Abstract
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 B(12) deficiency, modeled as a reduction in the V(max) 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 G(1)/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.
Highlights
From the Departments of ‡Biology and ¶Mathematics, Duke University, Durham, North Carolina 27708 and the ʈCancer Prevention Program, M4-B402, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109-1024
Steady-state Behavior—At steady state, with a total folate pool of 20 M, the concentrations of the folate metabolites and the fluxes are summarized in Table III in the first column under “Normal.” The values of the pool sizes and fluxes are within the ranges reported in the literature
Dependence on Parameters—Estimates for many of the kinetic parameters for enzymes of folate metabolism range over several orders of magnitude (Table II), which poses a serious difficulty for modeling
Summary
From the Departments of ‡Biology and ¶Mathematics, Duke University, Durham, North Carolina 27708 and the ʈCancer Prevention Program, M4-B402, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109-1024. 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. The model 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. The global behavior of the cycle can, be investigated through a mathematical model of the reactions of and interactions among the components of the cycle
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