Model Mathematics

Component: environment

Component: cell

i_Stim=-stim_amplitudeiftime-timestim_periodstim_periodstim_starttime-timestim_periodstim_periodstim_start+stim_duration0otherwise ddtimeV=-i_Na+i_Nab+i_NaK+i_Kr+i_Ks+i_tos+i_tof+i_K1+i_Kp+i_NaCa+i_Cl_Ca+i_Clb+i_CaL+i_Cab+i_Cap+i_Stim

Component: model_parameters

Cm=Cm_per_area2cell_radius10000πcell_length10000 Vol_Cell=3.141592654cell_radius10002cell_length10003 Vol_SR=0.035Vol_Cell Vol_SL=0.02Vol_Cell Vol_jct=0.00051Vol_Cell Vol_cytosol=0.65Vol_Cell Vol_mito=Vol_Cell-Vol_SR+Vol_SL+Vol_jct+Vol_cytosol

Component: reversal_potentials

E_Na_jct=RTFlnNaoNa_jct E_Na_SL=RTFlnNaoNa_SL E_Ca_jct=RT2FlnCaoCa_jct E_Ca_SL=RT2FlnCaoCa_SL E_K=RTFlnKoKi E_Cl=-RTFlnCloCli

Component: INa

openProb=m3hj i_Na_jct=Fx_Na_jctG_INaopenProbV-E_Na_jct i_Na_SL=Fx_Na_SLG_INaopenProbV-E_Na_SL i_Na=i_Na_jct+i_Na_SL

Component: INa_h_gate

alpha_h=0.13580+V-6.8ifV<-400otherwise beta_h=3.560.079V+3.1e50.35VifV<-4010.131+V+10.66-11.1otherwise tau_h=1alpha_h+beta_h h_infinity=alpha_halpha_h+beta_h ddtimeh=h_infinity-htau_h

Component: INa_j_gate

alpha_j=-1.2714e50.2444V-3.474e-5-0.04391VV+37.7811+0.311V+79.23ifV<-400otherwise beta_j=0.1212-0.01052V1+-0.1378V+40.14ifV<-400.3-2.535e-7V1+-0.1V+32otherwise tau_j=1alpha_j+beta_j j_infinity=alpha_jalpha_j+beta_j ddtimej=j_infinity-jtau_j

Component: INa_m_gate

alpha_m=0.32V+47.1311--0.1V+47.13 beta_m=0.08-V11 tau_m=1alpha_m+beta_m m_infinity=alpha_malpha_m+beta_m ddtimem=m_infinity-mtau_m

Component: INab

i_Nab_jct=Fx_NaBk_jctG_NaBkV-E_Na_jct i_Nab_SL=Fx_NaBk_SLG_NaBkV-E_Na_SL i_Nab=i_Nab_jct+i_Nab_SL

Component: INaK

Q_NaK=Q10_NaKT-31010 Q_Km_Nai=Q10_Km_NaiT-31010 sigma=Nao67.3-17 f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT i_NaK_jct=Fx_NaK_jctQ_NaKI_NaK_maxf_NaK1+Q_Km_NaiKm_NaiNa_jctH_NaKKoKo+Km_Ko i_NaK_SL=Fx_NaK_SLQ_NaKI_NaK_maxf_NaK1+Q_Km_NaiKm_NaiNa_SLH_NaKKoKo+Km_Ko i_NaK=i_NaK_jct+i_NaK_SL

Component: IKr

G_IKr=0.03Ko5.4 i_Kr=G_IKrXrRrV-E_K

Component: IKr_Xr_gate

ddtimeXr=Xr_infinity-Xrtau_Xr Xr_infinity=11+-50+V7.5 tau_Xr=10.00138V+71--0.123V+7+0.00061V+100.145V+10-1

