Model Mathematics

Component: environment

Component: Membrane

ddtimeVm=-i_K1+i_to+i_Kr+i_Ks+i_CaL+i_NaK+i_Na+i_NaCa+i_PCa+i_f+i_b_Na+i_b_Ca-i_stim

Component: stim_mode

i_stim_Period=60i_stim_frequency i_stim=stim_flagi_stim_AmplitudeCmiftimei_stim_Starttimei_stim_Endtime-i_stim_Start-time-i_stim_Starti_stim_Periodi_stim_Periodi_stim_PulseDuration0otherwise

Component: current_blockers

Component: electric_potentials

E_Na=RTFlnNaoNai E_K=RTFlnKoKi E_Ks=RTFlnKo+PkNaNaoKi+PkNaNai E_Ca=0.5RTFlnCaoCai

Component: i_Na

TTX_coeff=0.18ifTTX_3uM=10.06ifTTX_10uM=10.02ifTTX_30uM=11otherwise i_Na=TTX_coeffg_Nam3hjVm-E_Na

Component: i_Na_m_gate

m_inf=11+-Vm1000-34.15.913 alpha_m=11+-Vm1000-605 beta_m=0.11+Vm1000+355+0.11+Vm1000-50200 tau_m=1alpha_mbeta_m1000 ddtimem=m_inf-mtau_m

Component: i_Na_h_gate

h_inf=11+Vm1000+72.15.7 alpha_h=0.057-Vm1000+806.8ifVm<-0.040otherwise beta_h=2.70.079Vm1000+3.11050.3485Vm1000ifVm<-0.040.770.131+Vm1000+10.66-11.1otherwise tau_h=1.5alpha_h+beta_h1000ifVm<-0.042.5421000otherwise ddtimeh=h_inf-htau_h

Component: i_Na_j_gate

j_inf=11+Vm1000+72.15.7 alpha_j=-254280.2444Vm1000-6.94810-6-0.04391Vm1000Vm1000+37.781+0.311Vm1000+79.23ifVm<-0.040otherwise beta_j=0.02424-0.01052Vm10001+-0.1378Vm1000+40.14ifVm<-0.040.60.057Vm10001+-0.1Vm1000+32otherwise tau_j=7alpha_j+beta_j1000 ddtimej=j_inf-jtau_j

Component: i_CaL

nifed_coeff=0.93ifnifed_3nM=10.79ifnifed_10nM=10.56ifnifed_30nM=10.28ifnifed_100nM=11otherwise i_CaL=g_CaL4VmF2RTCai2VmFRT-0.341Cao2VmFRT-1df1f2fCa

Component: i_CaL_d_gate

d_infinity=11+-Vm1000+9.17 alpha_d=0.25+1.41+-Vm1000-3513 beta_d=1.41+Vm1000+55 gamma_d=11+-Vm1000+5020 tau_d=alpha_dbeta_d+gamma_d11000 ddtimed=d_infinity-dtau_d

Component: i_CaL_f1_gate

f1_inf=11+Vm1000+263 tau_f1=20+1102.5-Vm1000+272152+2001+13-Vm100010+1801+30+Vm100010constf11000 constf1=1+1433Cai-501 e -6iff1_inf-f1>01otherwise ddtimef1=f1_inf-f1tau_f1

Component: i_CaL_f2_gate

f2_inf=0.33+0.671+Vm1000+354 constf2=1 tau_f2=600-Vm1000+252170+311+25-Vm100010+161+30+Vm100010constf21000 ddtimef2=f2_inf-f2tau_f2

Component: i_CaL_fCa_gate

alpha_fCa=11+Cai0.00068 beta_fCa=0.11+Cai-0.00090.0001 gamma_fCa=0.31+Cai-0.000750.0008 fCa_inf=alpha_fCa+beta_fCa+gamma_fCa1.3156 constfCa=0ifVm>-0.06fCa_inf>fCa1otherwise ddtimefCa=constfCafCa_inf-fCatau_fCa

Component: i_Kr

E4031_coeff=0.77ifE4031_30nM=10.5ifE4031_100nM=11otherwise i_Kr=E4031_coeffg_KrVm-E_KXr1Xr2Ko5.4

Component: i_Kr_Xr1_gate

V_half=1000-RTFQln1+Cao2.64L01+Cao0.584-0.019 Xr1_inf=11+V_half-Vm10004.9 alpha_Xr1=4501+-45-Vm100010 beta_Xr1=61+30+Vm100011.5 tau_Xr1=1alpha_Xr1beta_Xr11000 ddtimeXr1=Xr1_inf-Xr1tau_Xr1

Component: i_Kr_Xr2_gate

Xr2_infinity=11+Vm1000+8850 alpha_Xr2=31+-60-Vm100020 beta_Xr2=1.121+-60+Vm100020 tau_Xr2=1alpha_Xr2beta_Xr21000 ddtimeXr2=Xr2_infinity-Xr2tau_Xr2

Component: i_Ks

Chromanol_coeff=0.7ifChromanol_iKs30=10.5ifChromanol_iKs50=10.3ifChromanol_iKs70=10.1ifChromanol_iKs90=11otherwise i_Ks=Chromanol_coeffg_KsVm-E_KsXs21+0.61+3.80.00001Cai1.4

Component: i_Ks_Xs_gate

Xs_infinity=11+-Vm1000-2016 alpha_Xs=11001+-10-Vm10006 beta_Xs=11+-60+Vm100020 tau_Xs=1alpha_Xsbeta_Xs1000 ddtimeXs=Xs_infinity-Xstau_Xs

Component: i_K1

alpha_K1=3.911+0.5942Vm1000-E_K1000-200 beta_K1=-1.5090.0002Vm1000-E_K1000+100+0.5886Vm1000-E_K1000-101+0.4547Vm1000-E_K1000 XK1_inf=alpha_K1alpha_K1+beta_K1 i_K1=g_K1XK1_infVm-E_KKo5.4

Component: i_f

i_f=g_fXfVm-E_f

Component: i_f_Xf_gate

Xf_infinity=11+Vm1000+77.855 tau_Xf=19001+Vm1000+15101000 ddtimeXf=Xf_infinity-Xftau_Xf

Component: i_b_Na

i_b_Na=g_b_NaVm-E_Na

Component: i_b_Ca

i_b_Ca=g_b_CaVm-E_Ca

Component: i_NaK

i_NaK=PNaKKoKo+Km_KNaiNai+Km_Na1+0.1245-0.1VmFRT+0.0353-VmFRT

Component: i_NaCa

i_NaCa=kNaCagammaVmFRTNai3Cao-gamma-1VmFRTNao3CaialphaKmNai3+Nao3KmCa+Cao1+Ksatgamma-1VmFRT

Component: i_PCa

i_PCa=g_PCaCaiCai+KPCa

Component: i_to

i_to=g_toVm-E_Kqr

Component: i_to_q_gate

q_inf=11+Vm1000+5313 tau_q=6.06+39.1020.57-0.08Vm1000+44+0.0650.1Vm1000+45.931000 ddtimeq=q_inf-qtau_q

Component: i_to_r_gate

r_inf=11+-Vm1000-22.318.75 tau_r=2.75352+14.405161.0370.09Vm1000+30.61+0.369-0.12Vm1000+23.841000 ddtimer=r_inf-rtau_r

Component: model_parameters

Component: sodium_dynamics

ddtimeNai=-Cmi_Na+i_b_Na+3i_NaK+3i_NaCaFVc1 e -18

Component: calcium_dynamics

i_rel=c_rel+a_relCa_SR2b_rel2+Ca_SR2dg0.0411 i_up=VmaxUp1+Kup2Cai2 i_leak=Ca_SR-CaiV_leak g_inf=11+Cai0.000356ifCai0.0003511+Cai0.0003516otherwise const2=0ifg_inf>gVm>-0.061otherwise ddtimeg=const2g_inf-gtau_g Cai_bufc=11+Buf_CKbuf_CCai+Kbuf_C2 Ca_SR_bufSR=11+Buf_SRKbuf_SRCa_SR+Kbuf_SR2 ddtimeCai=Cai_bufci_leak-i_up+i_rel-i_CaL+i_b_Ca+i_PCa-2i_NaCaCm2VcF1 e -18 ddtimeCa_SR=Ca_SR_bufSRVcV_SRi_up-i_rel+i_leak