Model Mathematics

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Component: environment

addbuffer = Par_97 pHstat = Par_98 pH_cy = \{\begin{matrix} pH_calc if time ≦ 1 \lor time > 1 \land addbuffer = 0 \\ pHstat otherwise \end{matrix}

Component: global_parameters

T = Par_94 I = Par_90

Component: parameters

Par_1 = 5 e -2 Par_2 = 0.4 Par_3 = 1.7 e -3 Par_4 = 4 e -3 Par_5 = \frac{2 e -3}{1.5} Par_6 = 4.7 e -3 Par_7 = 1.5 e -4 Par_8 = 2.7 e -3 Par_9 = 1.01 e -2 Par_10 = 2 e -4 Par_11 = 4.6 e -3 Par_12 = 1.5 e -2 Par_13 = 1.5 e -3 Par_14 = 7.4 e -3 Par_15 = 4.4 e -3 Par_16 = 0.00266054976219 Par_17 = 2 e -2 Par_18 = 1.7505240494613 Par_19 = 4.8 e -1 Par_20 = 6.3 e -5 Par_21 = 3 e -5 Par_22 = 8.8 e -1 Par_23 = 4.8 e -4 Par_24 = 1.19 e -4 Par_25 = 5.6 e -2 Par_26 = 1.8 e -4 Par_27 = 2 e -2 Par_28 = 8 e -5 Par_29 = 2.5 e -4 Par_30 = 4.02 e -3 Par_31 = 4.02 e -3 Par_32 = 2.7 e -3 Par_33 = 2.7 e -3 Par_34 = 8.7 e -4 Par_35 = 6 e -5 Par_36 = 1 e -2 Par_37 = 1 e -2 Par_38 = 13 Par_39 = 0.01065914307349 Par_40 = 5 e -5 Par_41 = 2 e -3 Par_42 = 1 e -3 Par_43 = 12 Par_44 = 3.2 e -4 Par_45 = 6.1 e -4 Par_46 = 8.25 e -2 Par_47 = 1.8 e -4 Par_48 = 1.2 e -5 Par_49 = 2.2 e -4 Par_50 = 8 e -6 Par_51 = 1.265 e 0 Par_52 = 2.5 e -6 Par_53 = 9 e -5 Par_54 = 2.9 e -4 Par_55 = 8 e -7 Par_56 = 3.3 e -6 Par_57 = 1.12 e 0 Par_58 = 2 e -3 Par_59 = 8 e -6 Par_60 = 1.2 e -3 Par_61 = 3.5 e -4 Par_62 = 1.12 e 0 Par_63 = 2 e -4 Par_64 = 1.4 e -5 Par_65 = 1.92 e -1 Par_66 = 1 e -4 Par_67 = 3.7 e -4 Par_68 = 1.44 e 0 Par_69 = 8 e -5 Par_70 = 3 e -4 Par_71 = 7.05 e -3 Par_72 = 1.13 e -3 Par_73 = 1.92 e 0 Par_74 = 3.35 e -4 Par_75 = 2 e -6 Par_76 = 1.7 e -2 Par_77 = 8.49 e -4 Par_78 = 5 e -1 Par_79 = 1.11 e -3 Par_80 = 3.5 e -3 Par_81 = 1.35 e -4 Par_82 = 3.9 e -3 Par_83 = 3.8 e -3 Par_84 = 8.8 e -1 Par_85 = 3.2 e -4 Par_86 = 2.7 e -4 Par_87 = 3.5 e -4 Par_88 = 0 Par_89 = 1 e -4 Par_90 = 1 e -1 Par_91 = 1.5 e -2 Par_92 = 2.5 e -2 Par_93 = 1 e -2 Par_94 = 303.15 Par_95 = 0.005 Par_96 = 0.08 Par_97 = 1 Par_98 = 7.4 Par_99 = 1 Par_100 = 29

