# Model Mathematics

### Component: environment

$ddtimeADP_m=V_ANT-V_ATPase+V_SL$

$ddtimeNADH=-V_O2+V_IDH+V_KGDH+V_MDH$

### 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

$ddtimeCa_m=f⁢1⁢V_uni-V_NaCa$

### Component: Ca_i

$Ca_i=pulse_valueiftime≥stim_start∧time≦stim_end∧time-stim_start-⌊time-stim_startstim_period⌋⁢stim_period≦stim_duration0.1otherwisestim_period=0.5iftime≥100∧time<3004otherwise$

### Component: ATP_m

$ATP_m=Cm-ADP_m$

$ADP_i=pulse_valueiftime≥100∧time<3000.05otherwise$

### Component: AcCoA

$NAD = C_PN - NADH$

### 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: oxidative_phosphorylation

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

### Component: calcium_dynamics

$V_ANT = Vmax_ANT ⁢ 1.0 - 0.05 ⁢ ATP_i ⁢ 0.45 ⁢ 0.8 ⁢ ADP_m 0.45 ⁢ ADP_i ⁢ 0.05 ⁢ ATP_m 1.0 + 0.05 ⁢ ATP_i 0.45 ⁢ ADP_i ⁢ⅇ- h ⁢ F ⁢ delta_psi_0 R ⁢ T ⁢ 1.0 + 0.45 ⁢ 0.8 ⁢ ADP_m 0.05 ⁢ ATP_m V_uni = Vmax_uni ⁢ Ca_i K_trans ⁢ 1.0 + Ca_i K_trans 3.0 ⁢ 2.0 ⁢ F ⁢ delta_psi_m - delta_psi_0 R ⁢ T 1.0 + Ca_i K_trans 4.0 + L 1.0 + Ca_i K_act na ⁢ 1.0 -ⅇ -2.0 ⁢ F ⁢ delta_psi_m - delta_psi_0 R ⁢ T V_NaCa = Vmax_NaCa ⁢ⅇ b ⁢ F ⁢ delta_psi_m - delta_psi_0 R ⁢ T ⁢ⅇln⁡ Ca_i Ca_m 1.0 + KNa Na_i n ⁢ 1.0 + KCa Ca_m$
Source
Derived from workspace Cortassa, Aon, Marban, Winslow, Orourke, 2003 at changeset a126ab075023.
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