanism as it affects starch accumulation as well as
carbon export, the [PI] tank is treated in the following section.
The Chloroplastic Inorganic Phosphate Balance, [PI]
In the experimental work summarized by the data in Table (12), dif¬
ferent levels of PI were maintained by manipulating the inorganic phosphate
concentrations in the medium, external to the chloroplasts. This was
equivalent to adjusting the cytoplasmic inorganic phosphate concentra¬
tion, [P2]. The correspondence between [PI] and [P2] is quite strong,
as can be seen in Table (12), and graphically in Figure (19).
This strong proportional dependence should be reflected in equation
(44), which is the chloroplastic inorganic phosphate balance equation:
d[P1] =
dt
Vdpmax [DHAP1] [P2]
([DHAP1] + Kd)([P2] + Kp2) + ¿k6
[DHAP1] [PGA1] [ATP1] / [PI]
- kg [LIGHT] [ADP1] [PI] - k4 [STARCH] [PI] .
(44)

[STARCH], umol C09/mg chl/hr
76
Figure 18. Measured and modelled inorganic phosphate-starch response.
Graph compares measured and modelled rates of starch formation as a
function of chloroplastic levels of inorganic phosphate, [PI]. Starch
accumulation rates are in units of ymol CC^ fixed as starch/mg
chiorophyll/hour.

IfJW ‘[2d]
77
[PI], mM
Figure 19. Comparison of chloroplastic and external concentrations of
inorganic phosphate. Based on data from Heldt et al. [1977].

78
In equation (44), the modelled dependence of [PI] for [P2] is in the
first term on the right hand side. This term represents the export of
DHAP1 from the chloroplast in strict counter exchange for inorganic
phosphate from the cytoplasm, P2. The second term on the right hand
side is the flux to the PI pool, resulting from the net dephosphorylation
of glucose phosphate in the accumulation of starch. Comparing the rates
of starch accumulation with C02 assimilation rates in Table (12), it is
clear that much more fixed carbon was being exported (term 1) than was
being stored as starch (term 2). This relationship is illustrated
graphically in Figure (20). Numerically, in the most extreme case with
[PI] equal to 2.2 mM in treatment 4, starch accumulation was approxi¬
mately 13% of the total carbon dioxide fixed and sucrose export was 87%
of C02 fixed.
In other experimental work, the maximum rates of starch buildup are
cited as being from 10% to 20% under normal conditions [Herold and
Walker, 1979]. Based on these data, the first term on the right hand
side of equation (44) is the primary process supplying inorganic phosphate
to the chloroplast. Therefore, the strong measured functional dependence
of [PI] on [P2] is also a predominant feature of the modelled [PI] balance.
In the discussion above, the modelled correspondence between the first
term on the right hand side and export of DHAP1 to the sucrose tank are
equated. This can be expressed as
[TRANSPORT]
(52)
where [TRANSPORT] equals the time rate of DHAP1 transport to the cytoplasm.
Equation (52) can be tested directly, using the data in Table (12), along
with assumed values for K
jl, Kp and Vdpmax. Results are shown in Figure (21).

CER, Mmol C02/mg chl/hr
79
120-r
100--
80..
60- â– 
40..
20-.
A
+—
2
Starch accumulation
4 6 8 10
[PI], mM
Figure 20. Comparison of carbon partitioning pathways. Compares total
C02 fixation rate with the rates of sucrose export and starch accumula¬
tion at various measured levels of chloroplastic inorganic phosphate,
[PI]. Based on data from Heldt et al. [1977]. CER is given in units
of micromoles CO2 fixed/mg chlorophyll/hr.

[TRANSPORT], ymol (XL/mg chl/hr
80
Figure 21. Measured and modelled inorganic phosphate-transport response.
Graphs compare the amount of fixed carbon transported from chloroplast
to cytoplasm as a function of [P2]. Modelled curve constants were
adjusted to intersect at the right most point. Measured values are
from Heldt et al. [1977].

81
For a comparison, a first order relationship is also tested and illus¬
trated in Figure (21). The first order function has the following form:
(53)
[TRANSPORT] = Kg [DHAP1] [P2] .
The modelled term based on two substrate Michaelis-Menten kinetics
clearly fits the observed data better than the first order relationship.
Under steady flow conditions, such that CC^ uptake (CER) equals carbo¬
hydrate production over a given period of time, concentrations of the
various cyclical intermediates are very nearly in steady state. With
this assumption, the [PI] balance can be analyzed in steady state, which
can be written as follows:
[DHAP1] [PGA1] [ATP1] / [PI]
- k4 [STARCH] [PI]) = kg [LIGHT] [ADP1] [PI] . (54)
In equation (54), the first term equals export from the chloroplast to
the sucrose tank, the second term is the net accumulation of starch
within the chloroplast. Taken together, the terms on the left hand
side represent total carbohydrate formation rate which, in steady flow,
must equal the carbon dioxide exchange rate. The right hand side of the
equation is simply the rate of [ATP 1] formation.
Using data from Table (12), equation (54) can be solved for the term
kg [LIGHT] [ADP1] at different values of [PI]. Since [LIGHT] is constant
in all four treatments, differences in the term reflect changing values
of [ADP1]. Results for the four treatments described in Table (12) are
listed in Table (13) and graphed in Figure (22).
The results show an increase in [ADP1]as [PI] decreases. If the sum
of [ADP1] and [ATP1] is assumed constant, then [ATP1] levels must decline

82
Table 13. Adenosine diphosphate formation as a function of inorganic
phosphate levels.
Val ue
1
Treatment
2 3
4
[PI] mM
9.6
7.0
4.0
2.2
CER mol CÜ2/mg chl/hr
91.3
108.4
113.9
59.7
kg [LIGHT] [ADP1]
9.5
15.5
28.5
27.2
Note: This table uses values from Table (12) to evaluate the relative
levels of ADP1 that result from changing PI levels. [LIGHT] and k are
constant in each treatment.

[LIGHT] [ADP1]
83
â– 1 1 1 1 1 1
2 4 6 8 10 12
[PI], mM
Figure 22. Modelled adenosine diphosphate-inorganic phosphate response.
Based on data from Heldt et al. [1977]. [PI] is the chloroplastic con¬
centration of inorganic phosphate. Adenosine diphosphate is a function
of [LIGHT] which was constant in the experimental work and the rate
constant, kg. Therefore, changes in the kg [LIGHT] [ADP1] term reflect
changes in the modelled concentration of AUPl.

84
as [ADP1] increases and the [ATP1] / [ADP1] ratio must therefore decrease
as [PI] decreases.
In general terms, the relationship found in Figure (22) is consis¬
tent with data presented by Kaiser and Urbach [1977], which detail the
interactions between [PI], [ATP1] and [ADP1]. In essence, they showed
that when internal levels of PI were reduced, the [ATP1] / [ADP1] ratio
responded immediately by decreasing dramatically. They further found
that the decline in [ATP1] / [ADP1] could be quickly reversed by
increasing the external supplies of inorganic phosphate, equivalent to
increasing [P2] in the model.
Further indirect evidence for the [ATP1] / [ADP1] ratio's dependence
on [PI] and [PGA1] is shown in Figure (23).
From Figures (22) and (23), the overall relationship that emerges
is a direct correspondence between [PI] and [ATP1] and an inverse pro¬
portionality between [PI] and [PGA1]. As explained in the model develop¬
ment section, the concentration of PGA1 is thermodynamically regulated.
For the forward cyclic PGA1 reaction to proceed against a relatively
large positive standard Gibbs' free energy change, the ratio in the
following function
must be very large. This constraint couples [PI] levels directly to
[PGA1] through its effect on the [ATP1] / [ADP1] ratio.
This explains the control path between chloroplasts and cytoplasm.
[PI] is closely dependent on [P2] and by regulating the level of ATP1,
[PI] can affect both the concentrations of intermediates and individual
reaction rates as was shown in Figure (19).

[PI], mM
85
6
4
2
O
N
\
\
\
S
\
\
o
o
o
[PGA1], mM
Figure 23. Measured chloroplastic PGA-inorganic phosphate response.
Based on data from Heldt et al. [1977],

86
The following section considers how the cytoplasmic inorganic
phosphate levels are regulated within the sucrose export system.
The Cytoplasmic Sucrose Balance, [SUCROSE]
Photosynthate that does not go to the starch tank flows to the cyto¬
plasmic sucrose tank, from which it is exported to the rest of the
plant. This balance is modelled by equation (43):
d[SUCR0SE] _ h Vdsmax [DHAP2]
dt " [DHAP2] + Kd2(l + [SUCROSE] / K )
- [EXPORT] ,
(43)
where [EXPORT] equals the time rate of sucrose export from the cytoplasm.
Under steady flow conditions, the sucrose tank is in steady state with
imports from the chloroplasts just offsetting exports to the rest of
the plant. In steady state, equation (18) can be simplified to the
following:
[EXPORT] =
h Vdsmax [DHAP2]
[DHAP2J + Kd2 (1 + LSUCROSEJ / K )
(55)
Equation (55) has two variables and three constants on the right hand
side. For purposes of analysis, assume that [DHAP2] is normalized by
some average concentration such that, at an average concentration
[DHAP2]n equals 1. Further assume that Vexmax is approximately equal
to the maximum rate of CO^ fixation, Vcrmax, which has been approximated
in Table (6) to equal 300 ymol CO^/mg chl/hr. and have been
assumed to equal 1.5 and 100 mM respectively, based partially on Hawker
[1967]. The responsiveness of equation (55) can be tested with these
values. Figure (24) illustrates the effect on [EXPORT] of varying

[EXPORT], ymol C0?/mg chl/hr
87
Figure 24. Measured and modelled sucrose concentration--[EXPORT] response.
Measured values (0) are from Hawker [1967]. Modelled values (•) are
modelled for different normalized DHAP2 concentrations. [EXPORT] is
given in units of ymol CO^ fixed and exported/mg chlorophyll/hour.

88
[SUCROSE] while [DHAP2]n is held constant, the dashed line is from data
taken by Hawker [1967], who did pioneering work on feedback inhibition
of sucrose formation.
Real World Scenarios
Much experimental work has been done on the relationships between
photosynthesis, starch and sucrose. A question of particular interest
is how partitioning between these photosynthetic end products and their
respective concentrations might functionally affect photosynthetic
rate. In researching this question, experimentalists have caused many
different techniques to alter levels of starch and sucrose in a wide
variety of plant materials and in settings ranging from laboratory to
field conditions.
Some of the more common methods of changing leaf carbohydrate levels
are manipulations of diurnal temperature regimes, ambient CO^ concentra¬
tions and by manipulating the source-sink balance of carbohydrates. In
each of these methods, enough work has been done to suggest certain
general response patterns, although there are numerous exceptions which
appear irreconcilable with the general trend. Direct manipulation of
source-sink balance fits into the model more simply than temperature
or CO^ manipulation and will be considered first.
Direct Manipulation; Sucrose Feeding
In two specific experiments [Moore et al., 1974; Habeshaw, 1973],
sucrose was directly applied to photosynthetic plant material. In both
cases, increased levels of external sucrose depressed photosynthetic
rate and increased carbohydrate concentrations in leaves. A large
fraction of the increased carbohydrate was in the form of starch. A
typical scenario can be applied to the model as follows.

