Michael C. Reed

A mathematical model of the folate cycle--new insights into folate homeostasis

A mathematical model is developed for the folate cycle based on standard biochemical kinetics. We use the model to provide new insights into several different mechanisms of folate homeostasis. The model reproduces the known pool sizes of folate substrates and the fluxes through each of the loops of the folate cycle and has the qualitative behavior observed in a variety of experimental studies. Vitamin B12 deficiency, modeled as a reduction in the Vmax of the methionine synthase reaction, results in a secondary folate deficiency via the accumulation of folate as 5-methyltetrahydrofolate (the “methyl trap”). One form of homeostasis is revealed by the fact that a 100-fold up-regulation of thymidylate synthase and dihydrofolate reductase (known to occur at the G1/S transition) dramatically increases pyrimidine production without affecting the other reactions of the folate cycle. The model also predicts that an almost total inhibition of dihydrofolate reductase is required to significantly inhibit the thymidylate synthase reaction, consistent with experimental and clinical studies on the effects of methotrexate. Sensitivity to variation in enzymatic parameters tends to be local in the cycle and inversely proportional to the number of reactions that interconvert two folate substrates. Another form of homeostasis is a consequence of the nonenzymatic binding of folate substrates to folate enzymes. Without folate binding, the velocities of the reactions decrease approximately linearly as total folate is decreased. In the presence of folate binding and allosteric inhibition, the velocities show a remarkable constancy as total folate is decreased.

The biological significance of substrate inhibition: a mechanism with diverse functions

Many enzymes are inhibited by their own substrates, leading to velocity curves that rise to a maximum and then descend as the substrate concentration increases. Substrate inhibition is often regarded as a biochemical oddity and experimental annoyance. We show, using several case studies, that substrate inhibition often has important biological functions. In each case we discuss, the biological significance is different. Substrate inhibition of tyrosine hydroxylase results in a steady synthesis of dopamine despite large fluctuations in tyrosine due to meals. Substrate inhibition of acetylcholinesterase enhances the neural signal and allows rapid signal termination. Substrate inhibition of phosphofructokinase ensures that resources are not devoted to manufacturing ATP when it is plentiful. In folate metabolism, substrate inhibition maintains reactions rates in the face of substantial folate deprivation. Substrate inhibition of DNA methyltransferase serves to faithfully copy DNA methylation patterns when cells divide while preventing de novo methylation of methyl‐free promoter regions.

Neural tube defects and folate pathway genes : Family-based association tests of gene-gene and gene-environment interactions

Background Folate metabolism pathway genes have been examined for association with neural tube defects (NTDs) because folic acid supplementation reduces the risk of this debilitating birth defect. Most studies addressed these genes individually, often with different populations providing conflicting results. Objectives Our study evaluates several folate pathway genes for association with human NTDs, incorporating an environmental cofactor: maternal folate supplementation. Methods In 304 Caucasian American NTD families with myelomeningocele or anencephaly, we examined 28 polymorphisms in 11 genes: folate receptor 1, folate receptor 2, solute carrier family 19 member 1, transcobalamin II, methylenetetrahydrofolate dehydrogenase 1, serine hydroxymethyl-transferase 1, 5,10-methylenetetrahydrofolate reductase (MTHFR), 5-methyltetrahydrofolate-homo-cysteine methyltransferase, 5-methyltetrahydrofolate-homocysteine methyltransferase reductase, betaine-homocysteine methyltransferase (BHMT), and cystathionine-beta-synthase. Results Only single nucleotide polymorphisms (SNPs) in BHMT were significantly associated in the overall data set; this significance was strongest when mothers took folate-containing nutritional supplements before conception. The BHMT SNP rs3733890 was more significant when the data were stratified by preferential transmission of the MTHFR rs1801133 thermolabile T allele from parent to offspring. Other SNPs in folate pathway genes were marginally significant in some analyses when stratified by maternal supplementation, MTHFR, or BHMT allele transmission. Conclusions BHMT rs3733890 is significantly associated in our data set, whereas MTHFR rs1801133 is not a major risk factor. Further investigation of folate and methionine cycle genes will require extensive SNP genotyping and/or resequencing to identify novel variants, inclusion of environmental factors, and investigation of gene–gene interactions in large data sets.

A mathematical model of glutathione metabolism

BackgroundGlutathione (GSH) plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimers disease, Parkinsons disease, cardiovascular disease, cancer, Down syndrome and autism.ApproachWe explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data.ConclusionWe show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.

