Model Mathematics

Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell=10003.1416radradL Ageo=23.1416radrad+23.1416radL Acap=2Ageo vmyo=0.68vcell vnsr=0.0552vcell vjsr=0.0048vcell vss=0.02vcell vsr=0.95vnsr+vjsr

Component: membrane

Istim=i_Stim_Amplitudeiftimei_Stim_Starttimei_Stim_Endtime-i_Stim_Start-time-i_Stim_Starti_Stim_Periodi_Stim_Periodi_Stim_PulseDuration0.0otherwise vffrt=vFFRT vfrt=vFRT ddtimev=-INa+INaL+Ito+ICaL+ICaNa+ICaK+IKr+IKs+IK1+INaCa_i+INaCa_ss+INaK+INab+IKb+IpCa+ICab+Istim

Component: CaMK

CaMKb=CaMKo1.0-CaMKt1.0+KmCaMcass CaMKa=CaMKb+CaMKt ddtimeCaMKt=aCaMKCaMKbCaMKb+CaMKt-bCaMKCaMKt

Component: intracellular_ions

cmdnmax=cmdnmax_b1.2ifcelltype=1cmdnmax_botherwise ddtimenai=-INa+INaL+3INaCa_i+3INaK+INabAcapcmFvmyo+JdiffNavssvmyo ddtimenass=-ICaNa+3INaCa_sscmAcapFvss-JdiffNa ddtimeki=-Ito+IKr+IKs+IK1+IKb+Istim-2INaKcmAcapFvmyo+JdiffKvssvmyo ddtimekss=-ICaKcmAcapFvss-JdiffK Bcai=11+cmdnmaxkmcmdnkmcmdn+cai2+trpnmaxkmtrpnkmtrpn+cai2 ddtimecai=Bcai-IpCa+ICab-2INaCa_iAcap2Fvmyo-Jupvsrvmyo+Jleakvsrvmyo+Jdiffvssvmyo Bcass=11+BSRmaxKmBSRKmBSR+cass2+BSLmaxKmBSLKmBSL+cass2 ddtimecass=Bcass-ICaL-2INaCa_ssAcap2Fvss+Jrelvsrvss-Jdiff Bcasr=11+csqnmaxkmcsqnkmcsqn+casr2 ddtimecasr=BcasrJup-Jleak-Jrel

Component: reversal_potentials

ENa=RTFlnnaonai EK=RTFlnkoki EKs=RTFlnko+PKNanaoki+PKNanai

Component: INa

mss=1.01.0+-v+mssV1mssV2 tm=1mtD1v+mtV1mtV2+mtD2-v+mtV3mtV4 ddtimem=mss-mtm hss=1.01.0+v+hssV1hssV2 thf=1.03.6860e-6-v+3.88757.8579+16v-0.49639.1843+0.075 ths=1.00.009794-v+17.9528.05+0.3343v+5.7356.66 Ahs=1.0-Ahf ddtimehf=hss-hfthf ddtimehs=hss-hsths h=Ahfhf+Ahshs jss=hss tj=4.8590+1.00.8628-v+116.72587.6005+1.1096v+6.27199.0358btj ddtimej=jss-jtj hssp=11+v+84.76.220 thsp=3ths ddtimehsp=hssp-hspthsp hp=Ahfhf+Ahshsp tjp=1.46tj ddtimejp=jss-jptjp fINap=1.01.0+KmCaMKCaMKa INa=GNabGNav-ENam31-fINaphj+fINaphpjp

Component: INaL

mLss=11+-v+42.855.264 tmL=tm ddtimemL=mLss-mLtmL hLss=1.01.0+v+87.617.488 thL=200.0bthL ddtimehL=hLss-hLthL hLssp=11+v+93.817.488 thLp=3.0thL ddtimehLp=hLssp-hLpthLp GNaL=GNaL_bbGnal0.7ifcelltype=1GNaL_bbGnalotherwise fINaLp=1.01.0+KmCaMKCaMKa INaL=GNaLv-ENamL1.0-fINaLphL+fINaLphLp

