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Model Mathematics

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Component: cai

\frac{d}{d time} (Cai) = Cai_bufc ((- i_up) + i_leak + i_rel - (\frac{Cm}{2.0 Vc F} (+ i_CaL_Ca + i_CaT + i_b_Ca + i_PCa - (2.0 i_NaCa)))) Cai_bufc = \frac{1.0}{1.0 + \frac{Buf_C Kbuf_C}{{(Cai + Kbuf_C)}^{2.0}}}

Component: casr

Buf_SR = 10.0 1.2 \frac{d}{d time} (Ca_SR) = \frac{Ca_SR_bufSR Vc}{V_SR} (i_up - i_rel - i_leak) Ca_SR_bufSR = \frac{1.0}{1.0 + \frac{Buf_SR Kbuf_SR}{{(Ca_SR + Kbuf_SR)}^{2.0}}}

Component: engine

Component: erev

E_Ca = 0.5 RTF \ln (\frac{Cao}{Cai}) E_K = RTF \ln (\frac{Ko}{Ki}) E_Na = RTF \ln (\frac{Nao}{Nai})

Component: extra

Component: geom

V_SR = V_tot \frac{VSR_tenT}{V_tot_tenT} V_tot_tenT = Vc_tenT + VSR_tenT Vc = V_tot \frac{Vc_tenT}{V_tot_tenT}

Component: ibca

g_b_Ca = 0.000592 0.62 i_b_Ca = g_b_Ca (V - E_Ca)

Component: ibna

g_b_Na = 0.00029 1.5 i_b_Na = g_b_Na (V - E_Na)

Component: ical

alpha_fCa = \frac{1.0}{1.0 + {(\frac{scale Cai}{0.000325})}^{8.0}} beta_fCa = \frac{0.1}{1.0 + ⅇ^{\frac{scale Cai - 0.0005}{0.0001}}} \frac{d}{d time} (d) = \frac{ical_d_inf - d}{ical_d_tau} d3 = d5 d1 d4 = \frac{1.0}{\frac{1.0}{d2} + \frac{1.0}{d6}} d6 = - 6.90988036924199989 \frac{d}{d time} (f) = \frac{ical_f_inf - f}{ical_f_tau} f2 = - 4.95057120338699974 e 1 f3 = f5 f1 f4 = \frac{1.0}{\frac{1.0}{f2} + \frac{1.0}{f6}} \frac{d}{d time} (fCa) = \frac{k_fca (fCa_inf - fCa)}{tau_fCa} fCa_inf = \frac{alpha_fCa + beta_fCa + gamma_fCa + 0.23}{1.46} gamma_fCa = \frac{0.2}{1.0 + ⅇ^{\frac{scale Cai - 0.00075}{0.0008}}} i_CaL = i_CaL_Ca + i_CaL_Na + i_CaL_K i_CaL_Ca = ibarca d f fCa i_CaL_K = ibark d f fCa i_CaL_Na = ibarna d f fCa ibarca = \frac{p_CaL_Ca 4.0 V FFRT (0.341 Cai ⅇ^{2.0 V FRT} - (0.341 Cao))}{ⅇ^{2.0 V FRT} - 1.0} ibark = \frac{p_CaL_K V FFRT (0.75 Ki ⅇ^{V FRT} - (0.75 Ko))}{ⅇ^{V FRT} - 1.0} ibarna = \frac{p_CaL_Na V FFRT (0.75 Nai ⅇ^{V FRT} - (0.75 Nao))}{ⅇ^{V FRT} - 1.0} ical_d_a = d1 ⅇ^{\frac{V}{d2}} ical_d_b = d3 ⅇ^{\frac{V}{d4}} ical_d_inf = \frac{ical_d_a}{ical_d_a + ical_d_b} ical_d_tau = \frac{1.0}{ical_d_a + ical_d_b} + taud_const ical_f_a = f1 ⅇ^{\frac{V}{f2}} ical_f_b = f3 ⅇ^{\frac{V}{f4}} ical_f_inf = \frac{ical_f_a}{ical_f_a + ical_f_b} ical_f_tau = \frac{1.0}{ical_f_a + ical_f_b} + tauf_const k_fca = \{\begin{matrix} 0.0 if fCa_inf > fCa \land V > - 60.0 \\ 1.0 otherwise \end{matrix} p_CaL_Ca = p_CaL_shannonCap p_CaL p_CaL_K = p_CaL_shannonKp p_CaL p_CaL_Na = p_CaL_shannonNap p_CaL p_CaL_shannonCap = \frac{p_CaL_shannonCa}{p_CaL_shannonTot} p_CaL_shannonKp = \frac{p_CaL_shannonK}{p_CaL_shannonTot} p_CaL_shannonNap = \frac{p_CaL_shannonNa}{p_CaL_shannonTot} p_CaL_shannonTot = p_CaL_shannonCa + p_CaL_shannonNa + p_CaL_shannonK

