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=ampiftimeduration0otherwise 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-CaMKt1+KmCaMcass CaMKa=CaMKb+CaMKt ddtimeCaMKt=aCaMKCaMKbCaMKb+CaMKt-bCaMKCaMKt

Component: intracellular_ions

cmdnmax=cmdnmax_b1.3ifcelltype=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_icmAcap2Fvmyo-Jupvnsrvmyo+Jdiffvssvmyo Bcass=11+BSRmaxKmBSRKmBSR+cass2+BSLmaxKmBSLKmBSL+cass2 ddtimecass=Bcass-ICaL-2INaCa_sscmAcap2Fvss+Jrelvjsrvss-Jdiff ddtimecansr=Jup-Jtrvjsrvnsr Bcajsr=11+csqnmaxkmcsqnkmcsqn+cajsr2 ddtimecajsr=BcajsrJtr-Jrel

Component: reversal_potentials

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

Component: INa

mss=11+-v+mssV1mssV2 tm=1mtD1v+mtV1mtV2+mtD2-v+mtV3mtV4 ddtimem=mss-mtm hss=11+v+hssV1hssV2 thf=11.432 e -5-v+1.1966.285+6.149v+0.509620.27 ths=10.009794-v+17.9528.05+0.3343v+5.7356.66 Ahs=1-Ahf ddtimehf=hss-hfthf ddtimehs=hss-hsths h=Ahfhf+Ahshs jss=hss tj=2.038+10.02136-v+100.68.281+0.3052v+0.994138.45 ddtimej=jss-jtj hssp=11+v+89.16.086 thsp=3ths ddtimehsp=hssp-hspthsp hp=Ahfhf+Ahshsp tjp=1.46tj ddtimejp=jss-jptjp fINap=11+KmCaMKCaMKa INa=GNav-ENam31-fINaphj+fINaphpjp

Component: INaL

mLss=11+-v+42.855.264 tmL=tm 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-14.3414.82 ta=1.051511.20891+-v-18.409929.3814+3.51+v+10029.3814 ddtimea=ass-ata iss=11+v+43.945.711 delta_epi=1-0.951+v+705ifcelltype=11otherwise tiF_b=4.562+10.3933-v+100100+0.08004v+5016.59 tiS_b=23.62+10.001416-v+96.5259.05+1.78 e -8v+114.18.079 tiF=tiF_bdelta_epi tiS=tiS_bdelta_epi AiF=11+v-213.6151.2 AiS=1-AiF ddtimeiF=iss-iFtiF ddtimeiS=iss-iStiS i=AiFiF+AiSiS assp=11+-v-24.3414.82 ddtimeap=assp-apta dti_develop=1.354+1 e -4v-167.415.89+-v-12.230.2154 dti_recover=1-0.51+v+7020 tiFp=dti_developdti_recovertiF tiSp=dti_developdti_recovertiS ddtimeiFp=iss-iFptiFp ddtimeiSp=iss-iSptiSp ip=AiFiFp+AiSiSp Gto=Gto_b4ifcelltype=1Gto_b4ifcelltype=2Gto_botherwise fItop=11+KmCaMKCaMKa Ito=Gtov-EK1-fItopai+fItopapip

