Model Mathematics

Component: environment

Component: membrane

RTONF=RTFi_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwiseddtimeV=-i_Stim+i_K1+i_b_Na+i_b_Ca+i_b_K+i_NaK+i_NaCa+i_Na+i_siC_m

Component: fast_sodium_current

E_mh=RTONFlnNa_o+0.12K_cNa_i+0.12K_ii_Na=g_Nam3hV-E_mh

Component: fast_sodium_current_m_gate

E0_m=V+41alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwisebeta_m=8000-0.056V+66ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=20-0.125V+75beta_h=20001+320-0.1V+75ddtimeh=alpha_h1-h-beta_hh

Component: sodium_potassium_pump

i_NaK=i_NaK_maxK_cK_mK+K_cNa_iK_mNa+Na_i

Component: sodium_background_current

E_Na=RTONFlnNa_oNa_ii_b_Na=g_b_NaV-E_Na

Component: calcium_background_current

E_Ca=0.5RTONFlnCa_oCa_ii_b_Ca=g_b_CaV-E_Ca

Component: Na_Ca_exchanger

i_NaCa=k_NaCagamman_NaCa-2VRTONFNa_in_NaCaCa_o-gamma-1n_NaCa-2VRTONFNa_on_NaCaCa_i1+d_NaCaCa_iNa_on_NaCa+Ca_oNa_in_NaCa1+Ca_i0.0069

Component: potassium_background_current

i_b_K=g_b_KV-E_K

Component: time_independent_potassium_current

E_K=RTONFlnK_cK_ii_K1=g_K1K_cK_c+K_m_K1V-E_K1+V-E_K-102RTONF

Component: second_inward_calcium_current

i_si=i_siCa+i_siK+i_siNai_siCa=4P_sidCaChonV-50RTONF1--1V-502RTONFCa_i100RTONF-Ca_o-2V-50RTONFi_siK=0.002P_sidCaChonV-50RTONF1--1V-50RTONFK_i50RTONF-K_c-1V-50RTONFi_siNa=0.01P_sidCaChonV-50RTONF1--1V-50RTONFNa_i50RTONF-Na_o-1V-50RTONF

Component: second_inward_calcium_current_d_gate

E0_d=V+24-5alpha_d=120if|E0_d|<delta_d30E0_d1--1E0_d4otherwisebeta_d=120if|E0_d|<delta_d12E0_dE0_d10-1otherwiseddtimed=alpha_d1-d-beta_dd

Component: second_inward_calcium_current_f_Ca_gate

E0_f=V+34alpha_f_Ca=25if|E0_f|<delta_f6.25E0_fE0_f4-1otherwisebeta_f_Ca=121+-E0_f4ddtimef_Ca=1201-f_CaCaChoff+1-f_Ca1-CaChoffbeta_f_Ca-alpha_f_Caf_CaCaChoff=Ca_i0.001+Ca_iCaChon=1-f_Ca1-CaChoff

Component: sarcoplasmic_reticulum_calcium_pump

K_1=K_cycaK_xcsK_srcaK_2=Ca_i+Ca_upK_1+K_cycaK_xcs+K_cycai_up=Ca_iK_2alpha_up-Ca_upK_1K_2beta_up

Component: calcium_release

PrecFrac=1-ActFrac-ProdFracVoltDep=0.08V-40RegBindSite=Ca_iCa_i+0.00052ActRate=600VoltDep+500RegBindSiteInactRate=60+500RegBindSiteddtimeActFrac=PrecFracActRate-ActFracInactRateddtimeProdFrac=ActFracInactRate-0.6ProdFraci_rel=ActFracActFrac+0.252K_m_rel+K_leak_rateCa_rel

Component: calcium_translocation

i_trans=Ca_up-Ca_relalpha_tr

Component: extracellular_sodium_concentration

Component: intracellular_sodium_concentration

ddtimeNa_i=-11V_iFi_Na+i_b_Na+i_NaK3+i_NaCa3+i_siNa

Component: extracellular_calcium_concentration

ddtimeCa_o=Cab-Ca_oK_diff-1i_siCa+i_NaCa+i_b_Ca21VeF

Component: extracellular_potassium_concentration

Component: intracellular_potassium_concentration

ddtimeK_i=-11V_iFi_K1+i_siK+i_b_K-2i_NaK

Component: intracellular_calcium_concentration

V_Cell=3.141592654radius2lengthV_i_ratio=1-V_e_ratio-V_up_ratio-V_rel_ratioV_i=V_CellV_i_ratioVe=V_CellV_e_ratioddtimeCa_i=-121V_iFi_siCa+i_b_Ca-2i_NaCa+i_relV_rel_ratioV_i_ratio-dCaCalmoddt-dCaTropdt-i_upddtimeCa_up=V_i_ratioV_up_ratioi_up-i_transddtimeCa_rel=V_up_ratioV_rel_ratioi_trans-i_relddtimeCa_Calmod=alpha_CalmodCa_iCalmod-Ca_Calmod-beta_CalmodCa_CalmodddtimeCa_Trop=alpha_TropCa_iTrop-Ca_Trop-beta_TropCa_TropdCaCalmoddt=alpha_CalmodCa_iCalmod-Ca_Calmod-beta_CalmodCa_CalmoddCaTropdt=alpha_TropCa_iTrop-Ca_Trop-beta_TropCa_Trop