Model Mathematics

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Component: environment

Component: COMPUTE_CONCENTRATION_AND_VOLTAGE_DERIVATIVES

RT_over_F = \frac{Rgas Temp}{Faraday} C = Acap 1.0 e -3 a1 = \frac{C}{Vmyo Faraday} a2 = \frac{C}{2 VSS Faraday} \frac{d}{d time} (Nai) = (- (INa + INab + 3 (INaCa + INaK) + IKv14_Na)) a1 \frac{d}{d time} (Ki) = (- ((IKr + IKs + IK1 + ICaK + i_Stim - (2 INaK)) + IKv43 + IKv14_K)) a1 \frac{d}{d time} (Cai) = beta_i (Jxfer - Jup - Jtrpn - (((ICab - (2 INaCa)) + IpCa) 0.5 a1)) \frac{d}{d time} (CaSS) = beta_SS (\frac{Jrel VJSR}{VSS} - (\frac{Jxfer Vmyo}{VSS}) - (ICa a2)) \frac{d}{d time} (CaJSR) = beta_JSR (Jtr - Jrel) \frac{d}{d time} (CaNSR) = \frac{Jup Vmyo}{VNSR} - (\frac{Jtr VJSR}{VNSR}) i_tot = INa + ICa + ICaK + IKr + IKs + IK1 + INaCa + INaK + Ito1 + IpCa + ICab + INab + i_Stim \frac{d}{d time} (V) = - i_tot

Component: I_stimulus

past = ⌊ \frac{time}{stim_period} ⌋ stim_period i_Stim = \{\begin{matrix} stim_amplitude if time - past \geq stim_offset \land time - past ≦ stim_offset + stim_duration \\ 0 otherwise \end{matrix}

Component: COMPUTE_INTRACELLULAR_CALCIUM_FLUXES

fb = {(\frac{Cai}{Kfb})}^{Nfb} rb = {(\frac{CaNSR}{Krb})}^{Nrb} Jup = \frac{KSR (vmaxf fb - (vmaxr rb))}{1 + fb + rb} Jrel = v1 (O1_RyR + O2_RyR) (CaJSR - CaSS) Jtr = \frac{CaNSR - CaJSR}{tautr} Jxfer = \frac{CaSS - Cai}{tauxfer}

Component: COMPUTE_Jtrpn_and_BUFFER_SCALE_FACTORS

dLTRPNCa = kltrpn_plus Cai (1 - LTRPNCa) - (kltrpn_minus LTRPNCa) dHTRPNCa = khtrpn_plus Cai (1 - HTRPNCa) - (khtrpn_minus HTRPNCa) \frac{d}{d time} (LTRPNCa) = dLTRPNCa \frac{d}{d time} (HTRPNCa) = dHTRPNCa Jtrpn = LTRPNtot dLTRPNCa + HTRPNtot dHTRPNCa beta_SS = \frac{1}{1 + \frac{CMDNtot KmCMDN}{{(CaSS + KmCMDN)}^{2}} + \frac{EGTAtot KmEGTA}{{(CaSS + KmEGTA)}^{2}}} beta_JSR = \frac{1}{1 + \frac{CSQNtot KmCSQN}{{(CaJSR + KmCSQN)}^{2}}} beta_i = \frac{1}{1 + \frac{CMDNtot KmCMDN}{{(Cai + KmCMDN)}^{2}} + \frac{EGTAtot KmEGTA}{{(Cai + KmEGTA)}^{2}}}

Component: COMPUTE_DERIVATIVES_OF_RyR_RECEPTOR_STATES

dC1_RyR = (- kaplus) {(CaSS 1000)}^{ncoop} C1_RyR + kaminus O1_RyR dO2_RyR = kbplus {(CaSS 1000)}^{mcoop} O1_RyR - (kbminus O2_RyR) dC2_RyR = kcplus O1_RyR - (kcminus C2_RyR) dO1_RyR = - (dC1_RyR + dO2_RyR + dC2_RyR) \frac{d}{d time} (C1_RyR) = dC1_RyR \frac{d}{d time} (O2_RyR) = dO2_RyR \frac{d}{d time} (C2_RyR) = dC2_RyR \frac{d}{d time} (O1_RyR) = dO1_RyR

