Model Mathematics

Component: time_component

Component: stimulus_current_component

Istim=stimCurrentiftimemodstimPeriod<stimDuration0.0otherwise

Component: interface

Component: parameters

Component: initial_values

Component: interface

Component: computed_constants

Vtotal=Vmyo+VJSR+VNSR+VSS0.64 Vmito=Vtotal0.36 f_01=3.0f_xb f_12=10.0f_xb f_23=7.0f_xb g0_01=1.0gmin_xb g0_12=2.0gmin_xb g0_23=3.0gmin_xb paths=g0_01g0_12g0_23+f_01g0_12g0_23+f_01f_12g0_23+f_01f_12f_23 P1max=f_012.0gmin_xb3.0gmin_xbpaths P2max=f_01f_123.0gmin_xbpaths P3max=f_01f_12f_23paths Fmax=P1max+2.0P2max+3.0P3max fnormmax=Fmax3.0 SLnorm=SL-1.70.6 Ktrop_Ca=kltrpn_minuskltrpn_plus Ktrop_half=1.01.0+Ktrop_Ca1.71000.0+0.91000.0-1.71000.02.3-1.7SL-1.7 Ntrop=3.5SL-2.0 fnormmax2=P1max+P2max+P3max La=1.0 Lm_prime=1.5 Lz=0.1 Lb=0.1 Lm=Lm_prime-Lb mod_factor=1.0+2.3-SL2.3-1.71.01.6 alpha_SL=min{1.0SL-2.0La+Lm_prime-LzLm}ifSL<2.21.0-SL-2.2Lmotherwise g_01_mod=g0_01mod_factor g_12_mod=g0_12mod_factor g_23_mod=g0_23mod_factor g_01_off=30.01000.0 g_01_off_mod=g_01_offmod_factor RT_over_F=RTFaraday G_Ks=0.282Ko5.4 G_K1=0.75Ko5.4 inv_5p98=1.05.98 FaradayE3=1000.0Faraday Cao_341=Cao341.0 ICamax_LHospital=2.0PCa1000.0Faraday1.0-341.0Cao Pca_4En3=4.01.0e-3PCa F_over_RT=1.0RT_over_F inv_ICahalf=1.0ICahalf PKFe3=FaradayE3PK sigma=0.0365Nao67.3-1.07.0 inv_KmNai=1.0KmNai INaKmax_Ko_Ko_KmKo=INaKmaxKoKo+KmKo inv_Ki1AD_NaK=1.0Ki1AD_NaK eta_1=eta-1.0 Nao_p3=Nao3.0Cao KmCa_Cao=KmCa+CaoKmNa3.0+Nao3.0kNaCaCao KmCa_Cao_ksat=KmCa_Caoksat inv_KiADP_CaP=1.0KiADP_CaP KmnsCa_p3=KmnsCa3.0 V_AM_scaler_max_1_f_01_12_23=V_AM_scalerV_AM_maxf_01+f_12+f_23 KmATP_AM_Ki_AM=KmATP_AMKi_AM DmuH_Constant=-2.303RT_over_FDpH VCS_C1=KCSEtCSAcCoAKmAcCoA+AcCoA one_inv_KACOeq=1.0+1.0KACOeq VIDH_Constant=1.0+Hkh_1+kh_2H kIDH_EtID=kIDHEtID inv_KADP=1.0KADP inv_KaCa=1.0KaCa inv_KidhNADH=1.0KidhNADH KmKGNAD_KmIDNAD=KmKGNADKmIDNAD Mg_Kmg_1=MgKmg+1.0 Mg_Kmg_1_Kca=Mg_Kmg_1Kca kKGDH_EtKG=kKGDHEtKG