Model Mathematics

Component: environment

Component: membrane

i_Stim=stim_amplitudeiftime0.05time0.05+stim_duration0otherwise ddtimeV=-1Cmi_Stim+i_K1+i_to+i_Kr+i_Ks+i_NaK+i_Na+i_b_Na+i_p_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

Component: reversal_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ks=RTFlnK_o+P_knaNa_oK_i+P_knaNa_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-10F1.25RT

Component: rapid_delayed_rectifier_potassium_current

i_Kr=g_Kr1xr1+g_Kr2xr211+V+922.4V-E_K

Component: rapid_delayed_rectifier_potassium_current_xr1_gate

alpha_xr1=501+-V-59 beta_xr1=0.05-V-2015 ddtimexr1=alpha_xr11-xr1-beta_xr1xr1

Component: rapid_delayed_rectifier_potassium_current_xr2_gate

alpha_xr2=501+-V-59 beta_xr2=0.4-V+30303 ddtimexr2=alpha_xr21-xr2-beta_xr2xr2

Component: slow_delayed_rectifier_potassium_current

i_Ks=g_Ksxs2V-E_Ks

Component: slow_delayed_rectifier_potassium_current_xs_gate

alpha_xs=141+-V-409 beta_xs=1-V45 ddtimexs=alpha_xs1-xs-beta_xsxs

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: persistent_sodium_current

i_p_Na=g_pna11+-V+528V-E_Na

Component: sodium_background_current

i_b_Na=g_bnaV-E_Na

Component: L_type_Ca_channel

i_Ca_L_Ca_cyt=1-FrICa4P_Ca_LdCaChoncytV-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_cyt=1-FrICaP_CaKP_Ca_LdCaChoncytV-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_cyt=1-FrICaP_CaNaP_Ca_LdCaChoncytV-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L_Ca_ds=FrICa4P_Ca_LdCaChondsV-50FRT1--V-50F2RTCa_i100FRT-Ca_o-V-50F2RT i_Ca_L_K_ds=FrICaP_CaKP_Ca_LdCaChondsV-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na_ds=FrICaP_CaNaP_Ca_LdCaChondsV-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+24-5 alpha_d=120if|E0_d|<0.000130E0_d1--E0_d4otherwise beta_d=120if|E0_d|<0.000112E0_dE0_d10-1otherwise ddtimed=speed_dalpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

E0_f=V+34 alpha_f=25if|E0_f|<delta_f6.25E0_fE0_f4-1otherwise beta_f=121+-1V+344 CaChoffcyt=Ca_iKCaChoff+Ca_i ddtimef=1201-fCaChoffcyt+1-f1-CaChoffcytspeed_fbeta_f-alpha_ff CaChoncyt=1-f1-CaChoffcyt CaChoffds=Ca_dsKmdsinact+Ca_ds CaChonds=1-f1-CaChoffds

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=0.033-V17 beta_s=331+-0.125V+10 ddtimes=alpha_s1-s-beta_ss

Component: transient_outward_current_r_gate

ddtimer=33311+-V+45-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+90RegBindSite2 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_p_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

Component: intracellular_potassium_concentration

ddtimeK_i=-11V_iFi_K1+i_Kr+i_Ks+i_Ca_L_K_cyt+i_Ca_L_K_ds+i_to-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 ddtimeCa_i=-121V_iFi_Ca_L_Ca_cyt+i_b_Ca-2i_NaCa_cyt-2i_NaCa_ds+Ca_dsV_ds_ratioKdecay+i_relV_rel_ratioV_i_ratio-ddtimeCa_Calmod-ddtimeCa_Trop-i_up ddtimeCa_ds=-1i_Ca_L_Ca_ds21V_ds_ratioV_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