ENHANCEMENT OF D-LACTATE PRODUCTION IN A
CONTINUOUS CULTURE OF A MUTANT ESCHERICHIA COLI
THROUGH PERIODIC OPERATION
JONATHAN BEN RODIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
UJ~aSIT'I : FURIDA LI
I would like to thank my committee chairmen, Professors Spyros Svoronos and
Gerasimos Lyberatos, for providing guidance above and beyond the call of duty. They are
appreciated for being there to help and encourage me during the bad times when the project
was going down seemingly blind alleys.
There are other faculty members who have truly been of great assistance. I would
like to thank my other committee members first, Professors Gerald Westermann-Clark,
Seymour Block, Ben Koopman, and Lonnie Ingram. Dr. Ingram is especially appreciated
for all of his very useful advice without which this project would not have been completed.
He has also been very generous with use of his laboratory and equipment. In addition to
my committee members, Professors Bitsanis and Crisalle are thanked for all of their
Several graduate students have helped me out during my research project. Three
deserve special mention, Jeff Mejia, Pratap Pullammanappallil, and Christina Stalhandske
for all the technical assistance they provided. If only one student was to be mentioned, Jeff
Mejia would be the one. He is the one who initially suggested the reversion problem with
this system. If not for his advice, I would still be in the dark as to the cause of all of the
problems associated with continuous anaerobic operation. Christina's help was
instrumental in the work performed on the aerobic characterization of bacterial growth.
Pratap, besides being one of my closest friends during my years in Gainesville, has been
an indispensable resource of information and help with my project. Additionally, Jeffrey
Harmon has lent a helping hand on several occasions. Lastly, in addition to those
mentioned above, I have been very fortunate to have had numerous other friends among the
graduate students in this department.
Several undergraduates from this department have assisted me at various times
during the duration of this project. I have been very fortunate to have had these people
work with me. The following undergraduates have worked as laboratory assistants or
completed small research projects with me: Dawn Mackland, Mike Hinson, Reann
Soodeen, Craig Moates, Erik Dunmire, and John Walker. Among these students, Dawn,
Craig, and Mike have each shown dedication above and beyond what was expected from
them. Like the graduate students that have gone through this department, I have been
fortunate to call several of the undergraduates, again in addition to those mentioned above,
This section would not be complete without mentioning Mr. Tracy Lambert, the
department's maintenance specialist. He has been of invaluable help to me during this
Finally, I would like to thank my parents, sister, brother, and sister-in-law.
Without their love, support, and encouragement, I probably would not have been able to
endure this whole ordeal. My brother was also generous with allowing me free use of the
facilities and equipment at his business, Gallery Graphics.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS .................................................................. ii
A B ST R A C T .................................................................................... vi
1 INTRODUCTION ........................................ ............. 1
2 THEORETICAL METHODS ............................................. 4
2.1 Overview ........................................... ......... 4
2.2 Determination of Optimal Steady-state Operation ............ 5
2.3 A New Method of Determining Optimal Periodic
Pulsing ............................ ......... ......... ......... 7
2.3.1 Carleman Linearization ......................... 7
2.3.2 Performance Measure Calculation .............. 10
2.4 Model Fitting with Nonlinear Least Squares Methods ....... 15
3 EXPERIMENTAL METHODS ......................................... 19
3.1 Organism Description ........................................... 19
3.2 Analytical Methods ............................................ 21
3.2.1 Biomass and Cell Number Determination ..... 21
3.2.2 Glucose Analysis ............................... 25
3.2.3 d-Lactate Measurement ........................ 26
3.2.4 Other Analyses .................................. 28
3.3 Feed Medium Composition ................................... 30
3.4 Feed Preparation ................................................ 32
3.5 Experimental Operation ......................................... 38
3.5.1 Operational Conditions ........................ 38
3.5.2 Shake Flask Experimental Procedure ......... 40
3.5.3 Reactor Experimental Procedure ............... 42
18.104.22.168 System Description ............ 42
22.214.171.124 System Startup and Operation 44
4 ANAEROBIC GROWTH OF E. COLI LCB898 ...................... 48
4.1 Background ...................................... ............ 48
4.2 Batch Growth ...................................... ......... 51
4.3 Continuous Growth ............................................. 65
4.4 Modeling .......................................................... 73
4.4.1 Presentation of Model ........................... 73
4.4.2 Model Parameter Fitting ....................... 74
5 AEROBIC GROWTH OF E. COL LCB898 ........................
5.1 Background ...................................................
5.2 Experimental and Modelling Results Introduction ............
5.3 Batch Growth .................................................
5.4 Continuous Growth ..........................................
5.5 M odeling ......................................................
5.5.1 Presentation of Model ........................
5.5.2 Model Parameter Fitting .....................
6 THE EFFECTS OF SHIFTS IN AERATION OF E. COLI LCB898 ..
6.1 Background ...................................................
6.2 Development of the Combined Aerobic-Anaerobic Model ...
6.3 Testing of the Model .........................................
7 EFFECTS OF AERATION CYCLING ON LACTATE
PRODUCTIVITY OF E. COLI LCB898 .............................
7.1 Background ...................................................
7.2 Theoretical Investigation into Cycling .....................
7.3 Experimetal Confirmation of Lactate Productivity
Optimization Results .........................................
8 REVERSION OF E. COL LCB898 AND A POSSIBLE NEW
METHOD OF AVOIDANCE OF REVERSION .......................
9 CONCLUSIONS ........................................................
MATHEMATICS PROGRAMS FOR COMPUTATION OF
CARLEMAN LINEARIZATION MATRICES .................................. 165
LIST OF REFERENCES ..................................................................... 171
BIOGRAPHICAL SKETCH ................................................................ 175
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ENHANCEMENT OF D-LACTATE PRODUCTION IN A
CONTINUOUS CULTURE OF A MUTANT ESCHERICHIA COLI
THROUGH PERIODIC OPERATION
Jonathan Ben Rodin
Chairman: S. Svoronos
Cochairman: G. Lyberatos
Major Department: Chemical Engineering
In some biological systems, the environmental conditions that are optimal for
microbial growth differ from the optimal conditions optimal for producing a desired
metabolite. If production of this metabolite were the process objective, one could
continuously operate a reactor system at the optimal production conditions. However, for a
given reactor volume, changing the conditions periodically could increase overall
production of the desired metabolite. This is possible since, due to higher growth rates
under the optimal growth conditions, one could operate the system at significantly higher
flowrates and, thus, obtain more product. A system involving E. coli mutant LCB898 was
used as a model system. Under anaerobic conditions this bacterium will produce large
amounts of d-lactic acid, whereas under aerobic conditions, this bacterium will grow faster.
The possibility of increasing total lactate production by cycling dissoved oxygen was
Before any optimization work could be done, an adequate model for describing the
behavior of this system under both steady-state and transient conditions had to be
developed and tested. Such a model was developed using batch and continuous data and
then tested by comparison with shifts between conditions.
A method for determining the optimal waveform for the proposed cycling was
developed by extending previous work by Lyberatos and Svoronos. The method involved
Carleman linearization of the model equations around a steady state and subsequent
development of a term for the performance measure. The system studied oscillated
between purely aerobic and anaerobic metabolisms with no intermediate conditions. Thus,
an "imaginary" steady state of intermediate metabolism had to be used for linearization.
In numerical simulation of the determined optimal cycling, significant improvement
over strictly anaerobic operation was found. Experimental verification of this was
performed and improvement, though not as significant as theoretical predictions would
indicate, was found. Additionally it was found that the mutant was probably reverting to a
form where little d-lactic acid was produced. Cycling of dissolved oxygen apparently helps
delay this reversion.
Chemical processes are usually operated in one of three different manners, batch,
fed-batch, or continuous, each with its own advantages and disadvantages. Batch
operation is advantageous when small quantities of a product are desired. This type of
operation is perhaps the simplest since it only involves charging the reactor with the
appropriate reactants at the start of the process and removal of the products at its
completion. Unfortunately, this type of operation includes frequent downtimes where the
reactor is being either charged or purged, and production is thus temporarily stopped. Fed-
batch operation, where feed is added continuously but nothing is being withdrawn, is also
advantageous when small quantities of a product are desired. This type of operation is
optimal, for example, when it is desired to keep reactant concentration low. Fed-batch
operation has the same downtime problems that batch operation does. Continuous
operation is typically used when large quantities of a product are desired. It has advantages
over the batch-type processes in that no downtimes for charging or purging the reactor are
necessary. However, higher control and instrumentation costs are incurred. When large
quantities of product are desired, continuous operation is the usual method of choice.
When continuous processes are used, they are usually operated, after start-up
transients die out, in a steady-state manner. This involves keeping the process variables
constant. This type of operation is relatively easy to model and control. However, optimal
operation may involve taking the reacting volume through multiple steps of processing, for
example, operating the system in a neutral environment for an amount of time, and then in
an acidic environment. The simplest solution to this type of problem for a two-step process
would be to have two tanks in series, where one has a particular set of environmental
conditions maintained in it, and the other has a different set of environmental conditions
maintained. However, this increases the total volume and instrumentation (and thus cost)
of the system. An alternative approach is periodic operation. This involves only one tank,
but the environmental conditions are manipulated with respect to time. In general chemical
systems small time constants are the rule. As a result, conditions in the reactor would have
to be changed frequently to observe a significant improvement over steady-state operation.
This would lead to substantial control costs. However, in biological systems the time
constants are relatively large. Thus conditions may not have to be changed rapidly.
Therefore, biological systems may be suitable for periodic operation.
Periodic operation of continuous culture systems has been investigated by other
workers [e.g. 1-8] and it has been found to be useful in achieving desired process goals.
For example, it has been used for enhancing the production of yeast in continuous cultures
 and for solving the problem of plasmid stability in continuous recombinant cultures .
To establish appropriate operating conditions, kinetic models are required that adequately
describe the transient behavior of the culture being investigated. Such models have been
developed previously [e.g. 9-11].
Biological reactors can be operated to achieve one of the following process
objectives: utilization of nutrient (e.g., wastewater treatment), biomass production,
production of a particular metabolite, or conversion of one chemical substance to another
(bioconversion). The productivity of a continuous culture is determined by two variables,
number and state of cells. To achieve high productivity or substrate utilization, it is
desirable to have a large number of cells in the optimal state for the particular objective. A
system can be manipulated to change the state of the cells through control of environmental
conditions. However, in microbial growth processes, the optimal cell state for maximum
growth of the cells is generally not the same as the optimal state for production of a desired
metabolite. A solution to this problem is cycling environmental conditions (and thus cell
state) in the reactor. A large number of cells producing the desired metabolite could result.
Previous efforts in cycling of conditions will be described later in this work.
As an example, an E. coli mutant (LCB898), which produces d-lactic acid in large
amounts, was examined in this work. Under aerobic growth conditions this organism
produces high amounts of biomass but insignificant amotints of d-lactic acid. Under
anaerobic conditions it produces significant amounts of d-lactic acid and less biomass. If
the goal is to maximize lactate production per reactor volume per time, one could simply
operate the system under strictly anaerobic conditions. Alternatively, cycling dissolved
oxygen level (and sometimes residence time) may improve productivity over that achieved
by strict anaerobic operation. This improvement, in the case of constant residence time, is
achieved by operating the system at higher flowrates. The higher flowrates are allowed by
the aerobic (faster growth) portion of the cycle. Improvement by cycling is explained
further in the chapter on cycling.