CoA_KSLeq=CoAKSLeq kSDH_EtSDH=kSDHEtSDH KmSucc_KiFUM=KmSuccKiFUM inv_KiOxaa=1.0KiOxaa kfFH_KFHeq=kfFHKFHeq kMDH_Fh_EtMD=1.01.0+Kh3H+Kh3Kh4H2.02.01.01.0+HKh1+H2.0Kh1Kh2+KoffkMDHEtMD Kmal_Kioaa=KmalKioaa VAAT_Constant=kfAATGLUkcnsASPKAATeqkfAAT kcnsASP_KAATeq_kfAAT=kcnsASPKAATeqkfAAT KfAAT_GLU=kfAATGLU KfAAT_KAATeq=kfAATKAATeq kres_sq_KmIDNAD=kreskresKmIDNAD exp_6_FRT_Dpsio=6.0DpsioF_over_RT FRT_6_g=6.0gF_over_RT ra_rc1_exp_6_FRT_Dpsio=ra+rc1exp_6_FRT_Dpsio r1_exp_6_FRT_Dpsio=r1exp_6_FRT_Dpsio rhoREN_ra_rc1_exp_6_FRT_Dpsio=0.5rhoRENra_rc1_exp_6_FRT_Dpsio rhoREN_rc2=0.5rhoRENrc2 rhoREN_ra=0.5rhoRENra rhoRen_6_ra=6.0rhoRENra rhoRen_6_ra_rb=6.0rhoRENra+rb AREF=RT_over_Flog10kresfFADH2FAD exp_AREF_FRT=AREFF_over_RT ra_rc2_exp_AREF_FRT=0.5ra+rc2exp_AREF_FRT VFO_C1=ra+rc1exp_6_FRT_Dpsioexp_AREF_FRT0.5 ra_exp_AREF_FRT=4.0raexp_AREF_FRT ra_rb=4.0ra+rb VFO_VHFe_C1=1.0+r1exp_AREF_FRTexp_6_FRT_Dpsio r2_r3_exp_AREF_FRT=r2+r3exp_AREF_FRT exp_3_FRT_Dpsio=3.0DpsioF_over_RT FRT_3=3.0F_over_RT kf1_Pi=kf1Pi VATPase_C1=100.0pa+pc1exp_3_FRT_Dpsio pa_pb_3=3.0pa+pb pa_300=300.0pa p1_exp_3_FRT_Dpsio=p1exp_3_FRT_Dpsio hm_F_over_RT=hmF_over_RT VmDT_75=0.75VmDT VmDT_20=20.0VmDT inv_Kfb=1.0Kfb inv_Krb=1.0Krb inv_tautr=1.0tautr inv_tauxfer=1.0tauxfer KmATP_SR_Ki_SR=KmATP_SRKi_SR inv_Ki_prime_SR=1.0Ki_prime_SR alpha_SL_fnormmax2=alpha_SLfnormmax2 alpha_SL_fnormmax=alpha_SLfnormmax3.0 inv_LTRPNtot_Ktrop_half=1.0LTRPNtotKtrop_half kTrop_pn_f_01=-kTrop_pn-f_01 kTrop_pn_f_12_g_01_mod=-kTrop_pn+f_12+g_01_mod f_23_g_12_mod=-f_23+g_12_mod CMDNtot_KmCMDN=CMDNtotKmCMDN CSQNtot_KmCSQN=CSQNtotKmCSQN inv_ktrans=1.0ktrans inv_kact=1.0kact Vmuni_ktrans=Vmuniktrans FRT2=2.0F_over_RT b_05=b0.5 Acap_Vmyo_F=AcapVmyoFaraday1000.0 Acap_VSS_F=Acap2.0VSSFaraday1000.0 VJSR_VSS=VJSRVSS Vmyo_VSS=VmyoVSS Vmyo_VNSR=VmyoVNSR VJSR_VNSR=VJSRVNSR inv_C_m=1.0C_m inv_bL=1.0bL inv_Cmito=1.0Cmito two_b=2.0b inv_keq=1.0keq zeta_alpha_SL_fnormmax=zetaalpha_SL_fnormmax

