Model Mathematics

H_e = 1 10^{- pH_e} W_x = 0.9 W_m W_i = 0.1 W_m H_i = H_e K_i = K_e k_dHPi = 1 10^{- 6.75} k_dHatp = 1 10^{- 6.48} k_dHadp = 1 10^{- 6.29}

dG_H = F dPsi + RT \ln (\frac{H_i}{H_x})

J_DH = \frac{x_DH (r NAD_x - NADH_x) (1 + \frac{Pi_x}{k_Pi1})}{1 + \frac{Pi_x}{k_Pi2}}

dG_C1op = dG_C1o - (RT \ln (\frac{H_x}{1 e -7})) - (RT \ln (\frac{Q}{QH2})) J_C1 = x_C1 (ⅇ^{\frac{- (dG_C1op + 4 dG_H)}{RT}} NADH_x - NAD_x)

dG_C3op = dG_C3o + 2 RT \ln (\frac{H_x}{1 e -7}) - (RT \ln (\frac{QH2}{Q})) 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 dPsi))}{2 RT}} Cox - Cred)

dG_C4op = dG_C4o - (2 RT \ln (\frac{H_x}{1 e -7})) - (\frac{RT}{2} \ln (\frac{O2}{1})) J_C4 = \frac{\frac{x_C4 1}{1 + \frac{k_O2}{O2}} Cred}{Ctot} (ⅇ^{\frac{- (dG_C4op + 2 dG_H)}{2 RT}} Cred - (Cox ⅇ^{\frac{F dPsi}{RT}}))

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))

Psi_x = (- 0.65) dPsi Psi_i = 0.35 dPsi J_ANT = \{\begin{matrix} \frac{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}}})) ADP_fi}{k_mADP + ADP_fi} if ADP_fi > mincond \lor ATP_fi > mincond \\ 0 otherwise \end{matrix}

ATP_fx = ATP_x - ATP_mx J_MgATPx = x_MgA (ATP_fx Mg_x - (K_DT ATP_mx))

ADP_fx = ADP_x - ADP_mx J_MgADPx = x_MgA (ADP_fx Mg_x - (K_DD ADP_mx))

ATP_fi = ATP_i - ATP_mi J_MgATPi = x_MgA (ATP_fi Mg_i - (K_DT ATP_mi))

ADP_fi = ADP_i - ADP_mi J_MgADPi = x_MgA (ADP_fi Mg_i - (K_DD ADP_mi))

J_ATP = gamma p_A (ATP_e - ATP_i)

J_ADP = gamma p_A (ADP_e - ADP_i)

J_AMP = gamma p_A (AMP_e - AMP_i)

J_Pi2 = gamma x_Pi2 (Pi_e - Pi_i)

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_x H2PIi - (H_i H2PIx))}{H2PIi + k_PiH}

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

J_Hle = \frac{x_Hle dPsi (H_i ⅇ^{\frac{F dPsi}{RT}} - H_x)}{ⅇ^{\frac{F dPsi}{RT}} - 1}

J_K = \frac{x_K dPsi (K_i ⅇ^{\frac{F dPsi}{RT}} - K_x)}{ⅇ^{\frac{F dPsi}{RT}} - 1}

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

NAD_x = NADtot - NADH_x

Q = Qtot - QH2

Cox = Ctot - Cred

ADP_fe = ADP_e - ADP_me ADP_me = \frac{K_DD + ADP_e + Mg_tot - (\sqrt{{(K_DD + ADP_e + Mg_tot)}^{2} - (4 Mg_tot ADP_e)})}{2}

Mg_e = Mg_tot - ADP_me Mg_i = Mg_e

\frac{d}{d t} (H_x) = \frac{x_buff H_x ((J_DH - (5 J_C1) - (2 J_C3) - (4 J_C4)) + (n_A - 1) J_F1 + 2 J_Pi1 + J_Hle - J_KH)}{W_x}

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

\frac{d}{d t} (Mg_x) = \frac{- J_MgATPx - J_MgADPx}{W_x}

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

\frac{d}{d t} (QH2) = \frac{J_C1 - J_C3}{W_x}

\frac{d}{d t} (Cred) = \frac{2 J_C3 - (2 J_C4)}{W_i}

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

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

\frac{d}{d t} (ATP_mx) = \frac{J_MgATPx}{W_x}

\frac{d}{d t} (ADP_mx) = \frac{J_MgADPx}{W_x}

\frac{d}{d t} (Pi_x) = \frac{(- J_F1) + J_Pi1}{W_x}

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

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

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

\frac{d}{d t} (ATP_mi) = \frac{J_MgATPi}{W_i}

\frac{d}{d t} (ADP_mi) = \frac{J_MgADPi}{W_i}

\frac{d}{d t} (Pi_i) = \frac{(- J_Pi1) + J_Pi2}{W_i}

\frac{d}{d t} (dPsi) = \frac{4 J_C1 + 2 J_C3 + 4 J_C4 - (n_A J_F1) - J_ANT - J_Hle - J_K}{C_im}

\frac{d}{d t} (O2) = 0