Component: Ito

ass=11+-v+EKshift-14.3414.82 ta=1.05151.01.20891.0+-v+EKshift-18.409929.3814+3.51.0+v+EKshift+100.029.3814 ddtimea=ass-ata iss=1.01.0+v+EKshift+43.945.711 delta_epi=1.0-0.951+v+EKshift+705ifcelltype=11.0otherwise tiF_b=4.562+1.00.3933-v+EKshift+100.0100.0+0.08004v+EKshift+50.016.59 tiS_b=23.62+10.001416-v+EKshift+96.5259.05+1.78e-8v+EKshift+114.18.079 tiF=tiF_bdelta_epi tiS=tiS_bdelta_epi AiF=1.01.0+v+EKshift-213.6151.2 AiS=1.0-AiF ddtimeiF=iss-iFtiF ddtimeiS=iss-iStiS i=AiFiF+AiSiS assp=1.01.0+-v+EKshift-24.3414.82 ddtimeap=assp-apta dti_develop=1.354+1e-4v+EKshift-167.415.89+-v+EKshift-12.230.2154 dti_recover=1.0-0.51+v+EKshift+70.020.0 tiFp=dti_developdti_recovertiF tiSp=dti_developdti_recovertiS ddtimeiFp=iss-iFptiFp ddtimeiSp=iss-iSptiSp ip=AiFiFp+AiSiSp Gto=bGtoGto_b4ifcelltype=1bGtoGto_b4ifcelltype=2Gto_bbGtootherwise fItop=1.01.0+KmCaMKCaMKa Ito=Gtov-EK1.0-fItopai+fItopapip