An unexpected problem that occurred while investigating this process was that of
reversion of the genotype of E. coli LCB898 under anaerobic continuous operation. This
reversion led the organism into a state where little d-lactic acid was produced. The
proposed cycling of aeration also appears to be a new method for avoiding reversion or
mutation of organisms under continuous operation.
This dissertation reports theoretical and experimental investigations on aeration
cycling for E. coli LCB898. First, the general theoretical problem of optimizing a system
undergoing cycling of environmental conditions will be formulated. A description of the
particular microbial system under anaerobic and aerobic conditions, including modeling
results, will then be given. Transient behavior of the system will then be discussed,
followed by cycling predictions and experimental results. The question of reversion delay
will subsequently be addressed. Conclusions will then be presented.
An important job of the engineer is to determine the best way to operate a system.
This usually will be the way that maximizes profitability within safety limits. It can involve
anything from deciding how best to place workers on an assembly line to finding the
optimal control setting for the temperature of a chemical reactor. The engineer will usually
attack this problem by devising a mathematical formulation of the system and then use one
or more optimization methods to design the best operation. The formulation will involve a
statement of some sort of performance criterion to be optimized, along with descriptions of
various equality and/or inequality constraints on the system. Examples of the performance
criterion include maximizing the number of automobiles produced or minimizing the
amount of byproduct from a reactor. Examples of constraints are the number of workers
available at any given time or the maximum operating temperature of a reactor. Two kinds
of constraints usually encountered are equality constraints, where some quantity of the
system must always be equal to some other quantity, and inequality constraints, where
some quantity of the system is bounded within certain valuess. The optimization method
used will be selected by the engineer based on several factors including the system under
study, available computing power, and others. Much work has been devoted to finding
such optimization methods [e.g. 12-14].
A class of optimization problems exists where the equality constraints are not
algebraic equations but differential equations. These are called optimal control problems
[13, page 364]. Frequently, for this type of system, the engineer will want to vary the
control settings with time to maximize the productivity. Many methods have been
developed for handling this kind of problem and one will be discussed later. Others can be
found elsewhere [e.g. 15,16].
Continuous-flow reactor systems are typically operated at optimal steady-state
conditions. However, several workers [17-23] have looked into operating systems at
nonconstant conditions by cycling control variables around the optimal steady-state control
settings and found improvement for certain performance criteria. Sometimes, though, there
may be a need to examine systems where there is no true optimal steady-state control
setting to cycle around [e.g. 8], and an imaginary intermediate state, only existing
mathematically, may be used to design the best cyclic operation. As an example of this
type of system one could imagine a reactor whose air pumps can be either on or off, with
the on setting resulting in complete aeration. A mathematical model of the system may
show that intermediate aeration is optimal for production. Then the engineer must decide
how to best operate the air pumps to get optimal production.
In this chapter, the problem of determining optimal steady-state operation will be
addressed first. The method used to determine optimal square-wave cycling will then be
discussed, and finally a short description of some of the model-fitting techniques will be
2.2 Determination of Optimal Steady-state Operation
The typical system examined is one described by a set of differential equations:
dxi fi(xl,x2,...n;U,U2,...Ur) (1)
where xi= state variable i
fi= function describing the rate of change of variable i
n= number of state variables
ui= control variable
r= number of control variables
Steady states for such a system are found by setting the right-hand side of equation
1 equal to a zero vector and solving (by algebraic manipulation or by use of numerical
methods ) for the values of xi. The optimum steady-state operating conditions (i. e. the
optimal control settings) for such a system can be found by treating the resulting steady-
state model equations as equality constraints, expressing necessary inequality constraints
and stating a performance measure. Since the equations become algebraic at steady state,
many methods of optimization can be used. If the steady-state model equations can be
solved to yield an explicit expression of the performance measure as a function solely of the
control variables (and if inequality constraints do not come into play), then classical
theories of determining the optimal control settings involving setting the partial derivatives
with respect to each control variable to zero and solving for the settings can be used .
Frequently an explicit expression cannot be found and other methods have to be used.
One can find the optimum steady-state settings by performing, when possible, a
simple numerical search for the control values giving the maximum (or minimum) value of
a stated performance measure, but it will frequently be necessary to use a different method
when the system increases in complexity. As stated before, many methods exist. A few of
them include quasi-Newton and conjugate gradient methods. These methods are described
2.3 A New Method of Determining Optimal Periodic Pulsing
This new method involves Carleman linearization of a general nonlinear system,
expression of an explicit formula of the performance measure for pulsed cycling of the
linearized system, and then a search, using the explicit performance measure, for the
optimal settings for the system.
2.3.1 Carleman Linearization
Carleman linearization is a method of describing a general nonlinear system of first
order differential equations in a linearized form. It was first introduced in 1932  and
has been applied to various problems in nonlinear system dynamics and control [17,26-
34]. A brief overview of this method is presented here. This description was composed
using earlier descriptions [17,35].
A restatement of equation 1 would be as follows:
x=f(x,u) ; f(0,0)= (2)
with xe Rn a vector of deviation state variables and ue Rm a vector of deviation control
variables from a nominal steady state. This system is defined to have n dimensions. It is
assumed that the functions f are differentiable up to order r at Q. Taylor expansion is then
performed on system (2) and the monomials of order up to r are introduced as new
variables. These monomials are then differentiated and terms of order up to r are retained.
The result is a linear system in the new variables and is called the nh order Carleman
linearization. For example, the system
xi = -xl +3x2 + x2
x2 = -xI + 4u
where the manipulated variable u is treated as a parameter, would have the following
monomials approximated as variables wi.
X2 W3 (4)
The second order Carleman linearization for the system in equation 3 is
-1 3 0 0 1 0
0 0 -1 0 0 4u
w= 0 0 -2 6 0 w+ 0 (5)
4u 0 0 -1 3 0
0 8u 0 0 0 0
The computation of the necessary partial derivatives for expressions of higher order
Carleman linearization can be tedious, and, in the case of elaborate differential equations,
can lead to errors. A new program written in Mathematica  has been developed for
computing the necessary Carleman matrices and vectors and is presented in Appendix A,
along with an associated program used to compute necessary Kronecker products (the
Kronecker package offered by Mathematica is not usable for this type of problem). This
program, using the capabilities of Mathematica, does not require the user to provide
necessary derivatives; it computes the derivatives analytically. A description of the
algorithm used in the program was given by Lyberatos and Svoronos , but will also be
Let 0 represent Kronecker multiplication. The Taylor series expansion about
x = 0 can be expressed as
x= Alkxk] + Alo (6)
where x[k] = x x 0 ... 0 x (k terms)
and 0 represents Kronecker multiplication
e.g. [27, page 11] if A is an mxn matrix and B is a pxq matrix then
allB a12B ... alnB
B= a21B a22B .." a2nB
amlB am2B .-. amnB
The resulting matrix has the dimensions mp x nq.
The following system then comprises the rh order Carleman approximation to the
A1,1 AI,2 A1,3 ... Ai,r A1,'
A2,0 A2.1 A2,2 --- A2,r-1 0
[2 0 A3,0 A3,1 A3,r-2 0
x =w= w+ (7)
S 0 0 A4,0o A4,r-3
0 0 -'" Ar,o Ar 0
where Ai,j = In G Ai_1,j + A,j 0 Ini-1
Ig=gxg Identity Matrix
The above system will have a dimensionality of n+n2+n3+...+nr. Since the vector
w will contain monomial redundancies (e.g. xlx2 and x2xl), the system should be
simplified. This is done by eliminating rows that correspond to the same monomial and
adding the corresponding columns together. The Carleman system will then have a
dimensionality of n+j-lCj or equivalently Y rCj nCj where mCq is the number of
combinations of m objects taken q at a time mCq = [14,23].
2.3.2 Performance Measure Calculation
In this section we will develop a method to determine an explicit performance
measure for a Carleman linearized system when we cycle our controls on a system between
two fixed settings. Consider the waveform in figure 1. In this figure uS and up are the two
control settings available, and ui represents a fixed intermediate (though not necessary
realistic) control setting. These settings can be vectors or scalars. 6 and p represent the
vector or scalar deviations of the two respective control settings from ui. T represents the
period of the cycle, and E represents the fraction of the period spent at one of the control
This problem is very similar to one looked at by Lyberatos and Svoronos . In
that work, they looked at square-wave cycling around an optimal steady state. The
deviations from that state were allowed to vary. The intermediate state mentioned above is
analogous to the optimal steady state that Lyberatos and Svoronos examined. Additionally,
in the present problem, the deviations from the intermediate are fixed. Thus, the previous
mathematical development that they performed can be used to a large extent here with only
minor changes. The main parts of their derivation will also be given here.
Again, the problem to be examined is (in deviation variables)
x = f(x,u); f(0,o) = 0 (8)
where f(x,u) is analytic in x at 0 for all admissible u vectors (or scalars). The u vectors
(scalars) are treated as staying constant for either part of the cycle. Taylor
KI- T -*|
K- eT 41)
Section of control waveform being analyzed
expansion around x-0 is performed on this system and the nh order Carleman linearization
I S(5)w + z(5) t e [nT, (n + E)T)
S S(p)w + z(p) t [(n + E)T, (n + 1)T) (9)
The performance measure under cyclic conditions can be represented as the
S=- oP(x,u)dt (10)
where J=time-averaged performance measure
T=period of the cycle
P=instantaneous performance measure
It is assumed that P(x, u) is analytic in x at 0, in which case it can be linearized.. This is
done by Taylor series expansion around x-0 and is cast in terms of the Carleman
coordinates w. The performance measure then takes the representation
J= I [ro () + r'(u)w(t)]dt (11)
where represents the matrix transpose.
In the derivation that follows, the following identities, which apply to any invertible
n x n matrices and were proved by Lyberatos and Svoronos , will be needed
(In AB)-A = A(In BA)-1 (12)
(In AB)- A(In BA)-'B = In
(In A)(In BA)- (In B) = (In B)(In AB)-'(In A)(14)
Now, equation 9 can be integrated to give the following ultimate periodic solution:
Se(5)(t-nT) w -I es(8)(t-nT)]S(8)-^z(6)
for t E [nT,(n + e)T)
-[I es(P)(1-n+E)T) s(p y-1z(P)
for t E [(n + E)T, (n + 1)T)
wo and we can be expressed as:
S= -[I- RD]-[[R RD]S()- z(8) + [I R]S(p)'z(p)] (17)
w = -[I- DR]-[[I- D]S()-' z(8)+ [D DR]S(p) z(p)] (18)
From (15) it can be seen that
wE = Dwo [I- D]S()-'z(6)
wo = Rw -[I R]S(p)z()
Using equation 15, the cycle average performance measure given in equation 11 can
be expressed as
J(T,e,5)= ir'(8) [eS()ET -] S()-'wO +
Ir'(p)[eS(p)(1-E)T_ I]S(p)- wE_
Tr'(8S)[()T + I es()E'T]S(5)-2 z() (21)
S'(p)[(p)(1- e)T + I eS()(-E)T]S(p)-2z(p) +
ro()E + ro(P)(1 -E)
Using that S(8)-1 commutes with D and S(p)-1 commutes with R along with
equations 19 and 20, equation 21 can be rewritten as:
J(T,E,8) = r()S()l wE 0w ETz(8)] +
r'(p)S(p)- [w w -(1 E)Tz(p)] + (22)
ro()E + ro(p)(l E)
Using equations 12-14, equation 17 and equation 18 the following is obtained:
wE w0 = (I- R)(I- DR)-(I D)
[S(p)-' (p)- S()- z(5)] (23)
Finally, from equations 22 and 23 follows
J(T, ,)= -[r'(p)S(p)-' -r'()S(8)-I
(I- R)(I-DR)-(I- D) [s( p) (p) S(8)' ()]
+-ro(8) r'()S(8 () (24)
+(1- E)[ro(p) r'(p)S(p)z()]
This is the form of the cyclic average performance measure that is the most useful.