Component: IKr_Rr_gate

Rr=11+33+V22.4

Component: IKs

pCa_jct=-log10Ca_jct1+3 pCa_SL=-log10Ca_SL1+3 G_Ks_jct=0.070.057+0.191+-7.2+pCa_jct0.6 G_Ks_SL=0.070.057+0.191+-7.2+pCa_SL0.6 E_Ks_jct=RTFlnKo+pKNaNaoKi+pKNaNa_jct E_Ks_SL=RTFlnKo+pKNaNaoKi+pKNaNa_SL E_Ks=RTFlnKo+pKNaNaoKi+pKNaNai i_Ks_jct=Fx_Ks_jctG_Ks_jctXs2V-E_Ks i_Ks_SL=Fx_Ks_SLG_Ks_SLXs2V-E_Ks i_Ks=i_Ks_jct+i_Ks_SL

Component: IKs_Xs_gate

ddtimeXs=Xs_infinity-Xstau_Xs Xs_infinity=11+-V-1.516.7 tau_Xs=17.19e-5V+301--0.148V+30+1.31e-4V+30-1+0.0687V+30

Component: Itos

i_tos=G_tosX_tosY_tos+0.5R_tosV-E_K

Component: Itos_X_gate

ddtimeX_tos=X_tos_infinity-X_tostau_X_tos X_tos_infinity=11+-V+315 tau_X_tos=91+V+315+0.5

Component: Itos_Y_gate

ddtimeY_tos=Y_tos_infinity-Y_tostau_Y_tos Y_tos_infinity=11+V+33.510 tau_Y_tos=30001+V+6010+30

Component: Itos_R_gate

R_tos_infinity=11+V+33.510 tau_R_tos=2.8e31+V+6010+220 R_tos=R_tos_infinity ddtimeR_tos_other=R_tos_infinity-R_tostau_R_tos

Component: Itof

i_tof=G_tofX_tofY_tofV-E_K

Component: Itof_X_gate

ddtimeX_tof=X_tof_infinity-X_toftau_X_tof X_tof_infinity=11+-V+315 tau_X_tof=3.5-V302+1.5

Component: Itof_Y_gate

ddtimeY_tof=Y_tof_infinity-Y_toftau_Y_tof Y_tof_infinity=11+V+33.510 tau_Y_tof=201+V+33.510+20

Component: IK1

G_K1=0.9Ko5.4 i_K1=G_K1K1_infinityV-E_K

Component: IK1_K1_gate

K1_infinity=alpha_K1alpha_K1+beta_K1 alpha_K1=1.021+0.2385V-E_K+59.215 beta_K1=0.491240.08032V-E_K+5.476+10.06175V-E_K+594.311+-0.5143V-E_K+4.753

Component: IKp

i_Kp=g_KpV-E_K1+7.488-V5.98

Component: ICl_Ca

i_Cl_Ca=G_ClV-E_ClFx_Cl_jct1+Kd_ClCaCa_jct+Fx_Cl_SL1+Kd_ClCaCa_SL

Component: IClb

i_Clb=G_ClBkV-E_Cl

Component: ICaL

Q_CaL=Q10_CaLT-31010 temp=dfQ_CaLVF2RT i_CaL_Ca_jct=tempfCa_jctFx_ICaL_jctPCa4gamma_CaiCa_jct2VFRT-gamma_CaoCao2VFRT-1 i_CaL_Na_jct=tempfCa_jctFx_ICaL_jctPNagamma_NaiNa_jctVFRT-gamma_NaoNaoVFRT-1 i_CaL_Ca_SL=tempfCa_SLFx_ICaL_SLPCa4gamma_CaiCa_SL2VFRT-gamma_CaoCao2VFRT-1 i_CaL_Na_SL=tempfCa_SLFx_ICaL_SLPNagamma_NaiNa_SLVFRT-gamma_NaoNaoVFRT-1 i_CaL_K=tempfCa_SLFx_ICaL_SL+fCa_jctFx_ICaL_jctPKgamma_KiKiVFRT-gamma_KoKoVFRT-1 i_CaL=i_CaL_Ca_SL+i_CaL_Ca_jct+i_CaL_Na_SL+i_CaL_Na_jct+i_CaL_K

Component: ICaL_d_gate

d_infinity=11+-V+14.56 tau_d=1d_infinity1--V+14.560.035V+14.5 ddtimed=d_infinity-dtau_d

