Model Mathematics

Component: environment

Component: membrane

dd time Em =- i_f + i_Kr + i_Ks + i_bNa + i_Na + i_NaK + i_NaCa + i_to + i_CaL + i_CaT + i_bK + i_bCl Cm

Component: reversal_potentials

E_Na = R T F ln Nao Nai E_Ca_rev = R T 2.0 F ln Cao Cai E_Cl = R T -1.0 F ln Clo Cli E_K = R T F ln Ko Ki

Component: L_type_calcium_current

i_CaL = g_CaL A_CaL Em - E_Ca_rev dd time A_CaL = alpha1 I3 + beta1 I1 - beta1 + alpha2 A_CaL dd time I1 = alpha2 A_CaL + beta3 I2 - beta2 + alpha3 + Cai 2.0 I1 dd time I2 = alpha3 Cai 2.0 I1 + beta4 Cai 2.0 I3 - beta3 + alpha4 I2 dd time I3 = beta1 A_CaL + alpha4 I2 - alpha1 + beta4 Cai 2.0 I3 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope beta2 = beta2_infinity + beta2_0 - beta2_infinity 1.0 + Em - beta2_E50 beta2_Eslope

Component: T_type_calcium_current

i_CaT = g_CaT A_CaT Em - E_Ca_rev dd time A_CaT = alpha1 I2 - beta1 + alpha2 A_CaT dd time I1 = alpha2 A_CaT + beta3 I2 - alpha3 I1 dd time I2 = alpha3 I1 + beta1 A_CaT - beta3 + alpha1 I2 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope beta3 = beta3_infinity + beta3_0 - beta3_infinity 1.0 + Em - beta3_E50 beta3_Eslope

Component: rapid_delayed_rectifying_potassium_current

i_Kr = i_Kr_Na + i_Kr_K i_Kr_Na = g_Kr A_Kr PKNa_r Em - E_Na i_Kr_K = g_Kr A_Kr Em - E_K dd time A_Kr = alpha1 I3 - beta1 + alpha2 A_Kr dd time I1 = alpha2 A_Kr - alpha3 I1 dd time I2 = alpha3 I1 + beta4 I3 - alpha4 I2 dd time I3 = beta1 A_Kr + alpha4 I2 - alpha1 + beta4 I3 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope alpha4 = alpha4_infinity + alpha4_0 - alpha4_infinity 1.0 + Em - alpha4_E50 alpha4_Eslope beta4 = beta4_infinity + beta4_0 - beta4_infinity 1.0 + Em - beta4_E50 beta4_Eslope

Component: slow_delayed_rectifying_potassium_current

i_Ks = i_Ks_Na + i_Ks_K i_Ks_Na = g_Ks A_Ks PKNa_s Em - E_Na i_Ks_K = g_Ks A_Ks Em - E_K dd time A_Ks = alpha1 I2 - beta1 + alpha2 A_Ks dd time I1 = alpha2 A_Ks + beta3 I2 - alpha3 I1 dd time I2 = alpha3 I1 + beta1 A_Ks - alpha1 + beta3 I2 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope beta3 = beta3_infinity + beta3_0 - beta3_infinity 1.0 + Em - beta3_E50 beta3_Eslope

Component: TTX_sensitive_sodium_current

i_Na = g_Na A_Na Em - E_Na dd time A_Na = alpha1 I3 - beta1 + alpha2 A_Na dd time I1 = alpha2 A_Na - alpha3 I1 dd time I2 = alpha3 I1 + beta4 I3 - alpha4 I2 dd time I3 = beta1 A_Na + alpha4 I2 - alpha1 + beta4 I3 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope alpha4 = alpha4_infinity + alpha4_0 - alpha4_infinity 1.0 + Em - alpha4_E50 alpha4_Eslope beta4 = beta4_infinity + beta4_0 - beta4_infinity 1.0 + Em - beta4_E50 beta4_Eslope

