Model Mathematics

Component: environment

Component: membrane

ddtimeV=-1Cmi_Na+i_Ca_L+i_Ca_T+i_Kv+i_BK+i_NCX+i_NaK+i_NsK+i_NsNa+I_stim

Component: I_stim

stim_start=period0iftimeperiod0timeperiod1period1iftimeperiod1timeperiod2period2iftimeperiod2time<period3period3iftimeperiod3time<period40otherwise local_time=time-stim_start I_stim=GcoupleV-V_ICCrest+V_ICCamplocal_timef_2iflocal_time<t_ICCpeakGcoupleV-V_ICCrest+V_ICCamp1+-f_12t_slope11+local_time-f_2-0.5f_1t_slopeotherwise

Component: L_type_Ca_channel

E_Ca=RT2FlnCaoCai i_Ca_L=g_CaLO_CaLV-E_Ca

Component: L_type_Ca_channel_states

T_correction_Ca=Q10CaT-31010 alpha=T_correction_Ca0.731V30 beta=T_correction_Ca0.2149-V40 alpha_0=4alpha alpha_1=3alpha alpha_2=2alpha alpha_3=1alpha beta_0=1beta beta_1=2beta beta_2=3beta beta_3=4beta phi_f=T_correction_Ca0.4742V10 phi_s=T_correction_Ca0.05956-V40 xi_f=T_correction_Ca0.01407-V300 xi_s=T_correction_Ca0.01213V500 psi_f=T_correction_Ca0.02197V500 psi_s=T_correction_Ca0.00232-V280 omega_f=beta_3xi_fphi_falpha_3psi_f omega_s=beta_3xi_sphi_salpha_3psi_s omega_sf=xi_spsi_fxi_f omega_fs=psi_s delta=T_correction_Ca0.01 theta=T_correction_Ca41+1Cai norm=C3+C2+C1+C0+C3Ca+C2Ca+C1Ca+C0Ca+O_CaL+ICa+IVs+IVf+IVsCa+IVfCa ddtimeC3=alpha_2C2norm-alpha_3+beta_2+phi_s+phi_f+thetaC3norm+beta_3O_CaLnorm+omega_fIVfnorm+omega_sIVsnorm+deltaC3Canorm ddtimeC2=alpha_1C1norm-alpha_2+beta_1+thetaC2norm+beta_2C3norm+deltaC2Canorm ddtimeC1=alpha_0C0norm-alpha_1+beta_0+thetaC1norm+beta_1C2norm+deltaC1Canorm ddtimeC0=-alpha_0+thetaC0norm+beta_0C1norm+deltaC0Canorm ddtimeC3Ca=thetaC3norm+alpha_2C2Canorm-alpha_3+beta_2+phi_f+phi_s+deltaC3Canorm+beta_3ICanorm+omega_fIVfCanorm+omega_sIVsCanorm ddtimeC2Ca=thetaC2norm+alpha_1C1Canorm-alpha_2+beta_1+deltaC2Canorm+beta_2C3Canorm ddtimeC1Ca=thetaC1norm+alpha_0C0Canorm-alpha_1+beta_0+deltaC1Canorm+beta_1C2Canorm ddtimeC0Ca=thetaC0norm-alpha_0+deltaC0Canorm+beta_0C1Canorm ddtimeO_CaL=alpha_3C3norm-beta_3+psi_f+psi_s+thetaO_CaLnorm+xi_fIVfnorm+xi_sIVsnorm+deltaICanorm ddtimeICa=thetaO_CaLnorm+alpha_3C3Canorm-beta_3+psi_f+psi_s+deltaICanorm+xi_fIVfCanorm+xi_sIVsCanorm ddtimeIVs=phi_sC3norm+psi_sO_CaLnorm+omega_fsIVfnorm-omega_s+xi_s+omega_sf+thetaIVsnorm+deltaIVsCanorm ddtimeIVf=phi_fC3norm+psi_fO_CaLnorm-omega_f+xi_f+omega_fs+thetaIVfnorm+omega_sfIVsnorm+deltaIVfCanorm ddtimeIVsCa=thetaIVsnorm+phi_sC3Canorm+psi_sICanorm+omega_fsIVfCanorm-omega_s+xi_s+omega_sf+deltaIVsCanorm ddtimeIVfCa=thetaIVfnorm+phi_fC3Canorm+psi_fICanorm-omega_f+xi_f+omega_fs+deltaIVfCanorm+omega_sfIVsCanorm