Component: ICaL

fICaLp=11+KmCaMKCaMKa r_down=1e-11-undo_CDI r_up=r_downnca1-nca1-undo_CDI jncass=1.01.0+v+19.58+253.696 ddtimejnca=jncass-jncatjnca km2n=jnca150 anca=1-nca1+Kmncass4 ddtimenca=ancak2n-ncakm2n dss=1.01.0+-v+3.9404.230 td=0.6+1-0.05v+6+0.09v+14 alpha=dsstd beta=1-dsstd jcass_new=1.01.0+v+19.583.696 jcass_VD=jcass_new jcass_CD=jcass_new jcass_VDp=jcass_new jcass_CDp=jcass_new tjca_new=35+350-v+2022100 tjca_VD=tjca_new tjca_CD=tjca_new tjca_VDp=tjca_new tjca_CDp=tjca_new psi_VD=jcass_VDtjca_VD psi_VDp=jcass_VDptjca_VDp psi_CD=jcass_CDtjca_CD psi_CDp=jcass_CDptjca_CDp omega_VD=1-jcass_VDtjca_VD omega_VDp=1-jcass_VDptjca_VDp omega_CD=1-jcass_CDtjca_CD omega_CDp=1-jcass_CDptjca_CDp f1ss_0=0.81.0+v+19.583.696+0.2 tf1_0=170+1.20.0045v+20-50+0.0045v+3010 ktaup=2.5 gamma_VD=1-f1ss_0tf1_0 delta_VD=f1ss_0tf1_0 gamma_VDp=gamma_VDktaup delta_VDp=delta_VDktaup gamma_CD=gamma_VDkCDI delta_CD=delta_VDkCDI gamma_CDp=gamma_VDpkCDI delta_CDp=delta_VDpkCDI tf1_VD=1gamma_VD+delta_VD tf1_CD=1gamma_CD+delta_CD f1ss_VD=gamma_VDgamma_VD+delta_VD f1ss_CD=gamma_CDgamma_CD+delta_CD tf2_new=1100+00.0035v+5-84+0.0035v+54 tf2_VD=tf2_new tf2_CD=tf2_VDkCDI tf2_VDp=tf2_newktaup tf2_CDp=tf2_VDkCDIktaup theta_VD=alphagamma_VDpsi_VDtf2_VDalphagamma_VDpsi_VD+betadelta_VDomega_VD theta_CD=alphagamma_CDpsi_CDtf2_CDalphagamma_CDpsi_CD+betadelta_CDomega_CD theta_VDp=alphagamma_VDppsi_VDptf2_VDpalphagamma_VDppsi_VDp+betadelta_VDpomega_VDp theta_CDp=alphagamma_CDppsi_CDptf2_CDpalphagamma_CDppsi_CDp+betadelta_CDpomega_CDp eta_VD=1tf2_VD-theta_VD eta_VDp=1tf2_VDp-theta_VDp eta_CD=1tf2_CD-theta_CD eta_CDp=1tf2_CDp-theta_CDp tf2post_VD=1eta_VD+theta_VD tf2post_CD=1eta_CD+theta_CD f2ss_VD=eta_VDeta_VD+theta_VD f2ss_CD=eta_CDeta_CD+theta_CD PhiCaL=4.0vffrt1.2cass2vfrt-0.341cao2.0vfrt-1.0 PhiCaNa=1.0vffrt0.75nass1.0vfrt-0.75nao1.0vfrt-1.0 PhiCaK=1.0vffrt0.75kss1.0vfrt-0.75ko1.0vfrt-1.0 PCa=PCa_b0.91.4ifcelltype=1PCa_b0.92.0ifcelltype=2PCa_b0.9otherwise PCap=1.1PCa PCaNa=0.00125PCa PCaK=3.574e-4PCa PCaNap=0.00125PCap PCaKp=3.574e-4PCap OCak=1-CCak-I1Cak-I2Cak-Ck-I1k-I2k-Ok OCakp=1-CCakp-I1Cakp-I2Cakp-Ckp-I1kp-I2kp-Okp ddtimeOk=alphaCk+delta_VDI1k-beta+gamma_VDOk-r_upOk+r_downOCak ddtimeI2k=eta_VDI1k+omega_VDCk-theta_VD+psi_VDI2k-r_upI2k+r_downI2Cak ddtimeI1k=theta_VDI2k+gamma_VDOk-eta_VD+delta_VDI1k-r_upI1k+r_downI1Cak ddtimeCk=betaOk+psi_VDI2k-omega_VD+alphaCk-r_upCk+r_downCCak ddtimeOkp=alphaCkp+delta_VDpI1kp-beta+gamma_VDpOkp-r_upOkp+r_downOCakp ddtimeI2kp=eta_VDpI1kp+omega_VDpCkp-theta_VDp+psi_VDpI2kp-r_upI2kp+r_downI2Cakp ddtimeI1kp=theta_VDpI2kp+gamma_VDpOkp-eta_VDp+delta_VDpI1kp-r_upI1kp+r_downI1Cakp ddtimeCkp=betaOkp+psi_VDpI2kp-omega_VDp+alphaCkp-r_upCkp+r_downCCakp ddtimeI2Cak=eta_CDI1Cak+omega_CDCCak-theta_CD+psi_CDI2Cak+r_upI2k-r_downI2Cak ddtimeI1Cak=theta_CDI2Cak+gamma_CDOCak-eta_CD+delta_CDI1Cak+r_upI1k-r_downI1Cak ddtimeCCak=betaOCak+psi_CDI2Cak-omega_CD+alphaCCak+r_upCk-r_downCCak ddtimeI2Cakp=eta_CDpI1Cakp+omega_CDpCCakp-theta_CDp+psi_CDpI2Cakp+r_upI2kp-r_downI2Cakp ddtimeI1Cakp=theta_CDpI2Cakp+gamma_CDpOCakp-eta_CDp+delta_CDpI1Cakp+r_upI1kp-r_downI1Cakp ddtimeCCakp=betaOCakp+psi_CDpI2Cakp-omega_CDp+alphaCCakp+r_upCkp-r_downCCakp ICaL_VD=PCaPhiCaLOk ICaL_VDp=PCapPhiCaLOkp ICaL_CD=PCaPhiCaLOCak ICaL_CDp=PCapPhiCaLOCakp ICaNa_VD=PCaNaPhiCaNaOk ICaNa_VDp=PCaNapPhiCaNaOkp ICaNa_CD=PCaNaPhiCaNaOCak ICaNa_CDp=PCaNapPhiCaNaOCakp ICaK_VD=PCaKPhiCaKOk ICaK_VDp=PCaKpPhiCaKOkp ICaK_CD=PCaKPhiCaKOCak ICaK_CDp=PCaKpPhiCaKOCakp ICaLnp=ICaL_VD+ICaL_CD ICaLp=ICaL_VDp+ICaL_CDp ICaLVD=ICaL_VD1-fICaLp+ICaL_VDpfICaLp ICaLCD=ICaL_CD1-fICaLp+ICaL_CDpfICaLp ICaNanp=ICaNa_VD+ICaNa_CD ICaNap=ICaNa_VDp+ICaNa_CDp ICaKnp=ICaK_VD+ICaK_CD ICaKp=ICaK_VDp+ICaK_CDp ICaL=ICaLpfICaLp+ICaLnp1-fICaLpbGCaL ICaNa=ICaNapfICaLp+ICaNanp1-fICaLpbGCaL ICaK=ICaKpfICaLp+ICaKnp1-fICaLpbGCaL gICaL=ICaLPhiCaL