89
The experimental plants are grown in some consistent environment,
resulting in a particular balance between the sucrose exported from
photosynthetic cells and the substrate and energy requirements of
plant's growing points. By direct external application of sucrose,
the concentration in the region around photosynthetic cells increases
and apparent demand for sucrose decreases (perhaps by disrupting a dif¬
fusion gradient). This results in decreased export and cytoplasmic
sucrose levels rise. High concentrations of sucrose cause [P2] to
decrease, which can subsequently decrease [PI] enough to reduce photo¬
synthesis. Low levels of PI are also directly linked to increased
levels of PGA1, which promote the accumulation of starch.
Direct Manipulation; Selective Shading
Another type of direct source-sink manipulation is the experimental
work done by Thorne and Koller [1974], in which experimental plants grown
in full light were completely shaded except for one leaf (the "source
leaf"). Control plants remained unshaded. The "source leaf" on the
experimental plant and a comparable leaf on a control plant were moni¬
tored for starch level, sucrose level, photosynthetic rate and inorganic
phosphate level.
After eight days, the source leaves from the shaded plants had much
lower levels of starch, higher levels of sucrose, higher levels of
inorganic phosphate, and higher photosynthetic rates than did the source
leaves from the unshaded control plants.
In terms of the model, this experiment poses an interesting problem.
The sink demand was much higher for the source leaves on shaded plants
than on the unshaded plants. According to the model, this should have
decreased the cytoplasmic SUCROSE levels, increasing [P2] and [PI],

90
and decreasing [PGA1], all of which would facilitate photosynthesis and
mobilization of starch.
All of these things happened, except [SUCROSE] increased steadily
from 1% to 3% dry weight after nine days. This apparent inconsistency
between the model and empirical results deserves close attention.
A central assumption in discussing the feedback biochemical controls
of the sucrose system is that cytoplasmic inorganic phosphate levels are
constant (in the short term). In this experiment, inorganic phosphate
levels were six times higher in the shaded plant's source leaves than
in the control plant after eight days of treatment. This means that both
sucrose and inorganic phosphate levels increased significantly at the
same time, which cannot be explained by the short term assumptions used
in the model as derived. This apparently paradoxical situation could
result simply from increased import of phosphate (perhaps being mined
from the shaded leaves which would have high levels available).
With higher levels of P2, larger pools of phosphorylated sucrose
antecedents can be maintained without affecting photosynthetic rates
via control of PI concentration. From Figure (24), it is clear that
export rates are increased by high concentrations of DHAP2, which rep¬
resents the pool of phosphorylated sucrose antecedents.
For the shaded plants in the Koller and Thomas experiment sink
demand was high. Even so, the source leaf maintained relatively higher
levels of sucrose than the control. This gradient promoted relatively
rapid export, which was evident in the higher CO^ exchange rates found
for the shaded plant's source leaves. At normal phosphate levels, the
high sucrose concentration maintained in these leaves would reduce avail¬
able inorganic phosphate, causing starch formation and reducing

91
photosynthesis. Importing phosphate would alter the balance of sucrose
to phosphorylated antecedents that could be tolerated without affecting
P2 and PI concentrations. Higher antecedent levels might drive sucrose
formation or appropriate enzyme levels might be increased, circumventing
the inhibition caused by the high sucrose levels. The model as derived
can mimic this experimental situation on any given day, but constants
related to enzyme levels and phosphate levels which are valid in the
short term could not follow the experiment through eight days.
Temperature Manipulation
As reviewed by Patterson [1980], temperature manipulation experi¬
ments frequently involve growing plants under one set of day/night
temperatures and then switching the acclimated plants to a different
pair of day/night temperatures. In general, changing the temperature
environment does affect photosynthetic rate, starch level and sucrose
level. One typical scenario might be as follows. Plants are grown in
a warm environment, for instance, 25/15° C day/night temperature.
Carbohydrate levels and CER are monitored. The temperature environment
is then changed to a cold night regime, 25/5° C, and as before, appro¬
priate measurements are taken. Expected results on the morning following
the first cold night might be as follows.
Photosynthetic rate would be suppressed [Rook, 1969], starch levels
would be higher than following a warm night [Hilliard and West, 1970],
and soluble carbohydrates, including sucrose concentrations would be rela¬
tively higher [Barlow and Boersma, 1976].
This proposed scenario is consistent with model behavior; increased
levels of sucrose should increase the concentrations of phosphorylated
sugars, decreasing [P2] which leads to increased starch accumulation and
decreased photosynthetic rate, as already described.

92
COq Concentration Manipulation
As reviewed by Guinn and Manney [1980], several C02 enrichment
experiments are described in which plants are grown in a particular C02
concentration and then exposed to a different C02 concentration.
An experiment by Mauney et al. [1980] is representative. Cotton
plants were grown in an atmosphere with 330 vpm C02, then were trans¬
ferred to an atmosphere of 630 vpm C02. During the first 2 hours after
transfer, the CER increased to a level 45% higher than the rate at low
C02 levels. The rate then began a slow decline "as starch accumulated,"
until net photosynthesis was only 15% above the rate at low C02 levels.
The plants were then switched back to 330 vpm C02 and photosynthetic
rate dropped below the initial rates in low C02 conditions. After three
days, the plants regained the initial rates of photosynthesis.
In terms of a modelled scenario, increased concentration of C02
causes proportionately more RuBP reduction of C02, and proportionately
less RuBP reduction of 02. Thus, more C02 can be fixed per molecule
of RuBP produced by the Calvin cycle and consequently, less ATP energy
units are required per unit of C02 fixed. The result is to increase
levels of important chloroplastic intermediates which facilitate increased
export to the cytoplasmic sucrose tank. As long as sink demand is high,
sucrose export rates are high and, as in the example above, the photo¬
synthetic rate is high. However, as the sink requirements are met, sucrose
exports decline and cytoplasmic sucrose levels increase until a new source-
sink balance is established; in the experiment above, the new balance had
a steady state photosynthetic rate 15% higher than the initial rate.
In the experiment's subsequent decrease in C0o level, the plants
were returned to initial external conditions, but internal starch level

93
was measurably higher. As a result the source-sink balance was altered.
In this model starch accumulation results from increased sucrose levels
which affect the chloroplastic levels of PI and PGA1 and increased
sucrose levels result from decreased export, which is a function of
low sink demand. In terms of the model, the plant's internal sink demand
was low and starch levels were high. Photosynthetic rates were lower
than had been the case initially. Until the plant was able to assimilate
the excess supplies of sucrose and starch, cytoplasmic sucrose levels
remained high, and [PI] remained low.
Finally, after three days, the starch levels dropped back to
initial levels, indicating that the excess carbohydrate had worked its
way through the system and the original source-sink balance was re¬
established.
The preceding scenarios have shown how the proposed biochemical model
could simulate alterations in carbohydrate production, utilization and
partitioning caused by diverse changes in external conditions. This
analysis emphasizes that starch and sucrose have integral roles in the
biochemistry of photosynthesis and are definitely not uninvolved products.
The proposed model offers a direct mechanistic explanation for end
product (starch and sucrose) inhibition of photosynthesis [Guinn and
Mauney, 1980]. Furthermore, this analysis indirectly offers some insight
into types of possible adaptation to changed environmental conditions.
This idea will be explored further in the results from the experimental
field work.

EXPERIMENTAL METHOD
Procedure
Field experiments designed to investigate short term photosynthetic
response and long term photosynthetic adaptation were conducted from
February through May of 1980. Data were taken which can be used for
further qualitative evaluation of the model developed in the preceding
chapters.
Soybeans (Glycine max L., cv. Bragg ) were planted on February 29,
1980 in four environmental control chambers located outdoors so that they
were irradiated by natural solar radiation. Plants were spaced equidis-
tantly 0.1 m from each other and 0.05 m from the chamber walls. This
arrangement produced a grid of 5 rows (N-S) and 20 columns (E-W) which
were designated by number (1-5) and letter (A-T). Plants along the
canopy edge were not used for any direct measurements or sampling. Each
unit was exposed equally to ambient irradiance, adequate nutrients and
similar soil water potentials throughout the experiment. Dry bulb
temperatures were controlled at 25° C both day and night. Chamber CO2
concentrations were maintained at 320 vpm in chamber 3 (Low-Low) and
at 640 vpm in chamber 2 (High-High). CO^ levels in chambers 1 (Low-High)
and 4 (High-Low) were held at 320 vpm and 640 vpm, respectively, until
7:00 a.m. on April 22, when their 00^ concentrations were reversed for
the remainder of the experiment. The experiment ended on May 10, 1980,
when the plants in all chambers were harvested.
94

95
From March 18 through April 9 vertical distribution of leaf area
was measured on four plants in specific grid positions within each
chamber. Measurements were made on the leaf area of the central leaf
in each trifoliate, internode lengths and overall height. These values
were used to calculate leaf expansion rates and to estimate leaf area
index, total leaf area per unit of projected ground area (LAI).
Diurnal samples were taken on six different days: April 11, April
16, April 21, April 22, April 29 and May 6. These days all had cloudless
mornings while afternoons had intermittent cloud coverage. Three tri-
foliates from upper sunlit leaves and three from lower shaded leaves
were sampled. These samples were taken three times during each diurnal
sampling period at 8 a.m., 2 p.m. and 5 p.m. In addition, at 11 a.m.,
two whole plant samples were taken from each chamber. All samples were
placed in labelled brown paper sacks and kept on ice until all four
chambers were sampled. Leaf area was measured with a Lambda Alpha digi¬
tal planimeter (model LI-3000). Samples were dried for 24 hours at 90° C,
placed in plastic bags and refrigerated until they could be weighed toan
accuracy of O.OOOg on a Mettler analytical balance.
The 11 a.m. whole plant samples were subdivided into groups based
on height distribution. The lower three trifoliates from both plants
were lumped together as subsample (A), the fourth and fifth trifoliates
were grouped as (B), the sixth and seventh (C), and so forth. Before
drying, these subsamples were measured for chlorophyll content, using
the procedure of Arnon [1949]. After drying, all samples were weighed
and specific leaf weights were calculated. Dry, weighed leaves were
ground in a Wiley Mill to a fine powder to pass a one mm screen in prepa¬
ration for laboratory analysis. The subsamples were measured for nitrogen

96
with micro Kjeldahl technique, and for inorganic phosphate with a
colorimetric technique [Tavssky and Shorr, 1953]. Selected samples were
analyzed for total available carbohydrates using the enzymatic pro¬
cedure described by Smith [1969] for extraction and a colorimetric test
for measurement [Nelson, 1944; Somogyi, 1952].
Physical Characteristics
Experiments were conducted in four plexiglás chambers similar to
the Soil Plant Air Research (SPAR) units developed at Clemson [Phene et al.,
1978]. The units measured 2.0 m by 0.5 m in cross section by 1.5 m tall.
The plexiglás panels were joined with aluminum angle braces and all
joints were well sealed with silicon caulk. The chambers could be
entered through the south panel (2.0 m by 1.5 m), which was secured
with bolts and sealed with a neoprene gasket, or through two small
panels (0.15 m by 0.15 m) on the north side, which were secured by
studs with wingnuts and sealed with neoprene gaskets. Air circulation
was provided at the rate of 4 air changes per minute by a continuously
operating squirrel cage fan housed in a duct on the chamber's north
wall. Inlet and exit baffles at chamber top and bottom insured good
mixing. The insulated duct work also contained a heat exchanger
(cooling coil), resistance heater, sample gas exit port, condensate
exit port and water injection system. The duct was also equipped with
a piston operated venting port (0.3 m by 0.2 m), which utilized pressure
gradients around the circulation fan to flush the chamber with ambient
air. A side view schematic of a chamber is given in Figure (25).
Each chamber was secured to a soil lysimeter 2.0 m by 0.5 m in
cross section by 1.0 m deep, constructed of steel and equipped with a
port for the pressurized injection of irrigation water and nutrient

97
SIDE VIEW
Figure 25. Control chamber schematic. Chamber environmentwas controlled
by a computer which was programmed to respond to four basic sensor signals:
quantum flux density, dry bulb temperature, dew point temperature and a
measurement of CCL concentration. Based on these signals the computer
regulated the input of CC^, H^O and heat to the chamber to maintain desired
conditions. The sample air flow line circulated air from the control
chamber to a gas analyzer which sent a millivolt signal to the computer.
More detail is provided in Figure (26).

