Model Mathematics

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Component: main

\frac{d}{d t} (a) = 1

Component: parameter

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

Component: parameter_Ikr

Component: parameter_Ik1

Component: parameter_Iks

Component: parameter_Ito

Component: parameter_Ica

Component: parameter_Ina

Component: parameter_If

Component: gating_Ikr

Xr1_3 = Xr1_5 Xr1_1 Xr2_3 = Xr2_5 Xr2_1 Xr1_4 = \frac{1}{\frac{1}{Xr1_2} + \frac{1}{Xr1_6}} Xr2_4 = \frac{1}{\frac{1}{Xr2_2} + \frac{1}{Xr2_6}} alpha_act = Xr1_1 ⅇ^{\frac{v}{Xr1_2}} beta_act = Xr1_3 ⅇ^{\frac{v}{Xr1_4}} x_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_act = \frac{1}{alpha_act + beta_act} + Xr1_7 alpha_inact = Xr2_1 ⅇ^{\frac{v}{Xr2_2}} beta_inact = Xr2_3 ⅇ^{\frac{v}{Xr2_4}} x_inf_inact = \frac{alpha_inact}{alpha_inact + beta_inact} tau_inact = \frac{1}{alpha_inact + beta_inact} + Xr2_7

Component: gating_Ik1

alpha_act = var_2 ⅇ^{\frac{v + var_4}{var_3}} beta_act = ⅇ^{\frac{v + var_6}{var_5}} x_inf_act_Ik1 = \frac{alpha_act}{alpha_act + beta_act}

Component: gating_Iks

ks_3 = ks_5 ks_1 ks_4 = \frac{1}{\frac{1}{ks_2} + \frac{1}{ks_6}} alpha_act = ks_1 ⅇ^{\frac{v}{ks_2}} beta_act = ks_3 ⅇ^{\frac{v}{ks_4}} x_ks_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_ks_act = \frac{1}{alpha_act + beta_act} + tau_ks_const

Component: gating_Ito

r_3 = r_5 r_1 s_3 = s_5 s_1 r_4 = \frac{1}{\frac{1}{r_2} + \frac{1}{r_6}} s_4 = \frac{1}{\frac{1}{s_2} + \frac{1}{s_6}} alpha_act = r_1 ⅇ^{\frac{v}{r_2}} beta_act = r_3 ⅇ^{\frac{v}{r_4}} x_to_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_to_act = \frac{1}{alpha_act + beta_act} + tau_r_const alpha_inact = s_1 ⅇ^{\frac{v}{s_2}} beta_inact = s_3 ⅇ^{\frac{v}{s_4}} x_to_inf_inact = \frac{alpha_inact}{alpha_inact + beta_inact} tau_to_inact = \frac{1}{alpha_inact + beta_inact} + tau_s_const

Component: gating_Ica

d_3 = d_5 d_1 f_3 = f_5 f_1 d_4 = \frac{1}{\frac{1}{d_2} + \frac{1}{d_6}} f_4 = \frac{1}{\frac{1}{f_2} + \frac{1}{f_6}} alpha_act = d_1 ⅇ^{\frac{v}{d_2}} beta_act = d_3 ⅇ^{\frac{v}{d_4}} x_ca_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_ca_act = \frac{1}{alpha_act + beta_act} + tau_d_const alpha_inact = f_1 ⅇ^{\frac{v}{f_2}} beta_inact = f_3 ⅇ^{\frac{v}{f_4}} x_ca_inf_inact = \frac{alpha_inact}{alpha_inact + beta_inact} tau_ca_inact = \frac{1}{alpha_inact + beta_inact} + tau_f_const scale_Ical_Fca_Cadep = 1.2 alpha_fCa = \frac{1.0}{1.0 + {(\frac{scale_Ical_Fca_Cadep ca_i}{.000325})}^{8}} beta_fCa = \frac{0.1}{1.0 + ⅇ^{\frac{scale_Ical_Fca_Cadep ca_i - .0005}{0.0001}}} gamma_fCa = \frac{0.2}{1.0 + ⅇ^{\frac{scale_Ical_Fca_Cadep ca_i - 0.00075}{0.0008}}} x_fca_inf_inact = \frac{alpha_fCa + beta_fCa + gamma_fCa + 0.23}{1.46}

Component: gating_Icat

x_cat_inf_act = \frac{1}{1 + ⅇ^{\frac{- (v + 26.3)}{6}}} tau_cat_act = \frac{1}{1.068 ⅇ^{\frac{v + 26.3}{30}} + 1.068 ⅇ^{\frac{- (v + 26.3)}{30}}} x_cat_inf_inact = \frac{1}{1 + ⅇ^{\frac{v + 61.7}{5.6}}} tau_cat_inact = \frac{1}{0.0153 ⅇ^{\frac{- (v + 61.7)}{83.3}} + 0.015 ⅇ^{\frac{v + 61.7}{15.38}}}

