Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_K_dr + i_K_ATP + i_Ca_f + i_Ca_s + i_NS)}{C}

i_K_dr = g_K_dr n I (V - V_K)

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{-20.0 - V}{5.3}}} tau_n = \frac{50.0}{ⅇ^{\frac{V + 75.0}{65.0}} + ⅇ^{\frac{- (V + 75.0)}{20.0}}}

\frac{d}{d time} (I) = - (\frac{I - I_infinity}{tau_I}) I_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{36.0 + V}{4.5}}}

i_K_ATP = g_K_ATP O_K_ATP (V - V_K) O_K_ATP = \frac{0.8 (1.0 + \frac{2.0 MgADP_i}{K_dd}) + 0.89 {(\frac{MgADP_i}{K_dd})}^{2.0}}{{(1.0 + \frac{MgADP_i}{K_dd})}^{2.0} (1.0 + \frac{ADP3_i}{K_td} + \frac{ATP4_i}{K_tt})} MgADP_i = 0.55 0.3 ADP_i

i_Ca_f = 0.27 g_Ca O_f \frac{Ca_o V}{1.0 - (ⅇ^{\frac{2.0 F V}{R T}})} O_f = 1.0 - (C + B) k_plus_1 = \frac{O_infinity}{tau_Ca_f} k_minus_1 = \frac{1.0 - O_infinity}{tau_Ca_f} O_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{- (15.0 + V)}{6.2}}} Ca_d = \frac{-3.02}{k_plus_2} \frac{Ca_o V}{1.0 - (ⅇ^{\frac{2.0 F V}{R T}})}

\frac{d}{d time} (C) = k_minus_1 \frac{k_minus_2}{k_plus_2 Ca_d V + k_minus_2} O_f - (k_plus_1 C)

\frac{d}{d time} (B) = k_plus_3 \frac{k_plus_2 Ca_d V}{k_plus_2 Ca_d V + k_minus_2} O_f - (k_minus_3 B)

i_Ca_s = 0.73 g_Ca O_s \frac{Ca_o V}{1.0 - (ⅇ^{\frac{2.0 F V}{R T}})} O_s = \frac{J}{1.0 + ⅇ^{\frac{- (11.0 + V)}{3.6}}}

\frac{d}{d time} (J) = - (\frac{J - J_infinity}{tau_J}) J_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V + 50.0}{6.3}}} tau_J = \frac{TJ}{ⅇ^{\frac{V + 50.0}{6.3}} + ⅇ^{\frac{- (V + 50.0)}{6.3}}} + Tmin

i_NS = \frac{g_NS}{1.0 + \frac{K_NS}{ATP_i}} \frac{Ca_o V}{1.0 - (ⅇ^{\frac{2.0 F V}{R T}})}

\frac{d}{d time} (ADP_i) = gamma1 (J_hyd - (J_ANT + Jp_gly)) ATP_i = 2.0 - ADP_i J_hyd = k_hyd ATP_i + delta_J_hyd Jp_gly = 2.0 delta_J_gly_total \frac{d}{d time} (delta_J_hyd) = \frac{1.0}{tau_hyd} (delta_J_hyd_ss - delta_J_hyd) delta_J_hyd_ss = \frac{delta_J_hyd_max}{1.0 + {(\frac{K_glu}{glu})}^{n_hyd}}

\frac{d}{d time} (Ca_i) = f_i ((- alpha) (i_NS + i_Ca_f + i_Ca_s) - (gamma2 (J_uni - J_NaCa) + k_Ca Ca_i))

\frac{d}{d time} (delta_psi) = \frac{-1.0}{60000.0 Cmito} ((- JH_res) + JH_F1 + J_ANT + JH_leak + J_uni 2.0 + J_NaCa) 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}} + ra {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 delta_psi}{R T}} + (r2 + r3 ⅇ^{\frac{F A_res}{R T}}) ⅇ^{\frac{g 6.0 F V}{R T}}} J_o = 30.0 rho_res \frac{((ra {10.0}^{6.0 delta_pH} + rc1 ⅇ^{\frac{6.0 F delta_psi}{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 delta_psi}{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 delta_psi}{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 delta_psi}{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 delta_psi}{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

\frac{d}{d time} (NADH_m) = \frac{1.0}{60000.0} (J_red - J_o) NAD_m = 8.0 - NADH_m J_red = J_red_basal + delta_J_red_I + 0.66 delta_J_red_II delta_J_red_I = 4.52 f_glu delta_J_gly_total delta_J_red_II = 2.84 f_glu delta_J_gly_total f_glu = f_PDHa f_PDHa = \frac{1.0}{1.0 + u2 (1.0 + u1 {(1.0 + \frac{Ca_m}{K_Ca2})}^{-2.0})} delta_J_gly_total = \frac{beta_max beta2 (1.0 + beta1 glu) glu ATP_i}{1.0 + beta3 ATP_i + (1.0 + beta4 ATP_i) beta5 glu + (1.0 + beta6 ATP_i) beta7 {glu}^{2.0}}

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})} ADP3_m = 0.45 0.8 ADP_m ADP3_i = 0.45 0.3 ADP_i ATP4_m = 0.05 ATP_m ATP4_i = 0.05 ATP_i

\frac{d}{d time} (ADP_m) = \frac{1.0}{60000.0} (J_ANT - (Jp_TCA + Jp_F1)) ATP_m = 12.0 - ADP_m

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 - delta_psi_offset)}{R T}}{1.0 - (ⅇ^{\frac{(-2.0) F (V - delta_psi_offset)}{R T}})}

J_NaCa = Jmax_NaCa \frac{ⅇ^{\frac{b F (V - delta_psi_offset)}{R T}}}{{(1.0 + \frac{K_Na}{Na_i})}^{n} (1.0 + \frac{K_Ca}{Ca_m})}

\frac{d}{d time} (Ca_m) = \frac{fm}{60000.0} (J_uni - J_NaCa)