Component: COMPUTE_DERIVATIVES_OF_LTYPE_CHANNEL_STATES

alpha = 4 1.2 0.416 ⅇ^{0.012 (V - 35)} beta = 4 0.45 0.049 ⅇ^{(- 0.065) (V - 22)} alpha_prime = aL alpha beta_prime = \frac{beta}{bL} gamma = 0.6 0.09233 CaSS omega = 0.25 0.01 C0_to_C1 = 4 alpha C1_to_C2 = 3 alpha C2_to_C3 = 2 alpha C3_to_C4 = alpha CCa0_to_CCa1 = 4 alpha_prime CCa1_to_CCa2 = 3 alpha_prime CCa2_to_CCa3 = 2 alpha_prime CCa3_to_CCa4 = alpha_prime C1_to_C0 = beta C2_to_C1 = 2 beta C3_to_C2 = 3 beta C4_to_C3 = 4 beta CCa1_to_CCa0 = beta_prime CCa2_to_CCa1 = 2 beta_prime CCa3_to_CCa2 = 3 beta_prime CCa4_to_CCa3 = 4 beta_prime C0_to_CCa0 = gamma C1_to_CCa1 = aL C0_to_CCa0 C2_to_CCa2 = aL C1_to_CCa1 C3_to_CCa3 = aL C2_to_CCa2 C4_to_CCa4 = aL C3_to_CCa3 CCa0_to_C0 = omega CCa1_to_C1 = \frac{CCa0_to_C0}{bL} CCa2_to_C2 = \frac{CCa1_to_C1}{bL} CCa3_to_C3 = \frac{CCa2_to_C2}{bL} CCa4_to_C4 = \frac{CCa3_to_C3}{bL} a1_C0 = (C0_to_C1 + C0_to_CCa0) C0 a2_C0 = C1_to_C0 C1 + CCa0_to_C0 CCa0 \frac{d}{d time} (C0) = a2_C0 - a1_C0 a1_C1 = (C1_to_C0 + C1_to_C2 + C1_to_CCa1) C1 a2_C1 = C0_to_C1 C0 + C2_to_C1 C2 + CCa1_to_C1 CCa1 \frac{d}{d time} (C1) = a2_C1 - a1_C1 a1_C2 = (C2_to_C1 + C2_to_C3 + C2_to_CCa2) C2 a2_C2 = C1_to_C2 C1 + C3_to_C2 C3 + CCa2_to_C2 CCa2 \frac{d}{d time} (C2) = a2_C2 - a1_C2 a1_C3 = (C3_to_C2 + C3_to_C4 + C3_to_CCa3) C3 a2_C3 = C2_to_C3 C2 + C4_to_C3 C4 + CCa3_to_C3 CCa3 \frac{d}{d time} (C3) = a2_C3 - a1_C3 a1_C4 = (C4_to_C3 + fL + C4_to_CCa4) C4 a2_C4 = C3_to_C4 C3 + gL Open + CCa4_to_C4 CCa4 \frac{d}{d time} (C4) = a2_C4 - a1_C4 \frac{d}{d time} (Open) = fL C4 - (gL Open) a1_Ca0 = (CCa0_to_CCa1 + CCa0_to_C0) CCa0 a2_Ca0 = CCa1_to_CCa0 CCa1 + C0_to_CCa0 C0 \frac{d}{d time} (CCa0) = a2_Ca0 - a1_Ca0 a1_Ca1 = (CCa1_to_CCa0 + CCa1_to_CCa2 + CCa1_to_C1) CCa1 a2_Ca1 = CCa0_to_CCa1 CCa0 + CCa2_to_CCa1 CCa2 + C1_to_CCa1 C1 \frac{d}{d time} (CCa1) = a2_Ca1 - a1_Ca1 a1_Ca2 = (CCa2_to_CCa1 + CCa2_to_CCa3 + CCa2_to_C2) CCa2 a2_Ca2 = CCa1_to_CCa2 CCa1 + CCa3_to_CCa2 CCa3 + C2_to_CCa2 C2 \frac{d}{d time} (CCa2) = a2_Ca2 - a1_Ca2 a1_Ca3 = (CCa3_to_CCa2 + CCa3_to_CCa4 + CCa3_to_C3) CCa3 a2_Ca3 = CCa2_to_CCa3 CCa2 + CCa4_to_CCa3 CCa4 + C3_to_CCa3 C3 \frac{d}{d time} (CCa3) = a2_Ca3 - a1_Ca3 a1_Ca4 = (CCa4_to_CCa3 + CCa4_to_C4) CCa4 a2_Ca4 = CCa3_to_CCa4 CCa3 + C4_to_CCa4 C4 \frac{d}{d time} (CCa4) = a2_Ca4 - a1_Ca4 a1_Cainf = 0.82 yCa_inf = \frac{a1_Cainf}{1 + ⅇ^{\frac{V + 28.5}{7.8}}} + 1 - a1_Cainf tau_yCa = \frac{1}{\frac{0.00653}{0.5 + ⅇ^{\frac{V}{- 7.1}}} + 0.00512 ⅇ^{\frac{V}{- 39.8}}} \frac{d}{d time} (yCa) = \frac{yCa_inf - yCa}{tau_yCa}