Component: gating_Ina

m_3 = m_5 m_1 h_3 = h_5 h_1 j_3 = j_5 j_1 m_4 = \frac{1}{\frac{1}{m_2} + \frac{1}{m_6}} h_4 = \frac{1}{\frac{1}{h_2} + \frac{1}{h_6}} j_4 = \frac{1}{\frac{1}{j_2} + \frac{1}{j_6}} j_5 = h_5 j_6 = h_6 alpha_m_act = m_1 ⅇ^{\frac{v}{m_2}} beta_m_act = m_3 ⅇ^{\frac{v}{m_4}} x_na_m_inf_act = \frac{alpha_m_act}{alpha_m_act + beta_m_act} tau_na_m_act = \frac{1}{alpha_m_act + beta_m_act} + tau_m_const alpha_h_inact = h_1 ⅇ^{\frac{v}{h_2}} beta_h_inact = h_3 ⅇ^{\frac{v}{h_4}} x_na_h_inf_inact = \frac{alpha_h_inact}{alpha_h_inact + beta_h_inact} tau_na_h_inact = \frac{1}{alpha_h_inact + beta_h_inact} + tau_h_const alpha_j_inact = j_1 ⅇ^{\frac{v}{j_2}} beta_j_inact = j_3 ⅇ^{\frac{v}{j_4}} x_na_j_inf_inact = \frac{alpha_j_inact}{alpha_j_inact + beta_j_inact} tau_na_j_inact = \frac{1}{alpha_j_inact + beta_j_inact} + tau_j_const

Component: gating_If

xf_3 = xf_5 xf_1 xf_4 = \frac{1}{\frac{1}{xf_2} + \frac{1}{xf_6}} alpha_act = xf_1 ⅇ^{\frac{v}{xf_2}} beta_act = xf_3 ⅇ^{\frac{v}{xf_4}} x_f_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_f_act = \frac{1}{alpha_act + beta_act} + xf_const

Component: Protocol

Ki = \{\begin{matrix} 150 if protocol = 1 \\ 148 if protocol = 2 \\ k_new if protocol = 0 \\ 125 otherwise \end{matrix}

Component: Nernst

E_K = \frac{R T}{F} \ln (\frac{Ko}{Ki}) E_Ca = \frac{0.5 R T}{F} \ln (\frac{Cao}{ca_i}) E_Na = \frac{R T}{F} \ln (\frac{Nao}{Na_i})

Component: Current_Ik1

g_k1 = var_1 i_k1 = g_k1 \sqrt{\frac{Ko}{5.4}} x_inf_act_Ik1 (v - E_K)

Component: Current_Ikr

dX_kr_act = \frac{x_inf_act - X_kr_act}{tau_act} dX_kr_inact = \frac{x_inf_inact - X_kr_inact}{tau_inact} g_Kr = Xr1_0 i_Kr = g_Kr \sqrt{\frac{Ko}{5.4}} X_kr_act X_kr_inact (v - E_K)

Component: Current_Iks

dX_ks_act = \frac{x_ks_inf_act - X_ks_act}{tau_ks_act} g_Ks = ks_0 i_Ks = g_Ks \sqrt{\frac{Ko}{5.4}} {X_ks_act}^{2} (v - E_K)

Component: Current_Ito

dX_to_act = \frac{x_to_inf_act - X_to_act}{tau_to_act} dX_to_inact = \frac{x_to_inf_inact - X_to_inact}{tau_to_inact} g_to = r_0 i_to = g_to \sqrt{\frac{Ko}{5.4}} X_to_act X_to_inact (v - E_K)

Component: Current_IcaL

k_fca = \{\begin{matrix} 0 if x_fca_inf_inact > X_fca_inact \land v > - 60 \\ 1 otherwise \end{matrix}

