Model Mathematics

Component: environment

Component: membrane

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-1Cmi_Stim+i_K1+i_to+i_K+i_NaK+i_Na+i_b_Na+i_Ca_L_Na_cyt+i_Ca_L_Na_ds+i_NaCa_cyt+i_NaCa_ds+i_Ca_L_Ca_cyt+i_Ca_L_Ca_ds+i_Ca_L_K_cyt+i_Ca_L_K_ds+i_b_Ca+i_b_K

Component: reversal_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ca=0.5RTFlnCa_oCa_i E_mh=RTFlnNa_o+0.12K_oNa_i+0.12K_i

Component: time_independent_potassium_current

i_K1=g_K1K_oK_o+K_mk1V-E_K1+V-E_K+10F1.67RT

Component: time_dependent_potassium_current

I_K=i_K_maxK_i-K_o-VFRT140 i_K=xI_K

Component: time_dependent_potassium_current_x_gate

E0_x=V+22-40 alpha_x=2.5if|E0_x|<delta_x30.5E0_x1--E0_x5otherwise beta_x=2.5if|E0_x|<delta_x30.178E0_xE0_x15-1otherwise ddtimex=alpha_x1-x-beta_xx

Component: fast_sodium_current

i_Na=g_Nam3hV-E_mh

Component: fast_sodium_current_m_gate

E0_m=V+41 alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwise beta_m=8000-0.056V+66 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

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

Component: sodium_background_current

i_b_Na=g_bnaV-E_Na

Component: potassium_background_current

i_b_K=g_bkV-E_K

Component: L_type_Ca_channel

i_Ca_L_Ca_cyt=1-FrICa4P_Ca_Ldff2V-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_cyt=1-FrICaP_CaKP_Ca_Ldff2V-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_cyt=1-FrICaP_CaNaP_Ca_Ldff2V-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L_Ca_ds=FrICa4P_Ca_Ldff2dsV-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_ds=FrICaP_CaKP_Ca_Ldff2dsV-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_ds=FrICaP_CaNaP_Ca_Ldff2dsV-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L=i_Ca_L_Ca_cyt+i_Ca_L_K_cyt+i_Ca_L_Na_cyt+i_Ca_L_Ca_ds+i_Ca_L_K_ds+i_Ca_L_Na_ds

Component: L_type_Ca_channel_d_gate

E0_d=V+24-20 alpha_d=120if|E0_d|<0.000130E0_d1--E0_d3otherwise beta_d=120if|E0_d|<0.000112E0_dE0_d7.5-1otherwise ddtimed=speed_dalpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

E0_f=V+34-10 alpha_f=25if|E0_f|<delta_f6.25E0_fE0_f5.5-1otherwise beta_f=121+-1V+345.5 ddtimef=speed_falpha_f1-f-beta_ff

Component: L_type_Ca_channel_f2_gate

ddtimef2=1-1Ca_iKm_f2+Ca_i+f2

Component: L_type_Ca_channel_f2ds_gate

ddtimef2ds=R_decay1-Ca_dsKm_f2ds+Ca_ds+f2ds

Component: calcium_background_current

i_b_Ca=g_bcaV-E_Ca

Component: transient_outward_current

i_to=g_tog_tos+s1-g_tosrV-E_K

Component: transient_outward_current_s_gate

alpha_s=0.260.033-V14.875 beta_s=0.26331+-V+107 ddtimes=alpha_s1-s-beta_ss

Component: transient_outward_current_r_gate

ddtimer=33311+-V+4-2410-r

Component: sodium_potassium_pump

i_NaK=i_NaK_maxK_oK_mK+K_oNa_iK_mNa+Na_i

Component: sodium_calcium_exchanger

i_NaCa_cyt=1-FRiNaCak_NaCagamman_NaCa-2VFRTNa_in_NaCaCa_o-gamma-1n_NaCa-2VFRTNa_on_NaCaCa_i1+d_NaCaCa_iNa_on_NaCa+Ca_oNa_in_NaCa1+Ca_i0.0069 i_NaCa_ds=FRiNaCak_NaCagamman_NaCa-2VFRTNa_in_NaCaCa_o-gamma-1n_NaCa-2VFRTNa_on_NaCaCa_ds1+d_NaCaCa_dsNa_on_NaCa+Ca_oNa_in_NaCa1+Ca_ds0.0069 i_NaCa=i_NaCa_cyt+i_NaCa_ds

Component: sarcoplasmic_reticulum_calcium_pump

K_1=K_cycaK_xcsK_srca K_2=Ca_i+Ca_upK_1+K_cycaK_xcs+K_cyca i_up=Ca_iK_2alpha_up-Ca_upK_1K_2beta_up

Component: calcium_translocation

i_trans=50Ca_up-Ca_rel

Component: calcium_release

VoltDep=0.08V-40 CaiReg=Ca_iCa_i+K_m_Ca_cyt CadsReg=Ca_dsCa_ds+K_m_Ca_ds RegBindSite=CaiReg+1-CaiRegCadsReg ActRate=0VoltDep+500RegBindSite2 InactRate=60+500RegBindSite2 SpeedRel=5ifV<-501otherwise PrecFrac=1-ActFrac-ProdFrac ddtimeActFrac=PrecFracSpeedRelActRate-ActFracSpeedRelInactRate ddtimeProdFrac=ActFracSpeedRelInactRate-SpeedRel1ProdFrac i_rel=ActFracActFrac+0.252K_m_rel+K_leak_rateCa_rel

Component: extracellular_sodium_concentration

Component: intracellular_sodium_concentration

ddtimeNa_i=-11V_iFi_Na+i_b_Na+3i_NaK+3i_NaCa_cyt+i_Ca_L_Na_cyt+i_Ca_L_Na_ds

Component: extracellular_calcium_concentration

Component: extracellular_potassium_concentration

ddtimeK_o=1i_K1+i_to+i_Ca_L_K_cyt+i_Ca_L_K_ds+-2i_NaK+i_K+i_b_K1V_eF-pfK_o-K_b

Component: intracellular_potassium_concentration

ddtimeK_i=-11V_iFi_K1+i_K+i_Ca_L_K_cyt+i_Ca_L_K_ds+i_to+i_b_K-2i_NaK

Component: intracellular_calcium_concentration

V_Cell=3.141592654radius10002length1000 V_i_ratio=1-V_e_ratio-V_up_ratio-V_rel_ratio V_i=V_CellV_i_ratio V_e=V_CellV_e_ratio ddtimeCa_i=-121V_iFi_Ca_L_Ca_cyt+i_b_Ca-2i_NaCa_cyt+Ca_dsV_ds_ratioKdecay+i_relV_rel_ratioV_i_ratio-ddtimeCa_Calmod-ddtimeCa_Trop-i_up ddtimeCa_ds=-1i_Ca_L_Ca_ds2V_ds_ratio1V_iF-Ca_dsKdecay ddtimeCa_up=V_i_ratioV_up_ratioi_up-i_trans ddtimeCa_rel=V_up_ratioV_rel_ratioi_trans-i_rel ddtimeCa_Calmod=alpha_CalmodCa_iCalmod-Ca_Calmod-beta_CalmodCa_Calmod ddtimeCa_Trop=alpha_TropCa_iTrop-Ca_Trop-beta_TropCa_Trop