Component: model_2

ADP=8.0-ATPi inv_ATPi=1.0ATPi VF_over_RT=VF_over_RT exp_VF_over_RT=VF_over_RT VFsq_over_RT=FaradayE3VF_over_RT exp2VFRT=exp_VF_over_RTexp_VF_over_RT O1_RyR=1.0-C1_RyR+C2_RyR+O2_RyR V_30=V+30.0 V_E_K=V-E_K INa=G_NamNamNamNahNajNaV-E_Na IKs=G_KsxKsxKsV-E_Ks1.0+V-40.040.0 K1Alpha=1.021.0+0.2385V_E_K-59.215 K1Beta=0.49120.08032V_E_K+5.476+0.06175V_E_K-594.311.0+-0.5143V-E_K+4.753 K1_inf=K1AlphaK1Alpha+K1Beta IK1=G_K1K1_infV_E_K INab=G_NabV-E_Na IKp=G_KpV_E_K1.0+7.488-Vinv_5p98 ICamax=Pca_4En3exp2VFRT-Cao_3410.5-0.02Vif|V|<LHospitalThresholdPca_4En3VFsq_over_RTexp2VFRT-Cao_341exp2VFRT-1.0otherwise ICaK=PKFe3Open+OCayCaKiexp2VFRT-Ko0.5-0.02V1.0+ICamaxinv_ICahalfif|V|<LHospitalThresholdPKFe3Open+OCayCaKiexp2VFRT-KoVF_over_RTexp2VFRT-1.01.0+ICamaxinv_ICahalfotherwise ICa=6.0ICamaxyCaOpen NaiP1p5=NaiNaiNai INaK=INaKmax_Ko_Ko_KmKoNaiP1p5NaiP1p5+KmNaiKmNaiKmNai1.0+0.1245-0.1VF_over_RT+sigmaexp_VF_over_RT1.0+Km1AT_NaKinv_ATPi1.0+ADPinv_Ki1AD_NaK exp_eta_VF_over_RT=etaVF_over_RT exp_eta1_VF_over_RT=exp_eta_VF_over_RTexp_VF_over_RT INaCa=exp_eta_VF_over_RTNaiNaiNai-exp_eta1_VF_over_RTNao_p3CaiKmCa_Cao+KmCa_Cao_ksatexp_eta1_VF_over_RT ICab=G_CabV-E_Ca IpCa=IpCamaxCaiKmpCa+Cai1.01.0+Km1ATP_CaPinv_ATPi1.0+ADPinv_KiADP_CaP+1.01.0+Km2ATP_CaPinv_ATPi CaiP3=CaiCaiCai common=0.75CaiP31.0-0.02VCaiP3+KmnsCa_p3if|V|<LHospitalThreshold0.75CaiP3VFsq_over_RTexp_VF_over_RT-1.0CaiP3+KmnsCa_p3otherwise InsNa=PnsNacommonNaiexp_VF_over_RT-Nao InsK=PnsKcommonKiexp_VF_over_RT-Ko InsCa=InsNa+InsK V_AM=V_AM_scaler_max_1_f_01_12_23f_01P0+f_12P1+f_23P21.0+inv_ATPiKmATP_AM+KmATP_AM_Ki_AMADP ATPm=Cm-ADPm DmuH=DmuH_Constant+Dpsi NAD=CPN-NADH KmIDNAD_NAD=KmIDNADNAD exp_FRT_6_g_DmuH=FRT_6_gDmuH FRT2_Dpsi=FRT2Dpsi-91.0 VCS=VCS_C1OaaOaa+KmOaa VACO=kfACOCIK-AKG+SCoA+Succ+FUM+MAL+Oaa+ISOCone_inv_KACOeq Fa=1.01.0+ADPminv_KADP1.0+Caminv_KaCa Fi=1.0+NADHinv_KidhNADH VIDH=kIDH_EtIDVIDH_Constant+KmIDNAD_NADFi+KmisoISOCnIDFa1.0+KmIDNAD_NADFi a__1=Mg_Kmg_1+Mg_Kmg_1_KcaCam VKGDH=kKGDH_EtKGa__1a__1+KmKGAKGnKG+KmKGNAD_KmIDNADKmIDNAD_NAD VSL=kfSLSCoAADPm-CoA_KSLeqSuccATPm VSDH=kSDH_EtSDHSuccSucc+KmSucc+KmSucc_KiFUMFUM1.0+inv_KiOxaaOaa VFH=kfFHFUM-kfFH_KFHeqMAL