Model Mathematics

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Component: Environment

Component: fixed_parameters

H_c = 1 10^{- pH_C} k_dHPI = 1 10^{- 6.75} k_dHatp = 1 10^{- 6.48} k_dHadp = 1 10^{- 6.29} W_m = 0.664 1.09 W_x = 0.9 W_m W_i = 0.1 W_m W_c = 0.807 1.044 H_i = H_c K_i = K_c Rm_cyto = \frac{V_mito}{V_cyto} Rm_cell = V_mito Rc_cell = V_cyto dG_H = F deltaPsi + RT \ln (\frac{H_i}{H_x}) dG_C1op = dG_C1o - (1 RT \ln (\frac{H_x}{1 e -7})) dG_C3op = dG_C3o + 2 RT \ln (\frac{H_x}{1 e -7}) dG_C4op = dG_C4o - (2 RT \ln (\frac{H_x}{1 e -7}))

Component: adjustable_parameters

Component: dNAD_x_dt

NAD_x = NAD_tot - NADH_x

Component: dQH2_x_dt

QH2_x = Q_tot - Q_x

Component: dCred_x_dt

Cred_x = C_tot - Cox_x

Component: dATP_fx_dt

ATP_fx = ATP_x - ATP_mx

Component: dADP_fx_dt

ADP_fx = ADP_x - ADP_mx

Component: dH_x_dt

H_x = 1 10^{- pH_x} \frac{d}{d time} (pH_x) = \frac{\frac{- 1}{2.303} x_buff (((J_DH - (5 J_C1) - (2 J_C3) - (4 J_C4)) + (n_A - 1) J_F1 + 2 J_PI1 - J_KH) + J_Hle)}{W_x}

Component: dK_x_dt

\frac{d}{d time} (K_x) = \frac{J_KH + J_K}{W_x}

Component: dMg_x_dt

\frac{d}{d time} (Mg_x) = \frac{- J_MgADP_x - J_MgATP_x}{W_x}

Component: dNADH_x_dt

\frac{d}{d time} (NADH_x) = \frac{J_DH - J_C1}{W_x}

Component: dQ_x_dt

\frac{d}{d time} (Q_x) = \frac{- (J_C1 - J_C3)}{W_x}

Component: dCox_x_dt

\frac{d}{d time} (Cox_x) = \frac{- (2 J_C3 - (2 J_C4))}{W_x}

Component: dATP_x_dt

\frac{d}{d time} (ATP_x) = \frac{J_F1 - J_ANT}{W_x}

Component: dADP_x_dt

\frac{d}{d time} (ADP_x) = \frac{(- J_F1) + J_ANT}{W_x}

Component: dATP_mx_dt

\frac{d}{d time} (ATP_mx) = \frac{J_MgATP_x}{W_x}

Component: dADP_mx_dt

\frac{d}{d time} (ADP_mx) = \frac{J_MgADP_x}{W_x}

Component: dPI_x_dt

\frac{d}{d time} (PI_x) = \frac{(- J_F1) + J_PI1}{W_x}

Component: dATP_fi_dt

ATP_fi = ATP_i - ATP_mi

Component: dADP_fi_dt

ADP_fi = ADP_i - ADP_mi

Component: dATP_i_dt

\frac{d}{d time} (ATP_i) = \frac{J_ATP + J_ANT + J_AKi}{W_i}

Component: dADP_i_dt

\frac{d}{d time} (ADP_i) = \frac{J_ADP - J_ANT - (2 J_AKi)}{W_i}

Component: dAMP_i_dt

\frac{d}{d time} (AMP_i) = \frac{J_AMP + J_AKi}{W_i}

Component: dATP_mi_dt

\frac{d}{d time} (ATP_mi) = \frac{J_MgATP_i}{W_i}

Component: dADP_mi_dt

\frac{d}{d time} (ADP_mi) = \frac{J_MgADP_i}{W_i}

Component: dPI_i_dt

\frac{d}{d time} (PI_i) = \frac{(- J_PI1) + J_PI2}{W_i}

Component: dMg_i_dt

\frac{d}{d time} (Mg_i) = \frac{- J_MgADP_i - J_MgATP_i}{W_i}

Component: dATP_c_dt

\frac{d}{d time} (ATP_c) = \frac{((- Rm_cyto) J_ATP + J_AKc - (\frac{J_AtC}{Rc_cell})) + J_CKc}{W_c}

Component: dADP_c_dt

\frac{d}{d time} (ADP_c) = \frac{((- Rm_cyto) J_ADP - (2 J_AKc)) + \frac{J_AtC}{Rc_cell} - J_CKc}{W_c}

Component: dAMP_c_dt

\frac{d}{d time} (AMP_c) = \frac{(- Rm_cyto) J_AMP + J_AKc}{W_c}

Component: dATP_mc_dt

\frac{d}{d time} (ATP_mc) = \frac{J_MgATP_c}{W_c}

Component: dADP_mc_dt

\frac{d}{d time} (ADP_mc) = \frac{J_MgADP_c}{W_c}

Component: dPI_c_dt

\frac{d}{d time} (PI_c) = \frac{(- J_PI2) Rm_cyto + \frac{J_AtC}{Rc_cell}}{W_c}

Component: dMg_c_dt

\frac{d}{d time} (Mg_c) = \frac{- J_MgATP_c - J_MgADP_c}{W_c}

Component: dPCr_c_dt

\frac{d}{d time} (PCr_c) = \frac{- J_CKc}{W_c}

Component: dATP_fc_dt

ATP_fc = ATP_c - ATP_mc

Component: dADP_fc_dt

ADP_fc = ADP_c - ADP_mc

Component: dCr_c_dt

Cr_c = CR_tot - PCr_c

Component: ddeltaPsi_dt

\frac{d}{d time} (deltaPsi) = \frac{4 J_C1 + 2 J_C3 + 4 J_C4 - (n_A J_F1) - J_ANT - J_Hle - J_K}{C_IM}