2.4 Model Fitting with Nonlinear Least Squares Methods
This topic is not directly related to the above discussion which led to an expression
for the performance measure, but this fitting, used in some parts of this work, is an
optimization technique and belongs in a chapter discussing the theory behind the overall
project. The type of problem that is being considered here is one where data are being
collected from some experiment and parameters for a model have to be determined. One
can manipulate the data in some fashion, such as semilog or log-log plotting, to find
necessary parameters, but, if no apparent manipulation exists for the proposed model, then
some other method must be used. One can attack such a problem by varying the
parameters of a model and determining how good the fit is to the data with those guessed
parameters. One can use methods of optimization to find the best way to vary the
parameters. The method of choice was Levenberg-Marquardt optimization due to its wide
use in prepackaged computer programs such as MATLAB and Kaleidagraph. A
description of the problem being examined, along with a short description of Levenberg-
Marquardt optimization, is appropriate here. A further description of the method of
optimization used can be found in numerical analysis texts such as Numerical Recipes .
Let us consider an experiment where data are taken at several times during the run.
In figure 2, an example experiment where three different types (x 1, x2, and x3) of data are
collected is shown.
In an experiment like that shown in figure 2, the experimenter collected all three
different types of data at the same instant. This type of collection is preferable for later
computational purposes, but is not necessary with the method to be described. In other
words, if one of the data types is difficult to collect simultaneously with the other data
types, then the following analysis still applies, but the computational effort may be
Let it be assumed that a general model for a system like that shown in figure 2 is
given in equation 2, but the vector of ordinary differential equations is also a function of
parameters. In other words
x=((x, ) ; x(0)= x (25)
where p=the vector of parameters for the model
For such a system, the parameter vector p and, occasionally, the initial condition
vector Xo (or just some parts of either of these vectors) must be determined. For any set of
guessed parameters and/or the initial conditions, the model equations can be integrated,
either analytically or by numerical methods such as Runge-Kutta integration, to show the
predictions for that set of guesses. The model predictions for this problem would be
computed for each time instant that data is available for comparison.
A performance measure for "goodness" of model fit then can be described as
nsp ndt ,2
P(Xd,,q)= nsp ndt Xdi(j)-i(j)) (26)
where P=performance measure
Xd. =one type of data point at time instant j (d is a vector of all data)
x )=corresponding model prediction for xd, (x is a vector of predictions)
qi=weight of one type of measurement (Q is the vector of the weights)
0= r -I
0 1 2 3 4
5 6 7
Figure 2. An example experiment where, at any time point, three different types of
data (xl, x2, and x3) are collected.
nsp=number of sampling points
ndt=number of data types
Our goal is to minimize the stated performance measure. The weighting factors q
serve two purposes. First, they can be used if one type of measurement is more "trusted"
than another. For example, one may give more weight to a simple measurement of
temperature taken with a thermistor than to a viscosity measurement taken with a poor
viscometer. This use of the weighting factor is going to be subject to the good judgment of
the experimenter and should be handled with caution. The other, more important, purpose
of the weighting factor is as a normalization constant. Alternative forms of the performance
measure, such as summing the logarithms of the squared residuals instead of the actual
squared residuals, (Xd i )2, can also be useful for normalizing.
Once the performance measure is expressed in the form of equation 26, the
optimization method of Levenberg and Marquardt can be used. This method is an elegant
combination of steepest gradient and inverse Hessian methods of optimization The
general algorithm involves use of steepest descent methods far from the minimum, and
then, as the minimum becomes more closely approximated, a smooth transition to the
inverse Hessian methods [24, page 523-524]. A prepackaged program was used in this
3.1 Organism Description
The organism used in this project was Escherichia coli strain LCB898. The original
culture was obtained from Dr. L.O. Ingram, Department of Microbiology and Cell Science,
University of Florida. The genotype is thrl leu6 ton A21 str lac Y1 sup E44pfll [37). The
important aspect of this organism is its mutation in the pfl gene causing lack of expression
of that gene. This is the gene for the production of pyruvate formate-lyase (pfl), an enzyme
which is primarily responsible for the conversion of pyruvate to acetyl-CoA and format
under anaerobic conditions.
The pertinent biochemical pathways for this organism are shown in figure 3 which
was prepared based on the diagram in Pascal . It points out the following important
features: lack of pfl activity , anaerobic inhibition of the pyruvate dehydrogenase
(PDH) pathway [38,39], and anaerobic induction of the d-lactate dehydrogenase (LDH)
pathway. Further descriptions of this organism's metabolism will be given in later
The culture was maintained on plates of rich broth agar with the following
composition in deionized water : 10 g/1 tryptone 5 g/l sodium chloride lg/l yeast
extract and 15 g/1 agar. The agar was prepared by mixing the ingredients together in
water, heating the solution to near boiling while stirring, and then pouring approximately
12 ml aliquots of the molten agar into individual 16X125 mm tubes. These tubes were
capped and autoclaved at 1210C for 30 minutes. Subculturing was performed on a monthly
Anaerbi- LDH -2 D-Lactate
Pertinent Biochemical Pathways in E. coli LCB898.
basis with the freshly inoculated plates being incubated at 370C in a Fisher Model 255D
incubator for 24 hours then being stored in a refrigerator.
3.2 Analytical Methods
3.2.1. Biomass and Cell Number Determination
The amount of biomass in the system was determined by two different methods,
cell counting and spectrophotometric turbidity (actually absorbance) measurement. The cell
counting involved serial dilution of a culture aseptically withdrawn from the culture vessel.
The dilutions were made in 8.5 g/1 solution of sodium chloride in water[41, p. 434] and the
agar used had the same composition as the rich broth agar used in culture storage.
Preparations involved pouring several 9 ml aliquots of the saline solution into 16X125 mm
tubes and pouring several 99 ml aliquots into bottles. Additionally, some empty capped
tubes were also prepared. These were all autoclaved for approximately 30 minutes.
Sterile, disposable, individually-wrapped borosilicate glass pipets (Fisher pipets) were
used in this procedure. A sample procedure for serial dilution and colony counting of a
culture is given in the two following paragraphs. The serial dilution procedure should be
performed under a laminar flow hood.
This sample procedure is designed for experiments where cell counts are expected
to be between thirty million and three hundred million cells/ml. Since it is desired to dilute
to 30-300 cells/ml, it is necessary to dilute samples 100000X, one million X, and ten
million X for later counting. Obviously this method can be modified for other expected cell
counts. Approximately 15 minutes before a sample is to be taken, three agar tubes are
placed in a boiling water bath in order to melt the tube contents. Immediately before the
measurement, the tubes are withdrawn from the water bath and stored in the laminar flow
hood, along with a propipettor, a pack of sterile gloves, three labeled sterile disposable
Fisher petri dishes, an appropriate number of pipets, dilution bottles, and tubes. A fresh
pipet should be used after each dilution step. The sample is removed from the culture (if
from a chemostat, the effluent sidearm tube (to be described later) is flamed and
approximately 10 ml are allowed to flow out into a presterilized empty tube; if from a
flask, the cap is removed under the laminar flow hood and a sample is aseptically pipetted
out) and one ml is pipetted from the tube or culture flask into a ninety nine ml saline bottle.
This bottle is then well shaken. At this point the original culture has been diluted 100 X. A
one ml sample is then aseptically transferred from the first dilution bottle to another ninety
nine ml saline bottle. Again, this bottle is well shaken. The culture sample has now been
diluted 10000 X. A one ml sample is then aseptically transferred to a 9 ml sample tube and
the tube is well shaken. 2 ml of the 100000X diluted sample is then taken. One ml is put
into the next 9 ml sterile tube and the other milliliter is pipetted onto the appropriately
labeled petri dish. One tubeful of agar, when it becomes lukewarm, is then poured into the
petri dish and the dish is subsequently mildly swirled in order to provide a more even
distribution of colony forming units. The new 1 million X dilution tube (now a 10 ml tube
with the one ml of sample added) is handled in the same way as the previous 100000X
tube. Lastly, the ten million X dilution tube has one ml transferred to the appropriate petri
dish. The agar in the petri dishes is allowed to solidify. The dishes are then inverted and
incubated at 370C for 24 hours.
Upon sufficient incubation, the petri dishes are taken out of the incubator and are
individually placed on a Quebec darkfield colony counter. A hand-held colony counter is
used to ensure accounting. A marking pen is used in order to make dots under each colony
appearing on the plate so that no colony gets counted twice. When counting, care must be
taken to count colonies on the edge of the petri dish and to check if some of the colonies are
growing directly underneath another colony. The results of each plate count are recorded,
and the cell counting procedure is finished.
Biomass concentration was measured spectrophotometrically using a Milton Roy
Spectronic 20D spectrophotometer. The procedure for this measurement is relatively
simple. The spectrophotometer is first set for operation at 550 nm. Deionized water is then
added to a clean cuvet, the cuvet is put into the sample chamber, and zeroing is performed.
The cuvet is then removed and the water is poured and then shaken out of the cuvet. Some
sample is then added and the cuvet is swirled. This sample is used to eliminate the effects
of residual water. At this point, the first amount of sample is poured out and at least three
ml of fresh sample are added. The cuvet is then placed into the sample chamber again and
an absorbance reading is then taken and recorded. If the absorbance reading is above 0.4,
appropriate dilution is performed. For example, in more dense samples, three ml of
deionized water would be added to one ml of sample for a 1/4 dilution. During the aerobic
operation experiments, 1/16 dilutions were necessary towards the end of the batch runs and
during continuous steady states.
In order to correlate the spectrophotometric absorbance reading to an actual dry
mass concentration, a calibration curve has to be obtained. A large (approximately 200 ml)
sample is taken from the reactor (at the end of a batch run). Eighty ml each of 75%, 25%,
and 12.5% dilutions are made in three separate beakers. The spectrophotometric
absorbances of each of these samples is then measured. In more turbid samples, when the
absorbance readings are significantly above 0.4, the diluted samples are used for
computation of the absorbance. Fifty ml of each of these dilutions are pipetted into
appropriately labeled centrifuge tubes. The tubes are then placed into a Precision Universal
Centrifuge set at 2000 rpm for 60 minutes. The supernatant is then decanted, the remaining
contents are washed with approximately 5 ml of deionized water, and the tubes are
centrifuged for 20 more minutes. The supernatant was pipetted off and the remaining
contents are then emptied into preweighed and labeled petri dishes for drying. These
dishes are dried at 1050C for 48 hours and the contents are weighed. In this manner, a
calibration curve was prepared. The calibration curve is shown in figure 4.