Component: equilibrium_constants

mgT = Par_95 k = Par_96 c0 = 1

Component: correction_factors

RT2dadT = 1.4775 B = 1.6 Icorr = \frac{RT2dadT \sqrt{I}}{1 + B \sqrt{I}} I1 = 0.1 alphadebye = 1.17582 IcorrpKa = \frac{1 alphadebye (\frac{\sqrt{I1}}{1 + B \sqrt{I1}} - (\frac{\sqrt{I}}{1 + B \sqrt{I}}))}{\ln 10} TcorrpKa = \frac{\frac{1}{T} - (\frac{1}{T1})}{\ln 10 R} RTalpha = 2.91482 IcorrdeltaGpof = \frac{RTalpha \sqrt{I}}{1 + B \sqrt{I}} pKak_Pi = 0.5 deltaH1o_Pi = 3 deltaHmgo_Pi = - 2.9 deltaH1_Pi = deltaH1o_Pi + Icorr (2^{2} + 1^{2} - (1^{2})) deltaHmg_Pi = deltaHmgo_Pi + Icorr (2^{2} + 2^{2} - (0^{2})) pKa1_Pi = 6.75 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaH1_Pi pKamg_Pi = 1.65 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaHmg_Pi P_Pi = 1 + 10^{(- pH_cy) + pKa1_Pi} + \frac{mg}{c0} 10^{pKamg_Pi} + \frac{k}{c0} 10^{pKak_Pi} HPi2 = \frac{1}{P_Pi} H2Pi1 = 10^{(- pH_cy) + pKa1_Pi} HPi2 kPi = \frac{k}{c0} 10^{pKak_Pi} HPi2 mgPi = \frac{mg}{c0} 10^{pKamg_Pi} HPi2 Navg_Pi = 1 H2Pi1 dNavgPidH = \frac{10^{pKa1_Pi} (P_Pi - (10^{(- pH_cy) + pKa1_Pi}))}{c0 {P_Pi}^{2}} dNavgPidmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_Pi + pKamg_Pi}}{{P_Pi}^{2}} dmgPidmg = \frac{\frac{P_Pi 10^{pKamg_Pi}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_Pi}}{c0})}{{P_Pi}^{2}} dmgPidpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_Pi + pKamg_Pi} \ln 10}{{P_Pi}^{2}} NH_HPi2 = 1 deltaGof_HPi2 = - 1096.1 deltaGpof_HPi2 = deltaGof_HPi2 + NH_HPi2 \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_HPi2)) deltaH1o_ATP = - 5 deltaHmgo_ATP = - 18 deltaHko_ATP = - 1 deltaH1_ATP = deltaH1o_ATP + Icorr (4^{2} + 1^{2} - (3^{2})) deltaHmg_ATP = deltaHmgo_ATP + Icorr (4^{2} + 2^{2} - (2^{2})) deltaHk_ATP = deltaHko_ATP + Icorr (4^{2} + 1^{2} - (3^{2})) pKa1_ATP = 6.48 + \frac{IcorrpKa}{1} (4^{2} + 1^{2} - (3^{2})) + TcorrpKa deltaH1_ATP pKamg_ATP = 4.19 + \frac{IcorrpKa}{1} (4^{2} + 2^{2} - (2^{2})) + TcorrpKa deltaHmg_ATP pKak_ATP = 1.17 + \frac{IcorrpKa}{1} (4^{2} + 1^{2} - (3^{2})) + TcorrpKa deltaHk_ATP P_ATP = 1 + 10^{(- pH_cy) + pKa1_ATP} + \frac{mg}{c0} 10^{pKamg_ATP} + \frac{k}{c0} 10^{pKak_ATP} ATP4 = \frac{1}{P_ATP} HATP3 = 10^{(- pH_cy) + pKa1_ATP} ATP4 mgATP2 = \frac{mg}{c0} 10^{pKamg_ATP} ATP4 kATP = \frac{k}{c0} 10^{pKak_ATP} ATP4 Navg_ATP = 0 ATP4 + 1 HATP3 + 0 mgATP2 + 0 kATP dNavgATPdH = \frac{10^{pKa1_ATP} (P_ATP - (10^{(- pH_cy) + pKa1_ATP}))}{c0 {P_ATP}^{2}} dNavgATPdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_ATP + pKamg_ATP}}{{P_ATP}^{2}} dmgATP2dmg = \frac{\frac{P_ATP 10^{pKamg_ATP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_ATP}}{c0})}{{P_ATP}^{2}} dmgATP2dpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_ATP + pKamg_ATP} \ln 10}{{P_ATP}^{2}} NH_ATP4 = 12 deltaGof_ATP4 = - 2768.1 deltaGpof_ATP4 = deltaGof_ATP4 + NH_ATP4 R T \ln 10 pH_cy - (IcorrdeltaGpof (16 - NH_ATP4)) pKak_ADP = 1 deltaH1o_ADP = - 3 deltaHmgo_ADP = - 15 deltaH1_ADP = deltaH1o_ADP + Icorr (3^{2} + 1^{2} - (2^{2})) deltaHmg_ADP = deltaHmgo_ADP + Icorr (3^{2} + 2^{2} - (1^{2})) pKa1_ADP = 6.38 + \frac{IcorrpKa}{1} (3^{2} + 1^{2} - (2^{2})) + TcorrpKa deltaH1_ADP pKamg_ADP = 3.25 + \frac{IcorrpKa}{1} (3^{2} + 2^{2} - (1^{2})) + TcorrpKa deltaHmg_ADP P_ADP = 1 + 10^{(- pH_cy) + pKa1_ADP} + \frac{mg}{c0} 10^{pKamg_ADP} + \frac{k}{c0} 10^{pKak_ADP} ADP3 = \frac{1}{P_ADP} HADP2 = 10^{(- pH_cy) + pKa1_ADP} ADP3 mgADP = \frac{ADP3 mg}{c0} 10^{pKamg_ADP} kADP = \frac{ADP3 k}{c0} 10^{pKak_ADP} Navg_ADP = 0 ADP3 + 1 HADP2 + 0 mgADP + 0 kADP dNavgADPdH = \frac{10^{pKa1_ADP} (P_ADP - (10^{(- pH_cy) + pKa1_ADP}))}{c0 {P_ADP}^{2}} dNavgADPdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_ADP + pKamg_ADP}}{{P_ADP}^{2}} dmgADPdmg = \frac{\frac{P_ADP 10^{pKamg_ADP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_ADP}}{c0})}{{P_ADP}^{2}} dmgADPdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_ADP + pKamg_ADP} \ln 10}{{P_ADP}^{2}} NH_ADP3 = 12 deltaGof_ADP3 = - 1906.13 deltaGpof_ADP3 = deltaGof_ADP3 + NH_ADP3 R T \ln 10 pH_cy - (IcorrdeltaGpof (9 - NH_ADP3)) deltaH1o_AMP = - 3 deltaHmgo_AMP = - 7.5 deltaH1_AMP = deltaH1o_AMP + Icorr (2^{2} + 1^{2} - (1^{2})) deltaHmg_AMP = deltaHmgo_AMP + Icorr (2^{2} + 2^{2} - (0^{2})) pKa1_AMP = 6.29 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaH1_AMP pKamg_AMP = 1.92 + \frac{IcorrpKa}{1} (2^{2} + 2^{2} - (0^{2})) + TcorrpKa deltaHmg_AMP P_AMP = 1 + 10^{pKa1_AMP - pH_cy} + \frac{mg}{c0} 10^{pKamg_AMP} AMP2 = \frac{1}{P_AMP} HAMP1 = AMP2 10^{pKa1_AMP - pH_cy} mgAMP = \frac{mg}{c0} 10^{pKamg_AMP} AMP2 Navg_AMP = 0 AMP2 + HAMP1 + 0 mgAMP dNavgAMPdH = \frac{10^{pKa1_AMP} (P_AMP - (10^{(- pH_cy) + pKa1_AMP}))}{c0 {P_AMP}^{2}} dNavgAMPdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_AMP + pKamg_AMP}}{{P_AMP}^{2}} dmgAMPdmg = \frac{\frac{P_AMP 10^{pKamg_AMP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_AMP}}{c0})}{{P_AMP}^{2}} dmgAMPdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_AMP + pKamg_AMP} \ln 10}{{P_AMP}^{2}} NH_AMP2 = 12 deltaGof_AMP2 = - 1040.45 deltaGpof_AMP2 = deltaGof_AMP2 + NH_AMP2 \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_AMP2)) pKak_PCR = 0.31 deltaH1o_PCR = 2.66 deltaHmgo_PCR = 8.19 deltaH1_PCR = deltaH1o_PCR + Icorr (2^{2} + 1^{2} - (1^{2})) deltaHmg_PCR = deltaHmgo_PCR + Icorr (2^{2} + 2^{2} - (0^{2})) pKa1_PCR = 4.5 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaH1_PCR pKamg_PCR = 1.6 + \frac{IcorrpKa}{1} (2^{2} + 2^{2} - (0^{2})) + TcorrpKa deltaHmg_PCR P_PCR = 1 + 10^{(- pH_cy) + pKa1_PCR} + \frac{mg}{c0} 10^{pKamg_PCR} + \frac{k}{c0} 10^{pKak_PCR} HPCR = \frac{1}{P_PCR} H2PCR = 10^{(- pH_cy) + pKa1_PCR} HPCR kPCR = \frac{k}{c0} 10^{pKak_PCR} HPCR mgPCR = \frac{mg}{c0} 10^{pKamg_PCR} HPCR Navg_PCR = H2PCR dNavgPCRdH = \frac{10^{pKa1_PCR} (P_PCR - (10^{(- pH_cy) + pKa1_PCR}))}{c0 {P_PCR}^{2}} dNavgPCRdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_PCR + pKamg_PCR}}{{P_PCR}^{2}} dmgPCRdmg = \frac{\frac{P_PCR 10^{pKamg_PCR}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_PCR}}{c0})}{{P_PCR}^{2}} dmgPCRdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_PCR + pKamg_PCR} \ln 10}{{P_PCR}^{2}} NH_HPCR = 8 pKa1_CR = 2.3 P_CR = 1 + 10^{(- pH_cy) + pKa1_CR} HCR = \frac{1}{P_CR} H2CR = HCR 10^{(- pH_cy) + pKa1_CR} Navg_CR = 0 HCR + 1 H2CR dNavgCRdH = \frac{10^{pKa1_CR} (P_CR - (10^{(- pH_cy) + pKa1_CR}))}{c0 {P_CR}^{2}} dNavgCRdmg = 0 NH_HCR = 9 deltaH1o_G1P = - 1.7 deltaHmgo_G1P = - 12 deltaH1_G1P = deltaH1o_G1P + Icorr (2^{2} + 