Component: COMPUTE_DERIVATIVES_OF_Kv4_3_CHANNEL_STATES

alpha_act43 = alphaa0Kv43 ⅇ^{aaKv43 V} beta_act43 = betaa0Kv43 ⅇ^{(- baKv43) V} alpha_inact43 = alphai0Kv43 ⅇ^{(- aiKv43) V} beta_inact43 = betai0Kv43 ⅇ^{biKv43 V} C0Kv43_to_C1Kv43 = 4 alpha_act43 C1Kv43_to_C2Kv43 = 3 alpha_act43 C2Kv43_to_C3Kv43 = 2 alpha_act43 C3Kv43_to_OKv43 = alpha_act43 CI0Kv43_to_CI1Kv43 = 4 b1Kv43 alpha_act43 CI1Kv43_to_CI2Kv43 = \frac{3 b2Kv43 alpha_act43}{b1Kv43} CI2Kv43_to_CI3Kv43 = \frac{2 b3Kv43 alpha_act43}{b2Kv43} CI3Kv43_to_OIKv43 = \frac{b4Kv43 alpha_act43}{b3Kv43} C1Kv43_to_C0Kv43 = beta_act43 C2Kv43_to_C1Kv43 = 2 beta_act43 C3Kv43_to_C2Kv43 = 3 beta_act43 OKv43_to_C3Kv43 = 4 beta_act43 CI1Kv43_to_CI0Kv43 = \frac{beta_act43}{f1Kv43} CI2Kv43_to_CI1Kv43 = \frac{2 f1Kv43 beta_act43}{f2Kv43} CI3Kv43_to_CI2Kv43 = \frac{3 f2Kv43 beta_act43}{f3Kv43} OIKv43_to_CI3Kv43 = \frac{4 f3Kv43 beta_act43}{f4Kv43} C0Kv43_to_CI0Kv43 = beta_inact43 C1Kv43_to_CI1Kv43 = f1Kv43 beta_inact43 C2Kv43_to_CI2Kv43 = f2Kv43 beta_inact43 C3Kv43_to_CI3Kv43 = f3Kv43 beta_inact43 OKv43_to_OIKv43 = f4Kv43 beta_inact43 CI0Kv43_to_C0Kv43 = alpha_inact43 CI1Kv43_to_C1Kv43 = \frac{alpha_inact43}{b1Kv43} CI2Kv43_to_C2Kv43 = \frac{alpha_inact43}{b2Kv43} CI3Kv43_to_C3Kv43 = \frac{alpha_inact43}{b3Kv43} OIKv43_to_OKv43 = \frac{alpha_inact43}{b4Kv43} a1_C043 = (C0Kv43_to_C1Kv43 + C0Kv43_to_CI0Kv43) C0Kv43 a2_C043 = C1Kv43_to_C0Kv43 C1Kv43 + CI0Kv43_to_C0Kv43 CI0Kv43 \frac{d}{d time} (C0Kv43) = a2_C043 - a1_C043 a1_C143 = (C1Kv43_to_C2Kv43 + C1Kv43_to_C0Kv43 + C1Kv43_to_CI1Kv43) C1Kv43 a2_C143 = C2Kv43_to_C1Kv43 C2Kv43 + CI1Kv43_to_C1Kv43 CI1Kv43 + C0Kv43_to_C1Kv43 C0Kv43 \frac{d}{d time} (C1Kv43) = a2_C143 - a1_C143 a1_C243 = (C2Kv43_to_C3Kv43 + C2Kv43_to_C1Kv43 + C2Kv43_to_CI2Kv43) C2Kv43 a2_C243 = C3Kv43_to_C2Kv43 C3Kv43 + CI2Kv43_to_C2Kv43 CI2Kv43 + C1Kv43_to_C2Kv43 C1Kv43 \frac{d}{d time} (C2Kv43) = a2_C243 - a1_C243 a1_C343 = (C3Kv43_to_OKv43 + C3Kv43_to_C2Kv43 + C3Kv43_to_CI3Kv43) C3Kv43 a2_C343 = OKv43_to_C3Kv43 OKv43 + CI3Kv43_to_C3Kv43 CI3Kv43 + C2Kv43_to_C3Kv43 C2Kv43 \frac{d}{d time} (C3Kv43) = a2_C343 - a1_C343 a1_O43 = (OKv43_to_C3Kv43 + OKv43_to_OIKv43) OKv43 a2_O43 = C3Kv43_to_OKv43 C3Kv43 + OIKv43_to_OKv43 OIKv43 \frac{d}{d time} (OKv43) = a2_O43 - a1_O43 a1_I043 = (CI0Kv43_to_C0Kv43 + CI0Kv43_to_CI1Kv43) CI0Kv43 a2_I043 = C0Kv43_to_CI0Kv43 C0Kv43 + CI1Kv43_to_CI0Kv43 CI1Kv43 \frac{d}{d time} (CI0Kv43) = a2_I043 - a1_I043 a1_I143 = (CI1Kv43_to_CI2Kv43 + CI1Kv43_to_C1Kv43 + CI1Kv43_to_CI0Kv43) CI1Kv43 a2_I143 = CI2Kv43_to_CI1Kv43 CI2Kv43 + C1Kv43_to_CI1Kv43 C1Kv43 + CI0Kv43_to_CI1Kv43 CI0Kv43 \frac{d}{d time} (CI1Kv43) = a2_I143 - a1_I143 a1_I243 = (CI2Kv43_to_CI3Kv43 + CI2Kv43_to_C2Kv43 + CI2Kv43_to_CI1Kv43) CI2Kv43 a2_I243 = CI3Kv43_to_CI2Kv43 CI3Kv43 + C2Kv43_to_CI2Kv43 C2Kv43 + CI1Kv43_to_CI2Kv43 CI1Kv43 \frac{d}{d time} (CI2Kv43) = a2_I243 - a1_I243 a1_I343 = (CI3Kv43_to_OIKv43 + CI3Kv43_to_C3Kv43 + CI3Kv43_to_CI2Kv43) CI3Kv43 a2_I343 = OIKv43_to_CI3Kv43 OIKv43 + C3Kv43_to_CI3Kv43 C3Kv43 + CI2Kv43_to_CI3Kv43 CI2Kv43 \frac{d}{d time} (CI3Kv43) = a2_I343 - a1_I343 a1_OI43 = (OIKv43_to_OKv43 + OIKv43_to_CI3Kv43) OIKv43 a2_OI43 = OKv43_to_OIKv43 OKv43 + CI3Kv43_to_OIKv43 CI3Kv43 \frac{d}{d time} (OIKv43) = a2_OI43 - a1_OI43