VMDH=kMDH_Fh_EtMDMALNADMAL+Kmal+OaaKmal_KioaaKmmNAD+NAD VAAT=VAAT_ConstantOaakcnsASP_KAATeq_kfAAT+AKG AREN=NADHkres_sq_KmIDNADKmIDNAD_NAD denominator1=1.0exp_6_FRT_Dpsio+r1_exp_6_FRT_DpsioAREN+r2+r3ARENexp_FRT_6_g_DmuH VNO=rhoREN_ra_rc1_exp_6_FRT_Dpsio+rhoREN_rc2exp_FRT_6_g_DmuHAREN-rhoREN_raexp_FRT_6_g_DmuHdenominator1 VHNe=rhoRen_6_raAREN-rhoRen_6_ra_rbexp_FRT_6_g_DmuHdenominator1 denominator2=rhoREFVFO_VHFe_C1+r2_r3_exp_AREF_FRTexp_FRT_6_g_DmuH VHFe=ra_exp_AREF_FRT-ra_rbexp_FRT_6_g_DmuHdenominator2 exp_3FRT_DmuH=FRT_3DmuH AF1=kf1_PiATPmADPm denominator3=-rhoF1exp_3_FRT_Dpsio+p1_exp_3_FRT_DpsioAF1+p2+p3AF1exp_3FRT_DmuH VATPase=VATPase_C1+pc2exp_3FRT_DmuHAF1-paexp_3FRT_DmuHdenominator3 Vhu=pa_300+pa_300AF1-pa_pb_3exp_3FRT_DmuHdenominator3 ATPi_ADP=ATPiADP ADPm_ATPm=ADPmATPm VANT=VmDT_75-VmDT_20ATPi_ADPADPm_ATPm-F_over_RTDpsi1.0+10.09.0ATPi_ADP-hm_F_over_RTDpsi1.0+18.0ADPm_ATPm Vhleak=ghDmuH MAlpha=3.2ifV=-47.130.32V+47.131.0--0.1V+47.13otherwise MBeta=0.08-V1.011.0 inv_MBeta_MAlpha=1.0MBeta+MAlpha tmNa=MAlphainv_MBeta_MAlphaifinv_MBeta_MAlpha<0.03mNaotherwise HAlpha=0.135-80.06.8-1.06.8VifV<-40.00.0otherwise HBeta=3.560.079V+310000.00.35VifV<-40.01.00.13+0.13-10.6611.1V-1.011.1otherwise JAlpha=-127140.00.2444V-3.474e-5-0.04391VV+37.781.0+0.311V+79.23ifV<-40.00.0otherwise JBeta=0.1212-0.01052V1.0+-0.1378V+40.14ifV<-40.00.3-2.535e-7V1.0+-0.1V-3.2otherwise ddtimemNa=MAlpha1.0-tmNa-MBetatmNa ddtimehNa=HAlpha1.0-hNa-HBetahNa ddtimejNa=JAlpha1.0-jNa-JBetajNa ddtimexKs=7.19e-5V_301.0--0.148V_301.0-xKs-1.31e-4V_300.0687V_30-1.0xKs fb=Caiinv_KfbNfb rb=CaNSRinv_KrbNrb Jup=KSRvmaxffb-vmaxrrb1.0+fb+rbinv_ATPiKmATP_SR+ADPKmATP_SR_Ki_SR+1.0+ADPinv_Ki_prime_SR Jrel=v1O1_RyR+O2_RyRCaJSR-CaSS Jtr=CaNSR-CaJSRinv_tautr Jxfer=CaSS-Caiinv_tauxfer P1_N1_P2_P3=P1+N1+P2+P3 FN_Ca=alpha_SL_fnormmax2P1_N1_P2_P3 force_norm=alpha_SL_fnormmaxP1_N1_P2_P3+P2+P3+P3 force=zeta_alpha_SL_fnormmaxP1_N1_P2_P3+P2+P3+P3 kTrop_np=kTrop_pnLTRPNCainv_LTRPNtot_Ktrop_halfNtrop ddtimeP0=P0_differential P0_differential=kTrop_pn_f_01P0+kTrop_npN0+g_01_modP1 ddtimeP1=P1_differential P1_differential=kTrop_pn_f_12_g_01_modP1+kTrop_npN1+f_01P0+g_12_modP2 ddtimeP2=P2_differential