0.000 0.300 0.600 0.900 1.200 1.500
Absorbance @ 550 nm
Figure 4. Dry Mass Calibration Curve. The linear fit shown is
Dry Mass Concentration (g/1)=0.565*Absorbance
with a squared regression coefficient of 0.998
3.2.2 Glucose Analysis
The device used for glucose concentration determination was an Analytical
Research Model 110 Glucose Monitor. The analyzer's main component is the
electrochemical sensor on which an immobilized glucose oxidase membrane is mounted.
This enzyme catalyzes the reaction between glucose and oxygen to produce hydrogen
peroxide. Hydrogen peroxide is detected by the sensor and an electrical signal proportional
to glucose concentration is produced [42, p. 52]. The analyzer's pumps will take a small
(approximately 1.5 ml) aliquot of the sample through a port and pass most of it by the
membrane, leaving only a small plug of fluid for the actual analysis. This analysis is
performed in approximately three minutes, at which time almost all the glucose will have
reacted. Usually three aliquots are measured and the results are averaged. The following
paragraph gives a brief description of the actual procedure.
In the description that follows, one cycle is defined as the time between glucose
analyzer samplings. The glucose analyzer is operated as follows. Glucose calibration
solutions of appropriate concentrations (operator's judgment) are prepared and allowed to
dissolve for at least 2 hours. Fifty percent dilutions of calibrations should also be
prepared. For example, if calibration is to be made with a 2 g/1 glucose solution, a 1 g/
glucose solution should also be prepared. Additionally, the glucose analyzer is switched
from idle to blank for 2 hours before calibrations are to be done. After these two hours the
calibration tube is placed in 100 ml of fresh water and the switch is set to "Cal". For the
next 15 minutes, water is allowed to pump through the system. After this 15 minutes, the
glucose analyzer is zeroed by setting the zero dial so that the peak readout during the
portion of the cycle between the ready light indicator coming on and the following sampling
reads ".000" g/1. One more cycle is observed to check for appropriate zeroing. At this
point, calibration of the glucose analyzer is performed. The sample tube is placed in the
appropriate calibration solution. The switch is then set to "Sample". Three cycles are
allowed to follow and the calibration is completed by setting the cal dial so that the peak
value of glucose read during the portion of the cycle between the ready light turning on and
the following sampling reads out the calibration value of the glucose solution. This
calibration is then checked with a 50% solution of the calibrator solution by putting the
sample tube into the appropriate calibrator solution. Three samples are taken and
calibration is checked by reading the appropriate peak value. If calibration is appropriate,
samples can than be measured for glucose content. Four samplings are taken, with the last
three peaks being recorded as data. Recalibration is performed once every hour that
sampling is done. If the calibration stays relatively accurate, a calibration check with 50%
calibration solution need not be completed. If glucose analysis results are below 1/2 of the
top calibration value, recalibration is performed at one half the calibration value.
3.2.3 d-Lactate Measurement
The measurement of d-lactate was based on a modification of Sigma procedure 816-
UV, which was designed for measurement of I-lactate. The major modification to this
method was the use of d-lactic dehydrogenase (Sigma L-2395) instead of 1-lactic
dehydrogenase, provided with the original Sigma kit. The principle of this test is explained
In the metabolism of E. coli and most other chemoheterotrophic bacteria, pyruvate
is converted by lactate dehydrogenase into lactate. This, however, is a reversible reaction.
In other words, the same enzyme can be used to convert lactate into pyruvate. The
conversion of d-lactate to pyruvate will be accompanied by a reduction of one molecule of
NAD+ into NADH. NADH shows strong spectrophotometric absorbance at 340 nm,
whereas NAD+ does not absorb at this wavelength. Thus, using the indirect method of
spectrophotometrically measuring NADH in a mixture, the amount of d-lactate can be
determined. The problem of backconversion of the pyruvate into d-lactate is handled by
adding hydrazine to the mixture. Hydrazine reacts with the pyruvate and forms a complex
that d-lactic dehydrogenase cannot convert back into d-lactate.
The experimental method involved preparation of a calibration curve of d-lactate
concentration against spectrophotometric absorbance at 340 nm. The spectrophotometer
used was a Milton Roy Spectronic 20D. A solution of approximately 200 mg/l d-lactic acid
(Sigma L0625) or the Lithium salt (Sigma LI000) in deionized water (approximately in this
case means that the experimenter knows the exact concentration within experimental
accuracy, but it is not necessarily exactly 200 mg/1 in concentration) was prepared when
calibration was performed. When the lithium salt was used, adjustments were made for the
weight of a lithium atom as opposed to a hydrogen atom in the free acid form. Dilutions of
approximately 87.5%, 75%, 62.5%, 50%, 37.5% and 25% were made of this solution.
Additionally, a solution of 2.50 g NAD+ (Sigma N7004) and 500 ml Glycine buffer
(Sigma 826-3) added to 1 liter of water was prepared. The mixture will be referred to as
"NAD solution" from this point. Since the NAD solution must be made immediately before
the lactate measurement, the actual amount prepared would depend on the number of lactate
samples to be analyzed. One would prepare 3 ml of the NAD solution (2 ml of water, 1 ml
of glycine, and 5 mg of NAD+) per sample, plus at least one extra 3 ml solution for
preparation of a blank. 2.8 ml aliquots of NAD solution were pipetted into the appropriate
number of labeled test cuvets plus one blank cuvet. Each labeled test cuvet had 0.2 ml of
the corresponding full strength or diluted calibration solution added and mixed .
Additionally, the blank cuvet had 0.2 ml of deionized water added and mixed. The 340 nm
spectrophotometric absorbances of each test cuvet against the blank were then measured
This value, which will be referred to as the zero absorbance, was used to compensate for
Sixty units of d-lactic dehydrogenase were then added to each of the test cuvets and
the blank cuvet. The cuvets were then incubated at 370C for 30 minutes. The new
absorbances against the blank were then measured, and the differences between the new
absorbances and the corresponding zero absorbances were then calculated and plotted
against the corresponding test lactate concentrations. The curve obtained is shown in figure
5, along with the results of a least squares fit to the data. Although the substance measured
is referred to as d-lactate throughout this work, the term d-lactate is actually slightly
inaccurate. D-lactic acid is the substance actually being measured. Frequently these The
relatively high correlation coefficient indicates that the assumption of a linear relationship in
this range of test lactate concentrations is satisfactory.
The procedure for measuring unknown lactate concentrations is essentially the same
as that for measuring the net absorbances of the calibration solutions. The key differences
will only be described. First, the unknowns must be diluted however many times to where
their lactate concentration is in the range between 50 and 200 mg/1. The amount of dilution
is usually based on previous methods, but for the first experiments this had to determined
by trial and error. Second, this dilution is also useful in diluting the effects of any residual
biomass or other substances in the filtered samples on the spectrophotometric readings.
Any remaining residuals would be taken into account by the zero absorbance measurement.
These residuals will not affect the net absorbance measurements as the enzyme used is
specific for d-lactate. Last, least, and most obvious, the calibration curve is used to
determine unknown concentrations, as opposed to the preparation of the curve when
3.2.4. Other Analyses
Other measurement methods were used in this research. These will only be
mentioned briefly as they were only seldomly used. These include amino acid analysis and
ethanol analysis. The amino acid measurements were made by an outside laboratory
(Interdisciplinary Center for Biotechnology Research, University of Florida, Gainesville,
Florida) on an amino acid analyzer. These amino acid measurements were used solely to
determine whether or not leucine or threonine nutritional limitations were encountered.
Ethanol concentrations, when measured, were determined using Sigma kit 332-UV.
*6 0nnnn -
" I '... I" . . I '
0.200 0.400 0.600
Test Absorbance @340 nm
d-Lactate Calibration Curve. The linear fit shown is
d-Lactate Concentration (mg/l)=260.144*Absorbance
with a squared regression coefficient of 0.998
3.3 Feed Medium Composition
Many factors had to be considered in the design of the feed composition and
preparation. The first consideration was whether to use a complex medium such as Luria
broth or a minimal medium. A glucose minimal medium was chosen as the probability of
interference of feed components with measurements is lower. Once a minimal medium was
chosen, other considerations had to be taken into account. These included pH, buffering,
nitrogen requirements, trace minerals and metals, genetic deficiencies, substrate amount,
and interactions between these components during heat sterilization. These interactions
must be considered when deciding which component solutions to autoclave in the same
flask. Ideally, each component solution should be autoclaved separately. However, in
order to maintain sterility during the mixing process, there should be as few separate flasks
as possible. Thus, given the considerations described below, a design was chosen
inbetween these two extremes. A general consideration given was the separation of
inorganic from organic components in order to avoid production of toxic byproducts during
autoclaving. Finally, all the ingredients were prepared in deionized water.
The medium should be buffered with target pH 7. Buffering lowers the amount of
base needed to maintain pH during the experiments. M9 medium [41, p. 431 and 43, p.
A.3] satisfies this requirement. Additionally the nitrogen and some of the trace mineral
requirements are satisfied by the use of M9 medium. M9 medium includes sodium
phosphate dibasic, potassium phosphate monobasic, sodium chloride, ammonium chloride,
calcium chloride and magnesium sulfate. The exact amounts used will be given later.
Miller [41, p. 431] suggests separate autoclaving of calcium chloride and of magnesium
sulfate from the rest of the salts.
Other trace metals were added to the medium as suggested elsewhere[40,44,45].
These included selenium oxide, hydrated ferrous sulfate, hydrated ammonium molybdate,
and hydrated manganese sulfate The amounts used will be given later. It was suggested
these should be sterilized by filtration, but sterility was a major concern in this work, so
these compounds were autoclaved together in solution. Bridson and Brecker 
suggested autoclaving metals separately from phosphates in order to avoid precipitation.
Genetic deficiencies of E. coli LCB898 had to be accounted for in the medium
formulation. The genotype mentioned in the organism description indicates requirements
for threonine, leucine, and thiamine. Additionally, as the pyruvate-formate lyase gene is
mutated, acetate may be required to satisfy some biosynthetic requirements of the cell.
Several batch experiments were performed under both aerobic and anaerobic conditions in
order to determine the amounts of these chemicals required to insure glucose limitation of
growth. Amino acid analysis was performed on a sample of the batch at the point where
growth was no longer seen to see if any residual amino acids were left in solution. The
final amounts chosen were those that allowed glucose limited growth up to at least a
concentration of 4 g/l glucose in the medium. This was indicated by the cessation of
growth when glucose became exhausted. Miller [41, p. 431] suggests separate
autoclaving of the amino acids and vitamin from the M9 salts, and Bridson and Brecker
suggest separate autoclaving of the amino acids from the carbohydrates to avoid Maillard
reactions. Thus the amino acids and vitamin solutions were autoclaved together separately
from all other components, and, to avoid any other possible feed reactions, the acetate was
also separately autoclaved.