98
solution, ports for tensiometers at 6 depths spaced 0.15 m apart, as
well as a drain valve from which accumulated water could be removed
through porous ceramic candles by vacuum pump. The lysimeters were
placed in pits 2.0 m by 2.0 m in cross section by 1.0 m deep, with an
access space on the north side of the system.
Controlled Environmental Factors
The main parameters controlled in this study were dry bulb temper¬
ature and COg concentration inside the chambers. Both were controlled
by digital computer, using feedback algorithms in conjunction with
appropriate sensors. Each chamber's dry bulb temperature was measured
with a thermocouple located near the exit air baffle at chamber bottom.
Every 10 seconds temperatures were measured and control decisions made
for each chamber. The control decision was whether the resistance heater
should be on or off since the cooling coils operated continuously. The
decision algorithm was based on both current temperature and the rate of
temperature change over the preceding 10 second interval.
00^ controls were somewhat more complex. They operated in two
automatic modes, one for daytime photosynthesis measurements and the
other for night time respiration measurements. In addition, the auto¬
matic controls could be overridden by manual controls, which allowed
special manipulations of chamber CO^ levels. CC^ concentration was
sensed with a Beckman Model 865 infrared gas analyzer housed 20.0 m
from the chambers in an instrumentation trailer. Each chamber was con¬
nected to the trailer by a continuous flow, closed gas sampling circuit.
Solenoids sequentially diverted sample gas from each of the four chambers
through the analyzer. Each circuit was sampled for 75 seconds to allow
for flushing and instrument stabilization. A complete sampling cycle

99
of the four chambers took 5 minutes. A schematic representation of the
control system is given in Figure (26).
Carbon dioxide exchange rate (CER) for each 5-minute cycling inter¬
val was calculated using conservation of mass as in the following equation
CER = (EMC02inj + MC02i - MC02e)/(.083)(AREA)(5 min) (56)
where zMC02inj = the sum of C02 injected during the 5-minute cycle,
kg/5 min,
MCO^i = the initial mass of chamber CO^ for current 5-minute
cycle, kg,
MCO^e = the mass of chamber CO^ at the end of the current
5-minute cycle, kg,
0.083 = the conversion of the 5-minute cycle time to units of
hours, hr/5 rnin, *
AREA = chamber ground surface area, m**2, and
CER = CO^ exchange rate, kg/hr/m**2.
An analysis of probable error is given in Appendix 5.
During the intervals between measurements, CO^ concentration was
maintained at desired levels using a control algorithm based on the level
of photosynthetically active radiation (PAR). Every 10 seconds PAR was
measured and used to predict CER for each chamber via an empirically
derived functional equation. The equation can be written as follows:
PCER = (PNMAX * PAR/(KPAR + PAR)) - RC (57)
where PCER = predicted CER, kg/m**2/hr,
PNMAX = maximum possible CER, kg/m**2/hr,
PAR = quantum flux density of photosynthetically active
radiation, pE/m**2/hr,

100
Figure 26. Control system schematic. Sensor signals were used in a
digital feedback circuit to control various inputs to the control cham¬
bers. The computer sampled [CO2] in each chamber by sequentially
opening sets of solenoids (H). Data were stored on disks. The system
was completed with a terminal which provided access to data and to the
control program in the computer.

101
KPAR = PAR for half maximal CER, yE/m**2/hr, and
RC = Respiration related correction coefficient, kg/m**2/hr.
Based on the predicted CO^ exchange rate, and a correction factor to
account for drifts detected by the 5-minute measurements, the 10-second
CO^ injection requirement, (MtX^Jinj, was calculated. In equation form,
MC02inj = PCER * AREA/360. + ([C02]d - [C02]m) * VOLUME/10 sec (58)
where PCER = predicted CER, kg/m**2/hr,
AREA = chamber ground surface area, m**2,
360.= conversion from an hourly to a 10 second basis, 10 sec/hr,
[COg^ = desired C02 concentration, kg/m**3,
[CO2]m = measured C02 concentration, kg/m**3
VOLUME = chamber volume, m**3, and
MCO2inj = mass of CO2 injection for current 10-second interval, kg/10 sec.
Dark respiration was measured at night over 15 minute periods each
hour. The chambers were each equipped with piston-operated venting
ports which were activated by computer control of solenoids in pressure
supply lines to the pistons. When the vents were opened, pressure
gradients created by the circulation fan flushed the chambers with
ambient air. Computer controls sequentially opened each chamber vent
for 15 minutes, closed the vent, and then CO2 concentrations were
measured continuously for 15 minutes. For this process, CC^ concentra¬
tion was recorded on strip charts that showed the increase in chamber
CC>2 concentration which resulted from dark respiration. One hour was
required to complete each cycle of respiration measurements for all
four chambers. As with photosynthetic rate, calculation of dark res¬
piration required a simple mass balance. The change in chamber CO2 level
during the 15-minute cycle was directly equated to dark respiration (RD) by:

102
RD = ([C02] - [CO,,] )* VOLUME * 4.0/AREA (59)
where [C023e = chamber C02 concentration at the end of the 15-minute
interval, kg/m**3/15 min,
VOLUME = chamber volume, m**3,
4.0 = the conversion factor from a 15-minute to an hourly basis,
AREA = chamber surface area, m**2,
RD = dark respiration rate, kg/m**2/hr, and
[C02]q = chamber C02 concentration at the beginning of the 15
minute interval, kg/m**3/15 min.
Since the chambers were not perfectly air tight, leakage exchanges
were expected. The following procedure was used to estimate leakage
exchange effects. After the respiration rate was determined with the
night time technique described above, C02 was injected until chamber
concentration was at 660 vpm. Then C02 level was continuously monitored
for 15 minutes and recorded by strip chart. The initial slops of the
tracings were always negative, indicating that leakage was removing CO^
from each chamber more rapidly than dark respiration could supply it.
The rate of total leakage loss (DL) was equal to the absolute sum of
the drawdown rate at 660 vpm (the slope of the recorded C02 concentra¬
tion) and the respiration rate.
DL = [C02]m660 * VOLUME/AREA + RD (60)
• 660
where [CO^ = chamber C02 drawdown rate measured at 660 vpm,
kg/m**3/hr,
VOLUME = chamber volume, m**3,
AREA = chamber surface area, m**2,

103
RD = dark respiration rate, kg/hr/m**2,
DL = diffusive leakage rate, kg/hr/m**2.
The leakage rate was considered to be a function of the gradient
between chamber and ambient levels of CO2. Since this driving force was
relatively stable and constant for each of the chambers, the differences
in leakage rate were treated as a function of differing resistances among
the chambers. Based on this assumption, diffusional leakage can be
expressed as follows:
DL = ([C02]d - [C02]a)/CR (61)
where [CO^]^ = desired chamber CO2 concentration, kg/m**3,
[C02]a = am^ient ^2 concentrat‘>on > kg/m**3,
CR = chamber resistance to diffusion, hr/m,
DL = diffusional leakage rate, kg/hr/m**2.
The resistance value for each chamber was obtained by combining equation
(60) and (61) to yield
CR = ([C02]d - [C02]a)/([CC)2]m660 *V0LUME/AREA + RD (62)
In order to approximate daytime chamber leakage, the resistance value
for each chamber was assumed to be constant. Then, using typical day¬
time ambient CO2 concentrations, 330 vpm (6.5 * 10-4 kg/m**3) for [C02]a
and the desired chamber values, [C02]d, the daytime leakage rate for each
chamber was calculated. The chambers were leak tested every 10 days to
reconfirm their resistance values. (See Appendix 5 for error analysis.)
Soil Respiration
The soil zone was separated from the upper canopy by a plexiglás
barrier supported about 25 mm above the lysimeter soil. Plants grew

104
through appropriately spaced holes which were sealed with foam and hot wax
when the plants were two weeks old. Air was drawn from a height of 6 m
and was pumped through a 30 gallon buffering tank to damp out local
fluctuations in ambient C02 concentrations. From the buffering tank,
air was pumped to each chamber through an inlet port at the east end of
each lysimeter, through the soil/plexiglas air space and out a port in
the west end of each lysimeter. CO^ flux from the soil was measured,
using an infrared gas analyzer (Beckman Model 865) which pulled reference
gas from the buffering tank and sample gas from each chamber's exit port.
Chambers were monitored automatically with a computer controlled multi¬
plexer which delivered sample gas from each chamber in sequence.
Water
Transpiration rates were measured manually by collecting condensate
from each chamber's cooling coils in a graduated cylinder for a speci¬
fied time interval (5 minutes). This was usually done three times each
day. When the overflow was not being caught in a cylinder, it flowed
into a large (18 liter) storage container. This system provided an
approximate measure of total daily transpiration. To maintain a soil
water balance, irrigation water was applied to replace the transpiration
losses. Vertical distribution of the soil water was measured with tensi¬
ometers. Accumulated water at the bottom of the lysimeter was periodi¬
cally removed through the drain valve. Dew point measurements were taken
using a dew point hygrometer which measured gas in the same sampling
circuit used for CO^ analysis. Tensiometer and dew point measurements
were taken simultaneously with the graduated cylinder transpiration
values.

105
Photosynthetically Active Radiation (PAR)
Quanta flux density of photosynthetically active radiation (PAR)
was measured above canopy with a Lambda Alpha quantum sensor (Model
LI-1905). Values were taken every 10 seconds and used for control of
C02 injection. At the end of a 5 minute CO^ sampling cycle, values were
averaged and stored as data on disks.
Problems
Diverse problems were encountered during the 10 weeks of field work.
Some of the difficulties arose from simple and unavoidable mechanical
failure, while others were technique or management errors. Each of the
problems affected results in a unique manner and to a different extent.
Some had a direct and recognizable effect, while others may have caused
biases over time which were not distinguishable.
In the control system, air conditioners were operated continuously
in every chamber, with the computer turning reheaters on or off based
on thermocouple readings from each chamber. On occasions when electrical
power was interrupted, the control program would crash, which left the
air conditioner running without any heater control. This caused chamber
temperatures to drop. In the worst case, temperatures fell to approxi¬
mately 13° C, at that point the air conditioner thermostats began to
control. Another difficulty with temperature control occurred when
computer storage disks were filled, which caused the computer to crash
without a power failure. This allowed heater control bits within the
computer to remain set. If a heater was on under these circumstances
it remained on until the program was brought up or power was interrupted.
Most of the time disks were changed before they were filled, however on
a few occasions the system did crash. At its worst, this problem

106
allowed the temperatures in two chambers to climb to approximately 45° C
for a period of several hours.
At the mechanical level, air conditioner coils occasionally froze,
which allowed daytime temperatures inside the chambers to climb. Even
without supplemental heating, chamber temperatures at midday rose above
40° C whenever an air conditioner was down. This problem occurred infre¬
quently.
A more troublesome mechanical problem occurred when diaphragms
ruptured in the sample line pumps. This allowed pumping to continue,
but mixed ambient with chamber air. Since CO^ levels were controlled
based on measurements of air in the sample lines, this caused the high
CO^ chamber air to be diluted and controls injected excessive CO^ into
those chambers. Usually, one diaphragm had to be replaced each week.
Another problem with CC^ controls resulted from the leaks that
developed in the chambers themselves which allowed outside air to dilute
CO^ levels in the high CO^ chambers. Leaks occurred in two ways:
plexiglás joints failed, and the automated mechanical port used for
night time respiration measurements failed to seat and seal properly.
The most damaging problem encountered during the experiment occurred
while searching for chamber leaks. The technique used was to inject freon
and use a freon detector to search for leaks around joints and seals on
the outside of each chamber. Unfortunately, the by-products of burning
freon are noxious. This caused no problem when burning outside the
chambers, but in one chamber the heater was on and the injected gas
severely burned the canopy's new growth. This occurred on the evening
of April 16 in chamber 2 (H-H) and affected the transpiration and photo¬
synthetic rates for several days. The plant canopy seemed to have
recovered by April 21.

