Model Mathematics

Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell=10003.14radradL Ageo=23.14radrad+23.14radL Acap=2Ageo vmyo=0.68vcell vnsr=0.0552vcell vjsr=0.0048vcell vss=0.02vcell

Component: membrane

Istim=i_Stim_Amplitudeiftimei_Stim_Starttimei_Stim_Endtime-i_Stim_Start-time-i_Stim_Starti_Stim_Periodi_Stim_Periodi_Stim_PulseDuration0otherwise vffrt=vFFRT vfrt=vFRT ddtimev=-INa+INaL+Ito+ICaL+ICaNa+ICaK+IKr+IKs+IK1+INaCa_i+INaCa_ss+INaK+INab+IKb+IpCa+ICab+IClCa+IClb+I_katp+Istim

Component: CaMK

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

Component: intracellular_ions

cmdnmax=cmdnmax_b1.3ifcelltype=1cmdnmax_botherwise ddtimenai=-INa+INaL+3INaCa_i+ICaNa_i+3INaK+INabAcapFvmyo+JdiffNavssvmyo ddtimenass=-ICaNa_ss+3INaCa_ssAcapFvss-JdiffNa ddtimeki=-Ito+IKr+IKs+IK1+IKb+I_katp+Istim-2INaK+ICaK_iAcapFvmyo+JdiffKvssvmyo ddtimekss=-ICaK_ssAcapFvss-JdiffK Bcai=11+cmdnmaxkmcmdnkmcmdn+cai2+trpnmaxkmtrpnkmtrpn+cai2 ddtimecai=Bcai-ICaL_i+IpCa+ICab-2INaCa_iAcap2Fvmyo-Jupvnsrvmyo+Jdiffvssvmyo Bcass=11+BSRmaxKmBSRKmBSR+cass2+BSLmaxKmBSLKmBSL+cass2 ddtimecass=Bcass-ICaL_ss-2INaCa_ssAcap2Fvss+Jrelvjsrvss-Jdiff ddtimecansr=Jup-Jtrvjsrvnsr Bcajsr=11+csqnmaxkmcsqnkmcsqn+cajsr2 ddtimecajsr=BcajsrJtr-Jrel

Component: reversal_potentials

ENa=RTznaFlnnaonai EK=RTzkFlnkoki EKs=RTzkFlnko+PKNanaoki+PKNanai ECl=RTzclFlnclocli

Component: I_katp

akik=koK_o_n0.24 bkik=11+A_atpK_atp2 I_katp=fkatpgkatpakikbkikv-EK

Component: INa

mss=11+-v+56.869.032 tm=0.1292-v+45.7915.542+0.06487-v-4.82351.122 ddtimem=mss-mtm hss=11+v+71.557.432 ah=0ifv-400.057-v+806.8otherwise bh=0.770.131+-v+10.6611.1ifv-402.70.079v+3.1e50.3485votherwise th=1ah+bh ddtimeh=hss-hth aj=0ifv-40-2.5428e40.2444v-6.948e-6-0.04391vv+37.781+0.311v+79.23otherwise bj=0.60.057v1+-0.1v+32ifv-400.02424-0.01052v1+-0.1378v+40.14otherwise jss=hss tj=1aj+bj ddtimej=jss-jtj hssp=11+v+77.557.432 ddtimehp=hssp-hpth tjp=1.46tj ddtimejp=jss-jptjp fINap=11+KmCaMKCaMKa INa=GNav-ENam31-fINaphj+fINaphpjp

Component: INaL

mLss=11+-v+42.855.264 tmL=0.1292-v+45.7915.542+0.06487-v-4.82351.122 ddtimemL=mLss-mLtmL hLss=11+v+87.617.488 ddtimehL=hLss-hLthL hLssp=11+v+93.817.488 thLp=3thL ddtimehLp=hLssp-hLpthLp GNaL=GNaL_b0.6ifcelltype=1GNaL_botherwise fINaLp=11+KmCaMKCaMKa INaL=GNaLv-ENamL1-fINaLphL+fINaLphLp