The final feed component to be discussed is the growth limiting substrate of
glucose. Glucose (Sigma) was used as the limiting substrate because of its relatively
straightforward measurement on the glucose analyzer previously mentioned. A main feed
concentration of 4 g/1 was decided on for several reasons. A feed glucose concentration too
low would make batch growth measurements difficult, as the analyzer available is
somewhat inaccurate at measuring glucose concentrations below 100 mg/1, and d-lactate
measurements below 25 mg/l are also of questionable accuracy. Another reason to avoid
low glucose concentrations is the desirability of visible turbidity in the reactor system. For
example, in a batch growth experiment, the onset of visible turbidity serves as a marker for
the beginning of more frequent measurements. This onset is still well before glucose
exhaustion and indicates the approximate point where glucose, d-lactate, and biomass
concentrations begin to measurably deviate from the starting values. On the other hand
high glucose concentrations also are not beneficial. First of all, autoclaving of high glucose
concentration solutions will lead to increased carmelization of the feed glucose. Also,
higher glucose concentrations represent higher biomass concentration. During aerobic
growth aeration may become insufficient at higher biomass concentrations. Buffering,
amino acid addition, and other feed components would have to be increased in
concentration. Finally, thick growth may cause other experimental problems such as
increased effluent tube wall growth, high amounts of base addition to maintain pH, and
more difficult sampling and cleanup. Thus, an intermediate glucose concentration of 4 g/
was picked. However, any glucose concentration from approximately 3 g/l to 10 g/1 would
also have satisfied the above criteria. Glucose solutions were autoclaved separately from
all other components to avoid all possible cross reactions (e.g. Maillard reactions). As
glucose concentration was the one feed component measured during all experiments, this
was the component that was most important to keep "pure".
The final feed composition used is given in Table 1.
3.4 Feed Preparation
The feed medium was prepared in three different configurations as follows: shake
flask, reactor batch, and continuous feed. Each will be discussed separately, and the flask
grouping listings in table 1 will be used. The term "2.7X concentrated" will hereafter be
used to refer to concentration higher than that listed in table 1 by a factor of 2.7. For
example, a 2.7X concentrated solution of flasking group 1 would be a solution of 10.8 g/1
glucose in water. One stock solution was used in all three configurations, a 100X
Table 1. Feed medium recipe with flasking divisions
Feed Ingredient Amount added per liter of
Glucose 4 g
KH2PO4 3 g
NaCI 0.5 g
NH4C1 1 g
Na2HPO4 6 g
Threonine 0.5 g
Leucine 0.5 g
Thiamine 5 mg
CH3COONa-3H20 1.66 g
MgSO4 0.24 g
CaC12 11.96 mg
SeO2 1.1 mg
FeSO4*7H20 27.8 mg
(NH4)6Mo7*4H20 1.765 mg
MnSO4-H20 1.69 mg
Note: For example flask 2 would include Na2HPO4, KH2PO4, NaCI, and NH4C1
concentrated solution of flasking group 7. One liter of this was prepared when necessary.
Ten milliliters of this solution were used for every liter of feed solution.
When shake flasks were prepared, stock solutions were used. The stock solutions
prepared were 100 ml bottles of 25X concentrated solutions of flasking groups 2-6.
Glucose solution was freshly prepared for each shake flask. In order to illustrate the
preparation of a shake flask, the preparation of the usual 250 ml amount of flask medium
will be given. 10 ml of each of the group 2-6 bottles are pipetted into separate tubes and
the tubes are capped. 2.5 ml of the group 7 flask are also pipetted into a tube. Finally,
197.5 ml of deionized water is poured into a shake flask and 1 g of glucose is added. The
flask is then capped with a paper towel and foil and tied with a string. All of these are then
autoclaved for 25 minutes. Finally, upon cooling of the ingredients, the ingredients are
poured together into the shake flask under a laminar flow hood.
The medium preparation for startup batches is described next. Although the startup
medium descriptions in this section do not appear to "add up" to the concentrations given in
Table 1, when the actual startup procedures are considered later, the final startup
composition does "add up" to the correct medium. Two liters of 1.4 X concentrated
flasking group 2 salts are prepared and poured into the chemostat and then autoclaved
within the reactor. A 56 ml aliquot of the flasking group 7 stock solution is pipetted into a
glass flask. Four additional glass flasks with 150 ml each of deionized water are set aside.
To each of those flasks 5.6 times the mass listed in table 1 for one flasking group is added,
for groups 3,4,5, and 6. These flasks are capped with paper towel and foil and then tied
with string. The glucose solution is prepared by adding 22.4 g of glucose to 944 ml of
water in the main feed flask, which is shown in figure 6. The main feed flask preparation
is as follows. A new Supor filter is placed in the Fisher 47 mm filter holder. The
connections are as follows: the flask outlet tube leads to its own filter holder, which leads
to the needle for puncturing into reactor. The needle is wrapped in foil wrap. Additionally,
there is a tube for a sterile nitrogen inlet into the flask for replacing the emptied fluid. The
Main Batch Feed Flask Diagram
Copper wire assembly on
nitrogen introduced passes through a Bacti-Vent air filter. The rods going through the
rubber stopper are made of glass. The main feed flask and the glass flasks are autoclaved
for 30 minutes. After these cool down, all of the flasks are placed under a laminar flow
hood. The metal clamp on the main feed flask is loosened and the contents of the glass
flasks are added. The metal clamp is then retightened and the feed is ready to be added to
the reactor, as will be described later in the description of reactor startup.
Finally, the continuous feed medium preparation will be described. Sixteen liters of
continuous feed medium were made in any single batch, thus sixteen times the amount of
each flasking group to be added per liter is added to separate amounts of water. The
procedure for a single batch is described. In three large flasks, 3.5 liter aliquots of
deionized water are added, along with separate additions of 16X of the Table 1 masses for
flasking groups 1, 2, and 3. For example, in the glucose flask, 64 g of glucose are added
to 3.5 liters of water. The group 7 flask has 160 ml of the appropriate stock solution added
and then filled with deionized water to 3 liters. The acetate flask has 26.56 g of
NaAcetate*3H20 added to 500 ml of water. The calcium chloride flask has 192 mg of
CaCI2 added to 250 ml of water and the last flask has 3.94.3 g of MgSO4*7H20 added to
250 ml of water. Finally, the feed carboy, diagrammed in figure 7 is prepared as follows.
Two fresh .22 [t Supor filters are placed in the appropriate filter holders, along with a fresh
Bacti-Vent air filter for sterile nitrogen introduction. The carboy is then autoclaved empty
and uncapped. One and a half liters of deionized water are then poured into the carboy and
it is capped. The tubes are then clamped, the needle and air filter are covered with foil
wrap, and the whole apparatus (except the N2 bag and the magnetic stirrer) is autoclaved
for 30 minutes. All of the flasks are covered with paper towel and foil wrap and then tied
with string. They are also autoclaved for 30 minutes. The cap of the carboy is removed
and the contents of the other flasks are added under a laminar flow hood.
0.22 p filters
Figure 7. Continuous Feed Carboy Diagram
3.5 Experimental Operation
3.5.1 Operational Conditions
The temperature that the experiments were operated at was 370C. This temperature was
chosen as it is the normal optimal temperature for growth of E. coli. The other major
environmental variable that was held constant was pH. It was suggested  that
somewhat acidic pH's gave higher batch yields of d-lactic acid. As pH 7 is the optimal pH
for E.coli growth, the possibility of cycling pH in addition to aeration was examined.
Preliminary experiments were performed early in this investigation to examine the effects of
pH on the anaerobic batch yield of d-lactate on glucose. The results will be described
briefly. These experiments were performed before any aerobic experiments were and,
thus, a slightly different medium formulation was used as shown in table 2. It should be
emphasized that the pH effects experiment was the only one described in this work using
the table 2 recipe. All other experiments used the main recipe given in Table 1.
The use of shake flasks will be described later. A starter flask with an initial medium
composition described in table 2 in 500 ml of deionized water was inoculated, placed in a
37C AO constant temperature shaker bath and kept there until the flask contents appeared
turbid. Three test flasks were prepared during the growth phase of the starter flask cultures
with 150 ml of medium in each. The medium ingredients of these three flasks were the
same as those in Table 2, but the concentrations of each were set so that, upon dilution with
100 ml of liquid, they were the same as those given in Table 2, except that the amounts of
potassium phosphate mono- and dibasic were varied to give the desired pH values.
Table 2. First Medium Recipe
Glucose 3.0 g/l
K2HPO4 4.9 g/
KH2PO4 3.0 g/1
NaAcetate 0.2 g/1
(NH4)2SO4 0.1 g/1
CaC12 0.2 g/1
MgSO4.7H20 0.1 g/1
FeS04-7H20 0.05 g/1
L-Threonine 0.05 g/1
L-Leucine 0.05 g/l
Thiamine 0.005 g/I\
When the starter flask reached the appropriate turbidity, the three test flasks were
each inoculated with 100 ml of the starter culture. Spectrophotometric absorbances, pH
values and lactic acid concentrations were then measured at half-hour intervals. The results
of this experiment are given in table 3. The large increase in lactate concentration in the pH
7 flask over a 5 hour period, along with the large increase in absorbance over a 26 hour
period, would indicate that the operating pH should be kept at a value around seven. An
additional benefit in choosing constant pH operation is that shifts in pH are difficult.
Buffering is generally desirable in microbial systems, but buffering would require higher
base or acid amounts to be added to cause a shift. High addition of these solutions have a
diluting effect on the culture and thus will interfere with measurements. This problem,
though, may possibly be overcome by use of gases such as C02 and N2 instead of acid or
base additions to manipulate pH.
3.5.2 Shake Flask Experimental Procedure
The shake flasks were prepared as described in the section on feed preparation.
Further procedural details will be given here. In a starter culture, after the contents were
poured together under a laminar flow hood, a small inoculum was taken off of the culture
storage agar dish with a sterile loop and then transferred into the combined medium flask.
In other types of shake flasks, liquid inocula may be used instead of the agar culture.
When liquid inocula were used, only small amounts (-1 ml) were usually added. After
inoculation, the flask was recapped with the paper towel/foil wrap cap and tied. The flask
was then placed in an AO shaker bath set at 370C. If the shake flask culture was to be used
for reactor inoculation, it was usually left in the bath for approximately 12 hours. For yield
experiments, the flasks would be left in for longer periods. The usual shake flask volume
used was 250 ml.
Table 3. Effects of pH on Lactate Production
Initial pH 7 6.4 5.85
Initial Lactate Conc. 105 110 110
Initial Absorbance 0.186 0.186 0.186
Lactate Conc. after 5 206 151 119
550 nm Absorbance 0.200 0.205 0.175
after 5 hours
pH after 5 hours 6.98 6.4 5.87
Lactate Conc. after 2900 1340 292
26 hours (mg/1)
550 nm Absorbance 0.49 0.37 0.22
after 26 hours
pH after 26 hours 5.24 5.26 5.38
3.5.3 Reactor Experimental Procedure
126.96.36.199 System Description
The reactor experimental procedures will now be described. The reactor, a
Bioengineering KLF 2000, was used for all of the batch and continuous experiments. A
diagram of the reactor system is shown in figure 8. In this figure the long dashed lines
represent measurements for the chemostat control unit, and the dotted lines represent
control outputs. Except where mentioned later, the reactor volume was always maintained
at 2 liters. If the system is in continuous mode, a load cell is used to determine the system
weight. A peristaltic pump maintains a constant effluent flowrate. The pumping rate is
calibrated by collection of the fluid in a graduated cylinder. When a small drop in weight is
detected the control unit activates the influent pump until the reactor is back up to its
operating weight. Only small deviations in the level were allowed. The pH value of the
system was measured with an Ingold Ag/AgCl pH electrode and controlled by a
Bioengineering M7832N pH controller. This pH control maintained constant pH by
controlling pumps for previously autoclaved 1 M HCI and NaOH solutions prepared
separately. The constant 370C temperature was maintained by a ptl00 temperature sensor,
a Bioengineering K54450 controller, and an 800 watt heater. Agitation for the reactor was
set at 700 rpm, and a baffle cage within the reactor helped insure good mixing. Dissolved
oxygen was monitored with a Cole-Parmer polarographic electrode and a Cole-Parmer
Model 5513 dissolved oxygen meter. When anaerobic conditions were necessary, filtered
(as shown in figure 8) Alphagaz oxygen-free nitrogen was bled over the top of the culture
at the rate of approximately 30 ml/min. When aeration was necessary, an Air Cadet pump
was used. It pumped air from underneath a UV hood, through a filter apparatus identical to
the same as that used for nitrogen, and through a sparging tube with the outlet bent
underneath the bottom rotor blade within the reactor. Two and a half vvm was the air
flowrate obtainable with this pump into the two liter reactor. When periodic switching of
Air vent filter
"-I I Air Pump
fluent UV Hood
Experimental Reactor Setup
the aeration was performed, a slow flow of nitrogen was continuously maintained over the
top of the culture so as to maintain a positive pressure (which helps prevent outside
contamination). Switching of conditions during the aeration cycling was performed by
simply plugging the Air Cadet pump into an X-10 wall module and setting switch times on
an X-10 computer interface (X-10 (USA) Inc. 185A LeGrand Ave. Northvale, NJ). The
gas was released through a Bioengineering gas outlet apparatus. This had a cooling jacket,
which was maintained at about 100C in order to minimize evaporation of culture volume.
