Group Title: Theoretical Biology and Medical Modelling 2006, 3:40
Title: In silico experimentation with a model of hepatic mitochondrial folate metabolism
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Title: In silico experimentation with a model of hepatic mitochondrial folate metabolism
Series Title: Theoretical Biology and Medical Modelling 2006, 3:40
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Creator: Nijhout HF
Reed MC
Lam SL
Shane B
Gregory JF
Ulrich CM
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Theoretical Biology and Medical 0

Modelling BioMed



Research

In silico experimentation with a model of hepatic mitochondrial
folate metabolism
H Frederik Nijhout*', Michael C Reed2, Shi-Ling Lam', Barry Shane3,
Jesse F Gregory III4 and Cornelia M Ulrich5


Address: 'Department of Biology, Duke University, Durham, NC 27708, USA, 2Department of Mathematics, Duke University, Durham, NC 27708,
USA, 3Department of Nutrition Sciences and Toxicology, University of California, Berkeley, CA 94720-3104, USA, 4Department of Food Science
and Human Nutrition, University of Florida, 32611-0370, USA and 5Cancer Prevention Program, Fred Hutchinson Cancer Research Center,
Seattle, WA 98109-1024, USA
Email: H Frederik Nijhout* hfn@duke.edu; Michael C Reed reed@math.duke.edu; Shi-Ling Lam shiling.lam@duke.edu;
Barry Shane bandie@berkeley.edu; Jesse F Gregory jfgy@ufl.edy; Comelia M Ulrich nulrich@fhcrc.org
* Corresponding author


Published: 06 December 2006
Theoretical Biology and Medical Modelling 2006, 3:40 doi: 0. 186/1742-4682-3-40


Received: 20 October 2006
Accepted: 06 December 2006


This article is available from: http://www.tbiomed.com/content/3/1/40
2006 Nijhout et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.



Abstract
Background: In eukaryotes, folate metabolism is compartmentalized and occurs in both the
cytosol and the mitochondria. The function of this compartmentalization and the great changes that
occur in the mitochondrial compartment during embryonic development and in rapidly growing
cancer cells are gradually becoming understood, though many aspects remain puzzling and
controversial.


Approach: We explore the properties of cytosolic and mitochondrial folate metabolism by
experimenting with a mathematical model of hepatic one-carbon metabolism. The model is based
on known biochemical properties of mitochondrial and cytosolic enzymes. We use the model to
study questions about the relative roles of the cytosolic and mitochondrial folate cycles posed in
the experimental literature. We investigate: the control of the direction of the mitochondrial and
cytosolic serine hydroxymethyltransferase (SHMT) reactions, the role of the mitochondrial
bifunctional enzyme, the role of the glycine cleavage system, the effects of variations in serine and
glycine inputs, and the effects of methionine and protein loading.
Conclusion: The model reproduces many experimental findings and gives new insights into the
underlying properties of mitochondrial folate metabolism. Particularly interesting is the remarkable
stability of format production in the mitochondria in the face of large changes in serine and glycine
input. The model shows that in the presence of the bifunctional enzyme (as in embryonic tissues
and cancer cells), the mitochondria primarily support cytosolic purine and pyrimidine synthesis via
the export of format, while in adult tissues the mitochondria produce serine for gluconeogenesis.


Background
Folate and one-carbon metabolism play a central role in
cellular physiology because they are intimately involved
in the control of purine, pyrimidine, and glutathione syn-


thesis, as well as the methylation of DNA, histones and a
host of other key cellular components. Deficiencies in
folate metabolism have been associated with a wide range
of diseases and pathologies such as anemia, spina bifida,


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central


^^3







Theoretical Biology and Medical Modelling 2006, 3:40



cancer, cardiovascular disease, and neuropsychiatric dis-
orders. Aberrant folate metabolism can be caused by pol-
ymorphisms in the genes for enzymes in the folate and
methionine cycles, environmental factors that increase
oxidative stress, and dietary deficiencies in B vitamins.
Thus, this part of cell metabolism is a locus where genetic,
environmental, and behavioral variables interact to affect
many aspects of health and disease [1-12].

It has been known for almost 50 years that some reactions
of the folate cycle in eukaryotes (Figure 1) are duplicated
in the cytosol and mitochondria [13], while other reac-
tions such as purine and pyrimidine synthesis occur only
in the cytosol, and the glycine cleavage system occurs only
in the mitochondria [14,15]. Two folate substrates, dihy-
drofolate (DHF) and 5-methyltetrahydrofolate (5mTHF),
occur only in the cytosol. Moreover, some enzymes of
mitochondrial folate metabolism are highly up-regulated
in embryos and cancer cells and virtually inactive in nor-
mal adult cells [16,17].