Component: Ito

ass=11+-v+EKshift-14.3414.82 ta=1.051511.20891+-v+EKshift-18.409929.3814+3.51+v+EKshift+10029.3814 ddtimea=ass-ata iss=11+v+EKshift+43.945.711 delta_epi=1-0.951+v+EKshift+705ifcelltype=11otherwise tiF_b=4.562+10.3933-v+EKshift+100100+0.08004v+EKshift+5016.59 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=11+v+EKshift-213.6151.2 AiS=1-AiF ddtimeiF=iss-iFtiF ddtimeiS=iss-iStiS i=AiFiF+AiSiS assp=11+-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=1-0.51+v+EKshift+70.020.0 tiFp=dti_developdti_recovertiF tiSp=dti_developdti_recovertiS ddtimeiFp=iss-iFptiFp ddtimeiSp=iss-iSptiSp ip=AiFiFp+AiSiSp Gto=Gto_b2ifcelltype=1Gto_b2ifcelltype=2Gto_botherwise fItop=11+KmCaMKCaMKa Ito=Gtov-EK1-fItopai+fItopapip

Component: ICaL

dss=1ifv31.49781.0763-1.0070-0.0829votherwise td=offset+0.6+1-0.05v+vShift+6+0.09v+vShift+14 ddtimed=dss-dtd fss=11+v+19.583.696 tff=7+10.0045-v+2010+0.0045v+2010 tfs=1000+10.000035-v+54+0.000035v+56 Afs=1-Aff ddtimeff=fss-fftff ddtimefs=fss-fstfs f=Affff+Afsfs fcass=fss tfcaf=7+10.04-v-47+0.04v-47 tfcas=100+10.00012-v3+0.00012v7 Afcaf=0.3+0.61+v-1010 Afcas=1-Afcaf ddtimefcaf=fcass-fcaftfcaf ddtimefcas=fcass-fcastfcas fca=Afcaffcaf+Afcasfcas jcass=1.01.0+v+18.082.7916 ddtimejca=jcass-jcatjca tffp=2.5tff ddtimeffp=fss-ffptffp fp=Affffp+Afsfs tfcafp=2.5tfcaf ddtimefcafp=fcass-fcafptfcafp fcap=Afcaffcafp+Afcasfcas km2n=jca1 anca_ss=1k2nkm2n+1+Kmncass4 ddtimenca_ss=anca_ssk2n-nca_sskm2n Io=0.5nao+ko+clo+4cao1000 Iss=0.5nass+kss+cli+4cass1000 constA=1.82e6dielConstantT-1.5 gamma_cass=-constA4Iss1+Iss-0.3Iss gamma_cao=-constA4Io1+Io-0.3Io gamma_nass=-constA1Iss1+Iss-0.3Iss gamma_nao=-constA1Io1+Io-0.3Io gamma_kss=-constA1Iss1+Iss-0.3Iss gamma_ko=-constA1Io1+Io-0.3Io PhiCaL_ss=4vffrtgamma_casscass2vfrt-gamma_caocao2vfrt-1 PhiCaNa_ss=1vffrtgamma_nassnass1vfrt-gamma_naonao1vfrt-1 PhiCaK_ss=1vffrtgamma_ksskss1vfrt-gamma_koko1vfrt-1 PCa=PCa_b1.2ifcelltype=1PCa_b2ifcelltype=2PCa_botherwise PCap=1.1PCa PCaNa=0.00125PCa PCaK=3.574e-4PCa PCaNap=0.00125PCap PCaKp=3.574e-4PCap fICaLp=11+KmCaMKCaMKa ICaL_ss=ICaL_fractionSS1-fICaLpPCaPhiCaL_ssdf1-nca_ss+jcafcanca_ss+fICaLpPCapPhiCaL_ssdfp1-nca_ss+jcafcapnca_ss ICaNa_ss=ICaL_fractionSS1-fICaLpPCaNaPhiCaNa_ssdf1-nca_ss+jcafcanca_ss+fICaLpPCaNapPhiCaNa_ssdfp1-nca_ss+jcafcapnca_ss ICaK_ss=ICaL_fractionSS1-fICaLpPCaKPhiCaK_ssdf1-nca_ss+jcafcanca_ss+fICaLpPCaKpPhiCaK_ssdfp1-nca_ss+jcafcapnca_ss anca_i=1k2nkm2n+1+Kmncai4 ddtimenca_i=anca_ik2n-nca_ikm2n Ii=0.5nai+ki+cli+4cai1000 gamma_cai=-constA4Ii1+Ii-0.3Ii gamma_nai=-constA1Ii1+Ii-0.3Ii gamma_ki=-constA1Ii1+Ii-0.3Ii PhiCaL_i=4vffrtgamma_caicai2vfrt-gamma_caocao2vfrt-1 PhiCaNa_i=1vffrtgamma_nainai1vfrt-gamma_naonao1vfrt-1 PhiCaK_i=1vffrtgamma_kiki1vfrt-gamma_koko1vfrt-1 ICaL_i=1-ICaL_fractionSS1-fICaLpPCaPhiCaL_idf1-nca_i+jcafcanca_i+fICaLpPCapPhiCaL_idfp1-nca_i+jcafcapnca_i ICaNa_i=1-ICaL_fractionSS1-fICaLpPCaNaPhiCaNa_idf1-nca_i+jcafcanca_i+fICaLpPCaNapPhiCaNa_idfp1-nca_i+jcafcapnca_i ICaK_i=1-ICaL_fractionSS1-fICaLpPCaKPhiCaK_idf1-nca_i+jcafcanca_i+fICaLpPCaKpPhiCaK_idfp1-nca_i+jcafcapnca_i ICaL=ICaL_ss+ICaL_i ICaNa=ICaNa_ss+ICaNa_i ICaK=ICaK_ss+ICaK_i

