Model Mathematics

\frac{d}{d time} (V) = \frac{-1.0}{Cmito} (JH_F1 + J_ant + JH_leak + J_uni 2.0 - JH_res) delta_pH = pH_i - pH_m proton_motive_force = V - (\frac{2.303 R T}{F} delta_pH)

JH_res = 360.0 rho_res \frac{ra {10.0}^{6.0 delta_pH} ⅇ^{\frac{F A_res}{R T}} + rb {10.0}^{6.0 delta_pH} - ((ra + rb) ⅇ^{\frac{g 6.0 F V}{R T}})}{(1.0 + r1 ⅇ^{\frac{F A_res}{R T}}) ⅇ^{\frac{6.0 F V_B}{R T}} + (r2 + r3 ⅇ^{\frac{F A_res}{R T}}) ⅇ^{\frac{g 6.0 F V}{R T}}} Jo = 30.0 rho_res \frac{((ra {10.0}^{6.0 delta_pH} + rc1 ⅇ^{\frac{6.0 F V_B}{R T}}) ⅇ^{\frac{F A_res}{R T}} - (ra ⅇ^{\frac{g 6.0 F V}{R T}})) + rc2 ⅇ^{\frac{F A_res}{R T}} ⅇ^{\frac{g 6.0 F V}{R T}}}{(1.0 + r1 ⅇ^{\frac{F A_res}{R T}}) ⅇ^{\frac{6.0 F V_B}{R T}} + (r2 + r3 ⅇ^{\frac{F A_res}{R T}}) ⅇ^{\frac{g 6.0 F V}{R T}}} A_res = \frac{R T}{F} \ln (\frac{K_res \sqrt{NADH_m}}{\sqrt{NAD_m}}) total_NAD_m = NADH_m + NAD_m

JH_leak = g_H proton_motive_force

JH_F1 = (-180.0) rho_F1 \frac{pa {10.0}^{3.0 delta_pH} ⅇ^{\frac{F A_F1}{R T}} + pb {10.0}^{3.0 delta_pH} - ((pa + pb) ⅇ^{\frac{3.0 F V}{R T}})}{(1.0 + p1 ⅇ^{\frac{F A_F1}{R T}}) ⅇ^{\frac{3.0 F V_B}{R T}} + (p2 + p3 ⅇ^{\frac{F A_F1}{R T}}) ⅇ^{\frac{3.0 F V}{R T}}} Jp_F1 = (-60.0) rho_F1 \frac{((pa {10.0}^{3.0 delta_pH} + pc1 ⅇ^{\frac{3.0 F V_B}{R T}}) ⅇ^{\frac{F A_F1}{R T}} - (pa ⅇ^{\frac{3.0 F V}{R T}})) + pc2 ⅇ^{\frac{F A_F1}{R T}} ⅇ^{\frac{3.0 F V}{R T}}}{(1.0 + p1 ⅇ^{\frac{F A_F1}{R T}}) ⅇ^{\frac{3.0 F V_B}{R T}} + (p2 + p3 ⅇ^{\frac{F A_F1}{R T}}) ⅇ^{\frac{3.0 F V}{R T}}} A_F1 = \frac{R T}{F} \ln (\frac{K_F1 ATP_m}{ADP_m_free Pi_m}) total_mitochondrial_adenosine_phosphate = ATP_m + ADP_m ADP_m_free = 0.8 ADP_m

J_ant = Jmax_ant \frac{1.0 - (\frac{ATP4_i ADP3_m}{ADP3_i ATP4_m} ⅇ^{\frac{(- F) V}{R T}})}{(1.0 + \frac{ATP4_i}{ADP3_i} ⅇ^{\frac{(- f) F V}{R T}}) (1.0 + \frac{ADP3_m}{ATP4_m})} \frac{d}{d time} (ADP_m) = J_ant - Jp_F1 ADP3_m = 0.45 0.8 ADP_m ADP3_i = 0.45 1.0 ADP_i ATP4_m = 0.05 ATP_m ATP4_i = 0.05 ATP_i

J_uni = Jmax_uni \frac{\frac{Ca_i}{K_trans} {(1.0 + \frac{Ca_i}{K_trans})}^{3.0}}{{(1.0 + \frac{Ca_i}{K_trans})}^{4.0} + \frac{L}{{(1.0 + \frac{Ca_i}{K_act})}^{na}}} \frac{\frac{2.0 F (V - V_offset)}{R T}}{1.0 - (ⅇ^{\frac{(-2.0) F (V - V_offset)}{R T}})}

J_Na_Ca = Jmax_Na_Ca \frac{ⅇ^{\frac{b F (V - V_offset)}{R T}}}{{(1.0 + \frac{K_Na}{Na_i})}^{n} (1.0 + \frac{K_Ca}{Ca_m})} \frac{d}{d time} (Ca_m) = fm (J_uni - J_Na_Ca)