1^{2} - (1^{2})) deltaHmg_G1P = deltaHmgo_G1P + Icorr (2^{2} + 2^{2} - (0^{2})) pKa1_G1P = 6.09 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaH1_G1P pKamg_G1P = 2.48 + \frac{IcorrpKa}{1} (2^{2} + 2^{2} - (0^{2})) + TcorrpKa deltaHmg_G1P P_G1P = 1 + 10^{- pH_cy} 10^{pKa1_G1P} + \frac{mg}{c0} 10^{pKamg_G1P} UG1P = \frac{1}{P_G1P} HG1P = UG1P 10^{(- pH_cy) + pKa1_G1P} mgG1P = \frac{UG1P mg}{c0} 10^{pKamg_G1P} Navg_G1P = HG1P dNavgG1PdH = \frac{10^{pKa1_G1P} (P_G1P - (10^{(- pH_cy) + pKa1_G1P}))}{c0 {P_G1P}^{2}} dNavgG1Pdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_G1P + pKamg_G1P}}{{P_G1P}^{2}} dmgG1Pdmg = \frac{\frac{P_G1P 10^{pKamg_G1P}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_G1P}}{c0})}{{P_G1P}^{2}} dmgG1PdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_G1P + pKamg_G1P} \ln 10}{{P_G1P}^{2}} NH_UG1P = 11 deltaGof_UG1P = - 1756.87 deltaGpof_UG1P = deltaGof_UG1P + NH_UG1P \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UG1P)) pKa1_G6P = 6.11 P_G6P = 1 + 10^{(- pH_cy) + pKa1_G6P} UG6P = \frac{1}{P_G6P} HG6P = UG6P 10^{(- pH_cy) + pKa1_G6P} Navg_G6P = HG6P dNavgG6PdH = \frac{10^{pKa1_G6P} (P_G6P - (10^{(- pH_cy) + pKa1_G6P}))}{c0 {P_G6P}^{2}} dNavgG6Pdmg = 0 NH_UG6P = 11 deltaGof_UG6P = - 1763.94 deltaGpof_UG6P = deltaGof_UG6P + NH_UG6P \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UG6P)) pKa1_F6P = 5.89 P_F6P = 1 + 10^{(- pH_cy) + pKa1_F6P} UF6P = \frac{1}{P_F6P} HF6P = UF6P 10^{(- pH_cy) + pKa1_F6P} Navg_F6P = HF6P dNavgF6PdH = \frac{10^{pKa1_F6P} (P_F6P - (10^{(- pH_cy) + pKa1_F6P}))}{c0 {P_F6P}^{2}} dNavgF6Pdmg = 0 NH_UF6P = 11 deltaGof_UF6P = - 1760.8 deltaGpof_UF6P = deltaGof_UF6P + NH_UF6P \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UF6P)) pKa1_FDP = 6.4 pKa2_FDP = 5.92 pKamg_FDP = 2.7 P_FDP = 1 + 10^{(- pH_cy) + pKa1_FDP} + 10^{(- 2) pH_cy + pKa1_FDP + pKa2_FDP} + \frac{mg}{c0} 10^{pKamg_FDP} UFDP = \frac{1}{P_FDP} HFDP = UFDP 10^{(- pH_cy) + pKa1_FDP} H2FDP = UFDP 10^{(- 2) pH_cy + pKa1_FDP + pKa2_FDP} mgFDP = \frac{UFDP mg}{c0} 10^{pKamg_FDP} Navg_FDP = HFDP + 2 H2FDP dNavgFDPdH = \frac{P_FDP (10^{pKa1_FDP} + 2 10^{(- pH_cy) + pKa1_FDP + pKa2_FDP}) - ((10^{(- pH_cy) + pKa1_FDP} + 2 10^{(- 2) pH_cy + pKa1_FDP + pKa2_FDP}) (10^{pKa1_FDP} + 2 10^{(- pH_cy) + pKa1_FDP + pKa2_FDP}))}{c0 {P_FDP}^{2}} dNavgFDPdmg = \frac{(- (10^{(- pH_cy) + pKa1_FDP} + 2 10^{(- 2) pH_cy + pKa1_FDP + pKa2_FDP})) 10^{pKamg_FDP}}{c0 {P_FDP}^{2}} dmgFDPdmg = \frac{\frac{P_FDP 10^{pKamg_FDP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_FDP}}{c0})}{{P_FDP}^{2}} dmgFDPdpH = \frac{\frac{mg}{c0} 10^{pKamg_FDP} (P_FDP 10^{(- pH_cy) + pKa1_FDP} \ln 10 - (10^{(- 2) pH_cy + pKa1_FDP + pKa2_FDP} 2 \ln 10))}{{P_FDP}^{2}} NH_UFDP = 10 deltaGof_UFDP = - 2601.4 deltaGpof_UFDP = deltaGof_UFDP + NH_UFDP \ln 10 R T pH_cy - (IcorrdeltaGpof (16 - NH_UFDP)) pKa1_GAP = 6.45 P_GAP = 1 + 10^{(- pH_cy) + pKa1_GAP} UGAP = \frac{1}{P_GAP} HGAP = UGAP 10^{(- pH_cy) + pKa1_GAP} Navg_GAP = HGAP dNavgGAPdH = \frac{10^{pKa1_GAP} (P_GAP - (10^{(- pH_cy) + pKa1_GAP}))}{c0 {P_GAP}^{2}} dNavgGAPdmg = 0 NH_UGAP = 5 deltaGof_UGAP = - 1288.6 deltaGpof_UGAP = deltaGof_UGAP + NH_UGAP \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UGAP)) pKamg_G3P = 1.63 deltaH1o_G3P = - 3.1 deltaH1_G3P = deltaH1o_G3P + Icorr (2^{2} + 1^{2} - (1^{2})) pKa1_G3P = 6.22 + \frac{IcorrpKa}{1} (2^{2} + 1^{2} - (1^{2})) + TcorrpKa deltaH1_G3P P_G3P = 1 + 10^{(- pH_cy) + pKa1_G3P} + \frac{mg}{c0} 10^{pKamg_G3P} UG3P = \frac{1}{P_G3P} HG3P = UG3P 10^{(- pH_cy) + pKa1_G3P} mgG3P = \frac{UG3P mg}{c0} 10^{pKamg_G3P} Navg_G3P = HG3P dNavgG3PdH = \frac{10^{pKa1_G3P} (P_G3P - (10^{(- pH_cy) + pKa1_G3P}))}{c0 {P_G3P}^{2}} dNavgG3Pdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_G3P + pKamg_G3P}}{{P_G3P}^{2}} dmgG3Pdmg = \frac{\frac{P_G3P 10^{pKamg_G3P}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_G3P}}{c0})}{{P_G3P}^{2}} dmgG3PdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_G3P + pKamg_G3P} \ln 10}{{P_G3P}^{2}} NH_UG3P = 7 deltaGof_UG3P = - 1339.25 deltaGpof_UG3P = deltaGof_UG3P + NH_UG3P \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UG3P)) pKa1_DHAP = 5.9 pKamg_DHAP = 1.57 P_DHAP = 1 + 10^{(- pH_cy) + pKa1_DHAP} + \frac{mg}{c0} 10^{pKamg_DHAP} UDHAP = \frac{1}{P_DHAP} HDHAP = UDHAP 10^{(- pH_cy) + pKa1_DHAP} mgDHAP = \frac{UDHAP mg}{c0} 10^{pKamg_DHAP} Navg_DHAP = HDHAP dNavgDHAPdH = \frac{10^{pKa1_DHAP} (P_DHAP - (10^{(- pH_cy) + pKa1_DHAP}))}{c0 {P_DHAP}^{2}} dNavgDHAPdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_DHAP + pKamg_DHAP}}{{P_DHAP}^{2}} dmgDHAPdmg = \frac{\frac{P_DHAP 10^{pKamg_DHAP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_DHAP}}{c0})}{{P_DHAP}^{2}} dmgDHAPdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_DHAP + pKamg_DHAP} \ln 10}{{P_DHAP}^{2}} NH_UDHAP = 5 deltaGof_UDHAP = - 1296.26 deltaGpof_UDHAP = deltaGof_UDHAP + NH_UDHAP \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_UDHAP)) pKa1_13DPG = 7.5 P_13DPG = 1 + 10^{(- pH_cy) + pKa1_13DPG} U13DPG = \frac{1}{P_13DPG} H13DPG = U13DPG 10^{(- pH_cy) + pKa1_13DPG} Navg_13DPG = H13DPG dNavg13DPGdH = \frac{10^{pKa1_13DPG} (P_13DPG - (10^{(- pH_cy) + pKa1_13DPG}))}{c0 {P_13DPG}^{2}} dNavg13DPGdmg = 0 NH_U13DPG = 4 deltaGof_U13DPG = - 2356.14 deltaGpof_U13DPG = deltaGof_U13DPG + NH_U13DPG \ln 10 R T pH_cy - (IcorrdeltaGpof (16 - NH_U13DPG)) pKa1_3PG = 6.21 P_3PG = 1 + 10^{(- pH_cy) + 6.21} U3PG = \frac{1}{P_3PG} H3PG = U3PG 10^{(- pH_cy) + 6.21} Navg_3PG = H3PG dNavg3PGdH = \frac{10^{pKa1_3PG} (P_3PG - (10^{(- pH_cy) + pKa1_3PG}))}{c0 {P_3PG}^{2}} dNavg3PGdmg = 0 NH_U3PG = 4 deltaGof_U3PG = - 1502.54 deltaGpof_U3PG = deltaGof_U3PG + NH_U3PG \ln 10 R T pH_cy - (IcorrdeltaGpof (9 - NH_U3PG)) pKa1_2PG = 7 pKamg_2PG = 2.45 pKak_2PG = 1.18 P_2PG = 1 + 10^{(- pH_cy) + pKa1_2PG} + \frac{mg}{c0} 10^{pKamg_2PG} + \frac{k}{c0} 10^{pKak_2PG} U2PG = \frac{1}{P_2PG} H2PG = U2PG 10^{(- pH_cy) + pKa1_2PG} mg2PG = \frac{U2PG mg}{c0} 10^{pKamg_2PG} k2PG = \frac{U2PG k}{c0} 10^{pKak_2PG} Navg_2PG = H2PG dNavg2PGdH = \frac{10^{pKa1_2PG} (P_2PG - (10^{(- pH_cy) + pKa1_2PG}))}{c0 {P_2PG}^{2}} dNavg2PGdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_2PG + pKamg_2PG}}{{P_2PG}^{2}} dmg2PGdmg = \frac{\frac{P_2PG 10^{pKamg_2PG}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_2PG}}{c0})}{{P_2PG}^{2}} dmg2PGdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_2PG + pKamg_2PG} \ln 10}{{P_2PG}^{2}} NH_U2PG = 4 deltaGof_U2PG = - 1496.38 deltaGpof_U2PG = deltaGof_U2PG + NH_U2PG \ln 10 R T pH_cy - (IcorrdeltaGpof (9 - NH_U2PG)) pKa1_PEP = 6.35 pKamg_PEP = 2.26 pKak_PEP = 1.08 P_PEP = 1 + 10^{pKa1_PEP - pH_cy} + \frac{mg}{c0} 10^{pKamg_PEP} + \frac{k}{c0} 10^{pKak_PEP} UPEP = \frac{1}{P_PEP} HPEP = UPEP 10^{pKa1_PEP - pH_cy} kPEP = \frac{UPEP k}{c0} 10^{pKak_PEP} mgPEP = \frac{UPEP mg}{c0} 10^{pKamg_PEP} Navg_PEP = HPEP dNavgPEPdH = \frac{10^{pKa1_PEP} (P_PEP - (10^{(- pH_cy) + pKa1_PEP}))}{c0 {P_PEP}^{2}} dNavgPEPdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_PEP + pKamg_PEP}}{{P_PEP}^{2}} dmgPEPdmg = \frac{\frac{P_PEP 10^{pKamg_PEP}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_PEP}}{c0})}{{P_PEP}^{2}} dmgPEPdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_PEP + pKamg_PEP} \ln 10}{{P_PEP}^{2}} NH_UPEP = 2 deltaGof_UPEP = - 1263.65 deltaGpof_UPEP = deltaGof_UPEP + NH_UPEP \ln 10 R T pH_cy - (IcorrdeltaGpof (9 - NH_UPEP)) pKa1_PYR = 2.49 P_PYR = 1 + 10^{(- pH_cy) + pKa1_PYR} UPYR = \frac{1}{P_PYR} HPYR = UPYR 10^{(- pH_cy) + pKa1_PYR} Navg_PYR = HPYR dNavgPYRdH = \frac{10^{pKa1_PYR} (P_PYR - (10^{(- pH_cy) + pKa1_PYR}))}{c0 {P_PYR}^{2}} dNavgPYRdmg = 0 NH_UPYR = 3 deltaGof_UPYR = - 472.27 deltaGpof_UPYR = deltaGof_UPYR + NH_UPYR \ln 10 R T pH_cy - (IcorrdeltaGpof (1 - NH_UPYR)) pKamg_LAC = 0.98 deltaH1o_LAC = - 0.33 deltaH1_LAC = deltaH1o_LAC + Icorr (1^{2} + 1^{2} - (0^{2})) pKa1_LAC = 3.67 + \frac{IcorrpKa}{1} (1^{2} + 1^{2} - (0^{2})) + TcorrpKa deltaH1_LAC P_LAC = 1 + 10^{(- pH_cy) + pKa1_LAC} + \frac{mg}{c0} 10^{pKamg_LAC} ULAC = \frac{1}{P_LAC} HLAC = ULAC 10^{(- pH_cy) + pKa1_LAC} mgLAC = \frac{mg}{c0} 10^{pKamg_LAC} ULAC Navg_LAC = HLAC dNavgLACdH = \frac{10^{pKa1_LAC} (P_LAC - (10^{(- pH_cy) + pKa1_LAC}))}{c0 {P_LAC}^{2}} dNavgLACdmg = \frac{\frac{- (10^{- pH_cy})}{c0} 10^{pKa1_LAC + pKamg_LAC}}{{P_LAC}^{2}} dmgLACdmg = \frac{\frac{P_LAC 10^{pKamg_LAC}}{c0} - (\frac{\frac{mg}{c0} 10^{2 pKamg_LAC}}{c0})}{{P_LAC}^{2}} dmgLACdpH = \frac{\frac{mg}{c0} 10^{(- pH_cy) + pKa1_LAC + pKamg_LAC} \ln 10}{{P_LAC}^{2}} NH_ULAC = 5 deltaGof_ULAC = - 516.72 deltaGpof_ULAC = deltaGof_ULAC + NH_ULAC \ln 10 R T pH_cy - (IcorrdeltaGpof (1 - NH_ULAC)) dNH_GLY = - 10 deltaGpo_GLY = 655.7 + dNH_GLY \ln 10 R T pH_cy NH_NAD = 26 deltaGof_NAD = 0 deltaGpof_NAD = deltaGof_NAD + NH_NAD \ln 10 R T pH_cy - (IcorrdeltaGpof (1 - NH_NAD)) NH_NADH = 27 deltaGof_NADH = 22.65 deltaGpof_NADH = deltaGof_NADH + NH_NADH \ln 10 R T pH_cy - (IcorrdeltaGpof (4 - NH_NADH)) NH_H2O = 2 deltaGof_H2O = - 237.19 deltaGpof_H2O = deltaGof_H2O + NH_H2O \ln 10 R T pH_cy - (IcorrdeltaGpof (0 - NH_H2O)) NH_H = 1 deltaGof_H = 0 deltaGpof_H = deltaGof_H + NH_H \ln 10 R T pH_cy deltaH_CK = (Navg_ATP + Navg_CR - Navg_PCR - Navg_ADP) + (NH_ATP4 + NH_HCR - NH_HPCR - NH_ADP3) Kref_CK = 2.58 e 8 deltaHo_CKo = - 17.55 deltaH1_CK = deltaHo_CKo + Icorr (2^{2} + 3^{2} + 1^{2} - (4^{2}) - (0^{2})) Kref_CKI = ⅇ^{\ln Kref_CK + \frac{alphadebye \sqrt{I} (2^{2} + 3^{2} + 1^{2} - (4^{2}) - (0^{2}))}{1 + B \sqrt{I}}} Kref_CKT = 10^{\log_{10} Kref_CKI - (TcorrpKa deltaH1_CK)} deltaGpo_CK = (- R) T \ln Kref_CKT Kapp_CK = \frac{ⅇ^{\frac{- deltaGpo_CK}{R T}} 10^{- pH_cy} P_ATP P_CR}{P_PCR P_ADP} deltaH_ADK = (2 Navg_ADP - Navg_ATP - Navg_AMP) + (2 NH_ADP3 - NH_ATP4 - NH_AMP2) deltaGpo_ADK = 2 deltaGpof_ADP3 - deltaGpof_ATP4 - deltaGpof_AMP2 Kapp_ADK = \frac{ⅇ^{\frac{- deltaGpo_ADK}{R T}} {P_ADP}^{2}}{P_ATP P_AMP} deltaH_GP = (Navg_G1P - Navg_Pi) + (1 - NH_HPi2) deltaGpo_GP = deltaGpo_GLY + deltaGpof_UG1P - deltaGpof_HPi2 Kapp_GP = \frac{ⅇ^{\frac{- deltaGpo_GP}{R T}} P_G1P}{P_Pi} deltaH_PGLM = (Navg_G6P - Navg_G1P) + (NH_UG6P - NH_UG1P) deltaGpo_PGLM = deltaGpof_UG6P - deltaGpof_UG1P Kapp_PGLM = \frac{ⅇ^{\frac{- deltaGpo_PGLM}{R T}} P_G6P}{P_G1P} deltaH_PGI = (Navg_F6P - Navg_G6P) + (NH_UF6P - NH_UG6P) deltaGpo_PGI = deltaGpof_UF6P - deltaGpof_UG6P Kapp_PGI = \frac{ⅇ^{\frac{- deltaGpo_PGI}{R T}} P_F6P}{P_G6P} deltaH_PFK = (Navg_ADP + Navg_FDP - Navg_F6P - Navg_ATP) + NH_ADP3 + NH_UFDP - NH_UF6P - NH_ATP4 deltaGpo_PFK = deltaGpof_UFDP + deltaGpof_ADP3 + deltaGpof_H - deltaGpof_UF6P - deltaGpof_ATP4 Kapp_PFK = \frac{ⅇ^{\frac{- deltaGpo_PFK}{R T}} P_FDP P_ADP}{P_F6P P_ATP 10^{- pH_cy}} deltaH_ALD = (Navg_DHAP + Navg_GAP - Navg_FDP) + (NH_UDHAP + NH_UGAP - NH_UFDP) deltaGpo_ALD = deltaGpof_UDHAP + deltaGpof_UGAP - deltaGpof_UFDP Kapp_ALD = \frac{1 ⅇ^{\frac{- deltaGpo_ALD}{R T}} P_GAP P_FDP}{P_DHAP} deltaH_TPI = (Navg_DHAP - Navg_GAP) + (NH_UDHAP - NH_UGAP) deltaGpo_TPI = deltaGpof_UDHAP - deltaGpof_UGAP Kapp_TPI = \frac{ⅇ^{\frac{- deltaGpo_TPI}{R T}} P_DHAP}{P_GAP} deltaH_GAPDH = (Navg_13DPG - Navg_GAP - Navg_Pi) + (NH_U13DPG + NH_NADH - NH_UGAP - NH_HPi2 - NH_NAD) deltaGpo_GAPDH = deltaGpof_U13DPG + deltaGpof_NADH + deltaGpof_H - deltaGpof_HPi2 - deltaGpof_UGAP - deltaGpof_NAD Kapp_GAPDH = \frac{ⅇ^{\frac{- deltaGpo_GAPDH}{R T}} P_13DPG}{P_Pi P_GAP 10^{- pH_cy} 1} deltaH_G3PDH = (Navg_DHAP - Navg_G3P) + (NH_UDHAP + NH_NADH - NH_NAD - NH_UG3P) deltaGpo_G3PDH = deltaGpof_H + deltaGpof_NADH + deltaGpof_UDHAP - deltaGpof_NAD - deltaGpof_UG3P Kapp_G3PDH = \frac{ⅇ^{\frac{- deltaGpo_G3PDH}{R T}} P_DHAP}{P_G3P 10^{- pH_cy}} deltaH_PGK = (Navg_3PG + Navg_ATP - Navg_13DPG - Navg_ADP) + (NH_U3PG + NH_ATP4 - NH_U13DPG - NH_ADP3) deltaGpo_PGK = deltaGpof_ATP4 + deltaGpof_U3PG - deltaGpof_U13DPG - deltaGpof_ADP3 Kapp_PGK = \frac{ⅇ^{\frac{- deltaGpo_PGK}{R T}} P_ATP P_3PG}{P_13DPG P_ADP} deltaH_PGM = (Navg_2PG - Navg_3PG) + (NH_U2PG - NH_U3PG) deltaGpo_PGM = deltaGpof_U2PG - deltaGpof_U3PG Kapp_PGM = \frac{ⅇ^{\frac{- deltaGpo_PGM}{R T}} P_2PG}{P_3PG} deltaH_ENOL = (Navg_PEP - Navg_2PG) + (NH_H2O + NH_UPEP - NH_U2PG) deltaGpo_ENOL = deltaGpof_H2O + deltaGpof_UPEP - deltaGpof_U2PG Kapp_ENOL = \frac{ⅇ^{\frac{- deltaGpo_ENOL}{R T}} P_PEP}{P_2PG} deltaH_PK = (Navg_PYR + Navg_ATP - Navg_PEP - Navg_ADP) + (NH_UPYR + NH_ATP4 - NH_UPEP - NH_ADP3) deltaGpo_PK = deltaGpof_UPYR + deltaGpof_ATP4 - deltaGpof_H - deltaGpof_UPEP - deltaGpof_ADP3 Kapp_PK = \frac{ⅇ^{\frac{- deltaGpo_PK}{R T}} P_PYR P_ATP 10^{- pH_cy}}{P_PEP P_ADP} deltaH_LDH = (Navg_LAC - Navg_PYR) + (NH_ULAC + NH_NAD - NH_UPYR - NH_NADH) deltaGpo_LDH = deltaGpof_ULAC + deltaGpof_NAD - deltaGpof_UPYR - deltaGpof_NADH - deltaGpof_H Kapp_LDH = \frac{ⅇ^{\frac{- deltaGpo_LDH}{R T}} P_LAC 10^{- pH_cy}}{P_PYR} deltaH_ATPase = (Navg_ADP + Navg_Pi - Navg_ATP) + (NH_ADP3 + NH_HPi2 - NH_ATP4 - NH_H2O) deltaGpo_ATPase = deltaGpof_ADP3 + deltaGpof_HPi2 + deltaGpof_H - deltaGpof_H2O - deltaGpof_ATP4 Kapp_ATPase = \frac{ⅇ^{\frac{- deltaGpo_ATPase}{R T}} P_ADP P_Pi}{P_ATP 10^{- pH_cy}}