Component: IKr

alpha=0.11610.2990vfrt beta=0.2442-1.604vfrt alpha_2=0.05780.9710vfrt beta_2=0.349e-3-1.062vfrt alpha_i=0.25330.5953vfrt beta_i=0.06525-0.8209vfrt alpha_C2ToI=0.52e-41.525vfrt beta_ItoC2=beta_2beta_ialpha_C2ToIalpha_2alpha_i ddtimeC3=betaC2-alphaC3 ddtimeC2=alphaC3+beta_1C1-beta+alpha_1C2 ddtimeC1=alpha_1C2+beta_2O+beta_ItoC2I-beta_1+alpha_2+alpha_C2ToIC1 ddtimeO=alpha_2C1+beta_iI-beta_2+alpha_iO ddtimeI=alpha_C2ToIC1+alpha_iO-beta_ItoC2+beta_iI GKr=GKr_b1.3ifcelltype=1GKr_b0.8ifcelltype=2GKr_botherwise IKr=GKrko5Ov-EK

Component: IKs

xs1ss=11+-v+11.68.932 txs1=817.3+12.326e-4v+48.2817.8+0.001292-v+210230 ddtimexs1=xs1ss-xs1txs1 xs2ss=xs1ss txs2=10.01v-5020+0.0193-v+66.5431 ddtimexs2=xs2ss-xs2txs2 KsCa=1+0.61+3.8e-5cai1.4 GKs=GKs_b1.4ifcelltype=1GKs_botherwise IKs=GKsKsCaxs1xs2v-EKs

Component: IK1

aK1=4.0941+0.1217v-EK-49.934 bK1=15.720.0674v-EK-3.257+0.0618v-EK-594.311+-0.1629v-EK+14.207 K1ss=aK1aK1+bK1 GK1=GK1_b1.2ifcelltype=1GK1_b1.3ifcelltype=2GK1_botherwise IK1=GK1ko5K1ssv-EK