Component: COMPUTE_DERIVATIVES_OF_Kv1_4_CHANNEL_STATES

alpha_act14 = alphaa0Kv14 ⅇ^{aaKv14 V} beta_act14 = betaa0Kv14 ⅇ^{(- baKv14) V} alpha_inact14 = alphai0Kv14 beta_inact14 = betai0Kv14 C0Kv14_to_C1Kv14 = 4 alpha_act14 C1Kv14_to_C2Kv14 = 3 alpha_act14 C2Kv14_to_C3Kv14 = 2 alpha_act14 C3Kv14_to_OKv14 = alpha_act14 CI0Kv14_to_CI1Kv14 = 4 b1Kv14 alpha_act14 CI1Kv14_to_CI2Kv14 = \frac{3 b2Kv14 alpha_act14}{b1Kv14} CI2Kv14_to_CI3Kv14 = \frac{2 b3Kv14 alpha_act14}{b2Kv14} CI3Kv14_to_OIKv14 = \frac{b4Kv14 alpha_act14}{b3Kv14} C1Kv14_to_C0Kv14 = beta_act14 C2Kv14_to_C1Kv14 = 2 beta_act14 C3Kv14_to_C2Kv14 = 3 beta_act14 OKv14_to_C3Kv14 = 4 beta_act14 CI1Kv14_to_CI0Kv14 = \frac{beta_act14}{f1Kv14} CI2Kv14_to_CI1Kv14 = \frac{2 f1Kv14 beta_act14}{f2Kv14} CI3Kv14_to_CI2Kv14 = \frac{3 f2Kv14 beta_act14}{f3Kv14} OIKv14_to_CI3Kv14 = \frac{4 f3Kv14 beta_act14}{f4Kv14} C0Kv14_to_CI0Kv14 = beta_inact14 C1Kv14_to_CI1Kv14 = f1Kv14 beta_inact14 C2Kv14_to_CI2Kv14 = f2Kv14 beta_inact14 C3Kv14_to_CI3Kv14 = f3Kv14 beta_inact14 OKv14_to_OIKv14 = f4Kv14 beta_inact14 CI0Kv14_to_C0Kv14 = alpha_inact14 CI1Kv14_to_C1Kv14 = \frac{alpha_inact14}{b1Kv14} CI2Kv14_to_C2Kv14 = \frac{alpha_inact14}{b2Kv14} CI3Kv14_to_C3Kv14 = \frac{alpha_inact14}{b3Kv14} OIKv14_to_OKv14 = \frac{alpha_inact14}{b4Kv14} a1_C0 = (C0Kv14_to_C1Kv14 + C0Kv14_to_CI0Kv14) C0Kv14 a2_C0 = C1Kv14_to_C0Kv14 C1Kv14 + CI0Kv14_to_C0Kv14 CI0Kv14 \frac{d}{d time} (C0Kv14) = a2_C0 - a1_C0 a1_C1 = (C1Kv14_to_C2Kv14 + C1Kv14_to_C0Kv14 + C1Kv14_to_CI1Kv14) C1Kv14 a2_C1 = C2Kv14_to_C1Kv14 C2Kv14 + CI1Kv14_to_C1Kv14 CI1Kv14 + C0Kv14_to_C1Kv14 C0Kv14 \frac{d}{d time} (C1Kv14) = a2_C1 - a1_C1 a1_C2 = (C2Kv14_to_C3Kv14 + C2Kv14_to_C1Kv14 + C2Kv14_to_CI2Kv14) C2Kv14 a2_C2 = C3Kv14_to_C2Kv14 C3Kv14 + CI2Kv14_to_C2Kv14 CI2Kv14 + C1Kv14_to_C2Kv14 C1Kv14 \frac{d}{d time} (C2Kv14) = a2_C2 - a1_C2 a1_C3 = (C3Kv14_to_OKv14 + C3Kv14_to_C2Kv14 + C3Kv14_to_CI3Kv14) C3Kv14 a2_C3 = OKv14_to_C3Kv14 OKv14 + CI3Kv14_to_C3Kv14 CI3Kv14 + C2Kv14_to_C3Kv14 C2Kv14 \frac{d}{d time} (C3Kv14) = a2_C3 - a1_C3 a1_O = (OKv14_to_C3Kv14 + OKv14_to_OIKv14) OKv14 a2_O = C3Kv14_to_OKv14 C3Kv14 + OIKv14_to_OKv14 OIKv14 \frac{d}{d time} (OKv14) = a2_O - a1_O a1_CI0 = (CI0Kv14_to_C0Kv14 + CI0Kv14_to_CI1Kv14) CI0Kv14 a2_CI0 = C0Kv14_to_CI0Kv14 C0Kv14 + CI1Kv14_to_CI0Kv14 CI1Kv14 \frac{d}{d time} (CI0Kv14) = a2_CI0 - a1_CI0 a1_CI1 = (CI1Kv14_to_CI2Kv14 + CI1Kv14_to_C1Kv14 + CI1Kv14_to_CI0Kv14) CI1Kv14 a2_CI1 = CI2Kv14_to_CI1Kv14 CI2Kv14 + C1Kv14_to_CI1Kv14 C1Kv14 + CI0Kv14_to_CI1Kv14 CI0Kv14 \frac{d}{d time} (CI1Kv14) = a2_CI1 - a1_CI1 a1_CI2 = (CI2Kv14_to_CI3Kv14 + CI2Kv14_to_C2Kv14 + CI2Kv14_to_CI1Kv14) CI2Kv14 a2_CI2 = CI3Kv14_to_CI2Kv14 CI3Kv14 + C2Kv14_to_CI2Kv14 C2Kv14 + CI1Kv14_to_CI2Kv14 CI1Kv14 \frac{d}{d time} (CI2Kv14) = a2_CI2 - a1_CI2 a1_CI3 = (CI3Kv14_to_OIKv14 + CI3Kv14_to_C3Kv14 + CI3Kv14_to_CI2Kv14) CI3Kv14 a2_CI3 = OIKv14_to_CI3Kv14 OIKv14 + C3Kv14_to_CI3Kv14 C3Kv14 + CI2Kv14_to_CI3Kv14 CI2Kv14 \frac{d}{d time} (CI3Kv14) = a2_CI3 - a1_CI3 a1_OI = (OIKv14_to_OKv14 + OIKv14_to_CI3Kv14) OIKv14 a2_OI = OKv14_to_OIKv14 OKv14 + CI3Kv14_to_OIKv14 CI3Kv14 \frac{d}{d time} (OIKv14) = a2_OI - a1_OI

Component: COMPUTE_REVERSAL_POTENTIALS

ENa = RT_over_F \ln (\frac{Nao}{Nai}) EK = RT_over_F \ln (\frac{Ko}{Ki}) a1 = Ko + 0.01833 Nao a2 = Ki + 0.01833 Nai EKs = RT_over_F \ln (\frac{a1}{a2}) ECa = 0.5 RT_over_F \ln (\frac{Cao}{Cai})