Component: IKr

ddtimeIC1=-A11B11vIC1Temp-293lnq1110-A21B21vIC2Temp-293lnq2110+A51B51vC1Temp-293lnq5110-A61B61vIC1Temp-293lnq6110 ddtimeIC2=A11B11vIC1Temp-293lnq1110-A21B21vIC2Temp-293lnq2110-A3B3vIC2Temp-293lnq310-A4B4vIOTemp-293lnq410+A52B52vC2Temp-293lnq5210-A62B62vIC2Temp-293lnq6210 ddtimeC1=-A1B1vC1Temp-293lnq110-A2B2vC2Temp-293lnq210-A51B51vC1Temp-293lnq5110-A61B61vIC1Temp-293lnq6110 ddtimeC2=A1B1vC1Temp-293lnq110-A2B2vC2Temp-293lnq210-A31B31vC2Temp-293lnq3110-A41B41vOTemp-293lnq4110-A52B52vC2Temp-293lnq5210-A62B62vIC2Temp-293lnq6210 ddtimeO=A31B31vC2Temp-293lnq3110-A41B41vOTemp-293lnq4110-A53B53vOTemp-293lnq5310-A63B63vIOTemp-293lnq6310-KmaxKunlnDnlnD+halfmaxO-KuObound ddtimeIO=A3B3vIC2Temp-293lnq310-A4B4vIOTemp-293lnq410+A53B53vOTemp-293lnq5310-A63B63vIOTemp-293lnq6310-KmaxKunlnDnlnD+halfmaxIO-KuA53B53vTemp-293lnq5310A63B63vTemp-293lnq6310IObound ddtimeIObound=KmaxKunlnDnlnD+halfmaxIO-KuA53B53vTemp-293lnq5310A63B63vTemp-293lnq6310IObound+Kt1+-v-Vhalf6.789Cbound-KtIObound ddtimeObound=KmaxKunlnDnlnD+halfmaxO-KuObound+Kt1+-v-Vhalf6.789Cbound-KtObound ddtimeCbound=-Kt1+-v-Vhalf6.789Cbound-KtObound-Kt1+-v-Vhalf6.789Cbound-KtIObound ddtimeD=0 GKr=GKr_bbGKr1.1ifcelltype=1GKr_bbGKr0.8ifcelltype=2GKr_bbGKrotherwise GKr_total=GKrko5.4 IKr=GKr_totalOv-EK

Component: IKs

xs1ss=11+-v+11.6+EKshift8.932 txs1=817.3+12.326e-4v+48.28+EKshift17.8+0.001292-v+210+EKshift230.0 ddtimexs1=xs1ss-xs1txs1 xs2ss=xs1ss txs2=10.01v-50+EKshift20+0.0193-v+66.54+EKshift31.0 ddtimexs2=xs2ss-xs2txs2 KsCa=1.0+0.61+3.8e-5cai1.4 GKs=bGKsGKs_b1.4ifcelltype=1bGKsGKs_botherwise IKs=GKsKsCaxs1xs2v-EKs

Component: IK1

xk1ss=11+-v+2.5538ko+144.59+EKshift1.5692ko+3.8115 txk1=122.2-v+EKshift+127.220.36+v+EKshift+236.869.33 ddtimexk1=xk1ss-xk1txk1 rk1=11+v+105.8-2.6ko+EKshiftkslope_rk19.493 GK1=bGK1GK1_b1.2ifcelltype=1bGK1GK1_b1.3ifcelltype=2bGK1GK1_botherwise IK1=GK1kork1xk1v-EK

