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Supplementary Material – Model DetailsforA mathematical model gives insights into nutritionaland genetic aspects of folate-mediated one-carbonmetabolismMichael C. Reed,1∗, H. Frederik Nijhout,2, Marian Neuhouser3,Jesse Gregory4,Barry Shane5, S. Jill James6, Alanna Boynton3,7, Cornelia M. Ulrich71Department of Mathematics, Duke University, Durham, NC 277082Department of Biology, Duke University, Durham, NC 277083Fred Hutchinson Cancer Research Center, Seattle, WA 98109- 1024.4Food Science & Human Nutrition Department , University of Florida, Gainsville, FL 32 6115Department of Nutritional Sciences & Toxicology, University of California, Berkeley, CA947206Department of Pediatrics, University of Arkansas f or Medical Sciences, Little Rock, AR722027Department of Epidemiology and the Interdiscisplinary Graduate Program in NutritionalSciences, University of Wa shington, WA 981951The model consists of 10 differential equations that express the rate of change of each ofthe substrates in the rectangular boxes in Figure 1.Figure 1: Folate and Methionine Metabolism. The enzymes are: AICART,aminoimidazolecarboxamide ribonucleotide transferase; BHMT, betaine-homocysteinemethyltransferase; CBS, cystathionine β-synthase; DHFR, dihydrofolate reductase;DNMT, DNA-methyltransferase; FTD, 10-formyltetrahydrofolate dehydrogenase; FTS, 10-formyltetrahydrofolate synthase; GNMT, glycine N-methyltransferase; MAT, methion-ine adenosyl t r ansferase; MS, methionine synthase; MTD, 5,10-methylenetetrahydrofolatedehydrogenase; MTCH, 5,10-methenyltetrahydrofolate cyclohydrolase; MTHFR, 5,10-methylenetetrahydrofolate reductase; PGT, Phosphoribo syl glycinamidetransformalase;SAHH, S-adenosylhomocysteine hydrolase; SHMT, serinehydroxymethyltransferase; TS:thymidylate synthase.The mathematical model merges two previously published models on the folate cycle [24]and the methionine cycle [23]. These cycles are connected not only by the MS reactions butalso by the inhibition of MTHFR bt SAM and GNMT by 5mTHF. In [23], [5mT HF ] wascalculted indirectly since the folate cycle was not present. Now it is calculated explicitlyby solving the differential equations for the folat e cycle. Because of these differences, it isnot surprising that the balance of some substrates in the initial combined model differedsomewhat from those reported in the literature and generated by the previous independentcycle models. We therefore modified somewhat a few parameters (within published ranges)to obtain appropriate concentrations. These changes were: the Vmaxof MTHFR was reducedfrom 6000 to 5000 µM/hr; the Vmaxof the CBS reaction was reduced from 100,000 to 90,000µM/hr; the Vmaxof the GNMT reaction was increased from 160 to 288 µM/hr; the inhibitionconstants for SAH on GNMT and DNMT were lowered from 18 to 10.8 µM and from 1.4to 0.84 µM, respectively; the Vmaxvalues of the TS and D HFR reactions were increased 1002fold (fro m 50 t o 5000 µM/hr) to simulate the conditions of rapid gr owth. In the in silicoexperiments described in the text, the model parameters and equations were those givenbelow, except for the parameter whose effect was being tested in a particular experiment.For simplicity o f