Component: INaCa

hca=qcavfrt hna=qnavfrt h1_i=1+naikna31+hna h2_i=naihnakna3h1_i h3_i=1h1_i h4_i=1+naikna11+naikna2 h5_i=nainaih4_ikna1kna2 h6_i=1h4_i h7_i=1+naokna31+1hna h8_i=naokna3hnah7_i h9_i=1h7_i h10_i=kasymm+1+naokna11+naokna2 h11_i=naonaoh10_ikna1kna2 h12_i=1h10_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=3E4_ik7_i-E1_ik8_i+E3_ik4pp_i-E2_ik3pp_i JncxCa_i=E2_ik2_i-E1_ik1_i Gncx=Gncx_b1.1ifcelltype=1Gncx_b1.4ifcelltype=2Gncx_botherwise INaCa_i=1-INaCa_fractionSSGncxallo_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=INaCa_fractionSSGncxallo_ssznaJncxNa_ss+zcaJncxCa_ss

Component: INaK

Knai=Knai0deltavfrt3 Knao=Knao01-deltavfrt3 P=eP1+HKhp+naiKnap+kiKxkur a1=k1pnaiKnai31+naiKnai3+1+kiKki2-1 b1=k1mMgADP a2=k2p b2=k2mnaoKnao31+naoKnao3+1+koKko2-1 a3=k3pkoKko21+naoKnao3+1+koKko2-1 b3=k3mPH1+MgATPKmgatp a4=k4pMgATPKmgatp1+MgATPKmgatp b4=k4mkiKki21+naiKnai3+1+kiKki2-1 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=Pnak_b0.9ifcelltype=1Pnak_b0.7ifcelltype=2Pnak_botherwise INaK=PnakznaJnakNa+zkJnakK

Component: IKb

xkb=11+-v-10.896823.9871 GKb=GKb_b0.6ifcelltype=1GKb_botherwise IKb=GKbxkbv-EK

Component: INab

INab=PNabvffrtnaivfrt-naovfrt-1

Component: ICab

ICab=PCab4vffrtgamma_caicai2vfrt-gamma_caocao2vfrt-1

Component: IpCa

IpCa=GpCacaiKmCap+cai

Component: ICl

IClCa_junc=FjuncGClCa1+KdClCacassv-ECl IClCa_sl=1-FjuncGClCa1+KdClCacaiv-ECl IClCa=IClCa_junc+IClCa_sl IClb=GClbv-ECl

Component: diff

JdiffNa=nass-naitauNa JdiffK=kss-kitauK Jdiff=cass-caitauCa

Component: ryr

a_rel=0.5bt1 Jrel_inf_b=-a_relICaL_ss11+cajsr_halfcajsr8 Jrel_inf=Jrel_inf_b1.7ifcelltype=2Jrel_inf_botherwise tau_rel_b=bt1+0.0123cajsr tau_rel=0.001iftau_rel_b<0.001tau_rel_botherwise ddtimeJrel_np=Jrel_inf-Jrel_nptau_rel btp=1.25bt a_relp=0.5btp1 Jrel_infp_b=-a_relpICaL_ss11+cajsr_halfcajsr8 Jrel_infp=Jrel_infp_b1.7ifcelltype=2Jrel_infp_botherwise tau_relp_b=btp1+0.0123cajsr tau_relp=0.001iftau_relp_b<0.001tau_relp_botherwise ddtimeJrel_p=Jrel_infp-Jrel_ptau_relp fJrelp=11+KmCaMKCaMKa Jrel=Jrel_b1-fJrelpJrel_np+fJrelpJrel_p

Component: SERCA

upScale=1.3ifcelltype=11otherwise Jupnp=upScale0.005425caicai+0.00092 Jupp=upScale2.750.005425caicai+0.00092-0.00017 fJupp=11+KmCaMKCaMKa Jleak=0.0048825cansr15 Jup=Jup_b1-fJuppJupnp+fJuppJupp-Jleak

Component: trans_flux

Jtr=cansr-cajsr60