This cooling was accomplished by continuous pumping of cooled Prestone antifreeze
through a Hotpoint refrigerator and freezer using a Manostat pump set on its lowest
pumping speed. The end of the effluent gas hose was placed in a dilute Betadine solution
in order to help prevent contamination.
188.8.131.52 System Startup and Operation
The following startup procedure was used for all batch and continuous
experiments. It should be emphasized that all continuous runs were started as batch runs.
The only variations were whether anaerobic or aerobic procedures were going to be used.
The cycling runs were all started up under aerobic conditions. Prior to startup, the effluent
tube, acid, base, and inlet gas filters were autoclaved. A batch feed was also prepared.
Additionally, a starter shake flask culture was prepared and inoculated 12 hours prior to
reactor inoculation. The chemostat was filled with the appropriate salts as described in the
batch feed description to the 2000 ml level. The topcap and bottom attachment rings were
secured in place. The pH electrode was precalibrated to pH 7 and 4 and inserted into the
topcap. The reactor was now ready for autoclaving.
The autoclaving of the reactor was done in situ. Here, the pH electrode was
pressurized to 30 psi by connecting it to an air cylinder, the stirrer was set to 800 rpm, the
gas outlet was opened, and temperature set-point of the chemostat was changed to 121 0C.
When the temperature reached 990C, the gas outlet was closed. The temperature was
allowed to reach 1210C, and was kept there for 30 minutes. After 121C was held for 30
minutes, the temperature set point was changed to 1040C. When reactor temperature
reached 1040C, the first thing that was done was to turn on the pump for the gas outlet
apparatus reflux coolant. The reactor pressure was raised by using either air from the Air
Cadet pump or nitrogen from a cylinder. The gas outlet was also opened immediately. The
reactor temperature set-point was then changed to 370C in preparation for the actual
After the reactor cooled down to 370C, the effluent, acid, and base tubes were each
placed through peristaltic pumps and then appropriate connections were made to the reactor
using aseptic technique. The effluent tube was immediately clamped to avoid loss of
reactor liquid. The main feed flask (described in the batch feed preparation) was then
connected to the reactor. Eight hundred milliliters were then pumped into the reactor for a
total volume of 2.8 liters. The reactor conditions were then set to pH 7, 370C, and 700 rpm
agitation. Finally, 20 ml of inoculum were taken by a sterile syringe from the starter flask
under a laminar flow hood and then injected through one of the reactor seals. The reactor at
this point was prepared and inoculated. A batch run was thus begun.
Immediately after inoculation a sample was aseptically taken through the effluent
sidearm aseptically into a previously autoclaved and capped tube. Serial dilution was
immediately performed and the remaining sample had its absorbance measured and then
was centrifuged for ten minutes in a Fisher Centrific 228 centrifuge. After centrifugation
the sample was filtered using a syringe and MSI Magna Nylon 66.22 p filters and then
heat shocked for five minutes in boiling water. Finally, the sample was allowed to cool to
room temperature and then stored in a freezer for later glucose and lactate analysis.
Frequent measurements were taken during batch runs. The acid and base levels
were monitored and recorded. Upon the absorbance values reaching above 0.4,
appropriate dilution with deionized water was performed in order to obtain a measurable
absorbance. The batch measurements were performed until absorbance stopped increasing.
Up to this point, the batch and continuous experiments were performed in a synonymous
manner (except for the obvious need for preparation of a continuous feed carboy during the
batch start of a continuous run). If a run was intended to be strictly batch, measurements
were continued for several hours into the stationary phase. If a run was intended to be a
continuous run, the system was switched into a continuous mode before the end of
exponential phase. The point of switching was usually about one hour before the expected
end of exponential phase. This end point was estimated using absorbance measurements
and comparing them with previous batch results.
The following procedure was used to switch the reactor from the initial batch mode
to a continuous mode. The feed carboy was connected to the reactor after its tube was led
through the influent peristaltic pump. Subsequently the reactor volume was lowered to 2
liters by draining through the effluent tube. The weight set point was entered into the
chemostat control unit, the effluent flowrate was set, and the reactor was then in a
Measurements were taken in the same fashion as in the batch runs. They were
taken at least three times on a daily basis, but usually the frequency was much higher.
Additional considerations during continuous operation were daily monitoring of the base
reservoir, checking of the tubing and overall system condition, contamination testing,
effluent disposal, and feed carboy preparation and changing.
Contamination testing was usually performed by the following two methods:
preparation of a shake flask deficient in the appropriate amino acids and inoculation with
reactor contents, and microscopic examination of a Gram-stained sample of the reactor
contents. In the former method, an additional control flask was prepared with the
appropriate amino acids. The two flasks were seeded with identical volumes of reactor
volume. They were then examined for growth after overnight shaker bath incubation. If
the deficient flask showed significant growth, then the reactor was declared contaminated.
This method is somewhat dubious, though, as the deficient flask could be selective for
leucine and threonine revertants. Thus, the primary method of contamination testing was
the mentioned microscopic examination. If the slide appeared to have only red rods, the
continuous operation was declared successful to that point.
When operating in continuous mode a new feed carboy had to be prepared daily.
The feed was changed by switching the quick connect fitting at the end of each carboy tube
while all ends were immersed in rubbing alcohol. The quick connect change in alcohol,
along with the second filter placed between this connect and the reactor inlet, helped insure
ANAEROBIC GROWTH OF E. COLI LCB898
Under anaerobic environmental conditions, where no alternate electron acceptors
such as nitrate, fumarate, or sulfate, are available, Escherichia coli uses fermentation as its
pathway for energy production. Fermentation, as defined by Brock [47, p.802], is a group
of catabolic reactions producing ATP in which organic compounds serve as both primary
electron donor and ultimate electron acceptor. When compared to aerobic or anaerobic
respiration, fermentation is not a very efficient method of producing ATP and, thus,
overall cell biomass [48, p. 54]. In order to understand fermentation, the reactions
involved are briefly described. The important reactions are diagrammed in figure 9 (this
diagram was drawn with the help of Neidhardt and Brock [49, p. 153 and 47, p. 126]).
First, the metabolic pathway common to both aerobic and anaerobic metabolism, pyruvate
formation, will be examined. After this, fermentative pyruvate dissimilation will be
The pathways of glucose degradation to pyruvate shown in figure 9 are the
Embden-Meyerhof-Pamas (EMP) pathway and the pentose-phosphate pathway. Typically,
in E. coli grown anaerobically on glucose, 92-95% of the glucose will be degraded by the
EMP pathway and 5-8% will be degraded by the pentose-phosphate pathway [50,51]. The
common first reaction to both pathways is the phosphorylation of glucose to glucose 6-
phosphate. After this point, the split between the two pathways occurs. The pentose-
phosphate pathway's major roles are formation of pentose phosphates for nucleotide
splits into two
Glyceraldehyde 3-phosphate --
6-Phospho- glucnate I
I LNADH NH4 a- Ketoglutarate
ATP pfl f- NADP
ATPy upv Acetyl c Citrate--.- )> Isocitrate
Pruvat7 CoA aolic Acetyl-P Acetate
S dh Formate Acetaldehyde Ethanol
NAD+4 CO +H NADH NAD+, CoA NADH NAD+
d-Lactate C +2
Figure 9. Main Anaerobic Biochemical Pathways in E. coli LCB898
biosynthesis and NADPH generation [48, p.31]. The EMP pathway will be described in
the following paragraph.
During pyruvate formation, a net yield of 2 moles of ATP per mole of glucose is
obtained by substrate-level phosphorylation. Additionally, 2 moles of NADH, the main
source of reducing power for biosynthesis, are generated. Some of the EMP pathway
intermediate metabolites also serve as biosynthetic precursors. These include fructose 6-
phosphate and phosphoenolpyruvate. The point at which aerobic and anaerobic
metabolisms differ is the degradation of pyruvate.
In wild-type E. coli cells, pyruvate is normally dissimilated under anaerobic
conditions by two pathways with no additional ATP generation, one being catalysed by
pyruvate formate-lyase (pfl), the other by d-lactate dehydrogenase (ldh) [52, p.151]. Pfl is
inactive under aerobic conditions . The products of the pfl degradation include
format, acetate, ethanol, C02, and H2 [49, p. 163]. The sole product of the lactate
dehydrogenase pathway is d-lactic acid. In anaerobic wild-type E. coli K12 batches ,
only traces of d-lactic acid are produced. This would indicate that the Idh pathway is not
In E. coli LCB898, a K12 mutant, a mutation exists in the gene responsible for
production of pyruvate-formate lyase, thus closing off that pathway for pyruvate
dissimilation [37,38,55]. High yields of d-lactic acid from glucose therefore are expected
in this mutant. An additional consequence is that when growth is anaerobic in a minimal
medium, the addition of acetate may be required since acetyl-CoA cannot be produced
without the action of pyruvate formate-lyase.
To summarize, two points must be reiterated. The first is that when glucose is
processed through the EMP pathway, a net yield of 2 ATP molecules for every glucose
molecule degraded is observed. During aerobic metabolism, which is to be described later,
oxidative phosphorylation can also be employed. It will be shown that the net ATP yield
per glucose is much higher when the additional phosphorylation is performed. Again, ATP
yield is directly proportional to growth yield. Thus, relatively low biomass yields under
anaerobic conditions are expected. The second main point is that E. coli LCB898 should
show high yields of d-lactate on glucose.
4.2 Batch Growth
In all of the following discussed batch results, time 0 represents the point at which
inoculation of the reactor was inoculated. The results for one of the anaerobic batch runs,
to be designated anaerobic batch run 1, are shown in figures 10 and 11. This was one of
the preliminary runs to help determine a final feed composition. It is clear that biomass
concentration stopped increasing well before glucose in the system was exhausted from the
results shown in figure 10. Any glucose consumed after 46 hours was strictly being used
for maintenance. The results shown in figure 11 indicate that the glucose was largely being
converted into lactate. In this experiment only 50 mg/l of each amino acid and no metals
were used in the medium. It was hypothesized (and later confirmed with amino acid
analysis) that threonine was exhausted at the point of entering stationary phase.