Component: J_DH

J_DH = \frac{X_DH (r NAD_x - NADH_x) (1 + \frac{PI_x}{k_PI1})}{1 + \frac{PI_x}{k_PI2}}

Component: J_C1

J_C1 = X_C1 (ⅇ^{\frac{- (dG_C1op + 4 dG_H)}{RT}} NADH_x Q_x - (NAD_x QH2_x))

Component: J_C3

J_C3 = \frac{X_C3 (1 + \frac{PI_x}{k_PI3})}{1 + \frac{PI_x}{k_PI4}} (ⅇ^{\frac{- (dG_C3op + 4 dG_H - (2 F deltaPsi))}{2 RT}} Cox_x \sqrt{QH2_x} - (Cred_x \sqrt{Q_x}))

Component: J_C4

J_C4 = \{\begin{matrix} 0 if O2_x < 1 e -12 \\ \frac{X_C4 O2_x}{O2_x + k_O2} \frac{Cred_x}{C_tot} (ⅇ^{\frac{- (dG_C4op + 2 dG_H)}{2 RT}} Cred_x {(\frac{O2_x}{1})}^{0.25} - (Cox_x ⅇ^{\frac{F deltaPsi}{RT}})) otherwise \end{matrix}

Component: J_F1

J_F1 = X_F1 (\frac{ⅇ^{\frac{- (dG_F1o - (n_A dG_H))}{RT}} K_DD}{K_DT} ADP_mx PI_x - (ATP_mx 1))

Component: J_ANT

Psi_x = (- 0.65) deltaPsi Psi_i = 0.35 deltaPsi J_ANT = \{\begin{matrix} X_ANT (\frac{ADP_fi}{ADP_fi + ATP_fi ⅇ^{\frac{(- F) Psi_i}{RT}}} - (\frac{ADP_fx}{ADP_fx + ATP_fx ⅇ^{\frac{(- F) Psi_x}{RT}}})) \frac{ADP_fi}{ADP_fi + k_mADP} if ADP_fi > mincon \lor ATP_fi > mincon \\ 0 otherwise \end{matrix}

Component: J_PI1

H2PIi = \frac{PI_i H_i}{H_i + k_dHPI} H2PIx = \frac{PI_x H_x}{H_x + k_dHPI} J_PI1 = \frac{X_PI1 (H_i H2PIi - (H_x H2PIx))}{H2PIi + k_PIH}

Component: J_Hle

J_Hle = \{\begin{matrix} \frac{X_Hle deltaPsi (H_i ⅇ^{\frac{F deltaPsi}{RT}} - H_x)}{ⅇ^{\frac{F deltaPsi}{RT}} - 1} if | deltaPsi | > mincond \\ \frac{X_Hle RT (H_i - H_x)}{F} otherwise \end{matrix}

Component: J_KH

J_KH = X_KH (K_i H_x - (K_x H_i))

Component: J_K

J_K = \{\begin{matrix} \frac{X_K deltaPsi (K_i ⅇ^{\frac{F deltaPsi}{RT}} - K_x)}{ⅇ^{\frac{F deltaPsi}{RT}} - 1} if | deltaPsi | > mincond \\ \frac{X_K RT (K_i - K_x)}{F} otherwise \end{matrix}

Component: J_AMP

J_AMP = gamma X_A (AMP_c - AMP_i)

Component: J_ADP

J_ADP = gamma X_A (ADP_c - ADP_i)

Component: J_ATP

J_ATP = gamma X_A (ATP_c - ATP_i)

Component: J_PI2

J_PI2 = gamma X_PI2 (PI_c - PI_i)

Component: J_MgATP_x

J_MgATP_x = X_MgA (ATP_fx Mg_x - (K_DT ATP_mx))

Component: J_MgADP_x

J_MgADP_x = X_MgA (ADP_fx Mg_x - (K_DD ADP_mx))

Component: J_MgATP_i

J_MgATP_i = X_MgA (ATP_fi Mg_i - (K_DT ATP_mi))

Component: J_MgADP_i

J_MgADP_i = X_MgA (ADP_fi Mg_i - (K_DD ADP_mi))

Component: J_MgATP_c

J_MgATP_c = X_MgA 1 (ATP_fc Mg_c - (K_DT ATP_mc))

Component: J_MgADP_c

J_MgADP_c = X_MgA 1 (ADP_fc Mg_c - (K_DD ADP_mc))

Component: J_AKi

J_AKi = X_AK (K_AK ADP_i ADP_i - (AMP_i ATP_i))

Component: J_AKc

J_AKc = X_AK 1 (K_AK ADP_c ADP_c - (AMP_c ATP_c))

Component: J_AtC

J_AtC = X_AtC

Component: J_CKc

J_CKc = X_CK 1 (K_CK ADP_c PCr_c H_c - (ATP_c Cr_c))