Component: INaCa_i

hca=qcavFRT hna=qnavFRT h1_i=1.0+naikna31.0+hna h2_i=naihnakna3h1_i h3_i=1.0h1_i h4_i=1.0+naikna11.0+naikna2 h5_i=nainaih4_ikna1kna2 h6_i=1.0h4_i h7_i=1.0+naokna31.0+1hna h8_i=naokna3hnah7_i h9_i=1h7_i h10_i=kasymm+1.0+naokna11+naokna2 h11_i=naonaoh10_ikna1kna2 h12_i=1.0h10_i k1_i=h12_icaokcaon k2_i=kcaoff k3p_i=h9_iwca k3pp_i=h8_iwnaca k3_i=k3p_i+k3pp_i k4p_i=h3_iwcahca k4pp_i=h2_iwnaca k4_i=k4p_i+k4pp_i k5_i=kcaoff k6_i=h6_icaikcaon k7_i=h5_ih2_iwna k8_i=h8_ih11_iwna x1_i=k2_ik4_ik7_i+k6_i+k5_ik7_ik2_i+k3_i x2_i=k1_ik7_ik4_i+k5_i+k4_ik6_ik1_i+k8_i x3_i=k1_ik3_ik7_i+k6_i+k8_ik6_ik2_i+k3_i x4_i=k2_ik8_ik4_i+k5_i+k3_ik5_ik1_i+k8_i E1_i=x1_ix1_i+x2_i+x3_i+x4_i E2_i=x2_ix1_i+x2_i+x3_i+x4_i E3_i=x3_ix1_i+x2_i+x3_i+x4_i E4_i=x4_ix1_i+x2_i+x3_i+x4_i allo_i=11+KmCaActcai2 JncxNa_i=3.0E4_ik7_i-E1_ik8_i+E3_ik4pp_i-E2_ik3pp_i JncxCa_i=E2_ik2_i-E1_ik1_i Gncx=bGncxGncx_b1.2ifcelltype=1bGncxGncx_b1.4ifcelltype=2bGncxGncx_botherwise INaCa_i=0.8Gncxallo_iznaJncxNa_i+zcaJncxCa_i h1_ss=1+nasskna31+hna h2_ss=nasshnakna3h1_ss h3_ss=1h1_ss h4_ss=1+nasskna11+nasskna2 h5_ss=nassnassh4_sskna1kna2 h6_ss=1h4_ss h7_ss=1+naokna31+1hna h8_ss=naokna3hnah7_ss h9_ss=1h7_ss h10_ss=kasymm+1+naokna11+naokna2 h11_ss=naonaoh10_sskna1kna2 h12_ss=1h10_ss k1_ss=h12_sscaokcaon k2_ss=kcaoff k3p_ss=h9_sswca k3pp_ss=h8_sswnaca k3_ss=k3p_ss+k3pp_ss k4p_ss=h3_sswcahca k4pp_ss=h2_sswnaca k4_ss=k4p_ss+k4pp_ss k5_ss=kcaoff k6_ss=h6_sscasskcaon k7_ss=h5_ssh2_sswna k8_ss=h8_ssh11_sswna x1_ss=k2_ssk4_ssk7_ss+k6_ss+k5_ssk7_ssk2_ss+k3_ss x2_ss=k1_ssk7_ssk4_ss+k5_ss+k4_ssk6_ssk1_ss+k8_ss x3_ss=k1_ssk3_ssk7_ss+k6_ss+k8_ssk6_ssk2_ss+k3_ss x4_ss=k2_ssk8_ssk4_ss+k5_ss+k3_ssk5_ssk1_ss+k8_ss E1_ss=x1_ssx1_ss+x2_ss+x3_ss+x4_ss E2_ss=x2_ssx1_ss+x2_ss+x3_ss+x4_ss E3_ss=x3_ssx1_ss+x2_ss+x3_ss+x4_ss E4_ss=x4_ssx1_ss+x2_ss+x3_ss+x4_ss allo_ss=11+KmCaActcass2 JncxNa_ss=3E4_ssk7_ss-E1_ssk8_ss+E3_ssk4pp_ss-E2_ssk3pp_ss JncxCa_ss=E2_ssk2_ss-E1_ssk1_ss INaCa_ss=0.2Gncxallo_ssznaJncxNa_ss+zcaJncxCa_ss

