In silico experimentation with a model of hepatic mitochondrial folate metabolism
© Nijhout et al; licensee BioMed Central Ltd. 2006
Received: 20 October 2006
Accepted: 06 December 2006
Published: 06 December 2006
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.
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.
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 formate 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 formate, while in adult tissues the mitochondria produce serine for gluconeogenesis.
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 synthesis, 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, cancer, cardiovascular disease, and neuropsychiatric disorders. Aberrant folate metabolism can be caused by polymorphisms 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].
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 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 mitochondrial 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 mitochondria? These questions have been the subject of extensive experimental investigation and theoretical discussions [16–26].
We have developed a mathematical model for mitochondrial 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 silico experiments that address many of the above questions and compare the results to experimental observations. The model gives insights into the mechanisms underlying the experimental results and allows us to test various hypotheses that have been proposed in the literature.
In the following section we give a brief overview of our model. Full details of the model and the full names of all abbreviations used in the text and in the model are given in additional file 1.
Figure 1 shows the biochemical pathways in the hepatic cellular model used in this paper. Rectangular boxes represent 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 substrates 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 concentrations 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. . Mitochondrial folate substrates and enzymes were added, and sarcosine and dimethylglycine are new variables (each is assumed to have the same concentrations in the cytosol and mitochondria). The extracellular serine, glycine, and methionine concentrations can be specified as functions of time. The cytosolic and mitochondrial serine and glycine concentrations can vary, as can the cytosolic methionine concentration. Appropriate kinetics are used for transport between the external, cytosolic, and mitochondrial compartments. The mitochondrial and cytosolic HCOOH concentrations are allowed to vary in the present model, and formate is transported between the mitochondrial and cytosolic compartments. 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.
Cytosolic and mitochondrial concentrations and velocities at steady-state.
5,10-CH = THF
5,10-CH = THF
Total cellular concentrations of folate metabolites and amino acids at steady-state
5,10-CH = THF
Transport rates at steady-state (μM/h).
Extracellular to cytosol
Mitochondria to cytosol
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 investigators to study the phenomenon of interest without omitting 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 pathway, 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 effect of these reactions is to maintain reaction velocities in the face of severe folate deficiency (studied in Nijhout et al. ). 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 synthesis 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.
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 methylation 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-methyleneTHF. 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 produces free formate 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 formate to the balance between serine and glycine? (3) How sensitive is the production of purines and pyrimidines in the cytosol to the supply of formate?
As external glycine rises, both the cytosolic and the mitochondrial 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 , who grew yeast in pure serine and pure glycine environments. In spite of great variations in the glycine and serine concentrations (Fig. 2A, middle panel, blue curve) and the reversals in both SHMT reactions, the rate at which formate is supplied to the cytosol remains remarkably constant (Fig. 2A). In addition, the rates of the TS and AICART reactions (for thymidylate and purine synthesis, respectively) 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 concentration is varied from 50 μM to 400 μM. As external serine increases, both the cytosolic and mitochondrial glycine concentrations increase, and there is an even greater increase in the cytosolic and mitochondrial serine concentrations. 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 formate 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 CBS reaction, which slows down and causes methionine cycle metabolites to accumulate, particularly as SAM, owing the internal regulatory mechanisms of the methionine cycle [27, 29].
Lewis et al.  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 substrates by the methylation reactions. However, when glycine 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 acceleration of the GNMT reaction so more of the radiolabeled methyl groups are put into sarcosine. Then, in the mitochondria, 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 reactions 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
C. SHMT expression
MacFarlane et al.  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 entirely. This resulted in a steady-state of [SAM] = 62.6 μM, [SAH] = 13.1 μM. Normal values of these metabolites are in the model [SAM] = 63.6 μM, [SAH] = 13.1 μM. This is not surprising because the normal net rate of the cSHMT reaction is very low (9.2 μM/h), as this enzyme is poised to modulate fluctuations in serine and glycine by interconverting them.
Herbig et al.  found that increasing the expression of cSHMT lowers the SAM concentration in a glycine-dependent manner. They suggested two possible alternative 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, lowering 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 external glycine concentration, which does not support the first hypothesis. When we add the binding of 5mTHF to SHMT to the model, and then up-regulate cSHMT, we find that the SAM concentration is substantially reduced, supporting the second hypothesis (simulations not shown).
Effects of variation in mSHMT and external glycine*
mSHMT = 0
Extenal gly = 0
mSHMT = 0 Extenal gly = 0
flux of glycine from mitochondria to cytosol
velocity of mSHMT
velocity of cSHMT
flux of HCOOH to cytosol
D. The GDC reaction
E. Eliminating the mitochondrial bifunctional enzyme
In the cytosol, thymidylate and purine synthesis are markedly 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 metabolism produces formate for the cytosol for purine and pyrimidine 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 gluconeogenesis.
F. Eliminating the mitochondria
E. Methionine and protein loading
To simulate a protein meal, we not only doubled methionine 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 mitochondrial SHMT reaction reverses direction. The increase in serine increases the CBS reaction and the fraction transsulfurated, 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 loading 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 formate from the mitochondria to the cytosol is remarkably constant.
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 different compartments. It is especially challenging, and in many cases impossible, to measure several different variables at the same time and to track changing concentrations or velocities over time. A mathematical representation of the substrates and reactions of folate metabolism allows one to conduct in silico 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 complexity of a real cell, and the usefulness of the model depends on how accurately it represents the known biology 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 pyrimidine synthesis, the directionality of the SHMT reactions, 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 significance of the mitochondria themselves. Our mathematical model has allowed us to explore these questions by in silico experimentation and we hope thereby to shed light on these questions and to contribute to the ongoing discussion.
Particularly interesting is the remarkable stability of formate 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 formate 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 serine and glycine concentrations by the reversible mitochondrial and cytosolic SHMT reactions.
Another highlight that we found is that eliminating the mitochondrial bifunctional enzyme did not lead to a runaway 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 cancer cells), the mitochondria primarily support cytosolic purine and pyrimidine synthesis via the export of formate, while in adult tissues the mitochondria produce serine for gluconeogenesis.
We plan to continue our investigations by conducting a complete fluctuation analysis  of the stability of formate production and purine and pyrimidine synthesis. In addition, we will continue to use the model to explore other important aspects of folate biochemistry and compartmentalization 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 compartmentalization of the metabolites of folate and methionine cycles between the liver and the blood.
- Additional File 1:
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.
We would like to thank Marian Neuhouser, Jill S. James, and Alanna Boynton 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 RO1 CA 105437(CMU) and NSF grant DMS 0109872 (MCR).
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