Because substrates, enzymes, and function differ between
the mitochondrial and cytosolic compartments, many
questions arise. What specific role does the mitochondrial
folate cycle play in overall cell metabolism? What is the


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reason for the down-regulation of mitochondrial MTD
and MTCH in adult tissues? Why does SHMT occur in
both compartments? What is the role of the mitochon-
drial GDC reaction? How does the system accommodate
changes in the input of serine and glycine? What happens
during protein or methionine loading? What are the roles
of folate-binding proteins in the cytosol and the mito-
chondria? These questions have been the subject of exten-
sive experimental investigation and theoretical
discussions [16-26].

We have developed a mathematical model for mitochon-
drial and cytosolic one-carbon metabolism. The model
extends our earlier models of cytosolic methionine and
folate metabolism [27-30]. We use the model to conduct
in silicon experiments that address many of the above ques-
tions and compare the results to experimental observa-
tions. The model gives insights into the mechanisms
underlying the experimental results and allows us to test
various hypotheses that have been proposed in the litera-
ture.

In the following section we give a brief overview of our
model. Full details of the model and the full names of all


Figure I
Diagram of the reactions modeled in the present paper. Pink rectangles represent variable metabolites and blue ellipses are
enzymes. Full names corresponding to acronyms are given in Additional file I.



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Theoretical Biology and Medical Modelling 2006, 3:40




abbreviations used in the text and in the model are given
in additional file 1.

Model overview
Figure 1 shows the biochemical pathways in the hepatic
cellular model used in this paper. Rectangular boxes rep-
resent the substrates that can vary in the model, and the
ellipses contain the acronyms of the enzymes that catalyze
specific reactions. Full names of the substrates and
enzymes appear in the Additional File 1. Non-boxed sub-
strates are taken to be constant. The model consists of 23
coupled differential equations for the time courses of the
boxed substrates. The formulae for the velocities of the
various reactions are taken, when possible, from the
experimental literature. In some cases we adjusted the rate
constants within experimental ranges so the concentra-
tions of folates in the cytosol and mitochondria would be
similar to those observed experimentally. In this model,
MTD, MTCH, FTD and FTS are active in the mitochondria,
and TS and DHFR are up-regulated in the cytosol, so the
model represents a liver cell that is actively dividing.

This model is an extension of the model used by Reed et
al. [30]. Mitochondrial folate substrates and enzymes
were added, and sarcosine and dimethylglycine are new
variables (each is assumed to have the same concentra-
tions in the cytosol and mitochondria). The extracellular
serine, glycine, and methionine concentrations can be
specified as functions of time. The cytosolic and mito-
chondrial serine and glycine concentrations can vary, as
can the cytosolic methionine concentration. Appropriate
kinetics are used for transport between the external,


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cytosolic, and mitochondrial compartments. The mito-
chondrial and cytosolic HCOOH concentrations are
allowed to vary in the present model, and format is trans-
ported between the mitochondrial and cytosolic compart-
ments. In addition, AICAR is a variable in the model that
couples the PGT and AICART reactions. Finally, we have
added a serine sink that corresponds to the use of
cytosolic serine in gluconeogenesis and the tricarboxylic
acid cycle. Full details of the model are given in Additional
file 1.

Table 1 shows the steady-state concentrations and veloci-
ties in the model assuming that the extracellular glycine,
serine, and methionine concentrations are held constant
at 300 [tM, 150 [tM, and 30 [tM respectively. For the
reversible reactions in Figure 1, the positive directions are
as follows: 5,10-CH2-THF to 5,10-CH = THF to 10f-THF
for MTD and MTCH; THF to 1 Of-THF for FTS; serine to gly-
cine for SHMT; SAH to homocysteine for SAAH. We refer
to the values shown in Table 1 as "normal" throughout
this paper. The computed distributions of folates in the
cytosol and mitochondria are similar to those reported by
Cook [15].

In the model, we express the quantities of substrates by
concentrations and we assume that the mitochondria
occupy 1/4 of the cell volume. So the same number of
molecules will have different concentrations in the two
compartments. For example, we assume that the total
"normal" cellular folate concentration is 20 [tM. If the
folate molecules are equally divided between the cytosol
and the mitochondria [15], then the total folate concen-


Table I: Cytosolic and mitochondrial concentrations and velocities at steady-state.