In the next batch experimental run, anaerobic batch run 2, the amino acid
concentrations were doubled, but metals were still not added to the medium. The results
for this experiment are shown in figures 12 and 13. Again, as can be seen in figure 13, the
bacteria appeared to enter a stationary growth phase before glucose was exhausted. Amino
acid analysis showed excess threonine and leucine. Other work with this organism
[40,44,45] was then reexamined and metals were then added to the final formulation of the
In figures 14-17 all of the experimental results for a batch run with sufficient amino
acids and metals added to the medium are shown. This run is designated anaerobic batch
run 3. At 27 hours, the point of glucose exhaustion, growth had essentially stopped, as
can be seen in figures 14-16. During this growth phase, as shown in figure 17, lactate was
being produced in what appears to be a growth-associated manner. Lactate concentration
20 30 40 50
Figure 10. Anaerobic batch run 1. Glucose and biomass concentration against time.
- - -
10 20 30
Figure 11. Anaerobic batch run 1. Lactate and biomass concentration against time.
* Lactate Concentration
A Biomass Concentration
4AA .. A
- .. .. . .. II
-4000- ** A
E 3500 <------
S3000 -. A 250
o :A -150 c.
S000lo 100 g
U : A
S500- A -50
0 A o. 0
0 5 10 15 20 25 30 35
Figure 12. Anaerobic batch run 2. Glucose and biomass concentration against time.
3500 Lactate Concentration A *
A Dry Mass Concentration 0
5 3000 A
E A -250
J 2000 A
8 A -150
6 1500- .
500 A -50
0- A -A0
0 5 10 15 20 25 30 35
Figure 13. Anaerobic batch run 2. Lactate and biomass concentration against time.
0 5 10 15 20 25 30 35
Figure 14. Anaerobic batch run 3. Biomass concentration against time.
0 5 10 15 20 25 30 35
Figure 15. Anaerobic batch run 3. Cell number concentration against time.
o 2500.000 *
0.000 5.000 10.000 15.000 20.000 25.000
Figure 16. Anaerobic batch run 3. Glucose concentration against time.
0.000- ., 1. 1
0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000
Figure 17. Anaerobic batch run 3. Lactate concentration against time.
did continue to increase beyond 27 hours, but this may be explained by a slow release of
the lactate from the cells. The low lactate concentration seen at 27 hours was probably due
to experimental error in the measurement, as the previous point indicated a lactate
concentration approximately 300 mg/l higher. Appropriate values for growth parameters
for this run will be given later in this chapter. Approximately 2 hours after entering the
stationary phase, the lactate measurements shown in figure 17 showed an interesting
response. The lactate showed a sharp dip with a subsequent increase. Ordinarily this may
have been simply dismissed as experimental error. A later experimental run was performed
under the same conditions as anaerobic batch run 3, to be designated anaerobic batch run 4,
and its results are shown in figures 18-21. The lactate results for this run are shown in
figure 21. The previously mentioned dip was also seen here. This dip was not of major
importance to this work as it occurs during stationary phase. This work primarily involved
exponential phase growth in continuous operation. However, possible explanations for it
are appropriate. The simplest hypothesis is experimental error. This hypothesis is not
probable though as it has been seen more than once. Another is that the cells may have
been growing diauxically on some other substance in the medium such as acetate, leucine,
or threonine. This would have been an unusual diauxy, though, as biomass concentration,
shown in figures 14 and 18, did not seem to increase during the period of glucose
exhaustion. The cells may have been using one of the listed substances in the medium for
maintenance while ingesting d-lactate along with this substance and later releasing the
lactate for some unknown reason. Still another hypothesis is that some of the cells may
have been genetically reverting to a pfl+ form (to be discussed further in a later chapter).
The properties of the revertant are not completely understood and this could have been
some effect of the revertant's growth alongside with the non-revertants. Again, whatever
the true explanation for this behavior may be, it was not of primary importance to this work
as most of the work performed in this project was on exponential phase growth.
* S S
5 10 15 20 25 30 35
Anaerobic batch run 4. Biomass concentration against time.
0 5 10 15 20 25 30
Figure 19. Anaerobic batch run 4. Cell number concentration against time.
5.000 10.000 15.000 20.000 25.000
Figure 20. Anaerobic batch run 4. Glucose concentration against time.
1 1 1 1 1
0 5 10 15 20
Figure 21. Anaerobic batch run 4. Lactate concentration against time.
25 30 35
I I I I I I I -
I . . .
4.3 Continuous Growth
All continuous anaerobic experiments were run with the standard feed medium
shown in table 1. In all of the following discussions of continuous results, time 0
represents the point at which the reactor was inoculated. The point of switch from batch to
continuous operation will be mentioned for each run. It should be reemphasized that all of
the continuous runs were started as anaerobic batch runs. The switching point was chosen
on the basis of reactor turbidity so as to avoid washout and glucose exhaustion. The
results for one of the anaerobic continuous experiments, anaerobic continuous run 1, are
shown in figures 22-25. This experiment was performed at a dilution rate of 0.164 hr1.
(Dilution rate is defined as the ratio of flowrate to reactor volume. In reactor engineering
terminology, this represents the reciprocal of the residence time.) The switch to continuous
operation in this run was done at 83 hours. In figure 22, it is seen that a steady state,
defined as where the state variables of the system are unchanging, was seen at
approximately 108 hours. Data collected past 130 hours show surprising results and these
will be presented and discussed in Chapter 8. Some of the results of another continuous
anaerobic experiment (with dilution rate of 0.17 hr-1), anaerobic continuous run 2, are
shown in figures 26 and 27. The increased number of data taken at the switch point show
the smooth change in system condition from batch to continuous operation. In this
experiment, a steady state was seen at approximately 44 hours.
Values for the averaged apparent steady-state values for various dilution rates of cell
number, biomass, lactate and glucose concentrations are given in table 4. These values
were taken from the shown continuous experiments along with other continuous anaerobic
experiments. The results show low values for residual glucose concentration and high
conversions to lactate. The biomass concentration is also consistently low. Surprisingly,
the biomass concentration seemed to rise with dilution rate, which is not in agreement with
normal Monod behavior. These increases were not very large though. In contrast to
biomass, glucose did follow the expected Monod behavior of increasing with dilution rate.
S I ' I
40.00 60.00 80.00
1 I 120.
Figure 22. Anaerobic continuous run 1. Biomass concentration against time.
I I --
0 20 40 60 80 100 120 140
Figure 23. Anaerobic continuous run 1. Cell number concentration against time.
0 20 40
Figure 24. Anaerobic continuous run 1. Glucose concentration against time.
I I -
Figure 25. Anaerobic continuous run
60 80 100 120
1. Lactate concentration against time.
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Figure 26. Anaerobic continuous run 2. Biomass concentration against time.
0.00 10.00 20.00 30.00 40.00 50.
Figure 27. Anaerobic continuous run 2. Lactate concentration against time.
Table 4. Apparent Anaerobic Continuous Steady States
Dilution Rate Biomass Cell Number Glucose
Concentration Concentration Concentration
(hr-1) (mg/1) (cells/) (mg/1)
.164 248 7.65x1011 136
.13 240 6.7xl011 86
4.4.1 Presentation of Model
The following model was proposed to describe this system under batch anaerobic
conditions during exponential growth
= maxanaerobic (27)
Ks,anaerobic + S
1 Pmax,anaerobicS (28)
s= ----x (28)
Yx/s,anaerobic Ks,anaerobic + S
p = max,anaerobic (29)
Ks,anaerobic + S
where q= time derivative of q
x=biomass (dry mass) concentration in the reactor
s=substrate (glucose) concentration in the reactor
p=product (d-lactate) concentration in the reactor
lrmax, anaerobic-maximum growth rate under anaerobic conditions
Ks, anaerobic=saturation parameter under anaerobic conditions
Yx/s, anaerobic=yield of biomass on substrate under anaerobic conditions
(=growth-associated lactate production parameter
The first model equation, equation 27, shows simple Monod dependence of biomass
growth rate on glucose concentration. Equation 28, representing the time derivative of
glucose concentration, was chosen with the assumption that all glucose consumed during
exponential growth was consumed for the purpose of producing biomass. The third
equation, equation 29, gives the time derivative of d-lactate concentration in such a system.
It was assumed that the d-lactate production under exponential growth conditions was
strictly anaerobically growth-associated.
A continuous form of this model is as follows
Ks,anaerobic + S
s = x + D(sp s) (31)
Yx/s,anaerobic Ksanaerobic + S
p = max,anaerobicS p
p = a x Dp (32)
Ks,anaerobic + s
where D=dilution rate= -
sF=feed substrate (glucose) concentration
The above continuous form of the model was developed for a continuous stirred tank
reactor under conditions of perfect mixing. No biomass or product was introduced in the
feed, so no feed lactate or biomass was accounted for in this model. Inlet substrate was
accounted for in the substrate equation. The equations were simply extensions of equations
27-29 with additional terms for dilution of the biomass, substrate, and product out of the
4.4.2 Model Parameter Fitting
The batch run measurements were the primary ones used for parameter
computation. The primary justification for this was that the anaerobic continuous runs
described previously were not performed until the ending of this work. Also, they showed
problems with reversion, which will be described in a later chapter, and measured steady
states were difficult to find. The parameters used in later modeling will be given here,
along with justification for their determination. Improved values for model parameters are
also given, but these were not the ones used in designing the later cycling operations still to
The first parameters to be discussed are the maximum growth rate, .Lmax, anaerobic,
and the saturation constant, Ks, anaerobic. These parameters would usually be determined
by use of a Lineweaver-Burke plot [56, p. 106] of continuous data. In these types of plots,
a large number of continuous steady states are necessary. Under steady-state conditions,
the time derivatives of the continuous form of the model are all equal to zero. By
manipulation of the steady-state version of 30, the following relation can be obtained
1_ Ks.anaerobic 1 1 (33)
D [ max,anaerobic Sss [ max,anaerobic
where sss=steady-state residual glucose concentration in the reactor
A plot could then be made of reciprocal dilution rate against reciprocal residual glucose
concentration. A least-squares fit would then be made to the data. The intercept would be
equivalent to the reciprocal of the maximum anaerobic growth rate, and the slope would be
equal to the saturation parameter divided by the maximum anaerobic growth rate.
Unfortunately, due to the reversion problems mentioned above, it was very difficult to
obtain continuous steady-state data. Equation 33 can be used on one data point to find one
of the two unknown parameters if the other can be satisfactorily estimated. It can be seen
that at a dilution rate equal to half of the maximum growth rate, the residual substrate in the
reactor is equal to Ks, anaerobic. In anaerobic batch run 3 the dry-mass growth rate was
0.190 hr1 and in anaerobic batch run 4 it was 0.23 hr1. These were obtained by simple
exponential fitting of the biomass data during exponential phase. For example, the data
used to calculate anaerobic batch run 3's growth rate was the dry mass data taken between
16 and 27 hours. The correlation coefficient for the fit (R2) was greater than 0.99. It was
assumed that these growth rates were at the maximum, as the glucose concentration was
very high during most of the duration of the runs. Were this not the case, the R2 would not
have been so close to 1. For the sake of consistency, anaerobic batch run 3 was the run
that served as the source of the data used for fitting model parameters. The reason why this
run was chosen over anaerobic batch run 4, was that the run 4's growth rate of 0.23 hr1
was significantly higher than that seen in other experiments performed. Most experiments,
including anaerobic batch run 1 and 2, indicated growth rates of the culture having values
between 0.19 and 0.20 hr-1. Therefore, the final value of I.max, anaerobic used was 0.190
hr1. The two Ks, anaerobic parameters then calculated using equation 33 for the anaerobic
continuous steady states given in table 4 are then 22.4 and 40.4 mg/1 for dilution rates
0.164 and 0.13 hr-1, respectively. An average Ks, anaerobic of 31.4 mg/1 would then be the
apparent value to be used. For several of the simulations described later the anaerobic
continuous experiments had not yet been performed. For these, a Ks, anaerobic value of 98
mg/l, based on preliminary continuous data using the feed medium listed in table 2, was
used for several of the later simulations in this dissertation. Use of the revised parameter
value of 31.4 mg/1 is suggested for future work with this model.
