Model Mathematics

Component: environment

Component: ADP_m

ddtimeADP_m=V_ANT-V_ATPase+V_SL

Component: NADH

ddtimeNADH=-V_O2+V_IDH+V_KGDH+V_MDH

Component: ISOC

ddtimeISOC=V_ACO-V_IDH

Component: alpha_KG

ddtimealpha_KG=V_AAT+V_IDH+-V_KGDH

Component: SCoA

ddtimeSCoA=V_KGDH-V_SL

Component: Suc

ddtimeSuc=V_SL-V_SDH

Component: FUM

ddtimeFUM=V_SDH-V_FH

Component: MAL

ddtimeMAL=V_FH-V_MDH

Component: OAA

ddtimeOAA=V_MDH-V_CS+V_AAT

Component: ASP

ddtimeASP=V_AAT-V_C_ASP

Component: Ca_m

ddtimeCa_m=f1V_uni-V_NaCa

Component: Ca_i

Ca_i=pulse_valueiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0.1otherwise stim_period=0.5iftime100time<3004otherwise

Component: Na_i

Component: ATP_i

Component: ATP_m

ATP_m=Cm-ADP_m

Component: ADP_i

ADP_i=pulse_valueiftime100time<3000.05otherwise

Component: GLU

Component: Mg

Component: H

Component: Pi

Component: CoA

Component: AcCoA

Component: FAD

Component: FADH2

Component: NAD

NAD = C_PN - NADH

Component: NADPH

Component: O2_m

dd time O2_m = shunt V_O2 - VTr_ROS

Component: O2_i

dd time O2_i = VTr_ROS - V_SOD

Component: H2O2

dd time H2O2 = V_SOD - V_CAT + V_GPX

Component: GSH

dd time GSH = V_GR - V_GPX

Component: GSSG

GSSG = 2.0 GT - GSH

Component: CIT

CIT = C_Kint - ISOC + alpha_KG + SCoA + Suc + FUM + MAL + OAA

Component: mitochondrial_membrane

dd time delta_psi_m = V_He + V_He_F +- V_Hu + V_ANT + V_Hleak + V_NaCa + 2.0 V_uni C_mito

Component: V_CS

V_CS = Kcat_CS ET_CS 1.0 + Km_AcCoA AcCoA + Km_OAA OAA + Km_AcCoA AcCoA Km_OAA OAA

Component: V_ACO

V_ACO = Kf_ACO CIT - ISOC KE_ACO

Component: V_IDH

V_IDH = Kcat_IDH ET_IDH 1.0 + H Kh_1 + Kh_2 H + Km_ISOC ISOC ni 1.0 + ADP_m Ka_ADP 1.0 + Ca_m Ka_Ca + Km_NAD NAD 1.0 + NADH Ki_NADH + Km_ISOC ISOC ni Km_NAD NAD 1.0 + NADH Ki_NADH 1.0 + ADP_m Ka_ADP 1.0 + Ca_m Ka_Ca

Component: V_KGDH

V_KGDH = Kcat_KGDH ET_KGDH 1.0 + Km_alpha_KG alpha_KG n_alpha_KG 1.0 + Mg Kd_Mg 1.0 + Ca_m Kd_Ca + Km_NAD NAD 1.0 + Mg Kd_Mg 1.0 + Ca_m Kd_Ca

Component: V_SL

V_SL = kf_SL SCoA ADP_m - Suc ATP_m CoA Ke_SL

Component: V_SDH

V_SDH = Kcat_SDH ET_SDH 1.0 + Km_Suc Suc 1.0 + OAA Kisdh_OAA 1.0 + FUM Ki_FUM

Component: V_MDH

V_MDH = Kcat_MDH ET_MDH fh_a fh_i 1.0 + Km_MAL MAL 1.0 + OAA Ki_OAA + Km_NAD NAD + Km_MAL MAL 1.0 + OAA Ki_OAA Km_NAD NAD fh_a = 1.0 1.0 + H kh1 + H 2.0 kh1 kh2 + k_offset fh_i = 1.0 1.0 + kh3 H + kh3 kh4 H 2.0 2.0