Component: glycogen_phosphorylase

Vfgly = Par_1 expno = Par_100 fracA = \{\begin{matrix} Par_2 if expno \neq 45 \\ 0.001 if time < 40 \\ 0.004 if time \geq 40 \land time < 80 \\ 0.01 if time \geq 80 \land time < 100 \\ 0.04 if time \geq 100 \end{matrix} KgpA_glyf = Par_3 KgpA_pi = Par_4 KgpA_igly = Par_5 KgpA_ipi = Par_6 KgpA_glyb = Par_7 KgpA_g1p = Par_8 KgpA_ig1p = Par_9 Dglya = 1 + \frac{Gly}{KgpA_glyf} + \frac{Pi}{KgpA_pi} + \frac{Gly Pi}{KgpA_glyf KgpA_ipi} + \frac{Gly}{KgpA_glyb} + \frac{G1P}{KgpA_g1p} + \frac{Gly G1P}{KgpA_ig1p KgpA_glyb} pa = \frac{1.404}{1 + 10^{5.94 - pH_cy} + 10^{pH_cy - 7.29}} VbglyA = \frac{pa Vfgly KgpA_glyb KgpA_ig1p}{KgpA_igly KgpA_pi Kapp_GP} glyAF = \frac{\frac{pa Vfgly Pi}{KgpA_igly KgpA_pi}}{Dglya} glyAR = \frac{\frac{VbglyA Gly}{KgpA_glyb KgpA_ig1p}}{Dglya} flux_GPa = fracA (Gly glyAF - (G1P glyAR))

