Model Mathematics

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Component: environment

CO2_in = 0.05 0.0425 (760 - 23.8) 1 e -3 HCO3_in = 30 e -3 pH_in = 6.157 + \log_{10} (\frac{HCO3_in}{CO2_in}) MOPSt = 0 pH_cy = pH_calc

Component: parameters

Vfgly = 0.0127 fracA = 1 e -2 KgpA_glyf = 1.7 e -3 KgpA_pi = 4 e -3 KgpA_igly = 2 e -3 KgpA_ipi = 4.7 e -3 KgpA_glyb = 1.5 e -4 KgpA_g1p = 2.7 e -3 KgpA_ig1p = 1.01 e -2 KgpB_pi = 2 e -4 KgpB_ipi = 4.6 e -3 KgpB_iglyf = 1.5 e -2 KgpB_g1p = 1.5 e -3 KgpB_ig1p = 7.4 e -3 KgpB_iglyb = 4.4 e -3 Kgp_amp = 3.875 e -6 nH = 1.8805 Vffpglm = 0.0177 Kpglm_g1p = 6.3 e -5 Kpglm_g6p = 3 e -5 Vbbpgi = 1.3155 Kpgi_g6p = 4.8 e -4 Kpgi_f6p = 1.19 e -4 Vffpfk = 0.0127 Kpfk_f6p = 1.8 e -4 Kpfk_f6pT = 2 e -2 Kpfk_atp = 8 e -5 Kpfk_atpT = 2.5 e -4 Kpfk_fbp = 4.02 e -3 Kpfk_fbpT = 4.02 e -3 Kpfk_adp = 2.7 e -3 Kpfk_adpT = 2.7 e -3 Kpfki = 8.7 e -4 10 Kmpfk = 6 e -5 d = 1 e -2 e_= 1 e -2 Lo = 13 Vffald = 0.0412 Kald_fbp = 5 e -5 Kald_dhap = 2 e -3 Kald_gap = 1 e -3 Vfftpi = 0.348 Ktpi_gap = 3.2 e -4 Ktpi_dhap = 6.1 e -4 Vbbg3pdh = 0.631 Kg3pdh_g3p = 1.8 e -4 Kg3pdh_nad = 1.2 e -5 Kg3pdh_dhap = 2.2 e -4 Kg3pdh_nadh = 8 e -6 Vffgad = 0.1865 Kgapdh_gap = 2.5 e -6 Kgapdh_nad = 9 e -5 Kgapdh_pi = 2.9 e -4 Kgapdh_bpg = 8 e -7 Kgapdh_nadh = 3.3 e -6 Vbbpgk = 0.0212 Kpgk_bpg = 2 e -3 Kpgk_adp = 8 e -6 Kpgk_3pg = 1.2 e -3 Kpgk_atp = 3.5 e -4 Vffpgm = 0.2046 Kpgm_3pg = 2 e -4 Kpgm_2pg = 1.4 e -5 Vffen = 1.943 Ken_2pg = 1 e -4 Ken_pep = 3.7 e -4 Vffpk = 0.0996 Kpk_pep = 8 e -5 Kpk_adp = 3 e -4 Kpk_pyr = 7.05 e -3 Kpk_atp = 1.13 e -3 Vffldh = 0.2687 Kldh_pyr = 3.35 e -4 Kldh_nadh = 2 e -6 Kldh_lac = 1.7 e -2 Kldh_nad = 8.49 e -4 VforCK = 11.1371 Kck_pcr = 1.11 e -3 Kck_iatp = 3.5 e -3 Kck_iadp = 1.35 e -4 Kck_ipcr = 3.9 e -3 Kck_cr = 3.8 e -3 Kck_Iadp = 0.015 e -3 Kck_Ipcr = 3.9 e -3 Kck_Icr = 58 e -3 Kck_Iatp = 4.346 e -3 Kck_Ii = 1 e -3 Vfadk = 2.5627 Kadk_amp = 3.2 e -4 Kadk_atp = 2.7 e -4 Kadk_adp = 3.5 e -4 kut = 0.0827 VmaxOxPhos = 0.0037 Kmadp = 4.8339 e -5 nnHH = 2.429 Vmax_MCT = 0.00462138 Klac1 = 25.5 e -3 pKmct1 = 8.89 PSVCO2 = 2.3084 X_CA = 740 kf_hydrCO2 = 0.0469 60 Keq_CA = 10^{- 6.157} kb_hydrCO2 = \frac{kf_hydrCO2}{Keq_CA} Flow = 4 e -3 V_cell = 55 e -3 0.67 1 e -3 V_ec = 0.149 e -3 - (\frac{55 e -3}{1.06} 1 e -3) bufcapfixed = 0.0141865