P2_differential=f_23_g_12_modP2+f_12P1+g_23_modP3 ddtimeP3=P3_differential P3_differential=-g_23_modP3+f_23P2 ddtimeN1=N1_differential N1_differential=kTrop_pnP1-kTrop_np+g_01_off_modN1 ddtimeN0=-P0_differential-P1_differential+P2_differential+P3_differential+N1_differential ddtimeLTRPNCa=LTRPNCa_differential LTRPNCa_differential=kltrpn_plusCaiLTRPNtot-LTRPNCa-kltrpn_minusLTRPNCa1.0-2.03.0FN_Ca ddtimeHTRPNCa=HTRPNCa_differential HTRPNCa_differential=khtrpn_plusCaiHTRPNtot-HTRPNCa-khtrpn_minusHTRPNCa Jtrpn=LTRPNCa_differential+HTRPNCa_differential beta_SS=1.01.0+CMDNtot_KmCMDNCaSS+KmCMDNCaSS+KmCMDN beta_JSR=1.01.0+CSQNtot_KmCSQNCaJSR+KmCSQNCaJSR+KmCSQN beta_i=1.01.0+CMDNtot_KmCMDNCai+KmCMDNCai+KmCMDN Cai_ktrans_plus1=1.0+Caiinv_ktrans Cai_ktrans_plus1_p3=Cai_ktrans_plus1Cai_ktrans_plus1Cai_ktrans_plus1 Vuni=Vmuni_ktransCaiFRT2_DpsiCai_ktrans_plus1_p3Cai_ktrans_plus1_p3Cai_ktrans_plus1+L1.0+Caiinv_kactna1.0--FRT2_Dpsi VnaCa=VmNCb_05FRT2_DpsiCamCai1.0+KnaNain1.0+KncaCam ddtimeNai=-INa+INab+InsNa+3.0INaCa+INaKAcap_Vmyo_F-VnaCa0.615 ddtimeKi=-InsK+IKs+IK1+IKp+ICaK+Istim-2.0INaKAcap_Vmyo_F ddtimeCai=beta_iJxfer-Jup+Jtrpn+0.25Acap_Vmyo_FICab-2.0INaCa+IpCa+VnaCa-Vuni0.615 ddtimeCaSS=beta_SSJrelVJSR_VSS-JxferVmyo_VSS+ICaAcap_VSS_F ddtimeCaJSR=beta_JSRJtr-Jrel ddtimeCaNSR=JupVmyo_VNSR-JtrVJSR_VNSR ddtimeV=-inv_C_mINa+ICa+ICaK+IKs+IK1+IKp+INaCa+INaK+InsCa+IpCa+ICab+INab+Istim ddtimeC1_RyR=-kaplusCaSSncoopC1_RyR+kaminusO1_RyR ddtimeO2_RyR=kbplusCaSSmcoopO1_RyR-kbminusO2_RyR ddtimeC2_RyR=kcplusO1_RyR-kcminusC2_RyR alpha=0.4V+2.00.1 beta=0.05V+2.0-1.013.0 alpha_prime=aLalpha beta_prime=betainv_bL C0_to_C1=4.0alpha C1_to_C2=3.0alpha C2_to_C3=2.0alpha C3_to_C4=alpha CCa0_to_CCa1=4.0alpha_prime CCa1_to_CCa2=3.0alpha_prime CCa2_to_CCa3=2.0alpha_prime CCa3_to_CCa4=alpha_prime C1_to_C0=beta C2_to_C1=2.0beta C3_to_C2=3.0beta C4_to_C3=4.0beta CCa1_to_CCa0=beta_prime CCa2_to_CCa1=2.0beta_prime CCa3_to_CCa2=3.0beta_prime CCa4_to_CCa3=4.0beta_prime gamma=0.1875CaSS C0_to_CCa0=gamma C1_to_CCa1=aLC0_to_CCa0 C2_to_CCa2=aLC1_to_CCa1 C3_to_CCa3=aLC2_to_CCa2 C4_to_CCa4=aLC3_to_CCa3 CCa0_to_C0=omega CCa1_to_C1=CCa0_to_C0inv_bL CCa2_to_C2=CCa1_to_C1inv_bL CCa3_to_C3=CCa2_to_C2inv_bL