notation, we will use the following abbreviations:5mT HF = 5-methyltetrahydrofolateT HF = tetrahydrofolateDHF = dihydrofolateCH2F = 5-10-methylenetetrahydrofolateCHF = 5-10-methenyltetrahydrofolate10fT HF = 1 0-formyltetrahydrofola t eMET = methionineSAM = S-adenosylmethionineSAH = S-a denosylhomocysteineHCY = homocysteinemetin = the rate of input of methionine to the system in µM/hrThe f ollowing other substrates are assumed t o have constant concentra t io ns (µM):[GAR] = 10 glycinamide ribonucleotide[AICAR] = 2.1 aminoimidazolecarboxamide ribonucleotide[NADP H] = 50 nicotinamide adenine dinucleotide phosphate[GLY ] = 1850 glycine[SER] = 468 serine[BET ] = 50 betaine[HCOOH] = 500 formate[H2C = O] = 500 formaldehyde[DUMP ] = 20 deoxyuridine monophophateFor each o f the biochemical reactions indicated by a reaction arrow in Figure 1, we denotethe velocity of the reaction (in µM/hr) by a capital V whose subscript is the acronym fo r theenzyme that catalyzes the reaction. Thus, for example, the velocity of the methione synthasereaction is denoted by VMS. Each of these velocities depends on the current values of one ormore of the metabolite concentrations and possibly also on one or more of the other inputsthat are assumed constant. The 10 differential equations express the time rate of change (inµM/hr) of each of the 10 substrates in terms of the velocities. One can see explicitly whateach of the velocities depends on.3d[5mT HF ]dt= VMT HF R([CH2F ], [NADP H], [SAM], [SAH]) − VMS([5mT HF ], [HCY ])d[T HF ]dt= VF T D([10fT HF ]) + VMS([5mT HF ], [HCY ]) + VP GT([10fT HF ], [GARP ])+VART([10fT HF ], [AICARP ]) − VF T S([T HF ], [HCOOH], [10fT HF ])−VSHM T([SER], [T HF ], [GLY ], [CH2F ]) − VNE([T HF ], [H2C = O], [CH2F ])+VDHF R([DHF ], [NADP H])d[DHF ]dt= VT S([DUMP ], [CH2F ]) − VDHF R([DHF R], [NADP H])d[CH2F ]dt= VSHM T([SER], [T HF ], [GLY ], [CH2F ]) + VNE([T HF ], [H2C = O], [CH2F ])−VT S([DUMP ], [CH2F ]) − VMT HF R([CH2F ], [NADP H], [SAM], [SAH])−VMHD([CH2F ], [CHF ])d[CHF ]dt= VMHD([CH2F ], [CHF ]) − VMCH([CHF ], [10fT HF ])d[10fT HF ]dt= VMCH([CH2], [10fT HF ]) + VF T S([T HF ], [HCOOH], [10fT HF ])−VP GT([10fT HF ], [GARP ]) − VART([10fT HF ], [AICARP ]) − VF T D([10fT HF ])d[MET ]dt= VBHMT([HCY ], [BET ], [SAM], [SAH]) + VMS([5mT HF ], [HCY ]) + metin(t)−VMAT I([MET ], [SAM]) − VMAT III([MET ], [SAM])d[SAM]dt= VMAT I([MET ], [SAM]) + VMAT III([MET ], [SAM])−VGNM T([SAM], [SAH], [5mT HF ]) − VDNM T([SAM], [SAH])d[SAH]dt= VGNM T([SAM], [SAH], [5mT HF ]) + VDNM T([SAM], [SAH])−VSAAH([SAH], [HCY ])d[HCY ]dt= VSAAH([SAH], [HCY ]) − VCBS([HCY ], [SAM], [SAH])−VBHMT([HCY ], [BET ], [SAM], [SAH]) − VMS([5mT HF ], [HCY ]);4For many of the velocities, we assume that their dependence on substrates has Michaelis-Menten form. VF T Dis uni-directional with one substrate and has the fo r m:V =Vmax[S]Km+ [S].VSAAH, VMCH, and VMHDare reversible Michaelis-Menten with one substrate in each term.VART, VT S, VDHF R, VP GT, and VMSare modeled by random order Michaelis-Menten with twosubstrates:V =Vmax[S1][S2](Km,1+ [S1])(Km,2+ [S2]).VSHM Tis assumed to be reversible random order Michaelis-Menten kinetics kinetics withtwo substrates in each term. For all these velocities the fo rm is clear and the Kmand