Component: icat

\frac{d}{d time} (d) = \frac{icat_d_inf - d}{icat_d_tau} \frac{d}{d time} (f) = \frac{icat_f_inf - f}{icat_f_tau} i_CaT = g_CaT d f (V - E_Ca) icat_d_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 26.3}{- 6.0}}} icat_d_tau = \frac{1.0}{1.068 ⅇ^{\frac{V + 26.3}{30.0}} + 1.068 ⅇ^{\frac{V + 26.3}{- 30.0}}} icat_f_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 61.7}{5.6}}} icat_f_tau = \frac{1.0}{0.0153 ⅇ^{\frac{- (V + 61.7)}{83.3}} + 0.015 ⅇ^{\frac{V + 61.7}{15.38}}}

Component: ifunny

Na_frac = \frac{NatoK_ratio}{NatoK_ratio + 1.0} \frac{d}{d time} (Xf) = \frac{ifunny_Xf_inf - Xf}{ifunny_Xf_tau} i_f = i_fNa + i_fK i_fK = (1.0 - Na_frac) g_f Xf (V - E_K) i_fNa = Na_frac g_f Xf (V - E_Na) ifunny_Xf_a = xF1 ⅇ^{\frac{V}{xF2}} ifunny_Xf_b = xF3 ⅇ^{\frac{V}{xF4}} ifunny_Xf_inf = \frac{ifunny_Xf_a}{ifunny_Xf_a + ifunny_Xf_b} ifunny_Xf_tau = \frac{1.0}{ifunny_Xf_a + ifunny_Xf_b} + xF_const xF2 = - 1.45897121702000003 e 1 xF3 = xF5 xF1 xF4 = \frac{1.0}{\frac{1.0}{xF2} + \frac{1.0}{xF6}}

Component: ik1

i_K1 = g_K1 \sqrt{\frac{Ko}{5.4}} \inf (V - E_K) ik1_inf_a = xK11 ⅇ^{\frac{V + xK13}{xK12}} ik1_inf_b = 1.0 ⅇ^{\frac{V + xK15}{xK14}} \inf = \frac{ik1_inf_a}{ik1_inf_a + ik1_inf_b}

Component: ikr

\frac{d}{d time} (Xr1) = \frac{ikr_Xr1_inf - Xr1}{ikr_Xr1_tau} Xr1_3 = Xr1_5 Xr1_1 Xr1_4 = \frac{1.0}{\frac{1.0}{Xr1_2} + \frac{1.0}{Xr1_6}} Xr1_6 = - 7.06808742965549008 \frac{d}{d time} (Xr2) = \frac{ikr_Xr2_inf - Xr2}{ikr_Xr2_tau} Xr2_2 = - 2.59944581644376989 e 1 Xr2_3 = Xr2_5 Xr2_1 Xr2_4 = \frac{1.0}{\frac{1.0}{Xr2_2} + \frac{1.0}{Xr2_6}} i_Kr = g_Kr \sqrt{\frac{Ko}{5.4}} Xr1 Xr2 (V - E_K) ikr_Xr1_a = Xr1_1 ⅇ^{\frac{V}{Xr1_2}} ikr_Xr1_b = Xr1_3 ⅇ^{\frac{V}{Xr1_4}} ikr_Xr1_inf = \frac{ikr_Xr1_a}{ikr_Xr1_a + ikr_Xr1_b} ikr_Xr1_tau = \frac{1.0}{ikr_Xr1_a + ikr_Xr1_b} + tau_1_offset ikr_Xr2_a = Xr2_1 ⅇ^{\frac{V}{Xr2_2}} ikr_Xr2_b = Xr2_3 ⅇ^{\frac{V}{Xr2_4}} ikr_Xr2_inf = \frac{ikr_Xr2_a}{ikr_Xr2_a + ikr_Xr2_b} ikr_Xr2_tau = \frac{1.0}{ikr_Xr2_a + ikr_Xr2_b} + tau_2_offset