Component: COMPUTE_INa_IKr_IKs_Ito1_IK1_INab_IKp

PKv14 = (1 - Kv43Frac) KvScale 4.2986 e -7 GKv43 = Kv43Frac KvScale 0.1 INa = GNa (na6 + na7) (V - ENa) fKo = \sqrt{\frac{Ko}{4}} IKr = GKr fKo OHerg (V - EK) IKs = GKs (O1ks + O2ks) (V - EK) IKv43 = GKv43 OKv43 (V - EK) VF_over_RT = \frac{V}{RT_over_F} VFsq_over_RT = 1000 Faraday VF_over_RT a1_K = Ki ⅇ^{VF_over_RT} - Ko a2 = ⅇ^{VF_over_RT} - 1 IKv14_K = \frac{PKv14 OKv14 VFsq_over_RT a1_K}{a2} a1_Na = Nai ⅇ^{VF_over_RT} - Nao IKv14_Na = \frac{0.02 PKv14 OKv14 VFsq_over_RT a1_Na}{a2} IKv14 = IKv14_K + IKv14_Na Ito1 = IKv43 + IKv14 K1_inf = \frac{1}{0.94 + ⅇ^{\frac{1.26}{RT_over_F} (V - EK)}} IK1 = GK1 \sqrt{\frac{Ko}{1}} K1_inf (V - EK) INab = GNab (V - ENa)

Component: COMPUTE_INaK_INaCa_ICab_IpCa

ICab = GCab (V - ECa) IpCa = \frac{IpCamax Cai}{KmpCa + Cai} VF_over_RT = \frac{V}{RT_over_F} sigma = \frac{ⅇ^{\frac{Nao}{67.3}} - 1}{7} a1_Na = 1 + 0.1245 ⅇ^{(- 0.1) VF_over_RT} a2_Na = 0.0365 sigma ⅇ^{(- 1.33) VF_over_RT} fNaK = \frac{1}{a1_Na + a2_Na} a1_K = \frac{Ko}{Ko + KmKo} a2_K = 1 + {(\frac{KmNai}{Nai})}^{1.5} INaK = \frac{INaKmax fNaK a1_K}{a2_K} a1_ncx = ⅇ^{eta VF_over_RT} {Nai}^{3} Cao a2_ncx = ⅇ^{(eta - 1) VF_over_RT} {Nao}^{3} Cai a3_ncx = 1 + ksat ⅇ^{(eta - 1) VF_over_RT} a4_ncx = KmCa + Cao a5_ncx = \frac{{KmNa}^{3} + {Nao}^{3}}{5000} INaCa = \frac{kNaCa (a1_ncx - a2_ncx)}{a4_ncx a3_ncx a5_ncx}

Component: COMPUTE_ICa_ICaK

PK = Pscale 4.574 e -7 PCa = Pscale 2.469 e -4 VF_over_RT = \frac{V}{RT_over_F} VFsq_over_RT = 1000 Faraday VF_over_RT a1_Ca = 1.0 e -3 ⅇ^{2 VF_over_RT} - (Cao 0.341) a2_Ca = ⅇ^{2 VF_over_RT} - 1 ICamax = \frac{PCa 4 VFsq_over_RT a1_Ca}{a2_Ca} ICa = ICamax yCa Open Icabar = \{\begin{matrix} 0 if ICamax \geq 0 \\ ICamax otherwise \end{matrix} PKprime = \frac{PK}{1 + \frac{Icabar}{ICahalf}} a1_K = Ki ⅇ^{VF_over_RT} - Ko a2_K = ⅇ^{VF_over_RT} - 1 ICaK = \frac{PKprime Open yCa VFsq_over_RT a1_K}{a2_K}