Cytosolic


Mitochondrial


Concentrations (ptM)


THF
5,10-CH = THF
5,10-CH2-THF
I0f-THF
5mTHF
DHF
Aicar


Ser
Gly
HCOOH
Met
SAM
SAH
Hcy


Velocities (ptM/h)


3.74
0.26
0.46
3.23
5.55
0.035
0.95


551
830
14.5
51.9
63.6
13.1
1.10


MTD
MTCH
FTS
FTD
SHMT
NE
AICART
DHFR
TS
MTHFR
PGT
MS
BHMT
CBS
DNMT
GNMT
MAT-I
MAT-ll1


Concentrations (ptM)


THF
5,10-CH = THF
5,10-CH2-THF
IOf-THF





Ser
Gly
HCOOH


Velocities (tiM/h)


MTD
MTCH
FTS
FTD
SHMT
NE
GDC
SDH
DMGD


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2106
2106
-1639
467
84.3
279
1560
122
60.7







Theoretical Biology and Medical Modelling 2006, 3:40



trations will be 13.3 [tM and 40 [tM in the cytosol and the
mitochondria, respectively. We assume that sarcosine and
dimethylglycine diffuse freely and thus have the same
concentrations in the cytosol and mitochondria. For
transport between compartments, the rates (in [tM/h) are
the rates of change of concentration in the cytosol. If a
substrate has concentration Cc in the cytosol and concen-
tration Cm in the mitochondria, then the observed total
cellular concentration (when the compartments are com-
bined) will be (0.75)C, + (0.25)Cm. Table 2 shows the
normal total cellular concentrations of the folate metabo-
lites and amino acids.

Table 3 shows the normal rates of transport of serine, gly-
cine, and HCOOH, between the compartments. For exam-
ple, at normal steady-state, the cytosol receives 799 [tM/h
of serine from the extracellular medium and loses 30.4
[tM/h to the mitochondria (Table 3). Of course, the
cytosol also loses 99.7 [tM/h through the CBS reaction,
8.19 [tM/h through the cytosolic SHMT reaction, and 662
[tM/h to gluconeogenesis (Tables 1 and 3).

Limitations of the model
The model we developed is intended specifically to study
the interaction among the folate cycles in the cytosol and
mitochondria. No mathematical model can include the
complete biological complexity of a system. Instead, a
model should contain sufficient detail to allow investiga-
tors to study the phenomenon of interest without omit-
ting features that are likely to affect the behavior of the
model dramatically. The model used in this paper, and
described in detail in Additional File 1, is no exception.
For instance, we do not include leucovorin as a cytosolic
folate substrate, we do not include the polyamine path-
way, and we use only two methyltransferase reactions
between SAM and SAH. We also do not include the fact
that some folate substrates can regulate gene expression of
some folate enzymes. We do not include the allosteric
binding of folates to folate enzymes, because the main

Table 2: Total cellular concentrations of folate metabolites and
amino acids at steady-state


Metabolite


Concentration (tM)


THF
5,10-CH = THF
5,10-CH2-THF
IOf-THF
5mTHF
DHF

Sarcosine
Dimethylglycine
Serine
Glycine


8.02
0.58
0.77
6.43
4.16
0.026

9.11
0.70
904
1087


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Table 3: Transport rates at steady-state (aM/h).

Serine Glycine


Extracellular to cytosol
Mitochondria to cytosol
To gluconeogenesis


HCOOH


546


effect of these reactions is to maintain reaction velocities
in the face of severe folate deficiency (studied in Nijhout
et al. [281). Our model assumes that cytosolic amino acids
are used only as substrates in the folate and methionine
cycles, and as a source for gluconeogenesis. We do not
include protein catabolism as a source, or protein synthe-
sis as a sink, for amino acids. Likewise, we do not include
the transport of homocysteine between the blood and the
cellular compartment. All these features are important
and interesting aspects of folate metabolism, and several
are currently under investigation, but they do not bear
directly on the role of mitochondrial folate metabolism
studied in this paper.