Component: glycogen_phosphorylase_B

fracB = 1 - fracA KgpB_pi = Par_10 KgpB_ipi = Par_11 KgpB_iglyf = Par_12 KgpB_g1p = Par_13 KgpB_ig1p = Par_14 KgpB_iglyb = Par_15 Kgp_amp = Par_16 interactioncoeff = Par_17 nH = Par_18 M = \frac{\frac{{(\frac{AMP}{Kgp_amp})}^{nH}}{interactioncoeff}}{1 + \frac{{(\frac{AMP}{Kgp_amp})}^{nH}}{interactioncoeff}} Dglyb = 1 + \frac{Gly}{KgpB_iglyf} + \frac{Pi}{KgpB_ipi} + \frac{Gly}{KgpB_iglyb} + \frac{G1P}{KgpB_ig1p} + \frac{Gly Pi}{KgpB_iglyf KgpB_pi} + \frac{Gly G1P}{KgpB_g1p KgpB_iglyb} pb = \frac{1.75}{1 + 10^{6.12 - pH_cy} + 10^{pH_cy - 7.03}} VbglyB = \frac{pb Vfgly KgpB_g1p KgpB_iglyb}{KgpB_iglyf KgpB_pi Kapp_GP} glyBF = \frac{\frac{pb M Vfgly Pi}{KgpB_iglyf KgpB_pi}}{Dglyb} glyBR = \frac{\frac{M VbglyB Gly}{KgpB_g1p KgpB_iglyb}}{Dglyb} flux_GPb = fracB (Gly glyBF - (G1P glyBR))

Component: PGLM

Vffpglm = Par_19 Kpglm_g1p = Par_20 Kpglm_g6p = Par_21 Vfpglm = \frac{Vffpglm 1.329}{1 + 10^{(- pH_cy) + 6.64} + 10^{pH_cy - 8.36}} Vbpglm = \frac{Vfpglm Kpglm_g6p}{Kpglm_g1p Kapp_PGLM} v_PGLM = \frac{\frac{Vfpglm G1P}{Kpglm_g1p} - (\frac{Vbpglm G6P}{Kpglm_g6p})}{1 + \frac{G1P}{Kpglm_g1p} + \frac{G6P}{Kpglm_g6p}}

Component: PGI

Vbbpgi = Par_22 Kpgi_g6p = Par_23 Kpgi_f6p = Par_24 Vbpgi = \frac{Vbbpgi}{1 + 10^{(- pH_cy) + 6.94} + 10^{pH_cy - 9.35}} Vfpgi = \frac{Vbpgi Kpgi_g6p}{Kpgi_f6p} Kapp_PGI v_PGI = \frac{\frac{Vfpgi G6P}{Kpgi_g6p} - (\frac{Vbpgi F6P}{Kpgi_f6p})}{1 + \frac{F6P}{Kpgi_f6p} + \frac{G6P}{Kpgi_g6p}}

Component: PFK

Vffpfk = Par_25 Kpfk_f6p = Par_26 Kpfk_f6pT = Par_27 Kpfk_atp = Par_28 Kpfk_atpT = Par_29 Kpfk_fbp = Par_30 Kpfk_fbpT = Par_31 Kpfk_adp = Par_32 Kpfk_adpT = Par_33 Kpfki = Par_34 Kmpfk = Par_35 d = Par_36 e_= Par_37 Lo = Par_38 Vfpfk = \frac{Vffpfk}{1 + {(\frac{pH_cy}{6.8})}^{- 30}} Vbpfk = \frac{Vfpfk Kpfk_fbp Kpfk_adp}{Kpfk_f6p Kpfk_atp Kapp_PFK} L = Lo {(\frac{\frac{1 + \frac{ATP}{Kpfki}}{1 + \frac{d ATP}{Kpfki}} (1 + \frac{e_AMP}{Kmpfk})}{1 + \frac{AMP}{Kmpfk}})}^{4} alpha = \frac{Kpfk_f6p Kpfk_atp}{Kpfk_f6pT Kpfk_atpT} Delta = (1 + \frac{F6P}{Kpfk_f6p}) (1 + \frac{ATP}{Kpfk_atp}) + \frac{FBP}{Kpfk_fbp} + \frac{ADP}{Kpfk_adp} (1 + \frac{FBP}{Kpfk_fbp}) Deltap = (1 + \frac{F6P}{Kpfk_f6pT}) (1 + \frac{ATP}{Kpfk_atpT}) + \frac{FBP}{Kpfk_fbpT} + \frac{ADP}{Kpfk_adpT} (1 + \frac{FBP}{Kpfk_fbpT}) v_PFK = \frac{(\frac{\frac{Vfpfk F6P ATP}{Kpfk_f6p Kpfk_atp}}{Delta} - (\frac{\frac{Vbpfk ADP FBP}{Kpfk_adp Kpfk_fbp}}{Delta})) (1 + alpha L {(\frac{Deltap}{Delta})}^{3})}{1 + L {(\frac{Deltap}{Delta})}^{4}}

Component: ALD

Vffald = Par_39 Kald_fbp = Par_40 Kald_dhap = Par_41 Kald_gap = Par_42 Vfald = \frac{Vffald 1.013}{1 + 10^{(- pH_cy) + 5.32} + 10^{pH_cy - 9.15}} Vbald = \frac{Vfald Kald_gap Kald_dhap}{Kald_fbp Kapp_ALD} v_ALD = \frac{\frac{Vfald FBP}{Kald_fbp} - (\frac{Vbald GAP DHAP}{Kald_gap Kald_dhap})}{1 + \frac{FBP}{Kald_fbp} + \frac{GAP}{Kald_gap} + \frac{DHAP}{Kald_dhap}}

Component: TPI

Vfftpi = Par_43 Ktpi_gap = Par_44 Ktpi_dhap = Par_45 Vftpi = Vfftpi Vbtpi = \frac{Vftpi Ktpi_dhap}{Ktpi_gap Kapp_TPI} v_TPI = \frac{\frac{Vftpi GAP}{Ktpi_gap} - (\frac{Vbtpi DHAP}{Ktpi_dhap})}{1 + \frac{GAP}{Ktpi_gap} + \frac{DHAP}{Ktpi_dhap}}

Component: G3PDH

Vbbg3pdh = Par_46 Kg3pdh_g3p = Par_47 Kg3pdh_nad = Par_48 Kg3pdh_dhap = Par_49 Kg3pdh_nadh = Par_50 Dg3pdh = (1 + \frac{G3P}{Kg3pdh_g3p} + \frac{NADH}{Kg3pdh_nadh}) (1 + \frac{DHAP}{Kg3pdh_dhap} + \frac{NAD}{Kg3pdh_nadh}) Vbg3pdh = Vbbg3pdh Vfg3pdh = \frac{Vbg3pdh Kg3pdh_g3p Kg3pdh_nad Kapp_G3PDH}{Kg3pdh_dhap Kg3pdh_nadh} v_G3PDH = \frac{\frac{Vfg3pdh G3P NAD}{Kg3pdh_g3p Kg3pdh_nad} - (\frac{Vbg3pdh DHAP NADH}{Kg3pdh_dhap Kg3pdh_nadh})}{Dg3pdh}