Component: T_type_Ca_channel

E_Ca=RT2FlnCaoCai i_Ca_T=g_CaTd_CaTf_CaTV-E_Ca

Component: T_type_Ca_channel_d_gate

T_correction_Ca=Q10CaT-29710 d_CaT_inf=11+-V+60.55.3 tau_d_CaT=1.9058T_correction_Ca ddtimed_CaT=d_CaT_inf-d_CaTtau_d_CaT

Component: T_type_Ca_channel_f_gate

T_correction_Ca=Q10CaT-29710 f_CaT_inf=11+V+75.54 tau_f_CaT=0.381178.6+14.7-V+50V+50900T_correction_Ca ddtimef_CaT=f_CaT_inf-f_CaTtau_f_CaT

Component: voltage_dep_K_channel

i_Kv=g_Kvx_Kvy_KvV-E_K E_K=RTFlnKoKi

Component: voltage_dep_K_channel_x_gate

T_correction_K=Q10KT-29710 x_Kv_inf=11+-V+4317.36 tau_x_Kv=4.7803T_correction_K ddtimex_Kv=x_Kv_inf-x_Kvtau_x_Kv

Component: voltage_dep_K_channel_y_gate

T_correction_K=Q10KT-29710 y_Kv_inf=11+V-44.912.0096 tau_y_Kv=763.7564T_correction_K ddtimey_Kv=y_Kv_inf-y_Kvtau_y_Kv

Component: Calcium_voltage_activated_potassium_channel

E_K=RTFlnKoKi i_BK=g_BKO4V-E_K

Component: Calcium_voltage_activated_potassium_channel_states

alpha=18.47188V1T beta=1-7.77556V1T k_on=40633 k_off_C=11 k_off_O=1.1 k_C0O0=0.02162alpha k_C1O1=0.000869alpha k_C2O2=0.0000281alpha k_C3O3=0.000781alpha k_C4O4=0.044324alpha k_O0C0=318.1084beta k_O1C1=144.1736beta k_O2C2=32.6594beta k_O3C3=0.095312beta k_O4C4=0.000106beta k_C0C1=4k_onCai k_C1C2=3k_onCai k_C2C3=2k_onCai k_C3C4=1k_onCai k_C4C3=4k_off_C k_C3C2=3k_off_C k_C2C1=2k_off_C k_C1C0=1k_off_C k_O0O1=4k_onCai k_O1O2=3k_onCai k_O2O3=2k_onCai k_O3O4=1k_onCai k_O4O3=4k_off_O k_O3O2=3k_off_O k_O2O1=2k_off_O k_O1O0=1k_off_O norm=C0+C1+C2+C3+C4+O0+O1+O2+O3+O4 ddtimeC4=-k_C4C3+k_C4O4C4norm+k_C3C4C3norm+k_O4C4O4norm ddtimeC3=-k_C3C2+k_C3O3+k_C3C4C3norm+k_C2C3C2norm+k_O3C3O3norm+k_C4C3C4norm ddtimeC2=-k_C2C1+k_C2O2+k_C2C3C2norm+k_C1C2C1norm+k_O2C2O2norm+k_C3C2C3norm ddtimeC1=-k_C1C0+k_C1O1+k_C1C2C1norm+k_C0C1C0norm+k_O1C1O1norm+k_C2C1C2norm ddtimeC0=-k_C0C1+k_C0O0C0norm+k_C1C0C1norm+k_O0C0O0norm ddtimeO4=-k_O4O3+k_O4C4O4norm+k_O3O4O3norm+k_C4O4C4norm ddtimeO3=-k_O3O2+k_O3C3+k_O3O4O3norm+k_O2O3O2norm+k_C3O3C3norm+k_O4O3O4norm ddtimeO2=-k_O2O1+k_O2C2+k_O2O3O2norm+k_O1O2O1norm+k_C2O2C2norm+k_O3O2O3norm ddtimeO1=-k_O1O0+k_O1C1+k_O1O2O1norm+k_O0O1O0norm+k_C1O1C1norm+k_O2O1O2norm ddtimeO0=-k_O0O1+k_O0C0O0norm+k_O1O0O1norm+k_C0O0C0norm