Results
A. Variation in serine and glycine
There is general agreement that one of the functions of the
mitochondrial folate cycle is to provide 1-C units to the
cytosol for purine and pyrimidine synthesis and the meth-
ylation reactions in rapidly dividing cells [14-16]. The two
primary sources of 1-C units are the mSHMT reaction,
which converts serine to glycine, and the GDC reaction,
which breaks down glycine, producing 5,10-methyl-
eneTHF. Additional contributions are made by the SDH
and the DMGD reactions. All four of these reactions use
THF to produce 5,10-methyleneTHF, which is converted
to 10f-THF. The FTS reaction regenerates THF and pro-
duces free format that is exported to the cytosol. There
are a number of natural questions here. (1) How does this
system operate at different levels of extracellular serine
and glycine? (2) How sensitive is the production of for-
mate to the balance between serine and glycine? (3) How
sensitive is the production of purines and pyrimidines in
the cytosol to the supply of format?

To investigate these questions, we systematically altered
the external concentrations of serine and glycine from
their normal values of 150 [tM and 300 [tM, respectively.
Figure 2A shows the cytosolic and mitochondrial glycine
and serine concentrations as the extracellular glycine con-
centration is varied from 100 [tM to 1000 [tM. As external
glycine increases, both the cytosolic and mitochondrial
glycine concentrations increase, but not as dramatically,
because the reverse transport out of the mitochondria and
cytosol increases as the concentrations rise. The cytosolic
serine concentrations also rise because of the interconver-
sion of glycine and serine by the SHMT reactions.


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Theoretical Biology and Medical Modelling 2006, 3:40


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0 200 400 600 800 1000

External [Gly] f(M)


A
mSER





cGLY


cSER


HCOOH



AICART


T^O',:SHMT


mSnMT


S"M


Met




10OHcy


0 100 200 300 400

External [Ser] (iM)


Figure 2
A: Response of selected model variables to variation in external glycine input. B: Response of model variables to variation in
external serine input.


As external glycine rises, both the cytosolic and the mito-
chondrial SHMT reactions reverse and run in the glycine
to serine direction (Fig. 2A); the mitochondrial reaction is
more sensitive to external glycine. This reversal was
observed by Kastanos, Woldman, and Appling [21], who
grew yeast in pure serine and pure glycine environments.
In spite of great variations in the glycine and serine con-
centrations (Fig. 2A, middle panel, blue curve) and the
reversals in both SHMT reactions, the rate at which for-
mate is supplied to the cytosol remains remarkably con-
stant (Fig. 2A). In addition, the rates of the TS and AICART
reactions (for thymidylate and purine synthesis, respec-
tively) change very little despite large changes in external
glycine. The metabolites of the methionine cycle also
change relatively little except for SAM, which rises at low
external glycine because the GNMT reaction rate declines
(Fig. 2A).


Figure 2B shows the cytosolic and mitochondrial serine
and glycine concentrations as the extracellular serine con-
centration is varied from 50 [tM to 400 [tM. As external
serine increases, both the cytosolic and mitochondrial gly-
cine concentrations increase, and there is an even greater
increase in the cytosolic and mitochondrial serine concen-
trations. As external serine decreases from normal, both
the cytosolic and the mitochondrial SHMT reactions
reverse and run in the glycine to serine direction (Fig. 2B);
as before, the mitochondrial reaction is more sensitive.
The rates of the TS and AICART reactions and the rate of
transport of format out of the mitochondria are again
remarkably stable.


The methionine cycle metabolites are more sensitive to
external serine than to external glycine, especially at low
external serine. This is because serine is required for the


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3500

3000

2500

2000

1500

1000

500

0

500

400

- 300

f 200

100

0

-100
90
80
70
60
5 50
40
30
20
10
0


2 1500


1000

500


0
500
400
300
S 200
100
0
-100
-200
70
60
50
2 40
30
20
10
0


B



-icSER
mGLY



cGLY





HCOOH




AICART
TS

/ I"'EhMMT






ScM

Met



10*Hcy







Theoretical Biology and Medical Modelling 2006, 3:40



CBS reaction, which slows down and causes methionine
cycle metabolites to accumulate, particularly as SAM,
owing the internal regulatory mechanisms of the methio-
nine cycle [27,29].

