Model Mathematics

\frac{d}{d time} (V) = \frac{i_VCa + i_Ca_pump + i_NaCa + i_CRAN + i_Na + i_NaK + i_KDr + i_KCa + i_KATP}{- Cm}

i_VCa = gm_VCa p_VCa (V - V_Ca) V_Ca = \frac{R T}{2.0 F} \ln (\frac{Cao}{Cai})

p_VCa = \frac{1.0}{1.0 + ⅇ^{\frac{V_Cah - V}{K_Cah}}}

i_Ca_pump = Pm_Cap \frac{{Cai}^{2.0}}{{K_Cap}^{2.0} + {Cai}^{2.0}}

i_NaCa = g_NaCa \frac{{Cai}^{5.0}}{{Cai}^{5.0} + {K_NaCa}^{5.0}} (V - V_NaCa) V_NaCa = \frac{R T}{F} (3.0 \ln (\frac{Nao}{Nai}) - (\ln (\frac{Cao}{Cai})))

i_CRAN = f_CRAN P_CRAN (V - V_Na) f_CRAN = \frac{- gm_CRAN}{1.0 + ⅇ^{\frac{CaER - K_Car}{3.0}}} P_CRAN = V - V_CRAN

i_Na = gm_Na p_Na (V - V_Na) V_Na = \frac{R T}{F} \ln (\frac{Nao}{Nai})

p_Na = \frac{1.0}{1.0 + ⅇ^{\frac{104.0 + V}{8.0}}}

i_NaK = P_NaK \frac{F1 f2 f3 F4 F5 f6 - (b1 B2 B3 B4 b5 B6)}{D} D = f2 f3 F4 F5 f6 + b1 f3 F4 F5 f6 + b1 B2 F4 F5 f6 + b1 B2 B3 F5 f6 + b1 B2 B3 B4 f6 + b1 B2 B3 B4 b5 F1 = f1 {Nai}^{3.0} F4 = f4 {Ko}^{2.0} F5 = f5 ATPi f5 = f5_ⅇ^{\frac{V F}{2.0 R T}} B2 = b2 ATPi B3 = b3 {Nai}^{3.0} B4 = b4 P B6 = b6 {K_supi}^{2.0} b5 = b5_ⅇ^{\frac{- (V F)}{2.0 R T}}

i_KDr = gm_KDr n (V - V_K) V_K = \frac{R T}{F} \ln (\frac{Ko}{Ki})

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{Vn - V}{Sn}}} tau_n = \frac{c}{ⅇ^{\frac{V - Vtau}{a}} + ⅇ^{\frac{Vtau - V}{b}}}

i_KCa = gm_KCa fCa (V - V_K)

fCa = \frac{{Cai}^{4.0}}{{Cai}^{4.0} + {K_KCa}^{4.0}}

i_KATP = gm_KATP O_KATP (V - V_K) O_KATP = \frac{0.08 (1.0 + \frac{0.33 ADPi}{Kdd}) + 0.89 {(0.165 + \frac{ADPi}{Kdd})}^{2.0}}{{(0.165 + \frac{ADPi}{Kdd})}^{2.0} (1.0 + \frac{0.135 ADPi}{Ktd} + \frac{0.05 ATPi}{Ktt})}

Jer_p = P_CaER \frac{{Cai}^{2.0}}{{Cai}^{2.0} + {K_Carp}^{2.0}}

\frac{d}{d time} (IP3i) = kIP \frac{{Cai}^{2.0}}{{Cai}^{2.0} + {K_IPCa}^{2.0}} - (kdIP IP3i)

J_out = (P_leak + P_IP3 O_infinity) (CaER - Cai) O_infinity = \frac{Cai}{Cai + K_RCa} \frac{{IP3i}^{3.0}}{{IP3i}^{3.0} + {K_IP3}^{3.0}}

\frac{d}{d time} (Cai) = fi ((\frac{(- i_VCa) + i_NaCa 2.0 - (i_Ca_pump 2.0)}{2.0 F Vi} - Jer_p) + \frac{J_out}{Vi}) - (ksg Cai) \frac{d}{d time} (CaER) = \frac{fer}{Ver} (Jer_p Vi - J_out) \frac{d}{d time} (Nai) = \frac{- (3.0 i_NaCa + 3.0 i_NaK + i_Na + i_CRAN)}{Vi F}

\frac{d}{d time} (ATPi) = k_ADP ADPi - (\frac{i_NaK + i_CRAN}{Vi F} + \frac{Jer_p}{2.0} + (k_ATP_Ca Cai + k_ATP) ATPi) ADPi = Ao - ATPi