Component: INa

FoverRT = \frac{1}{RToverF} KToverH = \frac{1.381 e -23 TNa}{6.626 e -31} RTNa = Rgas TNa RTNaF = \frac{Rgas TNa}{Faraday} Temp_Scale = 1.38862291252871 alpha1 = Temp_Scale KToverH ⅇ^{\frac{- 114007.462700232}{RTNa} + \frac{224.114}{Rgas} + \frac{0.286374268596235 V}{RTNaF}} beta1 = Temp_Scale KToverH ⅇ^{\frac{- 272470.273489681}{RTNa} + \frac{708.146}{Rgas} + \frac{(- 2.28528417586424) V}{RTNaF}} gamma1 = Temp_Scale KToverH ⅇ^{\frac{- 196336.575735923}{RTNa} + \frac{529.952}{Rgas} + \frac{2.78084918596045 V}{RTNaF}} Delta1 = Temp_Scale KToverH ⅇ^{\frac{- 133689.9304091}{RTNa} + \frac{229.205}{Rgas} + \frac{(- 1.55804214553883) V}{RTNaF}} On = Temp_Scale KToverH ⅇ^{\frac{- 62123.0784380481}{RTNa} + \frac{39.295}{Rgas} + \frac{0.288816042743232 V}{RTNaF}} Of = Temp_Scale KToverH ⅇ^{\frac{- 97657.8497137015}{RTNa} + \frac{1.51}{Rgas} + \frac{0.0684861993100685 V}{RTNaF}} GammaGamma = Temp_Scale KToverH ⅇ^{\frac{116431.142142348}{RTNa} + \frac{- 578.317}{Rgas} + \frac{0.764126011745707 V}{RTNaF}} DeltaDelta = Temp_Scale KToverH ⅇ^{\frac{- 55700.6624658307}{RTNa} + \frac{- 130.639}{Rgas} + \frac{(- 3.64981672927078) V}{RTNaF}} epsilon = Temp_Scale KToverH ⅇ^{\frac{- 85800.3675578326}{RTNa} + \frac{70.078}{Rgas}} omega_na = Temp_Scale KToverH ⅇ^{\frac{- 121955.166154864}{RTNa} + \frac{225.175}{Rgas}} rho = Temp_Scale KToverH ⅇ^{\frac{- 147813.990005035}{RTNa} + \frac{338.915}{Rgas} + \frac{2.1360043702126 V}{RTNaF}} mu = Temp_Scale KToverH ⅇ^{\frac{- 121322.143275242}{RTNa} + \frac{193.265}{Rgas} + \frac{(- 1.74290267020903) V}{RTNaF}} Cn = Temp_Scale KToverH ⅇ^{\frac{- 287913.446530953}{RTNa} + \frac{786.217}{Rgas}} Cf = Temp_Scale KToverH ⅇ^{\frac{- 59565.2236284584}{RTNa} + \frac{0.00711}{Rgas}} parameter_a = 1.40042625477401 k12 = 4 alpha1 k23 = 3 alpha1 k34 = 2 alpha1 k45 = alpha1 k56 = gamma1 k67 = epsilon k89 = k12 parameter_a k910 = k23 parameter_a k1011 = k34 parameter_a k1112 = k45 parameter_a k1213 = GammaGamma k57 = rho k21 = beta1 k32 = 2 beta1 k43 = 3 beta1 k54 = 4 beta1 k65 = Delta1 k76 = omega_na k98 = \frac{k21}{parameter_a} k109 = \frac{k32}{parameter_a} k1110 = \frac{k43}{parameter_a} k1211 = \frac{k54}{parameter_a} k1312 = DeltaDelta k75 = mu k81 = Cf k92 = \frac{k81}{parameter_a} k103 = \frac{k92}{parameter_a} k114 = \frac{k103}{parameter_a} k125 = \frac{k114}{parameter_a} k136 = Of k18 = Cn k29 = k18 parameter_a k310 = k29 parameter_a k411 = k310 parameter_a k512 = k411 parameter_a k613 = On \frac{d}{d time} (na1) = (- (k18 + k12)) na1 + k21 na2 + k81 na8 \frac{d}{d time} (na2) = (k12 na1 - ((k21 + k23 + k29) na2)) + k32 na3 + k92 na9 \frac{d}{d time} (na3) = (k23 na2 - ((k32 + k34 + k310) na3)) + k43 na4 + k103 na10 \frac{d}{d time} (na4) = (k34 na3 - ((k43 + k45 + k411) na4)) + k54 na5 + k114 na11 \frac{d}{d time} (na5) = (k45 na4 - ((k54 + k56 + k57 + k512) na5)) + k65 na6 + k75 na7 + k125 na12 \frac{d}{d time} (na6) = (k56 na5 - ((k65 + k67 + k613) na6)) + k76 na7 + k136 na13 \frac{d}{d time} (na7) = k57 na5 + k67 na6 - ((k75 + k76) na7) \frac{d}{d time} (na8) = (k18 na1 - ((k81 + k89) na8)) + k98 na9 \frac{d}{d time} (na9) = (k29 na2 + k89 na8 - ((k98 + k92 + k910) na9)) + k109 na10 \frac{d}{d time} (na10) = (k310 na3 + k910 na9 - ((k1011 + k103 + k109) na10)) + k1110 na11 \frac{d}{d time} (na11) = (k411 na4 + k1011 na10 - ((k1110 + k114 + k1112) na11)) + k1211 na12 \frac{d}{d time} (na12) = (k512 na5 + k1112 na11 - ((k1211 + k125 + k1213) na12)) + k1312 na13 \frac{d}{d time} (na13) = k613 na6 + k1213 na12 - ((k1312 + k136) na13)