Component: INaK

Knai=Knai0deltavF3.0RT Knao=Knao01.0-deltavF3.0RT P=eP1+HKhp+naiKnap+kiKxkur a1=k1pnaiKnai31+naiKnai3+1+kiKki2-1.0 b1=k1mMgADP a2=k2p b2=k2mnaoKnao31+naoKnao3+1+koKko2-1 a3=k3pkoKko21+naoKnao3+1+koKko2-1.0 b3=k3mPH1+MgATPKmgatp a4=k4pMgATPKmgatp1+MgATPKmgatp b4=k4mkiKki21+naiKnai3+1+kiKki2-1.0 x1=a4a1a2+b2b4b3+a2b4b3+b3a1a2 x2=b2b1b4+a1a2a3+a3b1b4+a2a3b4 x3=a2a3a4+b3b2b1+b2b1a4+a3a4b1 x4=b4b3b2+a3a4a1+b2a4a1+b3b2a1 E1=x1x1+x2+x3+x4 E2=x2x1+x2+x3+x4 E3=x3x1+x2+x3+x4 E4=x4x1+x2+x3+x4 JnakNa=3E1a3-E2b3 JnakK=2E4b1-E3a1 Pnak=bGnakPnak_b0.9ifcelltype=1bGnakPnak_b0.7ifcelltype=2bGnakPnak_botherwise INaK=PnakznaJnakNa+zkJnakK

Component: IKb

xkb=11+-v-14.4818.34 GKb=GKb_b0.6ifcelltype=1GKb_botherwise IKb=GKbxkbv-EK

Component: INab

INab=PNabvffrtnaivfrt-naovfrt-1.0

Component: ICab

ICab=1-undo_ICabPCab16vffrt1.2cai2vfrt-0.341cao2vfrt-1.0

Component: IpCa

IpCa=GpCacaiKmCap+cai

Component: diff

JdiffNa=nass-nai2.0 JdiffK=kss-ki2.0 Jdiff=cass-cai1.70.2

Component: ryr

RyRohalf=0.12-RyRa1-RyRa22 RyRchalf=0.10-RyRa1-RyRa22 RyRSRCass=1-11+casr-0.30.1 RyRainfss=RyRa1-RyRa21+1000cass-0.0430.0082 RyRtauadapt=1000 ddtimeRyRa=RyRainfss-RyRaRyRtauadapt RyRoinfss=1-11+1000cass-RyRa+RyRohalf0.003 RyRtauact=18.75e-11.875 ddtimeRyRo=RyRoinfss-RyRoRyRtauact RyRcinfss=11+1000cass-RyRa+RyRchalf0.001 RyRtauinact=287.510 ddtimeRyRc=RyRcinfss-RyRcRyRtauinact RyRtauinactp=RyRtauinact1.25 ddtimeRyRcp=RyRcinfss-RyRcpRyRtauinactp fJrelp=11+KmCaMKCaMKa g_irel_max_M=g_irel_max1.7 Jrelnp=g_irel_max_MRyRSRCassRyRoRyRccasr-cassifcelltype=2g_irel_maxRyRSRCassRyRoRyRccasr-cassotherwise g_irel_max_p=g_irel_max1.25 Jrelp=g_irel_max_p1.7RyRSRCassRyRoRyRcpcasr-cassifcelltype=2g_irel_max_pRyRSRCassRyRoRyRcpcasr-cassotherwise Jrel=1-fJrelpJrelnp+fJrelpJrelp

Component: SERCA

upScale=1.3ifcelltype=11otherwise Jupnp=upScale0.004375caicai+0.00092 Jupp=upScale2.750.004375caicai+0.00092-0.00017 fJupp=11+KmCaMKCaMKa Jleak=0.0123casr15.0 Jup=cJup1-fJuppJupnp+fJuppJupp Vmax_SRCaP=1.05.3114e-3 Kmf=0.246e-3 Kmr=1.7 hillSRCaP=1.787 Jup2=Vmax_SRCaPcaiKmfhillSRCaP-casrKmrhillSRCaP1+caiKmfhillSRCaP+casrKmrhillSRCaP

Component: trans_flux

Jtr=0