Component: GAPDH

Vffgad = Par_51 Kgapdh_gap = Par_52 Kgapdh_nad = Par_53 Kgapdh_pi = Par_54 Kgapdh_bpg = Par_55 Kgapdh_nadh = Par_56 Dgap = 1 + \frac{Pi}{Kgapdh_pi} + \frac{GAP}{Kgapdh_gap} + \frac{NAD}{Kgapdh_nad} + \frac{GAP NAD}{Kgapdh_gap Kgapdh_nad} + \frac{GAP NAD Pi}{Kgapdh_gap Kgapdh_nad Kgapdh_pi} + \frac{BPG}{Kgapdh_bpg} + \frac{NADH}{Kgapdh_nadh} + \frac{BPG NADH}{Kgapdh_nadh Kgapdh_bpg} Vfgad = Vffgad 0.0007 ⅇ^{pH_cy 0.8979} Vbgad = \frac{Vfgad Kgapdh_bpg Kgapdh_nadh}{Kgapdh_gap Kgapdh_pi Kgapdh_nad Kapp_GAPDH} v_GAPDH = \frac{\frac{Vfgad GAP NAD Pi}{Kgapdh_nad Kgapdh_gap Kgapdh_pi} - (\frac{Vbgad BPG NADH}{Kgapdh_bpg Kgapdh_nadh})}{Dgap}

Component: PGK

Vbbpgk = Par_57 Kpgk_bpg = Par_58 Kpgk_adp = Par_59 Kpgk_3pg = Par_60 Kpgk_atp = Par_61 Vbpgk = Vbbpgk Vfpgk = \frac{Vbpgk Kpgk_bpg Kpgk_adp}{Kpgk_3pg Kpgk_atp} Kapp_PGK D_PGK = 1 + \frac{ADP}{Kpgk_adp} + \frac{BPG}{Kpgk_bpg} + \frac{BPG ADP}{Kpgk_bpg Kpgk_adp} + \frac{P3G}{Kpgk_3pg} + \frac{ATP}{Kpgk_atp} + \frac{P3G ATP}{Kpgk_3pg Kpgk_atp} v_PGK = \frac{\frac{Vfpgk BPG ADP}{Kpgk_adp Kpgk_bpg} - (\frac{Vbpgk ATP P3G}{Kpgk_atp Kpgk_3pg})}{D_PGK}

Component: PGM

Vffpgm = Par_62 Kpgm_3pg = Par_63 Kpgm_2pg = Par_64 Vfpgm = \frac{Vffpgm 0.989}{1 + 10^{(- pH_cy) + 5.62} + 10^{pH_cy - 8.74}} Vbpgm = \frac{Vfpgm Kpgm_2pg}{Kpgm_3pg Kapp_PGM} v_PGM = \frac{\frac{Vfpgm P3G}{Kpgm_3pg} - (\frac{Vbpgm P2G}{Kpgm_2pg})}{1 + \frac{P3G}{Kpgm_3pg} + \frac{P2G}{Kpgm_2pg}}

Component: ENOL

Vffen = Par_65 Ken_2pg = Par_66 Ken_pep = Par_67 Vfen = Vffen Vben = \frac{Vfen Ken_pep}{Ken_2pg Kapp_ENOL} v_ENOL = \frac{\frac{Vfen P2G}{Ken_2pg} - (\frac{Vben PEP}{Ken_pep})}{1 + \frac{PEP}{Ken_pep} + \frac{P2G}{Ken_2pg}}

Component: PK

Vffpk = Par_68 Kpk_pep = Par_69 Kpk_adp = Par_70 Kpk_pyr = Par_71 Kpk_atp = Par_72 Vfpk = \frac{Vffpk 1.05}{1 + 10^{(- pH_cy) + 5.58} + 10^{pH_cy - 8.79}} Vbpk = \frac{Vfpk Kpk_pyr Kpk_atp}{Kpk_pep Kpk_adp Kapp_PK} v_PK = \frac{\frac{Vfpk PEP ADP}{Kpk_pep Kpk_adp} - (\frac{Vbpk PYR ATP}{Kpk_pyr Kpk_atp})}{1 + \frac{PEP}{Kpk_pep} + \frac{ADP}{Kpk_adp} + \frac{PEP ADP}{Kpk_pep Kpk_adp} + \frac{ATP}{Kpk_atp} + \frac{PYR}{Kpk_pyr} + \frac{PYR ATP}{Kpk_pyr Kpk_atp}}

Component: LDH

Vffldh = Par_73 Kldh_pyr = Par_74 Kldh_nadh = Par_75 Kldh_lac = Par_76 Kldh_nad = Par_77 Vfldh = Vffldh ((- 0.1134) pH_cy + 1.6069) Vbldh = \frac{Vfldh Kldh_lac Kldh_nad}{Kldh_pyr Kldh_nadh Kapp_LDH} v_LDH = \frac{\frac{Vfldh PYR NADH}{Kldh_pyr Kldh_nadh} - (\frac{Vbldh LAC NAD}{Kldh_lac Kldh_nad})}{1 + \frac{PYR}{Kldh_pyr} + \frac{NADH}{Kldh_nadh} + \frac{PYR NADH}{Kldh_pyr Kldh_nadh} + \frac{LAC}{Kldh_lac} + \frac{NAD}{Kldh_nad} + \frac{LAC NAD}{Kldh_lac Kldh_nad}}

Component: ATPase

VmaxATPase = \{\begin{matrix} Par_88 if expno \neq 5 \land expno \neq 45 \\ Par_88 if expno \neq 5 \land expno = 45 \land time \geq 110 \\ Par_88 if expno = 5 \land time > 30 \\ 0 otherwise \end{matrix} Katp_ATPase = Par_89 ATPase = \frac{VmaxATPase ATP}{Katp_ATPase + ATP}

Component: creatine_kinase

VforCK = Par_78 Kck_pcr = Par_79 Kck_iatp = Par_80 Kck_iadp = Par_81 Kck_ipcr = Par_82 Kck_cr = Par_83 VrevCK = \frac{\frac{VforCK}{Kapp_CK} Kck_iatp Kck_cr}{Kck_iadp Kck_pcr} CK = \frac{\frac{VrevCK ATP Cr}{Kck_iatp Kck_cr} - (\frac{VforCK ADP PCr}{Kck_iadp Kck_pcr})}{1 + \frac{ADP}{Kck_iadp} + \frac{PCr}{Kck_ipcr} + \frac{PCr ADP}{Kck_iadp Kck_pcr} + \frac{ATP}{Kck_iatp} + \frac{Cr ATP}{Kck_cr Kck_iatp}}

Component: adenylate_kinase

Vfadk = Par_84 Kadk_amp = Par_85 Kadk_atp = Par_86 Kadk_adp = Par_87 Vbadk = \frac{Vfadk {Kadk_adp}^{2}}{Kadk_amp Kadk_atp Kapp_ADK} ADK = \frac{\frac{Vfadk ATP AMP}{Kadk_atp Kadk_amp} - (Vbadk {(\frac{ADP}{Kadk_adp})}^{2})}{1 + \frac{ATP}{Kadk_atp} + \frac{AMP}{Kadk_amp} + \frac{ATP AMP}{Kadk_atp Kadk_amp} + \frac{2 ADP}{Kadk_adp} + \frac{{ADP}^{2}}{{Kadk_adp}^{2}}}