Component: equilibrium_constants

T = 298.15 I = 0.17 k = 0.14 c0 = 1 R = 8.314 e -3 B = 1.6 I1 = 0.1 alphadebye = 1.17582 IcorrpKa = \frac{alphadebye (\frac{\sqrt{I1}}{1 + B \sqrt{I1}} - (\frac{\sqrt{I}}{1 + B \sqrt{I}}))}{\ln 10} RTalpha = 2.91482 IcorrdeltaGpof = \frac{RTalpha \sqrt{I}}{1 + B \sqrt{I}} pKa1_Pi = 6.75 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) pKamg_Pi = 1.65 + IcorrpKa (2^{2} + 2^{2} - (0^{2})) pKak_Pi = 0.5 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 = H2Pi1 dNavgPidH = \frac{10^{pKa1_Pi} P_Pi (1 - H2Pi1)}{c0 {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)) pKa1_ATP = 6.48 + IcorrpKa (4^{2} + 1^{2} - (3^{2})) pKamg_ATP = 4.19 + IcorrpKa (4^{2} + 2^{2} - (2^{2})) pKak_ATP = 1.17 + IcorrpKa (4^{2} + 1^{2} - (3^{2})) 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 = HATP3 dNavgATPdH = \frac{10^{pKa1_ATP} P_ATP (1 - HATP3)}{c0 {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 pKa1_ADP = 6.38 + IcorrpKa (3^{2} + 1^{2} - (2^{2})) pKamg_ADP = 3.25 + IcorrpKa (3^{2} + 2^{2} - (1^{2})) 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 = HADP2 dNavgADPdH = \frac{10^{pKa1_ADP} P_ADP (1 - HADP2)}{c0 {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)) pKa1_AMP = 6.29 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) pKamg_AMP = 1.92 + IcorrpKa (2^{2} + 2^{2} - (0^{2})) 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 = HAMP1 dNavgAMPdH = \frac{10^{pKa1_AMP} (P_AMP - (10^{(- pH_cy) + pKa1_AMP}))}{c0 {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 pKa1_PCR = 4.5 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) pKamg_PCR = 1.6 + IcorrpKa (2^{2} + 2^{2} - (0^{2})) 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}} 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}} NH_HCR = 9 pKa1_G1P = 6.09 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) pKamg_G1P = 2.48 + IcorrpKa (2^{2} + 2^{2} - (0^{2})) 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}} 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 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) 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 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) 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}} 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 pKamg_FDP = 2.7 P_FDP = 1 + 10^{(- pH_cy) + pKa1_FDP} + \frac{mg}{c0} 10^{pKamg_FDP} UFDP = \frac{1}{P_FDP} HFDP = UFDP 10^{(- pH_cy) + pKa1_FDP} mgFDP = \frac{UFDP mg}{c0} 10^{pKamg_FDP} Navg_FDP = HFDP dNavgFDPdH = \frac{10^{pKa1_FDP} P_FDP (1 - HFDP)}{c0 {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 pKa1_G3P = 6.22 + IcorrpKa (2^{2} + 1^{2} - (1^{2})) 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}} 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}} 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}} 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}} 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}} 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}} 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 pKa1_LAC = 3.67 + IcorrpKa (1^{2} + 1^{2} - (0^{2})) 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}} 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) slopeint_1 = 1000 2.04742110212706 slopeint_2 = 1000 0.013838383371953 Kref_CKT = ⅇ^{\frac{slopeint_1}{T} + slopeint_2} I25 = 0.25 alphadebye1 = (1.10708 - (1.54508 e -3 T)) + 5.95584 e -6 T^{2} IcorrneglnKrefCK = alphadebye1 (\frac{\sqrt{I25}}{1 + 1.6 \sqrt{I25}} - (\frac{\sqrt{I}}{1 + 1.6 \sqrt{I}})) neglnKrefCK_Iexp = (- (\ln Kref_CKT)) + IcorrneglnKrefCK (4^{2} + 0^{2} - (2^{2}) - (3^{2}) - (1^{2})) Kref_CK = ⅇ^{- neglnKrefCK_Iexp} deltaGpo_CK = (- R) T \ln Kref_CK 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{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}} 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_A