Lewis et al. [18] radiolabeled the methyl group of SAM.
Very little of the radioactivity appeared in metabolites of
the folate and methionine cycles because most of these
radiolabeled methyl groups were transferred to other sub-
strates by the methylation reactions. However, when gly-
cine was elevated, the amount of radiolabel in HCOOH,
serine, and CO2 went up considerably. This can be easily
explained by the model. More glycine results in accelera-
tion of the GNMT reaction so more of the radiolabeled
methyl groups are put into sarcosine. Then, in the mito-
chondria, the sarcosine becomes either radiolabeled 5,10-
CH2-THF or CO2. The radiolabeled 5,10-CH2-THF makes
radiolabeled HCOOH via the MTD, MTCH, and FTS reac-
tions and radiolabeled CO2 via the FTD reaction. High
glycine increases the glycine-to-serine rate of the SHMT
reactions in both cytosol and the mitochondria, so more
radiolabel appears in serine.

B. Reduced folate status
Figure 3 shows the percentage change in the steady-state
concentrations or rates of various metabolites and reac-
tions in the presence of a 50% reduction in folate levels.
The concentration of 5mTHF drops, of course, and this
releases the inhibition of GNMT so the GNMT reactions
goes faster and depletes SAM. Methionine and SAM are
also depleted because less homocysteine is remethylated.
Because of the long-range regulations in the methionine
cycle [29], the rate of the DNMT methylation reaction
decreases only modestly. The transport of format from
the mitochondria decreases and thymidylate synthesis
and purine synthesis rates are reduced dramatically. The
rate of the GDC reaction in the mitochondria drops
because mitochondrial THF is much lower. Since the GDC
reaction catabolizes glycine, the concentration of glycine
rises, which also drives up the concentration of serine via
the SHMT reaction. It was observed by Allen et al. [31]
that both sarcosine and dimethylglycine are elevated in
patients with folate deficiency, clinical results that we
observe also in the model (Figure 3). More sarcosine is
produced in the cytosol because the GNMT rate is elevated
(because there is less inhibition by 5mTHF), and more
dimethylglycine is produced because the rate of the BHMT
reaction is elevated. Since the concentration of THF is
lower, sarcosine and dimethylglycine are used at lower
rates in the mitochondria.

C. SHMT expression
MacFarlane et al. [32] report that mice lacking liver
cytosolic SHMT have a normal SAM/SAH ratio. To test this
in the model, we eliminated the cytosolic SHMT reaction


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-60 -40 -20 0 20 40
% Change


60 80 100 120


Figure 3
Change in the steady-state concentrations of selected metab-
olites and steady-state reaction velocities of selected reac-
tions in the presence of a 50% reduction in folate levels.


entirely. This resulted in a steady-state of [SAM] = 62.6
[M, [SAH] = 13.1 [tM. Normal values of these metabolites
are in the model [SAM] = 63.6 [M, [SAH] = 13.1 [tM. This
is not surprising because the normal net rate of the cSHMT
reaction is very low (9.2 [tM/h), as this enzyme is poised
to modulate fluctuations in serine and glycine by inter-
converting them.

Herbig et al. [14] found that increasing the expression of
cSHMT lowers the SAM concentration in a glycine-
dependent manner. They suggested two possible alterna-
tive mechanisms: (1) that cSHMT is in competition with
MTHFR for 5,10-CH2-THF, and therefore higher SHMT
expression should lower [5mTHF] and thus lower the rate
of remethylation of homocysteine to methionine, lower-
ing SAM; or (2) that cSHMT sequesters 5mTHF, lowering
its free concentration and thereby lowering SAM as in (1).
In the current model, if SHMT does not bind to 5mTHF,
we found that the SAM concentration is quite insensitive
to the amount of cSHMT and also insensitive to the exter-
nal glycine concentration, which does not support the first
hypothesis. When we add the binding of 5mTHF to SHMT


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[DMG]
[SARC]
[SAM]
[5mTHF]
vAICART
vTS
[GLY]
[SER]
vDNMT
vMS
vBHMT
vGNMT
vGDC
vHCOOH







Theoretical Biology and Medical Modelling 2006, 3:40



to the model, and then up-regulate cSHMT, we find that
the SAM concentration is substantially reduced, support-
ing the second hypothesis (simulations not shown).