107
A second problem involving direct damage to plants occurred from
late April through early May. In chambers 1 (L-H) and 2 (H-H) there
was an infestation of spider mites. As before, one of the first indi¬
cations was a change in transpiration and photosynthetic rates. The
mites were eliminated by May 2 and some recovery was evident by May 6.
It is not clear how much effect these problems had on the overall
plant response in the chambers involved.
Finally, the experimental procedure itself had some shortcomings.
The chambers were planted thickly so the canopy would close quickly.
This worked well. However, it caused the plants to grow tall and
spindly. When whole plant samples were taken from the chambers, other
plants were damaged. They were not broken, but tended to fall over
somewhat, causing the canopy architecture to be changed. Secondly,
shading was not provided around the edge of the chambers as the canopy
grew which means that portions of the canopy leaf area exposed to direct
PAR changed during the day. This is probably unimportant on a relative
basis when comparing results between chambers, but undoubtedly affected
absolute values.
One of the values most affected was leaf area index. Values obtained
were at least twice as large as in normal field canopies. This is not
too surprising when the total exposed canopy area is considered. When
the canopies were half a meter tall the fully sunlit area was approxi¬
mately 2%m**2 with an additional lJsm**2 of indirectly exposed edges.
In a field canopy the fully sunlit area is lm**2. In future work edge
effects must be carefully considered and avoided if possible.

EXPERIMENTAL RESULTS
Controls
Controls worked well throughout the experimental procedure;
desired temperature and CO2 conditions seldom varied by more than 5%
from control levels. Temperature was maintained within ±1° of the
desired value of 25° C, as shown in Figure (27). CC>2 levels in the
high concentration chambers were usually within ±20 vpm of the desired
level of 640 vpm, while the low concentration chambers were usually
within ±10 vpm of the 320 vpm control level. Examples of [C02]masa
function of time for both high and low concentration chambers are given
in Figures (28) and (29). CO2 controls worked least well early in the
morning (until 7:30 a.m. or thereabouts) and under rapidly changing
light levels.
Carbon Balance
On April 22, the CO2 concentrations in chambers 1 (L-H) and 4 (H-L)
were switched from 320 vpm to 640 vpm and from 640 vpm to 320 vpm,
respectively. In order to compare canopy response before and after
the transition, the switch was made during a period of clear weather.
Time courses for photosynthetically active radiation (PAR) [CO^]1 ,
[00^34 and the carbon dioxide exchange rates (CER) for each chamber
on April 21 are given in Figure (28). A parallel set of measurements for
the period following the switch on April 22 is given in Figure (29).
Comparing the measured light levels in the two figures confirms that
the two days were virtually identical.
108

109
26
<-> 25
O
24
V°'V\
26--
O *
O
25-
24-â– 
CHAMBER 1 (L-H)
/
*
-l 26
25 °C
24
CHAMBER 2 (H-H)
xo-o/
cr0\ P o o-
\/ \'
,o—o
CHAMBER 3 (L-L)
* 'A'A-A'A-A -a'\a_a_a A'\a, A' A_AAa. A-A' XA'A.
^0_G CHAMBER 4 (H-L)
f \
â–¡ \ n
â–¡-Ov /
Na-n
A â–¡!
V'D'D''0^n// a~° D'
íf
-â– 26
o
25°
+ 24
24
12
TIME, EST
Figure 27. Diurnal temperature control. Hourly measured chamber air
temperatures from noon on April 21 until noon on April 22. The desired
control temperature was 25° C for all chambers.

CER, mg/dm**2/hr [C0?]1, vpm
110
Figure 28. Time courses of PAR, [COg] and CER on April 21. This is
the day preceding the transition in cO^ levels. CER is given in
units of mg C0£ fixed/dm**2 land area/hr.
[C09]4, vpm PAR, yE/m**2/sec

CER, mg/dm**2/hr [C02]1, vpm
111
Figure 29. Time courses of PAR, [C0?] and CER on April 22. This is
the day following the transition in levels. CER units are given
in units of mg CO^ fixed/dm**2 land area/hr.
[C0,]4, vpm PAR, uE/m**2/sec

112
The graphs of each chamber's CER on the two days demonstrate the
strong correspondence between CC^ concentration and net photosynthesis.
Before the switch, chambers 2 (H-H) and 4 (H-L) maintained a net photo¬
synthetic rate approximately twice as great as chambers 1 (L-H) and
3 (L-L). After the switch, chambers 1 (L-H) and 2 (H-H) had the high
CO2 levels and the high net photosynthetic rates, while the chamber 4
(H-L) rate dropped down to the level of chamber 3 (L-L). Response to
the change in CC^ concentration was immediate. Another feature
seen in these graphs is that CER seems to peak somewhat before light
level. This effect will be considered in a later section.
Figures (28) and (29) also demonstrate the close relationship
between PAR and CER. Figures (30) and (31) provide a closer exami¬
nation of this relationship over a 12 day period in a series of photo¬
synthetic light response curves given for each chamber. Curves for
April 16, 21, 22 and 28 are given for chambers 1 (L-H) and 2 (H-H) in
Figure (30) and for chambers 3 (L-L) and 4 (H-L) in Figure (31).
Looking first at chamber 1 (L-H) in Figure (30), the separation
between high [CO^] response on April 22 and 28 and low [CO^] response
on April 16 and 21 is striking. A less obvious feature is the increased
photosynthetic response to the same light level over time, indicating
the continued growth of the canopies, both before and after the switch.
Chamber 2 (H-H) does not show dramatic separation like chamber 1 (L-H)
since the CO^ concentration was constant at 640 vpm. However, the
increased photosynthetic response over time is clear, with the response
on April 16 being lowest and on April 28 being the highest. Before the
switch chamber 2 (H-H) was roughly twice as responsive as chamber 1
(L-H), but after the transition the chambers' responses became nearly
identical by April 28.

CER, mg/dm**2/hr
113
Figure 30. Photosynthetic light response curves; Chambers 1 (Low-
High) and 2 (High-High). Quantum flux densities (PAR) are measured
in microEinsteins/m**2 land area/sec. C0? exchange rates (CER) are
measured in mg CO^ fixed/dm**2 land area/nour.

CER, mg/dm**2/hr CER, mg/dm**2/hr
114
Figure 31. Photosynthetic light response curves; Chambers 3 (Low-Low)
and 4 (High-Low). PAR and CER are on a land area basis.

115
Chamber 3 (L-L) response, given in Figure (31), shows a steady
increase with time, consistent with the constant CO^ levels (320 vpm)
maintained. Chamber 4 (H-L) response decreased dramatically from its
high point on April 21 when C02 level was reduced on April 22. By
April 28, the response curves of chambers 3 (L-L) and 4 (H-L) were
very similar.
Dark respiration measurements taken at night corroborate and sup¬
plement the daytime net photosynthesis measurements. A comparison of
each chamber's dark respiration rates on selected dates around the
transition is given in Figure (32). Dark respiration is a measure of
metabolic activity which presumably increases as more C02 is photosyn-
thetically fixed. The graphs in Figure (32) show that before the switch,
chamber 4 (H-L) with high C02 had a significantly higher respiration
rate than did chamber 1 (L-H);after the switch this was reversed com¬
pletely.
Transpirati on
Another dramatic difference between high and low C02 concentrations
was in transpiration rates. Chambers with elevated C02 levels had
lower rates than the low C02 chambers. When [C02] was switched, the
transpiration rates adjusted to the new levels immediately. A time
course of rates is given in Figure (33). Chambers 1 (L-H) and 4 (H-L)
can be seen to rapidly switch on April 22, the transition date. This
is significant to the carbon balance, since transpiration is a direct
indicator of stomatal resistance to gas diffusion. Thus, reduced trans¬
piration rates in high C02 chambers indicate that the higher C02 gradient
is somewhat counter-balanced by increased resistance to the C02 flux.
This response has a beneficial side effect. High C02 chambers have

116
Figure 32. Time courses of dark respiration rates. Average measured
pre-dawn respiration rates for each chamber from April 6 to April 30.
C0„ concentrations were switched in chambers 1 (L-H) and 4 (H-L) on
April 22. Rates are measured in mg CO^ evolved/dm**2 land area/hour.

TRANSPIRATION RATE, g /dm**2/hr
117
16 18 20 22 24 26 28
APRIL
Figure 33. Time courses of transpiration rates. Measured midday
transpiration rates from April 16 through April 28. CO? concentrations
were switched in chambers 1 (L-H) and 4 (H-L) on April 22. Rates are
measured in g of H20/dm**2 land area/hour.

118
relatively greater photosynthetic rates than low CO^ chambers and they
have lower water requirements. To demonstrate this, a time course of
water use efficiency is given in Figure (34).
Plant Growth Parameters
Measurements of leaf area between March 20 and April 9 showed
that leaves in high CC^ chambers expanded more rapidly than those in low
CO2 chambers. In the case of the 2nd trifoliate, leaves in chambers 2
(H-H) and 4 (H-L) took 6 days to fully expand, while leaves in 1 (L-H)
and 3 (L-L) took 8 days. All of the leaves grew to about the same final
area. For the 4th trifoliate, leaves in chambers 2 (H-H) and 4 (H-L)
again expanded more rapidly, but their final area was smaller than the
low CO^ chamber leaves after 12 days of growth. These results are shown
graphically in Figure (35).
Total canopy leaf area index (LAI) has been estimated, based on
vertical leaf distribution data from whole plant samples taken through¬
out the experiment. The time course of LAI for each of the four chambers
is plotted in Figure (36). The results clearly show that high CC^
chambers had significantly greater leaf area per unit of land area (LAI)
than did the low CC^ chambers. After the switch in CC^ levels, the leaf
area in chamber 1 (L-H) continued to increase while chamber 4 (H-L)
began to decline. By May 3, chamber 1 (L-H) had a greater LAI than
chamber 4 (H-L).
The leaf area analysis can be put on a leaf mass basis using the
vertical distribution of specific leaf weights obtained in the whole
plant samplings. Results are given in Figure (37). As before, the
plants in low CC^ chambers had significantly less leaf mass than the
plants in high CC^ chambers before the switch. Also, as with leaf area,

WATER USE EFFICIENCY, mg CCL fixed/g ELO transpired
119
Figure 34. Time courses of water use efficiency. Measurements were
taken around noon on sunny days. The CCL levels were switched on
April 22 at 7:00 a.m.

LEAF AREA, cm**2
120
Figure 35. Time courses of individual leaf areas. The central leaf in
each trifoliate of four plants in each chamber was measured for length
and width. Values for leaf area are average values.

LEAF AREA INDEX
121
Figure 36. Time courses of leaf area index. LAI measurements are of
canopy leaf area divided by land area for each chamber from April 9
through May 6. Note that LAI measurements start at 4. The large values
for LAI resulted from light border effects which allowed crop surface
areas of 3.m**2 to be exposed to full sunlight for l.m**2 of ground area.

CANOPY LEAF MASS, g/m**2
122
Figure 37. Time courses of canopy leaf mass. Estimated total canopy
leaf mass for each chamber from April 11 through May 6. Leaf mass is
given on a land area basis.

123
the leaf mass of chamber 1 (L-H) increased and surpassed the leaf mass of
chamber 4 (H-L) after the transition. Overall, the leaf area index and
leaf mass time courses in Figures (36) and (37) appear rather similar;
however, there are distinctions. First, the leaf mass of chamber 1 (L-H)
seems to catch up with chamber 4 (H-L) on April 30, while the canopy leaf
areas are not equal until May 3. Furthermore, the final difference in
leaf areas gives chamber 1 (L-H) about 10% greater area, while the esti¬
mated leaf mass difference gives chamber 1 (L-H) more than 20% greater
mass than chamber 4 (H-L). These estimates are supported by the final
values for above ground biomass, harvested on May 10. Values are listed
in Table (14).
Variations in Photosynthetic Rate
As mentioned before, the daytime course of photosynthetic rates
given in Figures (28) and (29) appear to be somewhat skewed with respect
to the daytime course of solar radiation, such that photosynthetic rates
reach a maximum before the solar noon maximum at approximately 12:30 EST.
The implication is that photosynthetic rates in the morning were higher
than in the afternoon. For a more detailed consideration, morning and
afternoon data were used to generate separate photosynthetic light response
curves. In low light curves can be fitted using simple linear regression
techniques since response is linear. Typical results are given in Figure
(38), in which morning and afternoon regression 1ines for chambers 1 (L-H)
and 4 (H-L) are compared. The data used to generate these graphs are
listed in Table (15).
The results show that for chamber 1 (L-H), afternoon responses are
lower than the corresponding morning responses, particularly on April 22,
the day following transition. The responses in chamber 4 (H-L) are just

124
Table 14. Final above ground biomass.
l(L-H)
Chamber
2(H-H) 3(L-L)
4(H-L)
Mass, g.
863.
923. 730.
862.
Note: Values for total above ground dry weight are given. Biomass
includes stems, branches and leaves. Plants were harvested on May 10.