Component: iks

\frac{d}{d time} (Xs) = \frac{iks_Xs_inf - Xs}{iks_Xs_tau} i_Ks = g_Ks {Xs}^{2.0} (V - E_K) iks_Xs_a = ks1 ⅇ^{\frac{V}{ks2}} iks_Xs_b = ks3 ⅇ^{\frac{V}{ks4}} iks_Xs_inf = \frac{iks_Xs_a}{iks_Xs_a + iks_Xs_b} iks_Xs_tau = \frac{1.0}{iks_Xs_a + iks_Xs_b} + tauks_const ks3 = ks5 ks1 ks4 = \frac{1.0}{\frac{1.0}{ks2} + \frac{1.0}{ks6}} ks6 = - 1.88669715729099998 e 1

Component: ileak

V_leak = 8 e -05 0.02 i_leak = (Ca_SR - Cai) V_leak

Component: ina

\frac{d}{d time} (h) = \frac{ina_h_inf - h}{ina_h_tau} h2 = - 1.98393588600259996 e 1 h3 = h5 h1 h4 = \frac{1.0}{\frac{1.0}{h2} + \frac{1.0}{h6}} i_Na = g_Na m^{3.0} h j (V - E_Na) ina_h_a = h1 ⅇ^{\frac{V}{h2}} ina_h_b = h3 ⅇ^{\frac{V}{h4}} ina_h_inf = \frac{ina_h_a}{ina_h_a + ina_h_b} ina_h_tau = \frac{1.0}{ina_h_a + ina_h_b} + tau_h_const ina_j_a = j1 ⅇ^{\frac{V}{j2}} ina_j_b = j3 ⅇ^{\frac{V}{j4}} ina_j_inf = \frac{ina_j_a}{ina_j_a + ina_j_b} ina_j_tau = \frac{1.0}{ina_j_a + ina_j_b} + tau_j_const ina_m_a = m1 ⅇ^{\frac{V}{m2}} ina_m_b = m3 ⅇ^{\frac{V}{m4}} ina_m_inf = \frac{ina_m_a}{ina_m_a + ina_m_b} ina_m_tau = \frac{1.0}{ina_m_a + ina_m_b} + tau_m_const \frac{d}{d time} (j) = \frac{ina_j_inf - j}{ina_j_tau} j2 = - 6.65837555026519965 e 01 j3 = j5 j1 j4 = \frac{1.0}{\frac{1.0}{j2} + \frac{1.0}{j6}} j5 = h5 j6 = h6 \frac{d}{d time} (m) = \frac{ina_m_inf - m}{ina_m_tau} m3 = m5 m1 m4 = \frac{1.0}{\frac{1.0}{m2} + \frac{1.0}{m6}} m6 = - 7.91772628951300028

Component: inaca

alpha = 2.5 1.1 gamma = 0.35 2.0 i_NaCa = \frac{kNaCa (ⅇ^{gamma V FRT} {Nai}^{3.0} Cao - (ⅇ^{(gamma - 1.0) V FRT} {Nao}^{3.0} Cai alpha))}{({KmNai}^{3.0} + {Nao}^{3.0}) (KmCa + Cao) (1.0 + Ksat ⅇ^{(gamma - 1.0) V FRT})} kNaCa = 1000.0 1.1