The next parameter to be determined was the yield of biomass on glucose under
anaerobic conditions, Yx/s, anaerobic. Using equations 30 and 32 and the assumption of
steady state the following relation for continuous operation can be stated
xss=Yx/s, anaerobic(SF-Sss) (34)
where xss=steady-state biomass concentration in the reactor
Using this relation, yield values of .064 and .061 mg biomass were indicated for dilution
rates 0.164 and 0.13 hr1, respectively. Anaerobic batch run 3 was the base run used and
the biomass yield was computed for this using a material balance argument which is very
similar to equation 34.
where so=initial glucose concentration in the batch
In figure 28, a plot of biomass against consumed substrate is shown. The line fit to the
data and forced through zero is also exhibited. The slope of this line gives the value of
Yx/s, anaerobic determined by this experiment The fit indicates a yield value of
0.063 mg biomass. However, as can be seen from the large amount of scatter around the
line, this was not a very good fit. The correlation coefficient for this curve, R2, was only
0.90. Since the correlation coefficient was so low, the yield used in calculation was
computed by simply averaging the biomass concentrations found in the stationary phase
and dividing the average by the initial glucose concentration of 4000 mg/l. The yield
computed in this manner was 0.068 mg s. This was the value used in the modeling
work. The fit value of 0.063 mg biomass turned out to be in good agreement with the
later continuous results, and, thus, this result should be used in the future.
The final parameter to be discussed for the anaerobic model is the anaerobic growth
associated lactate production parameter, a. Using equations 30, 32, and the steady-state
assumption, the following continuous steady-state relationship holds
a = PSS (36)
where pss=steady-state product (d-lactate) concentration
mg d lactate
The continuous runs indicate values for a of 12.02, 12.95, and 14.15 mg d for
dilution rates of 0.17, 0.164, and 0.13 hr1, respectively. The variability in these values is
quite large and leaves some of the d-lactate measurements in question. The determination
of a for a batch run is done by using equation 27 and equation 29 to obtain
Figure 28. An
1000 1500 2000 2500 3000 3500 4000
Glucose consumed (mg/1)
run 3. Biomass concentration against glucose consumed.
p = ax (37)
Subsequent integration yields
where po=initial d-lactate concentration
Xo=initial biomass concentration
The slope of a plot of biomass against d-lactate concentration during exponential phase for
a batch run is equivalent to the a parameter. This plot for anaerobic batch run 3 is shown
in figure 29, along with the results of a linear least squares fit to the data. The problem
with this method is that, due to the scatter of the d-lactate values seen in figure 29, the final
value is very dependent on where exponential phase is declared to begin. For example, if
all of the data that were used for the computation of anaerobic batch run 3's growth rate
was used, an a parameter of 8.64 mg/mg (with a correlation coefficient, R2, of only 0.88)
would be the determined value. This correlation coefficient was unacceptably low. If the
last data point, due to its questionable reliability, was ignored the a parameter value
increased to 9.64. If the only points considered on this figure were those between 100 and
250 mg/1 biomass, an a parameter of 16.7 mg/mg would be found. Due to all of this
scatter, a batch value for a had to be determined by another batch run. Anaerobic batch run
4, in spite of its high growth rate, was then examined and used to obtain an estimate of a.
The results of the corresponding lactate against biomass curve are presented in figure 30,
along with linear least squares fitting results. The data showed a much higher degree of
linearity than that seen for anaerobic batch run 3. The a parameter fit for these data was
10.8 with a correlation coefficient, R2, of 0.98. This was the value used in later
simulations. Upon comparison of this value with those given by the continuous runs, this
0 50 100 150 200 250 3(
Biomass Concentration (mg/1)
Figure 29. Anaerobic batch run 3. Lactate concentration against biomass concentration.
value for a would underpredict lactate concentration by approximately 20%. Increased
values of a should be considered in future use of the model.
The parameter values are summarized in table 5. The suggested revised a
parameter was based on averaging the results for the determined o parameters of the three
continuous experiments. The large differences in updated parameter values for yield,
saturation and a parameters suggested that use of the model in designing any operation
must be checked for sensitivity to these parameters.
0 50 100 150 200 250
Biomass Concentration (mg/1)
Figure 30. Anaerobic batch run 4. Lactate concentration against biomass concentration.
Table 5. Anaerobic Model Parameter Values
Parameter Value used in later work
Plmax, anaerobic .19 hr-
Ks, anaerobic 98 mg/1
Yx/s, anaerobic .068 mg/mg
at 10.77 mg/mg
AEROBIC GROWTH OF E. COLI LCB898
Under aerobic conditions most facultative aerobes, such as E. coli, will adjust their
metabolism to take advantage of available oxygen and increase its production of biomass.
The first part of aerobic metabolism of glucose is production of pyruvate. This part
was described in the previous chapter on anaerobic growth. The only major difference to
be mentioned here is that 25% of the glucose will enter the pentose-phosphate pathway
under aerobic conditions [50,51]. Where the major difference between fermentation and
aerobic respiration on glucose lies, is in the fate of pyruvate. The aerobic metabolism of
glucose for a wild-type E. coli is shown in figure 31 [49, p. 155, 45]. The aerobic
metabolism of E. coli LCB898 shouldn't deviate significantly from this as no significant
aerobic metabolism genes are mutated in its genome. Pyruvate dehydogenase, which is
only produced aerobically , is the enzyme responsible for aerobic conversion of
pyruvate to acetyl-CoA. After it is formed, acetyl-CoA is sent through the TCA cycle. In
the TCA cycle only one ATP molecule (per molecule of pyruvate) is produced by substrate-
level phosphorylation, specifically the conversion of succinyl-CoA to succinate [48, p. 54].
All of the other ATP molecules are generated by oxidative phosphorylation, where the
energy is produced by the transfer of electrons from NADH, NADPH, and FADH2 to
oxygen . As can be seen in figure 31, from each turn of the cycle two molecules of
NAD+, one of NADP+, and one of FAD+ are reduced, with one additional NAD+
reduction occurring in the conversion of pyruvate to acetyl-CoA. In E. coli, two molecules
of ATP can be generated for each molecule of NADH or NADPH, and one molecule of
ATP can be produced for each molecule of FADH2 oxidized [48, p. 43]. To sum up, ten
molecules of ATP can be produced, when the TCA cycle is employed, for every molecule
of pyruvate processed. When one adds, per glucose molecule, the two ATP molecules
generated by fermentation, the 2 ATP's that can be generated from the 2 molecules of
NADH produced (and not needed in d-lactate formation) and the TCA generated ATP's
from the two pyruvate molecules formed, 26 molecules of ATP can be produced for every
glucose molecule, as opposed to the synthesis of just two molecules of ATP for each
glucose molecule strictly fermented.
Of course, these ATP yields are theoretical. Fermentative efficiency can be as high
as 50%, as opposed to the TCA cycle efficiency of 39% [47, p. 134]. Nonetheless, even
though pure fermentation has higher efficiency, the aerobic metabolism will give much
higher amounts of ATP per glucose molecule consumed than will pure fermentation. Since
growth requires ATP for energy, aerobic growth should show higher biomass yields on
There are two main products of aerobic growth of E. coli on glucose, specifically
biomass and CO2 [57, p.802]. Three CO2 molecules are produced by the TCA degradation
of each pyruvate molecule, and thus 6 CO2 molecules are produced for every glucose used
strictly for catabolism.
5.2 Experimental and Modeling Results Introduction
Most of the aerobic experiments were performed in conjunction with a master's
thesis project performed by Christina Stalhandske . The experiments were jointly
performed by this author and Stalhandske and the modeling work, while contained in that
work, was mostly performed by this author. Thus, most of the results, both experimental
and modeling, are taken from this thesis.
4 ) ADP
splits into two
Glyceraldehyde 3-phosphate ----
6-Phospho- gluc nate
v AIF ADU
ADP Succinate < Suc
ATP FADH 2
3-Phosphoglycerate 2 4
V NADH N '- Ketogl
APyruva Acetyl nitrate Isocitrate
Pyruva CoAli LCB898
Figure 31. Main Aerobic Biochemical Pathways in E. coli LCB898
5.3 Batch Growth
In all of the following discussed batch results, time 0 represents the point at which
the reactor was inoculated. The results for one of the aerobic batch runs, to be designated
aerobic batch run 1, are shown in figures 32-35. This was one of the preliminary runs to
help determine a final feed composition. As can be seen from figure 32, glucose was not
exhausted when biomass concentration stopped rapidly increasing at 14 hours. Biomass
did increase slightly after 14 hours, but not in an exponential manner. Glucose did
continue to drop, but it is hypothesized that this glucose was largely used for maintenance.
Amino acid analysis showed that threonine was exhausted before glucose The lactate and
ethanol concentrations of each sample were measured to see if they were produced in a
significant amount. These quantities turned out to be negligible. Thus, in the following
strictly aerobic batch and continuous runs ethanol and lactate measurements were not
The results of a batch run with sufficient amino acids aerobic batch run 2, are
shown in figures 36-38. This time the cells grew exponentially until glucose was
exhausted, which indicated that glucose was the limiting substrate. It appeared that 15
hours after starting the run, cell number and biomass concentration stopped increasing in an
exponential manner. Further increases in dry mass can be attributed to diauxy on
remaining amino acids or acetate present.
5.4 Continuous Growth
All continuous aerobic experiments were operated with the standard feed medium.
In all of the following discussed continuous results, time 0 represents the point at which the
reactor was inoculated. The point of switch from batch to continuous operation will be
mentioned. It should be reemphasized that all of the continuous runs were started as
aerobic batch runs. The switching point was determined on the basis of turbidity and
chosen so as to avoid washout and glucose exhaustion.
* Biomass Concentration
A Glucose Concentration
) 5 10 15 20 25 30 2
Figure 32. Aerobic batch run 1. Glucose and biomass concentration against time.
0 5 10 15 20 25 30 35
Figure 33. Aerobic batch run 1. Cell number concentration against time.
T T .
Figure 34. Aerobic batch run 1. Lactate concentration against time.
O l . Ia
u 3 1U 15 20 25
Figure 35. Aerobic batch run 1. Ethanol concentration against time.
0 a- AA O 6O0
0 5 10 15 20 25 30 35
Figure 36. Aerobic batch run 2. Biomass concentration against time.
Figure 37. Aerobic
1 ---* I- 1 l 1 1 1 1 1 1 I I.. I I I I- 1 1 I . .
5 10 15 20 25 30
batch run 2. Cell number concentration against time.