CER, mg/dm**2/hr
125
Figure 38. Morning and afternoon photosynthetic light response; Chambers
1 (L-H) and 4 (H-L). Curves result from data fitted by linear regression
techniques.

126
Table 15. Morning-afternoon photosynthetic data.
Date
KL-H)
Morning
CHAMBER
4(H-L)
Afternoon Morning
Afternoon
PAR
CER
PAR
CER
PAR
CER
PAR
CER
Apri 1
22
426.
56.3
324.
28.2
478.
27.7
332.
20.0
459.
57.7
353.
32.0
506.
28.4
360.
22.2
484.
57.9
381.
34.0
536.
30.8
390.
23.8
547.
63.0
422.
37.9
587.
33.4
431 .
25.6
599.
65.0
458.
40.5
637.
35.9
469.
27.7
0.
-3.4
0.
-3.4
0.
-3.2
0.
-3.2
Apri 1
26/25
338.
39.0
304.
34.4
330.
22.0
314.
23.0
368.
42.0
367.
41.1
360.
24.0
377.
27.7
397.
46.3
388.
42.0
389.
24.5
387.
28.0
444.
52.0
408.
43.9
432.
26.6
423.
30.7
491.
55.4
450.
48.2
481.
27.7
465.
33.0
0.
-3.7
0.
-3.7
0.
-3.5
0.
-3.5
Note:
These
data were
analyzed with
1 inear
regression techniques
to
generate the lines in Figure (38). Values for PAR are given in uE/m**2/hr
and for CER in mg CO^ fixed/dm**2 ground area/hr.

127
the opposite; afternoon regression lines are steeper than the corresponding
morning lines.
As a first indicator of the reliability of these regression lines,
their correlation coefficients have been calculated. They are listed
along with other regression data in Tables (16) and (17). The lowest
correlation coefficient found in either table is 0.981. This suggests
that the pattern is more than coincidental scatter. To test the null
hypothesis that the morning/afternoon pairs could be considered estimates
of a single true photosynthetic light response curve, a Student's t-
statistic has been calculated for each morning/afternoon pair. From the
t-statistic and the degrees of freedom for each pair, the level of con¬
fidence with which the null hypothesis can be rejected is prescribed.
The t-statistic and confidence level for each pair are listed in Tables
(16) and (17).
Results in Table (16) show that for chamber 1 (L-H), the difference
in morning and afternoon photosynthetic rates is significant on all five
dates shown, with a confidence level of at least 90% in every case. The
pattern of higher morning rates was unaffected by the CC^ transition on
April 22. Chamber 2 (H-H) also had higher morning photosynthetic rates,
as indicated by the positive t-statistics, however, the confidence levels
are not as consistently high as in chamber 1 (L-H).
Table (17) shows chamber 3 (L-L) to have a different pattern than
chambers 1 (L-H) and 2 (H-H). The t-statistic is negative on four of
the five days, indicating that afternoon photosynthetic rates were
greater than morning rates. The confidence level in all five cases is
excellent, higher than 95% in every case. Chamber 4 (H-L) has both
positive and negative t-statistics. Before the transition in CC^ levels,

Table 16. Regression analysis of photosynthesis data from Chambers 1 (Low-High) and 2 (High-Low).
CHAMBER
l(L-H) 2(H-H)
Morning, Date
A20
A21
A22
A26
M3
A20
A21
A22
A26
M3
CER @ 300 pE/m**2/sec
14.6
12.3
34.1
33.4
34.2
41.7
36.9
24.3
29.9
33.4
CER @ 500 pE/m**2/sec
27.0
22.7
58.1
58.0
60.0
71.5
66.0
44.3
54.7
58.5
Slope
.062
.052
.120
.122
.129
.149
.145
.099
.124
.126
Correlation Coefficient
.999
.999
.992
.998
.994
.990
.999
.993
.997
.998

Table 16. (contd.)
Afternoon, Date
A20
A21
A22
A25
M2
A20
A21
A22
A25
M2
CER @ 300 pE/m**2/sec
9.5
9.8
25.9
31.8
27.6
32.7
28.1
21.5
30.9
27.9
CER @ 500 pE/m**2/sec
18.3
18.6
45.4
55.2
49.2
57.9
50.8
40.0
55.4
50.3
Slope
.044
.044
.097
.117
.108
.126
.113
.093
.122
.112
Correlation Coefficient
.998
.998
.999
.998
.999
.992
.996
.998
.998
.999
t-Statistic
7.24
4.46
4.25
1.64
4.84
1.46
6.94
1.12
.32
2.95
Confidence Level
99%
99%
99%
90%
99%
90%
99%
85%
50%
99%
Note: Morning and afternoon photosynthetic response data under low PAR have been fitted by linear
regression. The hypothesis that morning and afternoon curves are both deviations from the same
"true" response curve has been tested. Dates are abbreviated: A for April and M for May.

Table 17. Regression analysis of photosynthesis data from Chambers 3 (Low-Low) and 4 (High-Low).
CHAMBER
3(L-L) 4(H-L)
Morning, Date
A20
A21
A22
A26
M3
A20
A21
A22
A26
M3
CER @ 300 uE/m**2/sec
14.7
9.5
11.6
11.8
11.9
50.4
42.0
15.7
18.0
20.2
CER @ 500 pE/m**2/sec
27.1
18.3
21.6
22.3
22.8
83.8
75.5
28.2
31.7
36.0
Slope
.062
.044
.050
.052
.055
.166
.153
.062
.068
.079
Correlation Coefficient
.999
.998
.998
.996
.992
.982
.997
.999
.988
.997

Table 17. (contd.)
Afternoon, Date
A20
A21
A22
A25
M2
A20
A21
A22
A25
M2
CER @ 300 pE/m**2/sec
13.4
12.9
13.8
16.4
14.8
46.7
34.8
17.3
20.9
20.9
CER @ 500 pE/m**2/sec
24.3
23.9
25.2
29.5
27.3
78.9
60.7
30.7
37.0
37.5
Slope
.054
.055
.057
.065
.063
.161
.128
.067
.080
.083
Correlation Coefficient
.996
.999
.998
.999
.999
.981
.993
.998
.998
.997
t-Statistic
2.94
-4.11
-2.62
-4.17
-1.62
.51
5.06
-2.32
-3.69
-1.03
Confidence Level
99%
99%
99%
99%
95%
50%
99%
99%
99%
80%
Note: Morning and afternoon photosynthetic response data under low PAR have been fitted by linear
regression. The hypothesis that morning and afternoon curves are both deviations from a single
"true" response curve has been tested. Dates are abbreviated: A for April and M for May.

132
chamber 4 (H-L) morning photosynthetic rates were higher, while after
the switch, afternoon rates were greater.
In the mechanism proposed in the model development section, photo¬
synthetic inhibition correlates directly with increasing carbohydrate
levels. Since carbohydrate levels typically increase during the day,
the observed afternoon inhibition was expected. However, the photosyn¬
thetic enhancement observed in chamber 3 (L-L) and in chamber 4 (H-L)
after its switch to low CC^ was not anticipated.
One possible explanation for the enhanced afternoon rates may be
found in variable canopy leaf temperatures. Although air temperature
was well controlled at 25° C, the variable energy budget experienced in
each canopy must have caused individual leaf temperatures to vary. Early
in the morning leaf temperatures were probably near 25° C, but late
afternoon leaf temperatures may have been higher than 25° C. If so,
photosynthetic rates may have been enhanced. In chambers 1 (L-H) and
2 (H-H), as well as chamber 4 (H-L) before the CO^ transition, the photo¬
synthetic inhibition related to carbohydrates could have overwhelmed
any enhancing temperature effects. However, chamber 3 (L-L) may have
been particularly vulnerable to temperature effects because photosyn¬
thetic rates (and presumably, carbohydrate levels) were low. In chamber
4 (H-L) leaf carbohydrate levels were measured and found to be signifi¬
cantly lowered after CO^ transition (see Figure 42). Therefore, tem¬
perature enhancement could have predominated in these two chambers.
Another interesting feature of Tables (16) and (17) are the time
courses of CER at 300 uE/m**2/sec and at 500 yE/m**2/sec, which show
the morning and afternoon response to the CO^ transition in chambers 1
(L-H) and 4 (H-L) in contrast to the constant chambers 2 (H-H) and

133
3 (L-L). The values show that each canopy's photosynthetic rate is
variable not only morning to afternoon but also from one morning to the
next. Figure (39) compares the morning time courses of photosynthetic
rates at 500 yE/m**2/sec for each chamber. Afternoon time courses are
graphed in Figure (40). Each figure also has time courses of total
integrated daily PAR and minimum daily air temperature.
Aside from the sharp responses to CO., transition, the graphs show
day to day variability which may result from residual source/sink patterns
established during preceding days. For instance, carbohydrate reserves
may have been used and not replaced during the cloudy weather on April
19. Therefore, leaf carbohydrate levels may have been unusually low on
April 20 causing a relative enhancement of photosynthesis.
Minimum ambient air temperatures may offer another clue to the
source/sink patterns. The root zone in each chamber was continuously
exposed to ambient air, in addition the canopies were flushed with
ambient air every hour for 15 minutes during the night. As a result,
the "control chambers" were not perfectly insulated from ambient condi¬
tions. Under low temperatures, metabolic processes slow down which
corserves carbohydrate levels. On April 21, air temperatures were very
low and photosynthesis declined in all chambers.
The underlying mechanism tying these variables together is assumed
to relate to carbohydrate levels and associated biochemical process
rates. This proposed mechanism is described in detail in the model
development and results sections. Briefly, carbohydrates originate in
photosynthesizing cells, from which they are exported to heterotrophic
cells throughout the plant. When more CO^ is fixed in the source leaves
than is utilized by the plant's distributed sinks, carbohydrates accumulate

CER, mg/dm**2/hr
134
Figure 39. Time courses of morning CERat500 yE/m**2/sec. Minimum
daily temperature values and integrated daily PAR are also given.
CER is given in mg CO^ fixed/dm**2 land area/hour.
DAILY PAR, E/m**2

135
Figure 40. Time courses of afternoon CERat 500 pE/m**2/sec. Minimum
daily temperature values and integrated daily PAR are also given. CER
is given in mg CO^ fixed/dm**2 land area/hour.
Daily PAR, E/m**2

136
in the photosynthesizing cells. Associated with the accumulated starch
and sucrose levels are feedback effects on the various biochemical cycles
which ultimately reduce the rate of carbon fixation. Via this mechanism,
the cloudy weather on April 19 may have sufficiently reduced carbohydrate
levels to cause enhanced photosynthetic rates on April 20, which caused
accumulation of starch and reduced CO^ uptake on April 21. In addition,
the low night time temperatures may have suppressed night time respira¬
tion on April 20 and 21, thereby reducing the breakdown of carbohydrates
and enhancing accumulation.
In summary, the low photosynthetic rates on April 21 resulted from
reduced sink demand caused by the high photosynthetic rates on April 20
(oversupplying carbohydrates) and the low temperature dependent metabolic
rates on the night of April 20/21 (reducing carbohydrate consumption).
After the [CO^] transition, the photosynthetic rates in chamber 2
(H-H), 3 (L-L), and 4 (H-L) increased from the morning of April 22 to
April 23; however, chamber 1 (L-H) declined. This is consistent with the
mechanism briefly outlined above. On April 22, chamber 1 (L-H) was
exposed for the first time to a high CC>2 environment and photosynthetic
rate soared, as did carbohydrate production. However, the canopy sinks
were still characteristic of the low CO^ environment and were not able
to utilize the amount of photosynthate that the sources provided. It
is assumed that starch accumulated and was still present on April 23 in
levels high enough to cause some inhibition. After April 23 inhibition
declined as the plants, which were in the vegetative phase, rapidly
increased sink strength as shown in the leaf mass measurements.
Phsyiological Responses
Specific leaf weights (SLW) were measured on selected dates for
chambers 1 (L-H) and 4 (H-L). Results are given in Table (18) and