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 M = \frac{{(\frac{AMP}{Kgp_amp})}^{nH}}{1 + {(\frac{AMP}{Kgp_amp})}^{nH}} 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

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

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

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

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 1} 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

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

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

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 1}{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

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

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

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

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

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: creatine_kinase

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

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: ATPase

ATPase = kut ATP

Component: OXPHOS

oxphos = \frac{VmaxOxPhos {(\frac{ADP}{Kmadp})}^{nnHH}}{1 + {(\frac{ADP}{Kmadp})}^{nnHH}}

Component: lactate_transport

Kh = 10^{- pKmct1} v_MCT = \frac{Vmax_MCT (\frac{LAC 10^{- pH_cy}}{Kh Klac1} - (\frac{LAC_ec 10^{- pH_ec}}{Kh Klac1}))}{\frac{LAC 10^{- pH_cy}}{Kh Klac1} + 2 + \frac{10^{- pH_cy}}{Kh} + \frac{LAC}{Klac1} + \frac{LAC_ec}{Klac1} + \frac{10^{- pH_ec}}{Kh} + \frac{LAC_ec 10^{- pH_ec}}{Klac1 Kh}}

Component: CO2_generation_transport

RQ = 1 PO2ratio = 4.2 fluxO2 = \frac{oxphos}{PO2ratio} fluxCO2 = RQ fluxO2

Component: Passive_permeation_flux

v_psCO2 = PSVCO2 (CO2_cy - CO2_ec) v_hydrCO2cy = X_CA (kf_hydrCO2 CO2_cy - (kb_hydrCO2 10^{- pH_cy} HCO3_cy)) v_hydrCO2ec = 1 (kf_hydrCO2 CO2_ec - (kb_hydrCO2 10^{- pH_ec} HCO3_ec))

Component: buffer_capacity

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)

Component: proton_flux

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 protons_consumed = (CKprtflux + glycprtflux + deltaH_ATPase ATPase + (- deltaH_ATPase) oxphos + deltaH_ADK ADK - v_hydrCO2cy) + v_MCT pHODEterm1 = \frac{protons_consumed}{bufcapfixed + bufcapmetab}