Several authors have observed that Chinese hamster ovary
(CHO) cells that lack mSHMT are glycine auxotrophs
(see, for example, [32,33]). These findings have been
interpreted as indicating that mitochondria normally sup-
ply glycine to the cytosol. The model suggests that the sit-
uation is more complicated and more interesting. In the
model, under normal conditions in hepatic cells, there is
a net influx of glycine into the mitochondria (Table 4). If
we eliminate the mSHMT reaction, there is a modest
decrease in cytosolic and mitochondrial glycine, but the
net flux remains from cytosol to mitochondria. On the
other, ifmSHMT is normal and we set the external glycine
to zero, the concentrations of glycine in the cytosol and
mitochondria decline to about one quarter of their nor-
mal value but not to zero. In addition, the mitochondria
become net exporters of glycine to the cytosol (Table 4).
This is because the velocity of mSHMT reaction from ser-
ine to glycine increases 10-fold. However, if mSHMT is
eliminated and the external glycine is set to zero, then the
glycine concentration declines to almost one tenth its nor-
mal value and format production by the mitochondria is
cut in half. Thus the elimination of mSHMT and external
glycine together is clearly very detrimental to the cell.
Interestingly, the net flux of glycine remains from cytosol
to mitochondria. If one adds glycine back into the exter-
nal medium the cell becomes almost normal (Table 4).

D. The GDC reaction
In order to study the contribution of the GDC reaction, we
set its velocity to zero in the model and calculated the per-
centage change in concentrations and fluxes at the new
steady state (Figure 4). Because the GDC reaction is turned
off, the concentration of 5,10-CH2-THF in the mitochon-
dria drops dramatically, which lowers the flux through the
MTD, MTCH, and FTS reactions. Thus, much less format
is produced in the mitochondria and therefore the rate of
export of format to the cytosol declines to about 50% of
its former value. Because of the reduced supply of format,
the concentration of cytosolic 10f-THF goes down. This
has two effects. First, fewer purines are produced and sec-

Table 4: Effects of variation in mSHMT and external glycine*


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ond, the net flux from 10f-THF to 5,10-CH2-THF reverses
so that the net flux is from 5,10-CH2-THF to 10f-THF. This
reduces the cytosolic concentration of 5,10-CH2-THF,
which causes thymidine synthesis to drop. It also makes
the concentration of 5mTHF drop, which causes the
homocysteine concentration to rise. The decline in
[5mTHF] releases the inhibition of GNMT, which draws
down [SAM].

E. Eliminating the mitochondrial bifunctional enzyme
The mitochondrial bifunctional enzyme is active during
embryonic development and in transformed cells [17,24],
but not in the adult liver. We examined the effect of elim-
inating the bifunctional enzyme by setting the Vlm, of the
mitochondrial MTD and MTCH reactions to zero. The sig-
nificant changes in mitochondrial and cytosolic one-car
bon metabolism are shown in Figure 5. The
mitochondrial GDC reaction slows down somewhat, and
the mSHMT reverses dramatically in the direction of ser-
ine production. Formate production by the mitochondria
is reduced to zero. Thus the mitochondria have switched
from being format factories to being serine factories.

In the cytosol, thymidylate and purine synthesis are mark-
edly reduced, and the cMTD and cMTCH reactions reverse
and now run strongly in the direction from 5,10-CH2-THF
to 10f-THF. The export of serine to gluconeogenesis is
greater than the serine import into the cell from the blood
(the opposite is true when the bifunctional enzyme is
present). Thus, when the bifunctional enzyme is present
(the case we call normal), mitochondrial folate metabo-
lism produces format for the cytosol for purine and pyri-
midine synthesis and methylation reactions. When the
bifunctional enzyme is absent, mitochondrial folate
metabolism produces serine for the cytosol and overall
folate metabolism is a net producer of serine for glucone-
ogenesis.

F. Eliminating the mitochondria
We examined the significance of the mitochondrial folate
cycle for overall one-carbon metabolism by eliminating
the mitochondrial folate reactions entirely (setting all the
velocities to zero). The significant changes in cytosolic
one-carbon metabolism are indicated in Figure 6. There is


Normal

cellular glycine 1087
flux of glycine from -451
mitochondria to cytosol
velocity of mSHMT 84
velocity of cSHMT 9.2
flux of HCOOH to cytosol 546


mSHMT = 0

1046
-474

0
19
524


Extenal gly = 0


mSHMT = 0 Extenal gly = 0


*Concentrations are in ptM and fluxes and velocities are in ^tM/h.


