Model Mathematics

\frac{d}{d time} (V) = \frac{-1.0}{C} (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)

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})}

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}})

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}) ADP_m_free = 0.8 ADP_m

J_ant = Jmax_ant \frac{1.0 - (\frac{ATP_i ADP_m}{ADP_i ATP_m} ⅇ^{\frac{(- F) V}{R T}})}{(1.0 + \frac{ATP_i}{ADP_i} ⅇ^{\frac{(- f) F V}{R T}}) (1.0 + \frac{ADP_m}{ATP_m})}

f_PDHa = \frac{1.0}{1.0 + u2 (1.0 + u1 {(1.0 + \frac{Ca_m}{K_Ca})}^{-2.0})} J_red = J_red_basal + 7.36 f_PDHa J_gly_tot

J_ptca = \frac{J_red_basal}{3.0} + 0.84 f_PDHa J_gly_tot

J_gly_tot = \frac{beta_max (1.0 + beta_1 Glc) Glc ATP_i}{1.0 + beta_3 ATP_i + 1.0 + beta_4 ATP_i} (beta_5 Glc + 1.0 + beta_6 ATP_i + beta_7 {Glc}^{2.0})

J_hyd = k_hyd ATP_i + J_hyd_ss J_hyd_ss = \frac{Jmax_hyd}{1.0 + {(\frac{K_Glc}{Glc})}^{n_hyd}}

J_erout = (Jmax_IP3 {(\frac{IP3}{IP3 + d_IP3})}^{3.0} {(\frac{Ca_i}{Ca_i + d_ACT})}^{3.0} h^{3.0} + JH_leak) (Ca_ER - Ca_i)

J_serca = Jmax_serca \frac{{Ca_i}^{2.0}}{{k_serca}^{2.0} + {Ca_i}^{2.0}}

\frac{d}{d time} (NADH_m) = \frac{M (J_red - Jo)}{Vm} total_NAD_m = NADH_m + NAD_m NAD_m = total_NAD_m - NADH_m \frac{d}{d time} (ADP_m) = \frac{M (J_ant - (J_ptca + Jp_F1))}{Vm} total_mitochondrial_adenosine_phosphate = ATP_m + ADP_m ATP_m = total_mitochondrial_adenosine_phosphate - ADP_m \frac{d}{d time} (ADP_i) = \frac{(- M) J_ant + C (J_hyd - J_gly_tot)}{Vc} ATP_i = 2.0 - ADP_i \frac{d}{d time} (Ca_m) = \frac{fm M (J_uni - J_Na_Ca)}{Vm} \frac{d}{d time} (Ca_ER) = \frac{fe E (J_serca - J_erout)}{Ve} \frac{d}{d time} (Ca_i) = \frac{fc (M (J_Na_Ca - J_uni) - (E (J_serca - J_erout)))}{Vc} \frac{d}{d time} (h) = \frac{d_INH - ((Ca_i + d_INH) h)}{tau}