Component: buffer_capacity

carnosine = Par_92 tris = Par_91 acetate = Par_93 bufcapfixed = \frac{\ln 10 carnosine 10^{- pH_cy - 6.87}}{{(10^{- pH_cy} + 10^{- 6.87})}^{2}} + \frac{\ln 10 tris 10^{- pH_cy - 8.3}}{{(10^{- pH_cy} + 10^{- 8.3})}^{2}} + \frac{\ln 10 acetate 10^{- pH_cy - 4.8}}{{(10^{- pH_cy} + 10^{- 4.8})}^{2}} bufcapmetab = \ln 10 10^{- pH_cy} c0 (1 + dNavgPidH Pi + dNavgATPdH ATP + dNavgADPdH ADP + dNavgAMPdH AMP + dNavgPCRdH PCr + dNavgCRdH Cr + dNavgG1PdH G1P + dNavgG6PdH G6P + dNavgF6PdH F6P + dNavgFDPdH FBP + dNavgGAPdH GAP + dNavgDHAPdH DHAP + dNavgG3PdH G3P + dNavg13DPGdH BPG + dNavg3PGdH P3G + dNavg2PGdH P2G + dNavgPEPdH PEP + dNavgPYRdH PYR + dNavgLACdH LAC) protons_consumed = deltaH_CK (- CK) + deltaH_ADK ADK + deltaH_PGLM v_PGLM + deltaH_GP (flux_GPa + flux_GPb) + deltaH_PGI v_PGI + deltaH_PFK v_PFK + deltaH_ALD v_ALD + deltaH_TPI v_TPI + deltaH_GAPDH v_GAPDH + deltaH_PGK v_PGK + deltaH_PGM v_PGM + deltaH_ENOL v_ENOL + deltaH_PK v_PK + deltaH_LDH v_LDH + deltaH_G3PDH v_G3PDH CKprtflux = deltaH_CK (- CK) glycprtflux = deltaH_PGLM v_PGLM + deltaH_GP (flux_GPa + flux_GPb) + deltaH_PGI v_PGI + deltaH_PFK v_PFK + deltaH_ALD v_ALD + deltaH_TPI v_TPI + deltaH_GAPDH v_GAPDH + deltaH_PGK v_PGK + deltaH_PGM v_PGM + deltaH_ENOL v_ENOL + deltaH_PK v_PK + deltaH_LDH v_LDH + deltaH_G3PDH v_G3PDH pHODEterm1 = \frac{protons_consumed}{bufcapfixed + bufcapmetab} pHODEterm2 = \frac{dNavgPidmg Pi + dNavgATPdmg ATP + dNavgADPdmg ADP + dNavgAMPdmg AMP + dNavgPCRdmg PCr + dNavgCRdmg Cr + dNavgG1Pdmg G1P + dNavgG6Pdmg G6P + dNavgF6Pdmg F6P + dNavgFDPdmg FBP + dNavgGAPdmg GAP + dNavgDHAPdmg DHAP + dNavgG3Pdmg G3P + dNavg13DPGdmg BPG + dNavg3PGdmg P3G + dNavg2PGdmg P2G + dNavgPEPdmg PEP + dNavgPYRdmg PYR + dNavgLACdmg LAC}{bufcapfixed + bufcapmetab} denom_mgODE = - 1 - (dmgATP2dmg ATP + dmgADPdmg ADP + dmgAMPdmg AMP + dmgPidmg Pi + dmgPCRdmg PCr + dmgG1Pdmg G1P + dmgFDPdmg FBP + dmgG3Pdmg G3P + dmgDHAPdmg DHAP + dmgPEPdmg PEP + dmg2PGdmg P2G + dmgLACdmg LAC) RHSterm1_mgODE = \frac{dmgATP2dpH ATP + dmgADPdpH ADP + dmgAMPdpH AMP + dmgPidpH Pi + dmgPCRdpH PCr + dmgG1PdpH G1P + dmgFDPdpH FBP + dmgG3PdpH G3P + dmgDHAPdpH DHAP + dmgPEPdpH PEP + dmg2PGdpH P2G + dmgLACdpH LAC}{denom_mgODE} denomMgpHODE = 1 - (RHSterm1_mgODE pHODEterm2)

Component: differential_equations

\frac{d}{d time} (PCr) = dPCrdt dPCrdt = CK \frac{d}{d time} (Cr) = dCrdt dCrdt = - CK \frac{d}{d time} (NAD) = dNADdt dNADdt = (- v_GAPDH - v_G3PDH) + v_LDH \frac{d}{d time} (NADH) = dNADHdt dNADHdt = v_GAPDH + v_G3PDH - v_LDH \frac{d}{d time} (ATP) = dATPdt dATPdt = (- CK - ADK - v_PFK) + v_PGK + v_PK - ATPase \frac{d}{d time} (ADP) = dADPdt dADPdt = (CK + 2 ADK + v_PFK - v_PGK - v_PK) + ATPase \frac{d}{d time} (AMP) = dAMPdt dAMPdt = - ADK \frac{d}{d time} (Pi) = dPidt dPidt = (- (flux_GPa + flux_GPb) - v_GAPDH) + ATPase \frac{d}{d time} (Gly) = dGlydt dGlydt = - (flux_GPa + flux_GPb) \frac{d}{d time} (G1P) = dG1Pdt dG1Pdt = flux_GPa + flux_GPb - v_PGLM \frac{d}{d time} (G6P) = dG6Pdt dG6Pdt = v_PGLM - v_PGI \frac{d}{d time} (F6P) = dF6Pdt dF6Pdt = v_PGI - v_PFK \frac{d}{d time} (FBP) = dFBPdt dFBPdt = v_PFK - v_ALD \frac{d}{d time} (DHAP) = dDHAPdt dDHAPdt = v_ALD + v_TPI + v_G3PDH \frac{d}{d time} (G3P) = dG3Pdt dG3Pdt = - v_G3PDH \frac{d}{d time} (GAP) = dGAPdt dGAPdt = v_ALD - v_TPI - v_GAPDH \frac{d}{d time} (BPG) = dBGPdt dBGPdt = v_GAPDH - v_PGK \frac{d}{d time} (P3G) = dP3Gdt dP3Gdt = v_PGK - v_PGM \frac{d}{d time} (P2G) = dP2Gdt dP2Gdt = v_PGM - v_ENOL \frac{d}{d time} (PEP) = dPEPdt dPEPdt = v_ENOL - v_PK \frac{d}{d time} (PYR) = dPYRdt dPYRdt = v_PK - v_LDH \frac{d}{d time} (LAC) = dLACdt dLACdt = v_LDH RHSterm2_mgODE = \frac{mgATP2 dATPdt + mgADP dADPdt + mgAMP dAMPdt + mgPi dPidt + mgPCR dPCrdt + mgG1P dG1Pdt + mgFDP dFBPdt + mgG3P dG3Pdt + mgDHAP dDHAPdt + mgPEP dPEPdt + mg2PG dP2Gdt + mgLAC dLACdt}{denom_mgODE} fixmg = 1 \frac{d}{d time} (Mg) = \{\begin{matrix} \frac{fixmg (RHSterm2_mgODE + RHSterm1_mgODE pHODEterm1)}{1 - (RHSterm1_mgODE pHODEterm2)} if time ≦ 1 \\ fixmg RHSterm2_mgODE otherwise \end{matrix} fixpH = Par_99 \frac{d}{d time} (pH_calc) = \frac{fixpH (pHODEterm1 + RHSterm2_mgODE pHODEterm2)}{1 - (RHSterm1_mgODE pHODEterm2)} \frac{d}{d time} (protonload) = - protons_consumed