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Theoretical Biology and Medical Modelling 2006, 3:40


Serlne


[Hcy]


vHCOOH

vAICART

vTS

[SAM]


m 5,10-CH2-THF

c 5,10-CH2-THF

[5mTHF]
[c Of-THF]


-60 -40 -20 0 20
% Change

Figure 4
Change in the steady-state concentrations of selected metab-
olites and steady-state velocities of selected reactions when
the GDC reaction is eliminated.



now no format at all being supplied by the mitochondria
so the rates of thymidylate synthesis and purine synthesis
are greatly reduced. The rate of the cytosolic SHMT
increases approximately 18-fold and the cytosolic MTD
and MTCH reactions reverse and now run in the direction
from 5,10-CH2-THF to 10f-THF (not shown). The
cytosolic concentration of 5,10-CH2-THF drops, causing
the concentration of5mTHF to drop, which in turn causes
homocysteine to rise. The concentrations of methionine
and SAM are not much affected. It is interesting to observe
that the elimination of the mitochondrial folate metabo-
lism does not completely disrupt cytosolic folate metabo-
lism; in fact the only major effects are on the rates of
thymidylate and purine synthesis, while the behavior of
the methionine cycle (including the DNMT reaction) is
largely unaffected. This is consistent with the hypothesis
that the main role of mitochondrial folate metabolism is
to supply extra 1-carbon units to the cytosol as format
[16,17,24].

E. Methionine and protein loading
The mathematical model allows us not only to compute
steady states but also to compute the time course of con-
centrations and fluxes as they respond dynamically to
changing inputs. We examined how the system responded
to a methionine load, which we simulated by doubling
the external methionine concentration from 30 to 60 tLM
during hours 5-10 of a 20 hour simulation (Figure 7A). As


Figure 5
Effect of eliminating the mitochondrial bifunctional enzyme.
A: selected reaction velocities when bifunctional enzyme is
active. B: reaction velocities when bifunctional enzyme is
eliminated. Reaction velocities are indicated with red num-
bers, and the units are [M/h.


expected [27,29], methionine rises modestly, SAM rises
substantially, but the DNA methylation rate is very stable
because the extra methyl groups are carried by an increase
in the rate of the GNMT reaction during loading. The rise
in SAM also causes an increase in the rate of the CBS reac-
tion during loading, so there is an increased removal of
serine from the system, which causes both cytosolic and
mitochondrial serine concentrations to decrease. Despite
the increase in the rate of the CBS reaction, homocysteine
almost doubles because SAM is inhibiting BHMT and
MTHFR, which decreases 5mTHF and slows the MS reac-
tion. Purine and thymidylate synthesis rise modestly dur-
ing loading because of modest increases in cytosolic 10f-
THF and 5,10-CH2-THF, and there is a decline of 5mTHF
accompanied by an increase in cytosolic THF. The mito-


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Serine


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Theoretical Biology and Medical Modelling 2006, 3:40


[Smthf]
[clOf-THF]
[cTHF]

[Hcy]
[SAM]
[methionine]


DNMT
Ts
AICART
cSHMT 1840

-100 -50 0 50 100
% change

Figure 6
Change in the steady-state concentrations of selected metab-
olites and steady-state reaction velocities of selected reac-
tions when the mitochondrial reactions are eliminated form
the model.



chondrial folates are virtually unchanged, as is the rate of
transport of format from the mitochondria to the
cytosol.

To simulate a protein meal, we not only doubled methio-
nine for five hours but also doubled the external serine
and glycine concentrations for the same five hours (Figure
7B). The major difference is that all the serine and glycine
concentrations rise during protein loading and the mito-
chondrial SHMT reaction reverses direction. The increase
in serine increases the CBS reaction and the fraction trans-
sulfurated, and the increase in glycine increases the GNMT
reaction. Both of these changes prevent SAM from rising
as high as it did under a pure methionine load. In turn, the
inhibition of MTHFR by SAM is diminished, so 5mTHF
does not fall as much as during a methionine load. The
joint effect is that homocysteine does not rise nearly as
much as during a pure methionine load. Purine and
thymidylate synthesis rise modestly during protein load-
ing because of modest increases in cytosolic 10f-THF and
5,10-CH2-THF. Compared to methionine loading, there
are smaller changes in the cytosolic folates and, as above,
the rate of transport of format from the mitochondria to
the cytosol is remarkably constant.

Discussion
Understanding the function of the compartmentalization
of the folate cycle between the cytosol and mitochondria


poses many challenges. Measuring concentrations and
especially reaction velocities is not easy in living cells, and
these measurements become particularly difficult when
substrates and some reactions are sequestered into differ-
ent compartments. It is especially challenging, and in
many cases impossible, to measure several different varia-
bles at the same time and to track changing concentra-
tions or velocities over time. A mathematical
representation of the substrates and reactions of folate
metabolism allows one to conduct in silicon experiments to
test ideas and hypotheses about how the system as a
whole operates. Of course, no such mathematical model
can represent the complete physical and biological com-
plexity of a real cell, and the usefulness of the model
depends on how accurately it represents the known biol-
ogy of the cell. Experiments with the mitochondrial
model in this paper show that its behavior is consistent
with a wide body of experimental findings.