dX_ca_act = \frac{x_ca_inf_act - X_ca_act}{tau_ca_act} dX_ca_inact = \frac{x_ca_inf_inact - X_ca_inact}{tau_ca_inact} dX_fca_inact = \frac{k_fca (x_fca_inf_inact - X_fca_inact)}{tau_fca} p_CaL = d_0 p_CaL_shannonTot = p_CaL_shannonCa + p_CaL_shannonNa + p_CaL_shannonK p_CaL_shannonCap = \frac{p_CaL_shannonCa}{p_CaL_shannonTot} p_CaL_shannonNap = \frac{p_CaL_shannonNa}{p_CaL_shannonTot} p_CaL_shannonKp = \frac{p_CaL_shannonK}{p_CaL_shannonTot} p_CaL_Ca = p_CaL_shannonCap p_CaL p_CaL_Na = p_CaL_shannonNap p_CaL p_CaL_K = p_CaL_shannonKp p_CaL ibarca = \frac{\frac{p_CaL_Ca 4.0 v F^{2}}{R T} (0.341 ca_i ⅇ^{\frac{2.0 v F}{R T}} - (0.341 Cao))}{ⅇ^{\frac{2.0 v F}{R T}} - 1.0} i_CaL_Ca = ibarca X_ca_act X_ca_inact X_fca_inact ibarna = \frac{\frac{p_CaL_Na v F^{2}}{R T} (0.75 Na_i ⅇ^{\frac{v F}{R T}} - (0.75 Nao))}{ⅇ^{\frac{v F}{R T}} - 1.0} i_CaL_Na = ibarna X_ca_act X_ca_inact X_fca_inact ibark = \frac{\frac{p_CaL_K v F^{2}}{R T} (0.75 Ki ⅇ^{\frac{v F}{R T}} - (0.75 Ko))}{ⅇ^{\frac{v F}{R T}} - 1.0} i_CaL_K = ibark X_ca_act X_ca_inact X_fca_inact i_CaL = i_CaL_Ca + i_CaL_Na + i_CaL_K

Component: Current_Icat

dX_cat_act = \frac{x_cat_inf_act - X_cat_act}{tau_cat_act} dX_cat_inact = \frac{x_cat_inf_inact - X_cat_inact}{tau_cat_inact} i_cat = g_cat X_cat_act X_cat_inact (v - E_Ca)

Component: Current_Ina

dX_na_m_act = \frac{x_na_m_inf_act - X_na_m_act}{tau_na_m_act} dX_na_h_inact = \frac{x_na_h_inf_inact - X_na_h_inact}{tau_na_h_inact} dX_na_j_inact = \frac{x_na_j_inf_inact - X_na_j_inact}{tau_na_j_inact} i_na = g_Na {X_na_m_act}^{3} X_na_h_inact X_na_j_inact (v - E_Na)

Component: Current_If

dX_f_act = \frac{x_f_inf_act - X_f_act}{tau_f_act} Na_frac = \frac{NatoK_ratio}{NatoK_ratio + 1} i_fNa = Na_frac g_f X_f_act (v - E_Na) i_fK = (1 - Na_frac) g_f X_f_act (v - E_K) i_f = i_fNa + i_fK

Component: Current_Inaca

i_naca = \frac{kNaCa (ⅇ^{\frac{gamma v F}{R T}} {Na_i}^{3.0} Cao - (ⅇ^{\frac{(gamma - 1.0) v F}{R T}} {Nao}^{3} ca_i alpha))}{({KmNai}^{3.0} + {Nao}^{3}) (KmCa + Cao) (1.0 + Ksat ⅇ^{\frac{(gamma - 1.0) v F}{R T}})}

Component: Current_Inak

i_nak = \frac{PNaK Ko Na_i}{(Ko + Km_K) (Na_i + Km_Na) (1.0 + 0.1245 ⅇ^{\frac{(- 0.1) v F}{R T}} + 0.0353 ⅇ^{\frac{(- v) F}{R T}})}

Component: Current_Iup

i_up = \frac{VmaxUp}{1.0 + \frac{{Kup}^{2}}{{ca_i}^{2}}}

Component: Current_leak

j_leak = (ca_SR - ca_i) V_leak

Component: Current_release

kCaSR = MaxSR - (\frac{MaxSR - MinSR}{1 + {(\frac{ec50SR}{ca_SR})}^{2.5}}) koSRCa = \frac{koCa}{kCaSR} kiSRCa = kiCa kCaSR CI = 1 - C - O - I dC = kim CI - (kiSRCa ca_i C) - (koSRCa {ca_i}^{2} C - (kom O)) dO = koSRCa {ca_i}^{2} C - (kom O) - (kiSRCa ca_i O - (kim I)) dI = kiSRCa ca_i O - (kim I) - (kom I - (koSRCa {ca_i}^{2} CI)) j_rel = \frac{ks O (ca_SR - ca_i) V_SR}{Vc}

Component: Current_bNa

i_b_Na = g_b_Na (v - E_Na)

Component: Current_bCa

i_b_Ca = g_b_Ca (v - E_Ca)

Component: Current_pCa

i_PCa = \frac{g_PCa ca_i}{ca_i + KPCa}

Component: ca_SR

Ca_SR_bufSR = \frac{1}{1 + \frac{Buf_SR Kbuf_SR}{{(ca_SR + Kbuf_SR)}^{2}}} dca_SR = \frac{Ca_SR_bufSR Vc}{V_SR} (i_up - (j_rel + j_leak))

Component: ca_buf

Cai_buf = \frac{1}{1.0 + \frac{Buf_C Kbuf_C}{{(ca_i + Kbuf_C)}^{2}}}