137
Table 18.
Specific
leaf weight
measurements
•
Morning
Date
Time
l(L-H)
2(H-H)
CHAMBER
3(L-L)
4(H-L)
All
9 AM
2.14
2.66
2.07
2.30
A16
8 AM
2.22
2.13
2.02
2.06
A17
9 AM
2.32
2.71
2.11
2.35
A21
9 AM
2.44
3.01
2.24
2.38
A22
8 AM
2.18
2.65
2.54
2.79
A29
9 AM
2.77
3.14
2.37
2.47
M6
9 AM
2.80
2.98
2.61
2.62
Afternoon
All
5 PM
2.42
2.45
2.17
2.56
A16
5 PM
2.51
2.75
2.38
3.15
A21
3 PM
2.78
3.87
2.90
3.02
A22
4 PM
3.20
4.00
2.52
3.51
A29
1 PM
2.81
2.99
2.65
3.79
M6
4 PM
3.76
4.15
3.59
3.81
Note: Morning and afternoon specific leaf weights from fully expanded
and sunlit leaves. Specific leaf weight, mg/cm**2. Dates are
abbreviated: A for April and M for May.

138
Figure (41). On April 16, SLW increased more rapidly in chamber 4 (H-L)
than in chamber 1 (L-H). On April 22, although the specific leaf weights
measured in chamber 4 (H-L) were greater than in chamber 1 (L-H), the
rate of increase and absolute increase were greater in chamber 1 (L-H).
By May 6, chamber 1 (L-H) had higher absolute values. The variability
in measurements, most notable on May 6, may have been caused by sampling
procedure. All measurements were made on fully expanded exposed leaves;
however, the samples were taken alternately from the east and west ends
of the chambers. This procedure may have introduced some variability
into leaf weights due to canopy architecture.
Variations in SLW are generally found to correspond somewhat to
leaf carbohydrate levels. Samples from chamber 1 (L-H) and 4 (H-L) were
analyzed for total soluble carbohydrate (primarily, sucrose and starch).
The results in Table (19) show specific leaf weights and carbohydrate
levels to be closely dependent. This is shown graphically in Figure (42).
The pattern is consistent for all dates in chamber 1 (L-H) and on April
22, in chamber 4 (H-L). On April 29 and May 2, the SLW/carbohydrate
pattern seems to break down for chamber 4 (H-L) and levels are uni¬
formly low. This probably reflects a continuing source/sink imbalance.
On April 22, chamber 4 (H-L) was switched from a high to a low CO2 envir¬
onment and source strength declined while sink demand remained high. On
April 29 and May 2, the sink demand remained high enough to keep leaf
carbohydrate levels low.
Leaf protein level is closely tied to total leaf nitrogen level.
Hence, total nitrogen was measured as an indicator of enzyme proteins.
Vertical distribution of total nitrogen was measured on dates when whole
plant samples were taken. Results are listed in Table (20). The data
are separated into vertical groups, 4 and 5 refer to the fourth and

SPECIFIC LEAF WEIGHT, mg/cm**2
139
Figure 41. Diurnal specific leaf weights; Chambers 1 (Low-High) and
4 (High-Low). Measurements were taken on exposed fully expanded leaves.
Specific leaf weigh (SLW) units are mg of leaf mass/cm**2 of leaf area.

140
Table 19.
Comparison
in Chambers
of specific
1 (L-H) and
leaf weight and
4 (H-L).
soluble carbohydrates
Chamber
1
(L-H)
4 (H-L)
Date
Node
SLW
% SC
SLW
% SC
A22
5
2.26
12.27
1.69
10.95
7
2.07
9.63
2.67
15.72
9
2.45
14.63
2.73
11.91
A29
5
1.81
10.73
1.98
4.79
7
1.74
9.87
2.08
5.89
9
1.57
6.47
2.63
6.07
M2
7
2.41
13.14
2.97
7.58
9
2.67
14.19
2.63
6.93
11
2.87
14.56
2.29
7.02
Note: Measurements were made on leaves from whole plant sample taken
at 11:00 EST on sunny days. Node refers to the vertical distribution
of the leaves sampled. Nodes were counted from the ground upward.
Specific leaf weight is in units of mg/cm**2 and soluble carbohydrate
(SC) values are given as % of dry weight.

Soluble Carbohydrates, % dry weight
141
Figure 42. Comparison of carbohydrate levels and specific leaf weight.
Graph compares measurements at 11:00 EST on April 22, April 29 and May 2
taken in chambers 1 (L-H) and 4 (H-L). The switch in CO^ level occurred
on April 22. The values in the lower right corner are for chamber 4
(H-L) on April 29 and May 2 several days after the CO^ transition.

Table 20. Vertical distribution of leaf nitrogen.
Nitrogen/Leaf Mass Total Nitrogen
Chamber Chamber
Node
Date
1 (L-H)
2 (H-H)
3 (L-L)
4 (H-L)
1 (L-H)
2 (H-H)
3 (L-L)
4 (H-L)
4,5
A22
5.10
4.85
5.17
4.48
4.42
4.85
4.20
4.56
A29
4.47
3.40
4.48
4.16
3.71
3.75
3.49
4.07
M6
3.36
3.80
4.32
3.89
2.71
5.36
3.29
3.70
6,7
A22
5.42
4.63
5.37
4.56
5.98
6.07
5.70
5.49
A29
5.03
4.89
5.20
4.34
5.31
6.15
5.29
5.11
M6
3.86
6.59
4.43
4.39
4.07
8.29
4.51
5.16
8,9
A22
5.63
3.60
5.78
5.57
4.76
3.18
3.47
6.34
A29
5.88
4.95
5.76
5.52
9.09
9.71
7.72
8.83
M6
4.56
7.40
5.26
5.15
6.93
9.33
5.56
7.93
10,11
A29
4.89
5.15
6.09
5.67
4.96
5.91
5.80
6.87
M6
4.56
6.08
5.70
5.31
6.56
9.25
4.94
6.33
a?
A22
15.1
14.0
13.4
16.4
4-> O
O C
A29
23.1
24.9
22.4
24.9
03
O
M6
24.4
31.1
24.2
25.8
Note: Nitrogen/leaf mass values are on a % basis and total nitrogen values are in grams.

143
fifth trifoliates counting from the ground upward. The measurements are
presented for each chamber on both a leaf area and a total canopy basis.
Comparing the nitrogen/leaf mass values on April 22, chamber 1 (L-H)
levels were clearly higher than chamber 4 (H-L). By May 6, the situation
was reversed. This is shown graphically in Figure (43). On a total
canopy nitrogen basis this disparity is much less evident. If there
was a significant difference, chamber 4 (H-L) had more total nitrogen
than chamber 1 (L-H). The relationship between the chambers on a total
nitrogen basis is summarized in the last three rows of Table (20). The
date for chamber 2 (H-H) cannot be accurately interpreted because of
physical damage and pest problems.
Chlorophyll was measured on the same dates from the same whole plant
samples as the nitrogen. Values are presented on a leaf area and total
canopy basis in Table (21). At the 4,5 nodes total chlorophyll values
declined over time, while at the 6,7 nodes the values climbed slightly
from April 22 to April 29 and then declined. In nodes 8 and 9, chloro¬
phyll increased sharply in all chambers from April 22 to April 29, then
dropped somewhat. The pattern suggests that the chlorophyll levels
peaked in higher nodes on later dates, perhaps due to leaf aging. The
estimates of total canopy chlorophyll given in the bottom rows show more
variability than did nitrogen levels. Total estimated chlorophyll con¬
tent increased in each chamber during the measurement period.
Inorganic phosphate levels were also measured on whole plant sample
dates (Table 22). Unlike chlorophyll and enzyme concentrations, inorganic
phosphate levels can fluctuate very quickly in response to changing light
levels. Since samples were taken several days apart under variable short
term conditions, the phosphate concentrations fluctuated enough to mask
any trends that may have been present.

Node
144
Figure (43). Vertical nitrogen distribution; Chambers! (Low-High) and
4 (High-Low). This graph shows the relative switch in leaf nitroqen
‘levels following the [CO^] transitions in chambers 1 (L-H) and 4 (H-L).

Table 21. Vertical distribution of leaf chlorophyll.
Chlorophyll/Leaf Area
Total
Chiorophyl1
Chamber
Chamber
Node
Date
1 (L-H)
2 (H-H)
3 (L-L)
4 (H-L)
1 (L-H)
2 (H-H)
3 (L-L)
4 (H-L)
4,5
A22
1.34
1.38
1.22
1.18
6.38
7.58
5.44
6.62
A29
1.16
1.28
1.34
1.30
5.30
6.74
5.04
7.00
M6
1.18
1.00
1.18
1.20
5.26
5.16
4.90
6.32
6,7
A22
1.26
1.52
1.40
1.38
7.64
10.98
8.18
9.16
A29
1.32
1.76
1.58
1.46
7.68
12.18
8.84
9.46
M6
1.20
1.26
1.22
1.38
6.82
8.52
6.68
8.60
8,9
A22
1.06
1.12
1.10
1.14
4.94
5.46
3.80
7.14
A29
1.20
1.52
1.62
1.60
10.68
16.36
11.94
14.10
M6
1.18
1.36
1.52
1.78
9.86
8.34
8.82
15.08
10,11
M6
1.50
1.00
1.42
1.52
11.88
8.36
6.78
9.94
Total
>>
CL
O
c
ra
o
A22
M6
18.96
35.50
87.
24.02
31.46
31.
17.42
27.20
56.
22.92
39.94
74.
Note: Chlorophyll/leaf area values are given in units of mg/cm**2 and total chlorophyll values are in
mg. %A indicates the percentage change in total chlorophyll from April 22 to May 6.

146
Table 22. Vertical distribution of leaf inorganic phosphate.
Phosphate-Leaf Mass
Chamber
Node
Date
1 (L-H)
2 (H-H)
3 (L-L)
4 (H-L)
4,5
A22
3.16
2.14
4.02
7.95
A29
1.26
1.30
1.50
1.53
M6
3.42
3.26
4.69
6.27
6,7
A22
4.62
2.50
3.85
3.47
A29
2.24
1.53
1.56
1.56
M6
2.88
5.25
7.73
1.48
8,9
A22
2.44
.92
11.26
2.94
A29
3.50
2.11
1.95
2.35
M6
5.29
4.45
5.06
1 .40
Note:
Phosphate-leaf
mass values
are in mg/gr dry
weight.