Component: ICaL_f_gate

f_infinity=11+V+35.063.6+0.61+50-V20 tau_f=10.0197-0.0337V+14.52+0.02 ddtimef=f_infinity-ftau_f

Component: ICaL_fCa_gate

fCa_SL=1-fCaB_SL fCa_jct=1-fCaB_jct ddtimefCaB_SL=1.7Ca_SL1-fCaB_SL-11.9fCaB_SL ddtimefCaB_jct=1.7Ca_jct1-fCaB_jct-11.9fCaB_jct

Component: INaCa

temp_jct=etaVFRTNa_jctHNaCao-eta-1VFRTNaoHNaCa_jct1+ksateta-1VFRT temp_SL=etaVFRTNa_SLHNaCao-eta-1VFRTNaoHNaCa_SL1+ksateta-1VFRT Q_NCX=Q10_NCXT-31010 Ka_SL=11+Kd_actCa_SL3 Ka_jct=11+Kd_actCa_jct3 i_NaCa_jct=Fx_NCX_jctV_maxKa_jctQ_NCXtemp_jctK_mCaiNaoHNa1+Na_jctK_mNaiHNa+K_mNaoHNaCa_jct1+Ca_jctK_mCai+K_mCaoNa_jctHNa+Na_jctHNaCao+NaoHNaCa_jct i_NaCa_SL=Fx_NCX_SLV_maxKa_SLQ_NCXtemp_SLK_mCaiNaoHNa1+Na_SLK_mNaiHNa+K_mNaoHNaCa_SL1+Ca_SLK_mCai+K_mCaoNa_SLHNa+Na_SLHNaCao+NaoHNaCa_SL i_NaCa=i_NaCa_jct+i_NaCa_SL

Component: ICap

V_maxAF_old=V_maxVol_cytosol2FCm Q_SLCaP=Q10_SLCaPT-31010 i_Cap_jct=Q_SLCaPV_maxAFFx_SLCaP_jct1+KmCa_jctH i_Cap_SL=Q_SLCaPV_maxAFFx_SLCaP_SL1+KmCa_SLH i_Cap=i_Cap_jct+i_Cap_SL

Component: ICab

i_Cab_jct=G_CaBkFx_CaBk_jctV-E_Ca_jct i_Cab_SL=G_CaBkFx_CaBk_SLV-E_Ca_SL i_Cab=i_Cab_SL+i_Cab_jct

Component: Jrel_SR

kCaSR=Max_SR-Max_SR-Min_SR1+EC50_SRCa_SRHSR koSRCa=koCakCaSR kiSRCa=kiCakCaSR RI=1-R-O-I ddtimeR=kimRI-kiSRCaCa_jctR-koSRCaCa_jct2R-komO ddtimeO=koSRCaCa_jct2R-komO-kiSRCaCa_jctO-kimI ddtimeI=kiSRCaCa_jctO-kimI-komI-koSRCaCa_jct2RI j_rel_SR=ksOCa_SR-Ca_jct

Component: Jleak_SR

j_leak_SR=KSRleakCa_SR-Ca_jct

Component: Jpump_SR

Q_SRCaP=Q10_SRCaPT-31010 j_pump_SR=Q_SRCaPV_maxVol_cytosolVol_SRCaiKmfH-Ca_SRKmrH1+CaiKmfH+Ca_SRKmrH

Component: ion_diffusion

j_Na_jct_SL=D_Na_jct_SLA_jct_SLx_jct_SL j_Na_SL_cytosol=D_Na_SL_cytosolA_SL_cytosolx_SL_cytosol j_Ca_jct_SL=D_Ca_jct_SLA_jct_SLx_jct_SL j_Ca_SL_cytosol=D_Ca_SL_cytosolA_SL_cytosolx_SL_cytosol j_Na_jct_SL_new=1.8313e-14 j_Na_SL_cytosol_new=1.6386e-12 j_Ca_jct_SL_new=8.2413e-13 j_Ca_SL_cytosol_new=3.7243e-12 J_Na_jct_SL=Na_jct-Na_SLj_Na_jct_SL J_Na_SL_cytosol=Na_SL-Naij_Na_SL_cytosol J_Ca_jct_SL=Ca_jct-Ca_SLj_Ca_jct_SL J_Ca_SL_cytosol=Ca_SL-Caij_Ca_SL_cytosol