Component: differential_equations

\frac{d}{d time} (PCr) = dPCrdt \frac{d}{d time} (Cr) = dCrdt \frac{d}{d time} (NAD) = dNADdt \frac{d}{d time} (NADH) = dNADHdt \frac{d}{d time} (ATP) = dATPdt \frac{d}{d time} (ADP) = dADPdt \frac{d}{d time} (AMP) = dAMPdt \frac{d}{d time} (Pi) = dPidt \frac{d}{d time} (Gly) = dglydt \frac{d}{d time} (G1P) = dG1Pdt \frac{d}{d time} (G6P) = dG6Pdt \frac{d}{d time} (F6P) = dF6Pdt \frac{d}{d time} (FBP) = dFBPdt \frac{d}{d time} (DHAP) = dDHAPdt \frac{d}{d time} (G3P) = dG3Pdt \frac{d}{d time} (GAP) = dGAPdt \frac{d}{d time} (BPG) = dBPGdt \frac{d}{d time} (P3G) = dP3Gdt \frac{d}{d time} (P2G) = dP2Gdt \frac{d}{d time} (PEP) = dPEPdt \frac{d}{d time} (PYR) = dPYRdt \frac{d}{d time} (LAC) = dLACdt \frac{d}{d time} (mg) = dmgdt \frac{d}{d time} (pH_calc) = dpH_calcdt \frac{d}{d time} (LAC_ec) = dLACecdt \frac{d}{d time} (HCO3_cy) = dHCO3cydt \frac{d}{d time} (CO2_cy) = dCO2cydt \frac{d}{d time} (HCO3_ec) = dHCO3ecdt \frac{d}{d time} (CO2_ec) = dCO2ecdt \frac{d}{d time} (MOPS) = dMOPSdt \frac{d}{d time} (MOPSH) = dMOPSHdt \frac{d}{d time} (pH_ec) = dpHecdt dPCrdt = clamp CK dCrdt = clamp (- CK) dNADdt = clamp ((- v_GAPDH - v_G3PDH) + v_LDH) dNADHdt = clamp (v_GAPDH + v_G3PDH - v_LDH) dATPdt = clamp (((- CK - ADK - v_PFK) + v_PGK + v_PK - ATPase) + oxphos) dADPdt = clamp ((CK + 2 ADK + v_PFK - v_PGK - v_PK) + ATPase - oxphos) dAMPdt = clamp (- ADK) dPidt = clamp ((- (flux_GPa + flux_GPb) - v_GAPDH) + ATPase - oxphos) dglydt = clamp (- (flux_GPa + flux_GPb)) dG1Pdt = clamp (flux_GPa + flux_GPb - v_PGLM) dG6Pdt = clamp (v_PGLM - v_PGI) dF6Pdt = clamp (v_PGI - v_PFK) dFBPdt = clamp (v_PFK - v_ALD) dDHAPdt = clamp (v_ALD + v_TPI + v_G3PDH) dG3Pdt = clamp (- v_G3PDH) dGAPdt = clamp (v_ALD - v_TPI - v_GAPDH) dBPGdt = clamp (v_GAPDH - v_PGK) dP3Gdt = clamp (v_PGK - v_PGM) dP2Gdt = clamp (v_PGM - v_ENOL) dPEPdt = clamp (v_ENOL - v_PK) dPYRdt = clamp (v_PK - v_LDH) dLACdt = clamp (v_LDH - v_MCT) dmgdt = clamp 0 dpH_calcdt = clamp pHODEterm1 dLACecdt = clamp (\frac{V_cell v_MCT}{V_ec} - (\frac{Flow LAC_ec}{V_ec})) dHCO3cydt = clamp v_hydrCO2cy dCO2cydt = clamp (fluxCO2 - v_hydrCO2cy - v_psCO2) dHCO3ecdt = clamp (\frac{Flow (HCO3_in - HCO3_ec)}{V_ec} + v_hydrCO2ec) dCO2ecdt = clamp (\frac{Flow (CO2_in - CO2_ec)}{V_ec} + \frac{v_psCO2 V_cell}{V_ec} - v_hydrCO2ec) MOPS_in = \frac{MOPSt}{2} MOPSH_in = \frac{MOPSt}{2} v_MOPSbuff = 1 e 7 (10^{- 7.184} MOPS - (MOPSH 10^{- pH_ec})) dMOPSdt = clamp (\frac{Flow (MOPS_in - MOPS)}{V_ec} - v_MOPSbuff) dMOPSHdt = clamp (\frac{Flow (MOPSH_in - MOPSH)}{V_ec} + v_MOPSbuff) dpHecdt = \frac{clamp (\frac{Flow (10^{- pH_in} - (10^{- pH_ec}))}{V_ec} + \frac{v_hydrCO2ec}{1} + \frac{v_MOPSbuff}{1} + \frac{V_cell v_MCT}{V_ec 1})}{(- (\ln 10)) 10^{- pH_ec}}