Component: ICaL

dss=11+-v+3.944.23 td=0.6+1-0.05v+6+0.09v+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 Aff=0.6 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 tjca=75 ddtimejca=fcass-jcatjca tffp=2.5tff ddtimeffp=fss-ffptffp fp=Affffp+Afsfs tfcafp=2.5tfcaf ddtimefcafp=fcass-fcafptfcafp fcap=Afcaffcafp+Afcasfcas km2n=jca1 anca=1k2nkm2n+1+Kmncass4 ddtimenca=ancak2n-ncakm2n PhiCaL=4vffrtcass2vfrt-0.341cao2vfrt-1 PhiCaNa=1vffrt0.75nass1vfrt-0.75nao1vfrt-1 PhiCaK=1vffrt0.75kss1vfrt-0.75ko1vfrt-1 PCa=PCa_b1.2ifcelltype=1PCa_b2.5ifcelltype=2PCa_botherwise PCap=1.1PCa PCaNa=0.00125PCa PCaK=3.574 e -4PCa PCaNap=0.00125PCap PCaKp=3.574 e -4PCap fICaLp=11+KmCaMKCaMKa ICaL=1-fICaLpPCaPhiCaLdf1-nca+jcafcanca+fICaLpPCapPhiCaLdfp1-nca+jcafcapnca ICaNa=1-fICaLpPCaNaPhiCaNadf1-nca+jcafcanca+fICaLpPCaNapPhiCaNadfp1-nca+jcafcapnca ICaK=1-fICaLpPCaKPhiCaKdf1-nca+jcafcanca+fICaLpPCaKpPhiCaKdfp1-nca+jcafcapnca

Component: IKr

xrss=11+-v+8.3376.789 txrf=12.98+10.3652v-31.663.869+4.123 e -5-v-47.7820.38 txrs=1.865+10.06629v-34.77.355+1.128 e -5-v-29.7425.94 Axrf=11+v+54.8138.21 Axrs=1-Axrf ddtimexrf=xrss-xrftxrf ddtimexrs=xrss-xrstxrs xr=Axrfxrf+Axrsxrs rkr=11+v+557511+v-1030 GKr=GKr_b1.3ifcelltype=1GKr_b0.8ifcelltype=2GKr_botherwise IKr=GKrko5.4xrrkrv-EK

Component: IKs

xs1ss=11+-v+11.68.932 txs1=817.3+12.326 e -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+3.8 e -5cai1.4 GKs=GKs_b1.4ifcelltype=1GKs_botherwise IKs=GKsKsCaxs1xs2v-EKs

Component: IK1

xk1ss=11+-v+2.5538ko+144.591.5692ko+3.8115 txk1=122.2-v+127.220.36+v+236.869.33 ddtimexk1=xk1ss-xk1txk1 rk1=11+v+105.8-2.6ko9.493 GK1=GK1_b1.2ifcelltype=1GK1_b1.3ifcelltype=2GK1_botherwise IK1=GK1kork1xk1v-EK

Component: INaCa_i

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=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=Knai0deltavF3RT Knao=Knao01-deltavF3RT 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-14.4818.34 GKb=GKb_b0.6ifcelltype=1GKb_botherwise IKb=GKbxkbv-EK

Component: INab

INab=PNabvffrtnaivfrt-naovfrt-1

Component: ICab

ICab=PCab4vffrtcai2vfrt-0.341cao2vfrt-1

Component: IpCa

IpCa=GpCacaiKmCap+cai

Component: diff

JdiffNa=nass-nai2 JdiffK=kss-ki2 Jdiff=cass-cai0.2

Component: ryr

a_rel=0.5bt Jrel_inf_temp=a_rel-ICaL1+11.5cajsr8 Jrel_inf=Jrel_inf_temp1.7ifcelltype=2Jrel_inf_tempotherwise tau_rel_temp=bt1+0.0123cajsr tau_rel=0.001iftau_rel_temp<0.001tau_rel_tempotherwise ddtimeJrelnp=Jrel_inf-Jrelnptau_rel btp=1.25bt a_relp=0.5btp Jrel_temp=a_relp-ICaL1+1.5cajsr8 Jrel_infp=Jrel_temp1.7ifcelltype=2Jrel_tempotherwise tau_relp_temp=btp1+0.0123cajsr tau_relp=0.001iftau_relp_temp<0.001tau_relp_tempotherwise ddtimeJrelp=Jrel_infp-Jrelptau_relp fJrelp=11+KmCaMKCaMKa 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=0.0039375cansr15 Jup=1-fJuppJupnp+fJuppJupp-Jleak

Component: trans_flux

Jtr=cansr-cajsr100
Source
Derived from workspace An encoding of the human ORd model by Steve Neiderer at changeset 2593df010620.
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