SUMMARY AND CONCLUSIONS
In this work photosynthesis has been studied on several distinct
levels. At the subcellular level a biochemical photosynthesis model
has been developed with very rapid time response. The model describes
the CO2 fixation and carbohydrate synthesis pathways in detail. In
addition, it offers a mechanistic explanation of the roles played by
starch and sucrose in the regulation of CO^ uptake. At the whole plant
level experiments have been conducted in environmental control chambers.
Both short term response and long term adaptation of soybean canopies
exposed to differing CO^ concentrations were monitored. Short term
measurements of variables such as CO^ exchange and specific leaf weight
were used to develop diurnal response patterns. In similar fashion,
long term measurements such as leaf area and biomass described growth
response integrated over time.
The model was evaluated quantitatively by comparing the responses
predicted by specific model equations with observed responsesas reported
in the literature. On this basis the model performs very well. The
model was used to successfully predict
1) CER as a function of CO^ concentration,
2) overall starch accumulation,
3) starch accumulation as a function of inorganic phosphate levels,
4) transport of fixed carbon from chloroplast to cytoplasm as a
function of cytoplasmic inorganic phosphate levels,
147

148
5) export of fixed carbon from the cytoplasm as a function of
sucrose concentration.
The model was also evaluated qualitatively and found to be generally
consistent with the results of whole plant source-sink experiments in the
literature. The model's mechanisms were able to account for sink strength
feedback regulation of photosynthetic rates. Decreased sucrose export
rates caused by reduced sink demand resulted in predicted starch accumu¬
lation and decreased photosynthetic rates while increased sink strength
resulted in decreased starch levels and enhanced photosynthetic rates.
Results from the experimental work showed definite reponse to both
short term changes in CO^ concentration and to long term exposure to
differing constant CC^ levels. It was found that soybean canopies grown
under elevated CC^ concentrations had
1) higher net photosynthesis rates,
2) higher dark respiration rates, and
3) lower transpiration rates.
Close analysis of each canopy's response found that photosynthetic light
response varied from morning to afternoon and from one morning to the
next. High [CO^] canopies exhibited afternoon inhibition of net photo¬
synthesis while low [CO^] canopies had a mixed response. On a leaf basis
the low [CO^] canopies seemed to have somewhat lower specific leaf weights
and the specific leaf weight increased less diurnally than in the high
[CO ] canopies. Changes in specific leaf weight were found to correspond
to changes in soluble carbohydrate levels.
On a longer time scale high [CO2D canopies responded morphologically
with
1) more rapid leaf expansion,

149
2) increased total leaf area, and
3) increased total biomass.
In addition, the total nitrogen levels on a leaf area basis were less in
high [CO2] canopies than in low [CO^] canopies. When CO^ levels were
switched all of the responses above slowly adapted to the new conditions.
There is an inherent difficulty in quantitatively comparing model and
experimental results because of the differences in detail of the modelled
state variables and the variables measured in the experiment. The model
includes internal variables at the subcellular level whereas experimental
measurements were on individual leaf and whole canopy levels. Experimen¬
tation at this level was necessary because source-sink balances that
directly affect and respond to changing photosynthetic rates occur on a
whole plant level. Modelling at this level was necessary because it
explicitly describes the mechanism linking source-sink balances and
photosynthetic rate regulation. The connection between model and experi¬
ment is in recognizing that canopy behavior is the integrated response
of each discrete cell in the system. Therefore, even across the large
gap in detail, model and experimental results must behave consistently.
Qualitatively the responses predicted by the model and measured in
the experiments were consistent. At the most fundamental level
increased [CO^] was shown in the model results to directly promote the
carboxylation reaction and to subsequently increase production of car¬
bohydrates. This was confirmed by the short term experimental results
which showed enhanced CO^ uptake rates and long term results which
showed enhanced biomass production under high [C02].
On a diurnal basis model results showed an increase in starch level
and experimental measurements showed a corresponding increase in specific

150
leaf weight which implied an increase in soluble carbohydrates. In
the long term soluble carbohydrate declined when [CO^] was switched in
Chamber 4 (H-L) from a high to a low level. This resulted from the
changing source-sink balance.
Canopy 4 (H-L) was grown in high [CO^] which enhanced its source
strength. In tandem with its higher CO^ fixing capacity the canopy
developed a matching sink capacity. When the chamber CO^ level suddenly
declined so did source strength but sink demand capacity remained high.
As a result sucrose levels in the photosynthetic tissue remained low
because of rapid export rates. Consequently, less starch accumulated
and soluble carbohydrate levels declined. The model results showed that
high sucrose export rates and reduced cytoplasmic sucrose levels
enhanced inorganic phosphate levels which favored export of fixed CO^
and inhibited starch formation. Thus, the model corresponds to experi¬
mental results in predicting lower soluble carbohydrate levels when
sink demand is high.
Experimental results also revealed a probable morning-afternoon
source-sink relationship. After a night of respiration, morning sink
demand was probably high relative to afternoon sink demand. Comparison
of relative morning-afternoon net photosynthesis showed significant
differences in rates. In Chamber 4 (H-L) with high absolute CO^
uptake rates, photosynthesis declined significantly in the afternoons.
In terms of the model sink requirements declined in the afternoon causing
increased sucrose levels and decreased inorganic phosphate levels,
which shifted the ATP/ADP ratio and slowed down the Calvin cycle
fixation of CO^.

151
After Chamber 4 (H-L) was switched to low C02 levels the experi¬
mental results showed no afternoon inhibition of photosynthesis. In
this case the canopy had excess sink demand capacity and sucrose levels
did not increase significantly enough to affect the rate regulating
ATP/ADP ratio.
To summarize, net photosynthesis is regulated directly by the
specific mix of biochemical substrate concentrations as shown in the
model and certain diurnal patterns exist which can affect these inter¬
dependent balances as shown in the short term experimental measurements.
Finally, the integrated effect of short term patterns over time controls
the development of whole canopy source-sink relationships.
In conclusion, the model and experimental results were found to
be in good qualitative agreement and to be well described in terms of
the source-sink concept. Measurements in the experimental work revealed
variations in the photosynthetic light response which have been reported
in terms of inhibition or enhancement of "normal" response. The model
developed in this work has shown how this dynamic photosynthetic response
can be mechanistically regulated by the fluctuating levels of inorganic
phosphate at the cellular level.
To further develop this model more complete data sets with emphasis
on starch, sucrose, and inorganic phosphate concentrations at frequent
time intervals are required. The model will also require a more complete
search of the biochemical literature for the various reaction rate con¬
stants. Finally, the model should be more realistically linked to the
rest of the plant via an export function which responds to sink demand.
Once these additions are made the model will be sufficiently complete
to be useful in larger scale plant growth models and ultimately in crop
simulation models.

1 52
In view of steadily increasing global CO^ levels further experi¬
mental work on CO^ enrichment is certainly justified. Several lines of
investigation can be suggested from the results of this research.
Specifically,
1. the canopies grown under elevated CO^ had a lower nitrogen
requirement per unit biomass,
2. the high CC^ plants were much more water efficient than their
low CO2 counterparts, and
3. canopies adapted their source-sink balances quickly when con¬
ditions changed.
These are all topics with important implications in both basic research
and applications which require more work.

APPENDIX 1
ABBREVIATIONS LISTING
A
starch accumulation coefficient
AMP
adenosine monophosphate
ADP
adenosine diphosphate
ADP1
chloroplastic ADP
ADP2
cytoplasmic ADP
AREA
chamber ground surface area
ATP
adenosine triphosphate
ATP1
chloroplastic ATP
ATP 2
cytoplasmic ATP
B
starch accumulation coefficient
BPGA
1,3-diphosphoglyceric acid
Cl
reaction rate constant 1
C2
reaction rate constant 2
C3
reaction rate constant 3
C4
reaction rate constant 4
C5
reaction rate constant 5
CER
C02 exchange rate, net photosynthesis
ch2o
C6H12°6
c12 H22011
co2
[C02]
[C02]a
[C02]d
QCO2]e
[C02]i
[co2]0
^C02^m
CR
carbohydrate or photosynthate
glucose
sucrose
carbon dioxide
chloroplastic (stromal) C02 concentration
ambient C02 concentration
desired C02 concentration
final C02 concentration
intercellular C02 concentration
initial C02 concentration
measured C02 concentration
chamber diffusion resistance
153

154
DHAP
dihydroxyacetone phosphate
DHAP1
chloroplastic DHAP
DHAP2
cytoplasmic DHAP
DL
diffusional leakage rate
E
enzyme
eco2
EC02RuBP
EMP
enzyme C02 complex
enzyme, C02, and RuBP complex
erythose 4 phosphate
EST
eastern standard time
[EXPORT]
rate of sucrose transport from cytoplasm
FBP
fructose-1,6-phosphate
FMP
fructose-6-phosphate
G
Gibbs' free energy
G°
Standard Gibbs' free energy
GAP
glyceraldehyde-3-phosphate
G1P
glucose-1-phosphate
G6P
glucose-6-phosphate
h
Planck's constant
H-H
high to high [C02]
H-L
high to low [C02]
h2o
ki ' kio
Kc
water
process rate constants 1 through 10
Michael is Menten constant for C02 process
Kd
M-M constant for DHAP1 transport process
Kd2
M-M constant for DHAP2 conversion process
Keq
equilibrium constant
Ko
M-M constant for 02 reduction process
Kp
Kr
M-M constant for P2 phosphorylation process
M-M constant for RuBP oxidation process
Ks
M-M constant for sucrose inhibition process
KPAR
PAR for half maximal CER
L-H
low to high [C02:
L-L
low to low [CO ]
LAI
leaf area index
LIGHT
PAR generated electron-H+ concentration
MC02e
final C02 mass
MC02inj
injected C02 mass

155
MC02o
initial CO2 mass
n
undefined number
NADP
nicotimamide adenine dinucleotide phosphate
NADPox
NADP oxidized state
NADPred
NADP reduced state
°2
oxygen
[o2]
chloroplastic (stromal) 02 concentration
P
inorganic phosphate
PI
chloroplastic P
P2
cytoplasmic P
PAR
photosynthetically active radiation
PCER
projected CER
PGA
phosphoglyceric acid
PGA1
chloroplastic PGA
PGA2
cytoplasmic PGA
PGly
phosphoglycolate
PNMAX
maximum CER-LIGHT response
R
universal gas constant
RC
respiration related coefficient
RD
dark respiration rate
Rm
membrane resistance to CO^ diffusion
RMP
ribose-5-phosphate
RuBP
ribulose-1,5-bisphosphate
RuBPc
RuBP carboxylase enzume
RuBPc-o
RuBP carboxylase-oxygenase enzyme
RuBPo
RuBP oxygenase enzyme
RuP
ri bul ose-5-phosphate
SDBP
sedoheptulose-1,7-bisphosphate
SDMP
sedoheptulose-7-phosphate
SLW
specific leaf weight
SMP
sucrose phosphate
SPAR
soi1-plant-air-research
STARCH
chloroplastic starch
SUCROSE
cytoplasmic sucrose
T
temperature
t
time
[TRANSPORT] DHAP1 transport to DHAP2

156
UDP
UDPG
UTP
Vc
Vcmax
V co
Vcomax
Vcr
Vcrmax
Vdpmax
Vdsmax
Vo
VOLUME
Vomax
Vor
Vormax
XMP
[ ]
[ 1]
C 2]
[ ]
C ]n
A
v
y
*
**
uridine diphosphate
uridine diphosphate glucose
uridine triphosphate
carboxylation reaction rate, 1 substrate
maximum Vc possible, 1 substrate
Vc with competitive inhibition
maximum Vco possible
carboxylation reaction rate, 2 substrates
maximum Vcr possible
maximum possible DHAP1-P2 [TRANSPORT]
maximum possible SUCROSE formation rate
0^ reduction rate, 1 substrate
chamber volume
maximum possible Vo, 1 substrate
O2 reduction reaction rate, 2 substrates
maximum possible Vor, 2 substrates
xylulose-5-phosphate
concentration
chloroplastic concentration
cytoplasmic concentration
time rate of change
normalized values
change in
frequency
mi cro
multiplier operand
power operand

APPENDIX 2
GLOSSARY OF TERMS
allosteric enzyme activity affected by inhibitors or promoters
autotrophic cells that can use CO^ directly as their sole
source of carbon and light as their sole source
of energy
carbohydrates compounds with the empirical formula [CP^Ojn
and their derivatives;wel1 known examples are
starch, sucrose, glucose, and cellulose
carboxylation any reaction process in which CC^ is reduced
chlorophylls light trapping pigments of photosynthetic cells
chloroplasts chlorophyll containing plastids suspended within
photosynthesizing cells
cofactor additional nonprotein structures required for
activation of an enzyme
cytoplasm the living component of cells in which organelles
are suspended
dark respiration the controlled release and utilization of energy
from the oxidation of carbohydrates in metabolism
processes of growth and maintenance in living
tissues
downhill reactions that have a negative standard free
energy change and will proceed spontaneously
under standard conditions; an exergonic process
157