Component: V_FH

V_FH = kf_FH FUM - MAL Ke_FH

Component: V_AAT

V_AAT = kf_AAT OAA GLU - alpha_KG ASP Ke_AAT

Component: V_C_ASP

V_C_ASP = k_C_ASP ASP

Component: V_SOD

V_SOD = 2.0 k1_SOD k5_SOD k1_SOD + k3_SOD 1.0 + H2O2 Ki_H2O2 ET_SOD O2_i k5_SOD 2.0 k1_SOD + k3_SOD 1.0 + H2O2 Ki_H2O2 + O2_i k1_SOD k3_SOD 1.0 + H2O2 Ki_H2O2

Component: V_CAT

V_CAT = 2.0 k1_CAT ET_CAT H2O2 - fr H2O2

Component: V_GPX

V_GPX = ET_GPX H2O2 GSH phi1_GPX GSH + phi2_GPX H2O2

Component: V_GR

V_GR = k1_GR ET_GR 1.0 + KM_GSSG GSSG + KM_NADPH NADPH + KM_GSSG GSSG KM_NADPH NADPH

Component: V_IMAC

V_IMAC = a + b 1.0 + Kcc O2_i GL + Gmax 1.0 + kappa delta_psi_bm - delta_psi_m delta_psi_m

Component: VTr_ROS

VTr_ROS = j V_IMAC delta_psi_m delta_psi_m - R T F log10 O2_m O2_i

Component: oxidative_phosphorylation

V_O2 = 0.5 rho_res ra + rc1 6.0 F delta_psi_B R T Ares F R T - ra g 6.0 F delta_mu_H R T + rc2 Ares F R T g 6.0 F delta_mu_H R T 1.0 + r1 F Ares R T 6.0 F delta_psi_B R T + r2 + r3 F Ares R T g 6.0 F delta_mu_H R T V_He = 6.0 rho_res ra F Ares R T - ra + rb g 6.0 F delta_mu_H R T 1.0 + r1 F Ares R T 6.0 F delta_psi_B R T + r2 + r3 F Ares R T g 6.0 F delta_mu_H R T Ares = R T F ln Kres NADH NAD 0.5 V_He_F = 6.0 rho_res_F ra F Ares_F R T - ra + rb g 6.0 F delta_mu_H R T 1.0 + r1 F Ares_F R T 6.0 F delta_psi_B R T + r2 + r3 F Ares_F R T g 6.0 F delta_mu_H R T Ares_F = R T F ln Kres_F FADH2 FAD 0.5 V_Hleak = gH delta_mu_H delta_mu_H = R T F delta_pH + delta_psi_m V_ATPase =- rho_F1 100.0 pa + pc1 3.0 F delta_psi_B R T AF1 F R T - pa 3.0 F delta_mu_H R T + pc2 AF1 F R T 3.0 F delta_mu_H R T 1.0 + p1 F AF1 R T 3.0 F delta_psi_B R T + p2 + p3 F AF1 R T 3.0 F delta_mu_H R T V_Hu = -3.0 rho_F1 100.0 pa 1.0 + F AF1 R T - pa + pb 3.0 F delta_mu_H R T 1.0 + p1 F AF1 R T 3.0 F delta_psi_B R T + p2 + p3 F AF1 R T 3.0 F delta_mu_H R T AF1 = R T F ln KF1 ATP_m ADP_m Pi

Component: calcium_dynamics

V_ANT = Vmax_ANT 1.0 - 0.05 ATP_i 0.45 0.8 ADP_m 0.45 ADP_i 0.05 ATP_m 1.0 + 0.05 ATP_i 0.45 ADP_i - h F delta_psi_0 R T 1.0 + 0.45 0.8 ADP_m 0.05 ATP_m V_uni = Vmax_uni Ca_i K_trans 1.0 + Ca_i K_trans 3.0 2.0 F delta_psi_m - delta_psi_0 R T 1.0 + Ca_i K_trans 4.0 + L 1.0 + Ca_i K_act na 1.0 - -2.0 F delta_psi_m - delta_psi_0 R T V_NaCa = Vmax_NaCa b F delta_psi_m - delta_psi_0 R T ln Ca_i Ca_m 1.0 + KNa Na_i n 1.0 + KCa Ca_m