Component: sodium_current

i_Na=g_NaO_NaV-E_Na E_Na=RTFlnNaoNai

Component: Na_channel_states

T_correction_Na=1Q10NaT-29710 k_I2I1=T_correction_Na0.00392392.6793+0.0061468V k_I1O=T_correction_Na0.12052-9.6028+0.083025V k_OC1=T_correction_Na2.391-13.335-0.25289V k_C1C2=T_correction_Na3.15660.36352+0.077193V k_C2C3=T_correction_Na0.55432-0.099074+0.036441V k_C3C2=T_correction_Na0.00052548-0.069102+0.0031945V k_C2C1=T_correction_Na1.4496-0.1566+0.058353V k_C1O=T_correction_Na1.53290.0093193+0.041075V k_OI1=T_correction_Na1.61640.30763+0.0060535V k_I1I2=T_correction_Na0.0277350.05149-0.046865V k_I1C1=T_correction_Na1.9046-2.484+0.020406V k_C1I1=T_correction_Na0.00021688-0.063438+0.0046683V norm=O_Na+C1+C2+C3+I1+I2 ddtimeC3=-k_C3C2C3norm+k_C2C3C2norm ddtimeC2=-k_C2C1+k_C2C3C2norm+k_C1C2C1norm+k_C3C2C3norm ddtimeC1=-k_C1C2+k_C1O+k_C1I1C1norm+k_OC1O_Nanorm+k_C2C1C2norm+k_I1C1I1norm ddtimeO_Na=-k_OC1+k_OI1O_Nanorm+k_C1OC1norm+k_I1OI1norm ddtimeI2=-k_I2I1I2norm+k_I1I2I1norm ddtimeI1=-k_I1O+k_I1I2+k_I1C1I1norm+k_I2I1I2norm+k_C1I1C1norm+k_OI1O_Nanorm

Component: Na_Ca_exchanger

i_NCX=P_NCXgammaVFRTNai3Cao-2.5gamma-1VFRTNao3CaiK_mNai3+Nao3K_mCa+Cao1+k_satgamma-1VFRT

Component: sodium_potassium_pump

i_NaK=P_NaKKoNaiKo+K_mKK_mNa+Nai1+0.1245-0.1VFRT+0.0353-VFRT

Component: non_specific_Na_current

E_Na=RTFlnNaoNai i_NsNa=g_NsNaV-E_Na

Component: non_specific_K_current

E_K=RTFlnKoKi i_NsK=g_NsKV-E_K

Component: ionic_concentrations

V_myo=3.5 e -12 ddtimeNai=-11 e 15i_Na+i_NsNa+i_NCX3+i_NaK3V_myoF ddtimeKi=-1 e -15i_Kv+i_BK+i_NsK+I_stim-i_NaK2V_myoF ddtimeCai=-1 e -15i_Ca_L+i_Ca_T-i_NCX22V_myoF1+n_CRTCRT_totalK_D_CRTCain_CRT-1Cain_CRT+K_D_CRT2+n_CaMCaM_totalK_D_CaMCain_CaM-1Cain_CaM+K_D_CaM2