Component: sodium_calcium_exchange_current

i_NaCa = kNaCa x2 k21 - x1 k12 x1 + x2 + x3 + x4 x1 = k41 k34 k23 + k21 + k21 k32 k43 + k41 x2 = k32 k43 k14 + k12 + k41 k12 k34 + k32 x3 = k14 k43 k23 + k21 + k12 k23 k43 + k41 x4 = k23 k34 k14 + k12 + k14 k21 k34 + k32 k43 = Nai K3ni + Nai k12 = Cai - Em Qci F R T Kci D1 k14 = Nai 2.0 1.0 + Nai K3ni Qn Em F 2.0 R T K1ni K2ni D1 k41 =- Em Qn F 2.0 R T D1 = 1.0 + Cai Kci 1.0 +- Em Qci F R T Cai Nai Kci Kcni + Nai K1ni 1.0 + Nai K2ni 1.0 + Nai K3ni k34 = Nao K3no + Nao k21 = Cao Kco Qco Em F R T D2 k23 = Nao 2.0 1.0 + Nao K3no - Qn Em F 2.0 R T K1no K2no D2 k32 = Qn Em F 2.0 R T D2 = 1.0 + Cao Kco 1.0 + Qco Em F R T + Nao K1no 1.0 + Nao K2no 1.0 + Nao K3no

Component: hyperpolarisation_activated_current

i_f = i_fNa + i_fK i_fNa = A_f Ko 1.83 Ko 1.83 + Km_f 1.83 g_f_Na Em - E_Na i_fK = A_f Ko 1.83 Ko 1.83 + Km_f 1.83 P_f_K g_f_K Em - E_K dd time A_f = alpha1 I2 - beta1 + alpha2 A_f dd time I1 = alpha2 A_f + beta3 I2 - alpha3 I1 dd time I2 = alpha3 I1 + beta1 A_f - beta3 + alpha1 I2 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope beta3 = beta3_infinity + beta3_0 - beta3_infinity 1.0 + Em - beta3_E50 beta3_Eslope

Component: sodium_potassium_pump_current

i_NaK = Ip_max Nai Nai + Km_Na Ko Ko + Km_K 1.0 - Em - 40.0 211.0 2.0

Component: transient_outward_current

i_to = g_to A_to Em - E_K dd time A_to = alpha1 I3 - beta1 + alpha2 A_to dd time I1 = alpha2 A_to - alpha3 I1 dd time I2 = alpha3 I1 + beta4 I3 - alpha4 I2 dd time I3 = beta1 A_to + alpha4 I2 - alpha1 + beta4 I3 alpha1 = alpha1_infinity + alpha1_0 - alpha1_infinity 1.0 + Em - alpha1_E50 alpha1_Eslope beta1 = beta1_infinity + beta1_0 - beta1_infinity 1.0 + Em - beta1_E50 beta1_Eslope alpha2 = alpha2_infinity + alpha2_0 - alpha2_infinity 1.0 + Em - alpha2_E50 alpha2_Eslope alpha3 = alpha3_infinity + alpha3_0 - alpha3_infinity 1.0 + Em - alpha3_E50 alpha3_Eslope alpha4 = alpha4_infinity + alpha4_0 - alpha4_infinity 1.0 + Em - alpha4_E50 alpha4_Eslope beta4 = beta4_infinity + beta4_0 - beta4_infinity 1.0 + Em - beta4_E50 beta4_Eslope

Component: background_currents

i_bNa = g_Na Em - E_Na i_bK = Kb_K Ko 0.41 Ki - Ko - Em F R T i_bCl = g_bCl Em - E_Cl

Component: calcium_dynamics

i_Ca_up = Iup_max 1.0 1.0 + Km_Caup Cai 2.0 i_Ca_rel = 2.0 F Vrel tau_rel Carel 1.0 1.0 + Km_Carel Cai 2.0 i_Ca_tr = 2.0 F Vrel tau_tr Caup

Component: ion_concentrations

dd time Cai =- i_CaL + i_CaT + i_Ca_up - 2.0 i_NaCa + i_Ca_rel 2.0 F Vi dd time Caup = i_Ca_up - i_Ca_tr 2.0 F Vup dd time Carel = i_Ca_tr - i_Ca_rel 2.0 F Vrel dd time Cao = i_CaL + i_CaT - 2.0 i_NaCa 2.0 F Ve + Cab - Cao tau_b dd time Nai =- i_Kr_Na + i_Ks_Na + i_Na + 3.0 i_NaCa + i_bNa + i_fNa + 3.0 i_NaK F Vi dd time Nao = i_Kr_Na + i_Ks_Na + i_Na + 3.0 i_NaCa + i_bNa + i_fNa + 3.0 i_NaK F Ve + Nab - Nao tau_b dd time Ki =- i_Kr_K + i_Ks_K + i_bK + i_fK + i_to - 2.0 i_NaK F Vi dd time Ko = i_Kr_K + i_Ks_K + i_bK + i_fK + i_to - 2.0 i_NaK F Ve + Kb - Ko tau_b dd time Cli = i_bCl F Vi dd time Clo = i_bCl F Ve + Clb - Clo tau_b