Component: Na_buffer

dNa_jct_buf=konNa_jctBmax_jct-Na_jct_buf-koffNa_jct_buf dNa_SL_buf=konNa_SLBmax_SL-Na_SL_buf-koffNa_SL_buf ddtimeNa_jct_buf=dNa_jct_buf ddtimeNa_SL_buf=dNa_SL_buf ddtimeNa_jct=-Cmi_Na_jct+3i_NaCa_jct+i_Nab_jct+3i_NaK_jct+i_CaL_Na_jctVol_jctF-J_Na_jct_SLVol_jct-dNa_jct_buf ddtimeNa_SL=-Cmi_Na_SL+3i_NaCa_SL+i_Nab_SL+3i_NaK_SL+i_CaL_Na_SLVol_SLF+J_Na_jct_SL-J_Na_SL_cytosolVol_SL-dNa_SL_buf ddtimeNai=J_Na_SL_cytosolVol_cytosol

Component: Ca_buffer

dCalsequestrin=kon_CalsequestrinCa_SRBmax_CalsequestrinVol_cytosolVol_SR-Ca_Calsequestrin-koff_CalsequestrinCa_Calsequestrin ddtimeCa_Calsequestrin=dCalsequestrin dCa_SLB_SL=kon_SLCa_SLBmax_SLB_SLVol_cytosolVol_SL-Ca_SLB_SL-koff_SLBCa_SLB_SL dCa_SLB_jct=kon_SLCa_jctBmax_SLB_jctVol_cytosolVol_jct-Ca_SLB_jct-koff_SLBCa_SLB_jct dCa_SLHigh_SL=kon_SLCa_SLBmax_SLHigh_SLVol_cytosolVol_SL-Ca_SLHigh_SL-koff_SLHighCa_SLHigh_SL dCa_SLHigh_jct=kon_SLCa_jctBmax_SLHigh_jctVol_cytosolVol_jct-Ca_SLHigh_jct-koff_SLHighCa_SLHigh_jct ddtimeCa_SLB_SL=dCa_SLB_SL ddtimeCa_SLB_jct=dCa_SLB_jct ddtimeCa_SLHigh_SL=dCa_SLHigh_SL ddtimeCa_SLHigh_jct=dCa_SLHigh_jct dCa_jct_tot_bound=dCa_SLB_jct+dCa_SLHigh_jct dCa_SL_tot_bound=dCa_SLB_SL+dCa_SLHigh_SL i_Ca_jct_tot=i_CaL_Ca_jct-2i_NaCa_jct+i_Cab_jct+i_Cap_jct i_Ca_SL_tot=i_CaL_Ca_SL-2i_NaCa_SL+i_Cab_SL+i_Cap_SL ddtimeCa_SR=j_pump_SR-j_leak_SRVol_cytosolVol_SR+j_rel_SR-dCalsequestrin ddtimeCa_jct=-i_Ca_jct_totCmVol_jct2F-J_Ca_jct_SLVol_jct+j_rel_SRVol_SRVol_jct+j_leak_SRVol_cytosolVol_jct-1dCa_jct_tot_bound ddtimeCa_SL=-i_Ca_SL_totCmVol_SL2F+J_Ca_jct_SL-J_Ca_SL_cytosolVol_SL-1dCa_SL_tot_bound ddtimeCai=-j_pump_SRVol_SRVol_cytosol+J_Ca_SL_cytosolVol_cytosol-1dCa_cytosol_tot_bound