Component: inak

PNaK = 1.362 1.818 i_NaK = \frac{PNaK Ko Nai}{(Ko + Km_K) (Nai + Km_Na) (1.0 + 0.1245 ⅇ^{(- 0.1) V FRT} + 0.0353 ⅇ^{(- V) FRT})}

Component: ipca

g_PCa = 0.025 10.5 i_PCa = \frac{g_PCa Cai}{Cai + KPCa}

Component: irel

\frac{d}{d time} (I) = (kiSRCa Cai O - (kim I) - (kom I)) + koSRCa {Cai}^{2.0} RI \frac{d}{d time} (O) = (koSRCa {Cai}^{2.0} R - (kom O) - (kiSRCa Cai O)) + kim I \frac{d}{d time} (R) = (kim RI - (kiSRCa Cai R) - (koSRCa {Cai}^{2.0} R)) + kom O RI = 1.0 - R - O - I i_rel = ks O (Ca_SR - Cai) \frac{V_SR}{Vc} kCaSR = MaxSR - (\frac{MaxSR - MinSR}{1.0 + {(\frac{ec50SR}{Ca_SR})}^{2.5}}) kiCa = 54.0 0.3425 kiSRCa = kiCa kCaSR kim = 0.001 0.5571 koCa = 56320.0 11.43025 koSRCa = \frac{koCa}{kCaSR} kom = 1.5 0.1429

Component: ito

i_to = g_to r s (V - E_K) ito_r_a = r1 ⅇ^{\frac{V}{r2}} ito_r_b = r3 ⅇ^{\frac{V}{r4}} ito_r_inf = \frac{ito_r_a}{ito_r_a + ito_r_b} ito_r_tau = \frac{1.0}{ito_r_a + ito_r_b} + tau_r_const ito_s_a = s1 ⅇ^{\frac{V}{s2}} ito_s_b = s3 ⅇ^{\frac{V}{s4}} ito_s_inf = \frac{ito_s_a}{ito_s_a + ito_s_b} ito_s_tau = \frac{1.0}{ito_s_a + ito_s_b} + tau_s_const \frac{d}{d time} (r) = \frac{ito_r_inf - r}{ito_r_tau} r3 = r5 r1 r4 = \frac{1.0}{\frac{1.0}{r2} + \frac{1.0}{r6}} r6 = - 1.10471393012032006 e 1 \frac{d}{d time} (s) = \frac{ito_s_inf - s}{ito_s_tau} s2 = - 1.76344722898096009 e 1 s3 = s5 s1 s4 = \frac{1.0}{\frac{1.0}{s2} + \frac{1.0}{s6}}

Component: iup

Kup = 0.00025 0.702 VmaxUp = 0.000425 0.26 i_up = \frac{VmaxUp}{1.0 + \frac{{Kup}^{2.0}}{{Cai}^{2.0}}}

Component: ki

\frac{d}{d time} (Ki) = \frac{- Cm}{F Vc} ((+ i_K1 + i_to + i_Kr + i_Ks + i_fK - (2.0 i_NaK)) + i_CaL_K)

Component: membrane

\frac{d}{d time} (V) = - (+ i_K1 + i_to + i_Kr + i_Ks + i_CaL + i_CaT + i_NaK + i_Na + i_NaCa + i_PCa + i_f + i_b_Na + i_b_Ca + i_stim)

Component: nai

\frac{d}{d time} (Nai) = \frac{- Cm}{F Vc} (+ i_Na + i_b_Na + i_fNa + 3.0 i_NaK + 3.0 i_NaCa + i_CaL_Na)

Component: phys

FFRT = F FRT FRT = \frac{F}{R T} RTF = \frac{R T}{F}

Component: stimulus

amplitude = - 3.0 i_stim = pace amplitude

Source: Derived from workspace Kernik et al. 2019 at changeset 2c123f3eba5b.

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