CCa4_to_C4=CCa3_to_C3inv_bL ddtimeC0=C1_to_C0C1+CCa0_to_C0CCa0-C0_to_C1+C0_to_CCa0C0 ddtimeC1=C0_to_C1C0+C2_to_C1C2+CCa1_to_C1CCa1-C1_to_C0+C1_to_C2+C1_to_CCa1C1 ddtimeC2=C1_to_C2C1+C3_to_C2C3+CCa2_to_C2CCa2-C2_to_C1+C2_to_C3+C2_to_CCa2C2 ddtimeC3=C2_to_C3C2+C4_to_C3C4+CCa3_to_C3CCa3-C3_to_C2+C3_to_C4+C3_to_CCa3C3 ddtimeC4=C3_to_C4C3+gLOpen+CCa4_to_C4CCa4-C4_to_C3+fL+C4_to_CCa4C4 ddtimeOpen=fLC4-gLOpen ddtimeCCa0=CCa1_to_CCa0CCa1+C0_to_CCa0C0-CCa0_to_CCa1+CCa0_to_C0CCa0 ddtimeCCa1=CCa0_to_CCa1CCa0+CCa2_to_CCa1CCa2+C1_to_CCa1C1-CCa1_to_CCa0+CCa1_to_CCa2+CCa1_to_C1CCa1 ddtimeCCa2=CCa1_to_CCa2CCa1+CCa3_to_CCa2CCa3+C2_to_CCa2C2-CCa2_to_CCa1+CCa2_to_CCa3+CCa2_to_C2CCa2 ddtimeCCa3=CCa2_to_CCa3CCa2+CCa4_to_CCa3CCa4+C3_to_CCa3C3-CCa3_to_CCa2+CCa3_to_CCa4+CCa3_to_C3CCa3 ddtimeCCa4=CCa3_to_CCa4CCa3+gprimeOCa+C4_to_CCa4C4-CCa4_to_CCa3+fprime+CCa4_to_C4CCa4 ddtimeyCa=1.01.0+V+55.01.07.5+0.51.0+21.0-V1.06.0-yCa20.0+600.01.0+V+30.01.09.5 ddtimeOCa=fprimeCCa4-gprimeOCa Vt_CRP2=kt_2CrPi_mito-CrPi_cyto VCK_cyto=kf_2CRT_cyto-CrPi_cytoATPi_cyto-CrPi_cyto8.0-ATPi_cytoinv_keq VCK_mito=kf_3CRT_mito-CrPi_mitoATPi-CrPi_mitoADPinv_keq ddtimeCrPi_mito=VCK_mito-Vt_CRP2 ddtimeCrPi_cyto=Vt_CRP2+VCK_cyto ddtimeATPi=1.0-clamp_ATPi0.615VANT-V_AM+0.5Jup+6.371e-5INaK+IpCa+VCK_mito ddtimeATPi_cyto=1.0-clamp_ATPi_cyto-VCK_cyto-VATPase_cyto ddtimeCam=fmVuni-VnaCa ddtimeADPm=VANT-VATPase+VSL ddtimeDpsi=--VHNe-VHFe+Vhu+VANT+Vhleak+two_bVnaCa+2.0Vuniinv_Cmito ddtimeNADH=-VNO+VIDH+VKGDH+VMDH ddtimeISOC=VACO-VIDH ddtimeAKG=VIDH+VAAT-VKGDH ddtimeSCoA=VKGDH-VSL ddtimeSucc=VSL-VSDH ddtimeFUM=VSDH-VFH ddtimeMAL=VFH-VMDH ddtimeOaa=VMDH-VCS+VAAT ddtimeASP=VAAT-kcnsASPASP

Component: one_ion

reversal_potential=RTzFlnextracellular_concentrationintracellular_concentration

Component: one_ion

reversal_potential=RTzFlnextracellular_concentrationintracellular_concentration

Component: one_ion

reversal_potential=RTzFlnextracellular_concentrationintracellular_concentration

Component: two_ions

reversal_potential=RTzFlnmultiplier_1extracellular_concentration_1+multiplier_2extracellular_concentration_2multiplier_1intracellular_concentration_1+multiplier_2intracellular_concentration_2