Component: IKr

C2H_to_C3H = T_Const_HERG 0.02608362043337 C3H_to_C2H = T_Const_HERG 0.14832978132145 C1H_to_C2H = T_Const_HERG A0_HERG ⅇ^{B0_HERG V} C2H_to_C1H = T_Const_HERG A1_HERG ⅇ^{B1_HERG V} C3H_to_OH = T_Const_HERG A2_HERG ⅇ^{B2_HERG V} OH_to_C3H = T_Const_HERG A3_HERG ⅇ^{B3_HERG V} OH_to_IH = T_Const_HERG A4_HERG ⅇ^{B4_HERG V} IH_to_OH = T_Const_HERG A5_HERG ⅇ^{B5_HERG V} C3H_to_IH = T_Const_HERG A6_HERG ⅇ^{B6_HERG V} IH_to_C3H = \frac{OH_to_C3H IH_to_OH C3H_to_IH}{C3H_to_OH OH_to_IH} \frac{d}{d time} (C1Herg) = C2H_to_C1H C2Herg - (C1H_to_C2H C1Herg) a1_C2 = C1H_to_C2H C1Herg + C3H_to_C2H C3Herg a2_C2 = (C2H_to_C1H + C2H_to_C3H) C2Herg \frac{d}{d time} (C2Herg) = a1_C2 - a2_C2 a1_C3 = C2H_to_C3H C2Herg + OH_to_C3H OHerg + IH_to_C3H IHerg a2_C3 = (C3H_to_IH + C3H_to_OH + C3H_to_C2H) C3Herg \frac{d}{d time} (C3Herg) = a1_C3 - a2_C3 a1_O = C3H_to_OH C3Herg + IH_to_OH IHerg a2_O = (OH_to_C3H + OH_to_IH) OHerg \frac{d}{d time} (OHerg) = a1_O - a2_O a1_I = C3H_to_IH C3Herg + OH_to_IH OHerg a2_I = (IH_to_C3H + IH_to_OH) IHerg \frac{d}{d time} (IHerg) = a1_I - a2_I

Component: IKs

C0ks_C1ks = 0.00795600798004 C1ks_O1ks = 0.03966720676071 O1ks_O2ks = 0.00767254363063 ⅇ^{0.08662945914655 V} O1ks_C1ks = 0.00700806628929 ⅇ^{(- 0.14999754700285) V} O2ks_O1ks = 0.00379737998368 ⅇ^{(- 0.01425668126881) V} C1ks_C0ks = 0.2162557589585 ⅇ^{(- 0.00001889123021) V} \frac{d}{d time} (C0ks) = (- C0ks_C1ks) C0ks + C1ks_C0ks C1ks \frac{d}{d time} (C1ks) = (C0ks_C1ks C0ks - ((C1ks_C0ks + C1ks_O1ks) C1ks)) + O1ks_C1ks O1ks \frac{d}{d time} (O1ks) = (C1ks_O1ks C1ks - ((O1ks_C1ks + O1ks_O2ks) O1ks)) + O2ks_O1ks O2ks \frac{d}{d time} (O2ks) = O1ks_O2ks O1ks - (O2ks_O1ks O2ks)

Model Mathematics

Component: environment

Component: COMPUTE_CONCENTRATION_AND_VOLTAGE_DERIVATIVES

Component: I_stimulus

Component: COMPUTE_INTRACELLULAR_CALCIUM_FLUXES

Component: COMPUTE_Jtrpn_and_BUFFER_SCALE_FACTORS

Component: COMPUTE_DERIVATIVES_OF_RyR_RECEPTOR_STATES

Component: COMPUTE_DERIVATIVES_OF_LTYPE_CHANNEL_STATES

Component: COMPUTE_DERIVATIVES_OF_Kv4_3_CHANNEL_STATES

Component: COMPUTE_DERIVATIVES_OF_Kv1_4_CHANNEL_STATES

Component: COMPUTE_REVERSAL_POTENTIALS

Component: COMPUTE_INa_IKr_IKs_Ito1_IK1_INab_IKp

Component: COMPUTE_INaK_INaCa_ICab_IpCa

Component: COMPUTE_ICa_ICaK

Component: INa

Component: IKr

Component: IKs

Component: cell

Component: transmembrane_currents

Component: intracellular_currents

Component: Ions_n_reversal_potentials