Among the important questions investigated or discussed
by experimentalists in recent years are: the role of the
mitochondrial bifunctional enzyme, the effect of cytosolic
and mitochondrial SHMT expression on purine and pyri-
midine synthesis, the directionality of the SHMT reac-
tions, the relative roles of serine and glycine as one-carbon
donors, the effects of protein and methionine loading, the
significance of the GDC reaction and, indeed, the signifi-
cance of the mitochondria themselves. Our mathematical
model has allowed us to explore these questions by in sil-
ico experimentation and we hope thereby to shed light on
these questions and to contribute to the ongoing discus-
sion.

Particularly interesting is the remarkable stability of for-
mate production in the mitochondria in the face of large
changes in serine and glycine input. As a consequence, the
cytosol has an almost constant input of format for purine
and pyrimidine synthesis, despite short term and long
term variations in glycine and serine availability. This
effect is largely due to the efficient rebalancing of the ser-
ine and glycine concentrations by the reversible mito-
chondrial and cytosolic SHMT reactions.

Another highlight that we found is that eliminating the
mitochondrial bifunctional enzyme did not lead to a run-
away accumulation of 5,10-CH2-THF in the mitochondria
as might be expected. Instead, the mitochondrial SHMT
reaction reverses direction strongly and the mitochondria
become net exporters of serine. Thus, in the presence of
the bifunctional enzyme (as in embryonic tissues and can-
cer cells), the mitochondria primarily support cytosolic
purine and pyrimidine synthesis via the export of format,
while in adult tissues the mitochondria produce serine for
gluconeogenesis.




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Theoretical Biology and Medical Modelling 2006, 3:40


0 5 10
Time (hours)


10 15 20 0 5 10 15
Time (hours) Time (hours)


-UMT


50


cSHMT


-100

[mTHFJ

15 [m1OfTHF]

10
[cTHF]

[CIOITHFI
0 5 10 15 20
Time (hours)


Figure 7
A: Response of selected model variables to a 5-hour pulse of elevated external methionine. B: Response to a 5-hour pulse of
elevated external methionine, glycine and serine. The pulses consisted of a doubling of the external amino-acid concentrations
from 5 to 10 hours after initiation of the simulation.


We plan to continue our investigations by conducting a
complete fluctuation analysis [29] of the stability of for-
mate production and purine and pyrimidine synthesis. In
addition, we will continue to use the model to explore
other important aspects of folate biochemistry and com-
partmentalization by studying the roles of folate-protein
binding, substrate channeling, and the interactions of
simultaneous genetic polymorphisms with variation in
dietary input and vitamin status. We plan to investigate
the dynamic properties and potential interactions among
the many methyltransferases that act in parallel using
SAM as a substrate. Finally, we plan to investigate the
dynamic transport processes that determine the compart-
mentalization of the metabolites of folate and methio-
nine cycles between the liver and the blood.

Abbreviations
The attached Additional File 1 contains a complete
description of the mathematical model as well as full


names of all abbreviations used in the text and in the
model.

Competing interests
The authors) declare that they have no competing inter-
ests.

Authors' contributions
HN, MR, BS, JG and CU participated in the formulation of
the questions and made substantial contributions to the
design of the project and revised the intellectual content
of the manuscript. HN, MR and SL wrote the code and car-
ried out the in silicon experimentation. HN and MR wrote
the first draft of the manuscript. All authors read and
approved the final manuscript.


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15 20








Theoretical Biology and Medical Modelling 2006, 3:40


Additional material


Acknowledgements
We would like to thank Marian Neuhouser, Jill S. James, and Alanna Boyn-
ton for their many contributions to the mathematical modeling project, and
Dean Appling for useful comments on a draft of this paper. This work was
supported by NIH grant ROI CA 105437(CMU) and NSF grant DMS
0109872 (MCR).

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Additional File 1
contains a complete description of the mathematical model as well as full
names of all abbreviations used in the text and in the model.
Click here for file
[http://www.biomedcentral.com/content/supplementary/1742-
4682-3-40-Sl.pdf]


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