Long-Range Allosteric Interactions between the Folate and Methionine Cycles Stabilize DNA Methylation Reaction Rate

Several metabolites in the folate and methionine cycles influence the activities of distant enzymes involved in one-carbon metabolism. Many hypotheses have been advanced about the functional impact of these long-range interactions. Using both steady-state and fluctuation analyses of a mathematical model of methionine metabolism, we investigate the biochemical basis for several of these hypotheses. We show that the long-range interactions provide remarkable stabilization of the DNA methylation rate in the face of large fluctuations in methionine input. In particular, they enable the system to maintain methylation in the face of low and extremely low protein input. These interactions may therefore have evolved primarily to stabilize DNA methylation under conditions of methionine starvation. In silico experimentation allows us to evaluate the independent effects of various combinations of the long-range interactions, and thereby propose a plausible evolutionary scenario.

Serotonin synthesis, release and reuptake in terminals: a mathematical model

BackgroundSerotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system.MethodsWe construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data.ResultsWe compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine.ConclusionsSerotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.

A model for the computation and encoding of azimuthal information by the lateral superior olive

A structural model is proposed for the processing of interaural intensity differences by the lateral superior olive. One fundamental assumption is that the incoming excitatory projections from the ipsilateral anteroventral cochlear nucleus innervate columns of LSO neurons serially according to threshold. A second fundamental assumption is that the inhibitory innervation from the ipsilateral medial nucleus of the trapezoid body is also serially arranged according to threshold but in the opposite direction along the LSO column. Using neurophysiological and neuroanatomical data for neuronal response curves, connectional patterns, and cell and synapse numbers, the model was formulated quantitatively and implemented for machine computation. Azimuthal location is encoded by the position along the LSO column where LSO cell firing first goes to zero. Accuracy of coding was tested for three different connectional schemes, for variations in neuronal parameters, and for cell and synapse death. Encoding is shown to be independent of absolute sound level and to vary linearly with interaural intensity difference.

Homeostatic mechanisms in dopamine synthesis and release: a mathematical model

BackgroundDopamine is a catecholamine that is used as a neurotransmitter both in the periphery and in the central nervous system. Dysfunction in various dopaminergic systems is known to be associated with various disorders, including schizophrenia, Parkinsons disease, and Tourettes syndrome. Furthermore, microdialysis studies have shown that addictive drugs increase extracellular dopamine and brain imaging has shown a correlation between euphoria and psycho-stimulant-induced increases in extracellular dopamine [1]. These consequences of dopamine dysfunction indicate the importance of maintaining dopamine functionality through homeostatic mechanisms that have been attributed to the delicate balance between synthesis, storage, release, metabolism, and reuptake.MethodsWe construct a mathematical model of dopamine synthesis, release, and reuptake and use it to study homeostasis in single dopaminergic neuron terminals. We investigate the substrate inhibition of tyrosine hydroxylase by tyrosine, the consequences of the rapid uptake of extracellular dopamine by the dopamine transporters, and the effects of the autoreceoptors on dopaminergic function. The main focus is to understand the regulation and control of synthesis and release and to explicate and interpret experimental findings.ResultsWe show that the substrate inhibition of tyrosine hydroxylase by tyrosine stabilizes cytosolic and vesicular dopamine against changes in tyrosine availability due to meals. We find that the autoreceptors dampen the fluctuations in extracellular dopamine caused by changes in tyrosine hydroxylase expression and changes in the rate of firing. We show that short bursts of action potentials create significant dopamine signals against the background of tonic firing. We explain the observed time courses of extracellular dopamine responses to stimulation in wild type mice and mice that have genetically altered dopamine transporter densities and the observed half-lives of extracellular dopamine under various treatment protocols.ConclusionDopaminergic systems must respond robustly to important biological signals such as bursts, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of tyrosine hydroxylase, the dopamine transporters, and the dopamine autoreceptors.

In silico experimentation with a model of hepatic mitochondrial folate metabolism

BackgroundIn 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.ApproachWe 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.ConclusionThe 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.

Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: Creation and propagation

AbstractThe creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {xi}i=1n, of jump discontinuities. LetS be the smallest closed set which satisfies:(i)S is a union of forward characteristics.(ii)S contains all the forward characteristics from the points {xi}i=1n.(iii)if two forward characteristics inS intersect, then all forward characteristics from the point of intersection lie inS. We prove that the singular support of the solution lies inS. We derive a sum law which gives a lower bound on the smoothness of the solution across forward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound.