Model Mathematics

Component: environment

Component: membrane

I_st=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=dVdt dVdt=-i_Na+i_Ca_L+i_Ca_T+i_Kr+i_Ks+i_K_ATP+i_to+i_K1+i_Kp+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_NaCa+i_ns_Ca+I_st

Component: fast_sodium_current

E_Na=RTFlnNaoNai i_Na=g_Nam3hjV-E_Na

Component: fast_sodium_current_m_gate

E0_m=V+47.13 alpha_m=0.32E0_m1--0.1E0_mif|E0_m|delta_m3.2otherwise beta_m=0.08-V11 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=0.13580+V-6.8ifV<-400otherwise beta_h=3.560.079V+3100000.35VifV<-4010.131+V+10.66-11.1otherwise ddtimeh=alpha_h1-h-beta_hh

Component: fast_sodium_current_j_gate

alpha_j=-1271400.2444V+3.474 e -5-0.04391VV+37.781+0.311V+79.23ifV<-400otherwise beta_j=0.1212-0.01052V1+-0.1378V+40.14ifV<-400.3-2.535 e -7V1+-0.1V+32otherwise ddtimej=alpha_j1-j-beta_jj

Component: L_type_Ca_channel

I_CaCa=P_Ca22VF2RTgamma_CaiCai2VFRT-gamma_CaoCao2VFRT-1 I_CaNa=P_Na12VF2RTgamma_NaiNai1VFRT-gamma_NaoNao1VFRT-1 I_CaK=P_K12VF2RTgamma_KiKi1VFRT-gamma_KoKo1VFRT-1 i_CaCa=dff_CaI_CaCa i_CaNa=dff_CaI_CaNa i_CaK=dff_CaI_CaK i_Ca_L=i_CaCa+i_CaK+i_CaNa

Component: L_type_Ca_channel_d_gate

E0_d=V+10 d_infinity=11+-E0_d6.24 tau_d=10.0356.24if|E0_d|<1 e -5d_infinity1--E0_d6.240.035E0_dotherwise alpha_d=d_infinitytau_d beta_d=1-d_infinitytau_d ddtimed=alpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

f_infinity=11+V+328+0.61+50-V20 tau_f=10.0197-0.0337V+102+0.02 alpha_f=f_infinitytau_f beta_f=1-f_infinitytau_f ddtimef=alpha_f1-f-beta_ff

Component: L_type_Ca_channel_f_Ca_gate

f_Ca=11+CaiKm_Ca

Component: T_type_Ca_channel

i_Ca_T=g_CaTbbgV-E_Ca

Component: T_type_Ca_channel_b_gate

b_inf=11+-V+1410.8 tau_b=3.7+6.11+V+254.5 ddtimeb=b_inf-btau_b

Component: T_type_Ca_channel_g_gate

g_inf=11+V+605.6 tau_g=-0.875V+12ifV012otherwise ddtimeg=g_inf-gtau_g

Component: rapid_delayed_rectifier_potassium_current

g_Kr=0.02614Ko5.4 Rect=11+V+922.4 i_Kr=g_KrxrRectV-E_K

Component: rapid_delayed_rectifier_potassium_current_xr_gate

xr_infinity=11+-V+21.57.5 tau_xr=10.00138V+14.21--0.123V+14.2+0.00061V+38.90.145V+38.9-1 ddtimexr=xr_infinity-xrtau_xr

Component: slow_delayed_rectifier_potassium_current

E_Ks=RTFlnKo+PNaKNaoKi+PNaKNai g_Ks=0.4331+0.61+3.8 e -5Cai1.4 i_Ks=g_Ksxs1xs2V-E_Ks

Component: slow_delayed_rectifier_potassium_current_xs1_gate

xs1_infinity=11+-V-1.516.7 tau_xs1=17.19 e -5V+301--0.148V+30+0.000131V+300.0687V+30-1 ddtimexs1=xs1_infinity-xs1tau_xs1

Component: slow_delayed_rectifier_potassium_current_xs2_gate

xs2_infinity=11+-V-1.516.7 tau_xs2=47.19 e -5V+301--0.148V+30+0.000131V+300.0687V+30-1 ddtimexs2=xs2_infinity-xs2tau_xs2

Component: time_independent_potassium_current

g_K1=0.75Ko5.4 E_K=RTFlnKoKi i_K1=g_K1K1_infinityV-E_K

Component: time_independent_potassium_current_K1_gate

alpha_K1=1.021+0.2385V-E_K-59.215 beta_K1=10.491240.08032V-E_K+5.476+0.06175V-E_K-594.311+-0.5143V-E_K+4.753 K1_infinity=alpha_K1alpha_K1+beta_K1

Component: plateau_potassium_current

Kp=11+7.488-V5.98 i_Kp=g_KpKpV-E_K

Component: ATP_sensitive_potassium_current

g_K_ATP=0.000193nicholsarea pATP=11+ATPikATPhATP GKbaraATP=g_K_ATPpATPKo4nATP i_K_ATP=GKbaraATPV-E_K

Component: transient_outward_current

g_to=00.5 rvdv=V100 i_to=g_tozdv3ydvrvdvV-E_K

Component: transient_outward_current_zdv_gate

alpha_zdv=10V-40251+V-4025 beta_zdv=10-V+90251+-V+9025 tau_zdv=1alpha_zdv+beta_zdv zdv_ss=alpha_zdvalpha_zdv+beta_zdv ddtimezdv=zdv_ss-zdvtau_zdv

Component: transient_outward_current_ydv_gate

alpha_ydv=0.0151+V+605 beta_ydv=0.1V+2551+V+255 tau_ydv=1alpha_ydv+beta_ydv ydv_ss=alpha_ydvalpha_ydv+beta_ydv ddtimeydv=ydv_ss-ydvtau_ydv

Component: sarcolemmal_calcium_pump

i_p_Ca=I_pCaCaiK_mpCa+Cai

Component: sodium_background_current

i_Na_b=g_NabV-E_Na

Component: calcium_background_current

E_Ca=RT2FlnCaoCai i_Ca_b=g_CabV-E_Ca

Component: sodium_potassium_pump

sigma=17Nao67.3-1 f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT i_NaK=I_NaKf_NaK11+K_mNaiNai2KoKo+K_mKo

Component: non_specific_calcium_activated_current

P_ns_Ca=01.75 e -7 I_ns_Na=P_ns_Ca12VF2RTgamma_NaiNai1VFRT-gamma_NaoNao1VFRT-1 I_ns_K=P_ns_Ca12VF2RTgamma_KiKi1VFRT-gamma_KoKo1VFRT-1 i_ns_Na=I_ns_Na11+K_m_ns_CaCai3 i_ns_K=I_ns_K11+K_m_ns_CaCai3 i_ns_Ca=i_ns_Na+i_ns_K

Component: Na_Ca_exchanger

i_NaCa=K_NaCagamman_NaCa-2VFRTNain_NaCaCao-gamma-1n_NaCa-2VFRTNaon_NaCaCai1+d_NaCaCaiNaon_NaCa+CaoNain_NaCa1+Cai0.0069

Component: calcium_dynamics

V_JSR=0.00480.68V_myo V_NSR=0.05520.68V_myo ddtimeAPtrack=1001-APtrack-0.5APtrackifdVdt>150-0.5APtrackotherwise ddtimeAPtrack2=1001-APtrack2-0.5APtrack2ifAPtrack<0.2APtrack>0.18-0.5APtrack2otherwise ddtimeAPtrack3=1001-APtrack3-0.5APtrack3ifAPtrack<0.2APtrack>0.18-0.01APtrack3otherwise ddtimeCainfluxtrack=-1A_capi_CaCa+i_Ca_T-i_NaCa+i_p_Ca+i_Ca_b2V_myoFifAPtrack>0.20ifAPtrack2>0.01APtrack0.2-0.5Cainfluxtrackotherwise ddtimeOVRLDtrack=501-OVRLDtrackif11+K_mCSQNCa_JSR>CSQNthreshOVRLDtrack3<0.37APtrack3<0.37-0.5OVRLDtrackotherwise ddtimeOVRLDtrack2=501-OVRLDtrack2ifOVRLDtrack>LogicthreshOVRLDtrack2<Logicthresh-0.5OVRLDtrack2otherwise ddtimeOVRLDtrack3=501-OVRLDtrack3ifOVRLDtrack>LogicthreshOVRLDtrack3<Logicthresh-0.01OVRLDtrack3otherwise G_rel=G_rel_maxCainfluxtrack-delta_Ca_ithK_mrel+Cainfluxtrack-delta_Ca_ith1-APtrack2APtrack2ifCainfluxtrack>delta_Ca_ithG_rel_overload1-OVRLDtrack2OVRLDtrack2ifCainfluxtrackdelta_Ca_ithOVRLDtrack2>00otherwise i_rel=G_relCa_JSR-Cai i_up=I_upCaiCai+K_mup K_leak=I_upCa_NSR_max i_leak=K_leakCa_NSR i_tr=Ca_NSR-Ca_JSRtau_tr ddtimeCa_JSR=0.0011+CSQN_maxK_mCSQNK_mCSQN+Ca_JSR2i_tr-i_rel ddtimeCa_NSR=0.001-i_trV_JSRV_NSR-i_leak+i_up ddtimeCai=0.0011+CMDN_maxK_mCMDNK_mCMDN+Cai2+Tn_maxK_mTnK_mTn+Cai2-1A_capi_CaCa+i_Ca_T-i_NaCa+i_p_Ca+i_Ca_b2V_myoF+i_relV_JSRV_myo+i_leak-i_upV_NSRV_myo

Component: ionic_concentrations

volume=πpreplengthradius2 V_myo=0.68volume ddtimeNai=-0.001i_Na+i_CaNa+i_Na_b+i_ns_Na+i_NaCa3+i_NaK3A_capV_myoF ddtimeKi=-0.001i_CaK+i_Kr+i_Ks+i_K1+i_Kp+i_K_ATP+i_to+i_ns_K+-i_NaK2A_capV_myoF