Component: cytosolic_Ca_buffer

dCa_TroponinC=kon_TroponinCCaiBmax_TroponinC-Ca_TroponinC-koff_TroponinCCa_TroponinC dCa_TroponinC_Ca_Mg=kon_TroponinC_Ca_Mg_CaCaiBmax_TroponinC_Ca_Mg_Ca-Ca_TroponinC_Ca_Mg+Mg_TroponinC_Ca_Mg-koff_TroponinC_Ca_Mg_CaCa_TroponinC_Ca_Mg dMg_TroponinC_Ca_Mg=kon_TroponinC_Ca_Mg_MgMgiBmax_TroponinC_Ca_Mg_Mg-Ca_TroponinC_Ca_Mg+Mg_TroponinC_Ca_Mg-koff_TroponinC_Ca_Mg_MgMg_TroponinC_Ca_Mg dCa_Calmodulin=kon_CalmodulinCaiBmax_Calmodulin-Ca_Calmodulin-koff_CalmodulinCa_Calmodulin dCa_Myosin=kon_Myosin_CaCaiBmax_Myosin_Ca-Ca_Myosin+Mg_Myosin-koff_Myosin_CaCa_Myosin dMg_Myosin=kon_Myosin_MgMgiBmax_Myosin_Mg-Ca_Myosin+Mg_Myosin-koff_Myosin_MgMg_Myosin dCa_SRB=kon_SRBCaiBmax_SRB-Ca_SRB-koff_SRBCa_SRB dCa_cytosol_tot_bound=dCa_TroponinC+dCa_TroponinC_Ca_Mg+dMg_TroponinC_Ca_Mg+dCa_Calmodulin+dCa_Myosin+dMg_Myosin+dCa_SRB ddtimeCa_TroponinC=dCa_TroponinC ddtimeCa_TroponinC_Ca_Mg=dCa_TroponinC_Ca_Mg ddtimeMg_TroponinC_Ca_Mg=dMg_TroponinC_Ca_Mg ddtimeCa_Calmodulin=dCa_Calmodulin ddtimeCa_Myosin=dCa_Myosin ddtimeMg_Myosin=dMg_Myosin ddtimeCa_SRB=dCa_SRB

Component: indo_fluo_Ca_buffer_not_connected

Indo1Bound=Ca_Indo1_Cytosol+Ca_Indo1_jctVol_jctVol_cytosol+Ca_Indo1_SLVol_SLVol_cytosol Fluo3Bound=Ca_Fluo3_Cytosol+Ca_Fluo3_jctVol_jctVol_cytosol+Ca_Fluo3_SLVol_SLVol_cytosol dCa_Indo1_Cytosol=kon_Indo1Indo1-Indo1BoundCaiBmax_Indo1_Cytosol-Ca_Indo1_Cytosol-koff_Indo1Ca_Indo1_Cytosol dCa_Indo1_jct=kon_Indo1Indo1-Indo1BoundCa_jctBmax_Indo1_jctVol_cytosolVol_jct-Ca_Indo1_jct-koff_Indo1Ca_Indo1_jct dCa_Indo1_SL=kon_Indo1Indo1-Indo1BoundCa_SLBmax_Indo1_SLVol_cytosolVol_SL-Ca_Indo1_SL-koff_Indo1Ca_Indo1_SL dCa_Fluo3_Cytosol=kon_Fluo3Fluo3-Fluo3BoundCaiBmax_Fluo3_Cytosol-Ca_Fluo3_Cytosol-koff_Fluo3Ca_Fluo3_Cytosol dCa_Fluo3_jct=kon_Fluo3Fluo3-Fluo3BoundCa_jctBmax_Fluo3_jctVol_cytosolVol_jct-Ca_Fluo3_jct-koff_Fluo3Ca_Fluo3_jct dCa_Fluo3_SL=kon_Fluo3Fluo3-Fluo3BoundCa_SLBmax_Fluo3_SLVol_cytosolVol_SL-Ca_Fluo3_SL-koff_Fluo3Ca_Fluo3_SL ddtimeCa_Indo1_Cytosol=dCa_Indo1_Cytosol ddtimeCa_Indo1_SL=dCa_Indo1_SL ddtimeCa_Indo1_jct=dCa_Indo1_jct ddtimeCa_Fluo3_Cytosol=dCa_Fluo3_Cytosol ddtimeCa_Fluo3_SL=dCa_Fluo3_SL ddtimeCa_Fluo3_jct=dCa_Fluo3_jct

Component: Ions_n_reversal_potentials

Component: transmembrane_currents

Component: intracellular_currents