158
endergonic reactions that have a positive standard free
energy change and will not proceed spontaneously
in the direction written under standard condi¬
tions; an uphill process
enzymes highly specialized class of protein molecules
which catalyze virtually all metabolic reactions
equilibrium state that exists when no changes take place in
a system's properties over time
exergonic reactions that have a negative standard free
energy change and will proceed spontaneously in
the direction written; a downhill process
fluorescence the loss of energy originally absorbed by
reemission of light quanta; the emitted light is
of longer wavelength than the absorbed light's
wavelength
Gibb's free energy....a measure of a system's total energy changes rela¬
tive to changes in entropy
gross photosynthesis..total C02 taken up by the Calvin cycle carboxyla-
tion process
glucose the most abundant simple sugar and the precursor
of sucrose and starch; its chemical formula is
C6H12°6
heterotrophic cells that cannot use C02 but must obtain carbon
and energy from relatively complex reduced com¬
pounds such as sucrose
in vitro procedures that occur outside the living cell;
in an artifical environment

159
in vivo procedures that occur within the living cell;
in natural conditions
organelles the highest level of intracellular organization;
various supramolecular complexes such as nuclei,
mitochondria and chloroplasts
oxidation the chemical loss of electrons
phloem system for transport from organ to organ and
storage of photosynthetic products found in higher
plants
phosphorylation a chemical process in which a phosphate group is
coupled to another compound; in biological systems
phosphate groups relate to chemical energy status
photorespiration the reduction of O2 by RuBP; a process that
directly competes with photosynthesis for available
RuBP
photosynthate the general products of photosynthesis such as
starch and sucrose; carbohydrates produced by
photosynthesis
photosynthesis the chemical reduction of CO2 with RuBP as a
reducing agent, RuBP being the product of a
biochemical cycle driven by light energy
photosynthetically
active radiation electromagnetic radiation with wavelengths in the
range 400 to 700 nanometers; wavelengths that can
be absorbed by photosynthetic pigments
pool the available supply of a compound in the chloro-
plastic reaction tank or the cytoplasmic reaction
tank

160
reduction the chemical gain of electrons
reversible thermodynamically, a process that occurs without
change in entropy or biochemically, a process
that enzymatically and energetically can proceed
in either direction
standard conditions... conditions in which standard free energy change
occurs for a reaction; 1.0 molar concentration
for all reactants, pH equal to 7.0 and 25° C
starch a carbohydrate characterized by long chains with
chemical formula (C6H-|2°6)n " H2° where n 1S any
number
steady flow condition that occurs in an open system when flow
out of the system equals flow into the system
steady state condition that occurs when there are no net changes
in a system's characteristics with time
stoichiometry the mass relationships in chemical formulas and
equations
stroma the fluid component of a chloroplast; the
chloroplastic site of the Calvin cycle and various
other biochemical processes
substrate components, reactants or precursors involved in a
chemical reaction
sucrose a carbohydrate with chemical formula, 2^22^11 ’
the primary photosynthate transported throughout
the plant
tank a term used synonomously with pool referring to
the available supply of a compound

161
thylokoid the chloroplastic structure housing pigments where
the light reactions take place
trifoliates the three leaf structural units common to soybean
pi ants
uphill synonomous with energonic; an energy requiring
reactions under standard conditions

APPENDIX 3
UNITS LISTING
Length
m
meters
cm
centimeters
nm
nanometers
Area
m**2
meters squared
dm* *2
decimeters squared
cm**2
centimeters squared
Volume
m**3
meters cubed
1
1 iters
ul
microliters
Time
hr
hours
min
mi ñutes
sec
seconds
Mass
kg
kilograms
g
grams
mg
milligrams
mg chi
milligrams chlorophyll
yg
micrograms
ymol
micromoles
Concentration
kg/m**3
kilograms/meter cubed
vpm
volumetric parts/million
mM
mi 11imolar
PM
mi cromolar
Pressure
mbar
millibars
162

163
APPENDIX 3 (contd.)
Flux
Total Flux
kg/m**2/hr kilograms/meter squared/hour
mg/dm**2/hr milligrams/decimeter
squared/hour
pmol/mg chl/hr micromoles/mi Hi gram
chlorophyll/hour
yE/m**2/sec
microEinsteins/meter
squared/seconds
E/m**2
Einsteins/meter squared
Note: In the units notation the double asterisk (**) and the slash (/)
are read "to the power of" and "per," respectively. All mole quantities
refer to gram moles.

APPENDIX 4
SYMBOL LISTING
Source
mass or energy source outside of system; a
forcing function
Tank
a compartment of mass or energy storage within
the system storing a quantity as the balance of
inflows and outflows; a state variable
Interaction
interactive intersection of two pathways coupled
to produce an outflow in proportion to a function
of both; limiting factor action
Interaction
Michaelis-Menten form
Pathway indicator
defines specific pathways
164

APPENDIX 5
PROBABLE ERROR ANALYSIS OF C02 MASS BALANCE MEASUREMENTS
The primary experimental result from the chamber control system was
the carbon dioxide exchange rate (CER) or less precisely, the photo¬
synthetic rate. To control chamber C02 concentration, the C02 injection
rate was discretely adjusted to equal CER. Equation (56) is a quanti¬
tative statement of this mass balance control algorithm.
CER = UMC02inj + MC02i - MC02e) /(0.415) (AREA)
(56)
A more explicit version of this equation must be more detailed:
MC02inj = FL0W * TIME’
MC0o• = [CO,] * VOLUME, and
21 2 m
MC0o = [CO,] * VOLUME
2e L 2 m
where FLOW is the injection mass flow rate, TIME is the time that the
injection solenoid is open, [C02]m is the infrared gas analyzer measure¬
ment of chamber C02 concentration and VOLUME is the chamber bolume. An
additional consideration not included at all in equation (56) is a
correction for diffusion leakage (DL) made on a chamber by chamber basis.
Expanding equation (56) yields
(FLOW * TIME) + ([ACOJ * VOLUME)
2Jm
CER =
(0.415) (AREA)
+ DL .
Functionally, this equation can be written
CER = f[FLOW, TIME, [aCO^, VOLUME, AREA, DL].
165

166
Partial derivatives from this relationship are as follows:
9f
3^= TIME/ (0.41 5) (AREA),
9f
= FLOW/(0.41 5) (AREA),
9f
VOLUME/(0.415) (AREA)
9f
9VOLUME ~ ^C02V(°-415) (AREA)>
-FLOW * TI ME/ (0.415) (AREA)2 and
9f
9 DL
1.
Probable error as a fraction of CER is given by
2
ACER 1
CER f [(9FL0W
_9_f
l-LAc02Jm
9f
f^FT^TT A FLOW
3f
9FL0W
A TIME
3[AC0?]m A [AC02]m,
2
9f
9AREA
A AREA
+ 1 3DT a DL
9VOLUME
2] %
A VOLUME
To solve this equation the accuracies of each variable have been esti¬
mated either by using direct calibration, manufacturers calibration or
best guess. Approximations of accuracies are as follows:
-8
aFLOW = 9.4 * 10 kg/sec--this value is based on direct calibrations
which consistently showed a secular drift in flow rate that was
larger than the manufacturers calibrated accuracy,

167
aTIME = 3.2 * 10 ^ sec--this value is based on the manufacturer's cali¬
bration of the computer's real time clock,
a[aC0o] = 7.8 * 10 ^ kg/m**3--this value is based on the manufacturer's
2 m
calibrated accuracy which had a larger uncertainty than was obtained
in direct calibrations,
aVOLUME =0.05 m**3--this value is relatively large because of uncertainty
over the exact volume of duct work in the control chamber; the value
is a best guess,
aAREA =0.0001 m**2--this value is also a best guess conservatively
assuming that length and width were known to within 1 cm,
_5
aDL = 2.0 * 10 kg/m**2/hr--this value is a best guess of uncertainty
in the graphical techniques used to measure the diffusion leakage
rate.
Two calculations will be made for different cases. First, the case
of continuous injection into a high [CO^]^ chamber with a large leakage
rate will be considered. Values are
FLOW =2.8*10"6 kg/sec,
TIME = 300 sec,
[AC0J = 5.9 * 10-5 kg/m**3,
2 m
VOLUME =1.6 m**3,
AREA =1.0 m**2 and
DL = -2.0 * 10"4 kg/m**2/hr.
Using these values and the uncertainties outlined above probable error
can be calculated. Individual terms are
= A FLOW = 6.8 * 10'5 kg/m**2/hr,

168
A TIME = 1.3 * TO"12 kg/m**2/hr,
~3~[aC0' T" a [aC024 = 3-° * 10"5 kg/m**2/hrs
L 2Jm
3~VÜLU'ME A V0LUME = 7J * 10’6 kg/m**2/hr,
A AREA = 2.0 * 10-7 kg/m**2/hr.
8f A DL = 2.0 * 10‘5 kq/m**2/hr, and
3DL
CER 2.1 * 10 kg/m**2/hr., a typical measured rate,
Substituting into the probable error equation the following ratio
is obtained:
=0.037 = 3.7%
Second, the case of a low [CO^]^ chamber with a typical injection
time will be considered. For this case, CO2 levels inside and outside
the control chambers are nearly equal allowing DL to be dropped since no
net diffusion occurs. Values are
FLOW = 2.8 * 10-6 kg/sec,
TIME = 50 sec,
[aC02] = 2.5 * 10“5 kg/m**3,
VOLUME = 1.6 m**3,
AREA =1.0 m**2.
Using these values the probable error can be calculated. Individual
terms are

169
FLOW = 1.1 * 10-5 kg/m**2/hr,
gjf^-A TIME = 1.3 * 10"12 kg/m**2/hr3
4 [4C02]m ' 3'° * ,0'5 kg/m**2/hr,
Jvolijhe 4 VOLUME = 3.0 * Kf6 kg/m**2/hr,
3f
3AREA
A AREA = 3.4 * 10-8 kg/m**2/hr, and
CER = 4.3 * 10-4 kg/m**2/hr, a typical measured rate.
Substituting into the probable error equation the following ratio
is obtained:
ACER
CER
=0.075 = 7.5%.
Looking at the contributing terms, the FLOW term and the [aCO^] term
are important in both examples. In addition diffusion leakage in the high
[C02] case is important. Of these uncertainties diffusion leakage and
the injection flow rate have the greatest room for improvement through
careful experimental design. Even though uncertainty in [CO^]^ is based
on the manufacturers calibration it too can be improved by dedicating a
different gas analyzer to each CO2 level allowing full scale to be reduced.
Overall the probable error in C02 mass balance measurements is acceptable.

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BIOGRAPHICAL SKETCH
Pierce Jones was born October 19, 1946, in Jacksonville, Florida.
In June 1968, he received a Bachelor of Science degree in agricultural
economics from the University of Florida. In September 1976, he
received a Master of Science degree in astronomy from the University
of South Florida. He began a program in mechanical engineering in
September 1976 and expects to receive the degree of Doctor of Philosophy
in June 1981.
176

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
G.L. Zacharnah, .Chairman
Affiliate Wmessor of Mechanical
Engineering and
Professor of Agricultural Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
C.K. Hsieh
Professor of Mechanical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
R.K. Irey
Professor of Mechanica
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
L.H. Allen, Jr. ^
Associate Professor of Agronomy

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
D.E. Buffijjgion^
Associate Profesor of Agricultural
Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
JJÍ/ Jonesy
Pryfessos!/of Agricultural Engineering
This dissertation was submitted to the Graduate Faculty of the College
of Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
June 1981
/Ú.
Dean, College of Engineering
Dean, Graduate School

I
UNIVERSITY OF FLORIDA
3 1262 08556 7526