Model Mathematics

Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell=1000⁢3.14⁢rad⁢rad⁢L Ageo=2⁢3.14⁢rad⁢rad+2⁢3.14⁢rad⁢L Acap=2⁢Ageo vmyo=0.68⁢vcell vnsr=0.0552⁢vcell vjsr=0.0048⁢vcell vss=0.02⁢vcell

Component: membrane

Istim=ampiftime≦duration0otherwise vffrt=v⁢F⁢FR⁢T vfrt=v⁢FR⁢T ddtimev=-INa+INaL+Ito+ICaL+ICaNa+ICaK+IKr+IKs+IK1+INaCa_i+INaCa_ss+INaK+INab+IKb+IpCa+ICab+Istim

Component: CaMK

CaMKb=CaMKo⁢1-CaMKt1+KmCaMcass CaMKa=CaMKb+CaMKt ddtimeCaMKt=aCaMK⁢CaMKb⁢CaMKb+CaMKt-bCaMK⁢CaMKt

Component: intracellular_ions

cmdnmax=cmdnmax_b⁢1.3ifcelltype=1cmdnmax_botherwise ddtimenai=-INa+INaL+3⁢INaCa_i+3⁢INaK+INab⁢Acap⁢cmF⁢vmyo+JdiffNa⁢vssvmyo ddtimenass=-ICaNa+3⁢INaCa_ss⁢cm⁢AcapF⁢vss-JdiffNa ddtimeki=-Ito+IKr+IKs+IK1+IKb+Istim-2⁢INaK⁢cm⁢AcapF⁢vmyo+JdiffK⁢vssvmyo ddtimekss=-ICaK⁢cm⁢AcapF⁢vss-JdiffK Bcai=11+cmdnmax⁢kmcmdnkmcmdn+cai2+trpnmax⁢kmtrpnkmtrpn+cai2 ddtimecai=Bcai⁢-IpCa+ICab-2⁢INaCa_i⁢cm⁢Acap2⁢F⁢vmyo-Jup⁢vnsrvmyo+Jdiff⁢vssvmyo Bcass=11+BSRmax⁢KmBSRKmBSR+cass2+BSLmax⁢KmBSLKmBSL+cass2 ddtimecass=Bcass⁢-ICaL-2⁢INaCa_ss⁢cm⁢Acap2⁢F⁢vss+Jrel⁢vjsrvss-Jdiff ddtimecansr=Jup-Jtr⁢vjsrvnsr Bcajsr=11+csqnmax⁢kmcsqnkmcsqn+cajsr2 ddtimecajsr=Bcajsr⁢Jtr-Jrel

Component: reversal_potentials

ENa=R⁢TF⁢ln⁡naonai EK=R⁢TF⁢ln⁡koki EKs=R⁢TF⁢ln⁡ko+PKNa⁢naoki+PKNa⁢nai

Component: INa

mss=11+ⅇ-v+mssV1mssV2 tm=1mtD1⁢ⅇv+mtV1mtV2+mtD2⁢ⅇ-v+mtV3mtV4 ddtimem=mss-mtm hss=11+ⅇv+hssV1hssV2 thf=11.432 e -5⁢ⅇ-v+1.1966.285+6.149⁢ⅇv+0.509620.27 ths=10.009794⁢ⅇ-v+17.9528.05+0.3343⁢ⅇv+5.7356.66 Ahs=1-Ahf ddtimehf=hss-hfthf ddtimehs=hss-hsths h=Ahf⁢hf+Ahs⁢hs jss=hss tj=2.038+10.02136⁢ⅇ-v+100.68.281+0.3052⁢ⅇv+0.994138.45 ddtimej=jss-jtj hssp=11+ⅇv+89.16.086 thsp=3⁢ths ddtimehsp=hssp-hspthsp hp=Ahf⁢hf+Ahs⁢hsp tjp=1.46⁢tj ddtimejp=jss-jptjp fINap=11+KmCaMKCaMKa INa=GNa⁢v-ENa⁢m3⁢1-fINap⁢h⁢j+fINap⁢hp⁢jp

Component: INaL

mLss=11+ⅇ-v+42.855.264 tmL=tm ddtimemL=mLss-mLtmL hLss=11+ⅇv+87.617.488 ddtimehL=hLss-hLthL hLssp=11+ⅇv+93.817.488 thLp=3⁢thL ddtimehLp=hLssp-hLpthLp GNaL=GNaL_b⁢0.6ifcelltype=1GNaL_botherwise fINaLp=11+KmCaMKCaMKa INaL=GNaL⁢v-ENa⁢mL⁢1-fINaLp⁢hL+fINaLp⁢hLp

Component: Ito

ass=11+ⅇ-v-14.3414.82 ta=1.051511.2089⁢1+ⅇ-v-18.409929.3814+3.51+ⅇv+10029.3814 ddtimea=ass-ata iss=11+ⅇv+43.945.711 delta_epi=1-0.951+ⅇv+705ifcelltype=11otherwise tiF_b=4.562+10.3933⁢ⅇ-v+100100+0.08004⁢ⅇv+5016.59 tiS_b=23.62+10.001416⁢ⅇ-v+96.5259.05+1.78 e -8⁢ⅇv+114.18.079 tiF=tiF_b⁢delta_epi tiS=tiS_b⁢delta_epi AiF=11+ⅇv-213.6151.2 AiS=1-AiF ddtimeiF=iss-iFtiF ddtimeiS=iss-iStiS i=AiF⁢iF+AiS⁢iS assp=11+ⅇ-v-24.3414.82 ddtimeap=assp-apta dti_develop=1.354+1 e -4ⅇv-167.415.89+ⅇ-v-12.230.2154 dti_recover=1-0.51+ⅇv+7020 tiFp=dti_develop⁢dti_recover⁢tiF tiSp=dti_develop⁢dti_recover⁢tiS ddtimeiFp=iss-iFptiFp ddtimeiSp=iss-iSptiSp ip=AiF⁢iFp+AiS⁢iSp Gto=Gto_b⁢4ifcelltype=1Gto_b⁢4ifcelltype=2Gto_botherwise fItop=11+KmCaMKCaMKa Ito=Gto⁢v-EK⁢1-fItop⁢a⁢i+fItop⁢ap⁢ip

Component: ICaL

dss=11+ⅇ-v+3.944.23 td=0.6+1ⅇ-0.05⁢v+6+ⅇ0.09⁢v+14 ddtimed=dss-dtd fss=11+ⅇv+19.583.696 tff=7+10.0045⁢ⅇ-v+2010+0.0045⁢ⅇv+2010 tfs=1000+10.000035⁢ⅇ-v+54+0.000035⁢ⅇv+56 Aff=0.6 Afs=1-Aff ddtimeff=fss-fftff ddtimefs=fss-fstfs f=Aff⁢ff+Afs⁢fs fcass=fss tfcaf=7+10.04⁢ⅇ-v-47+0.04⁢ⅇv-47 tfcas=100+10.00012⁢ⅇ-v3+0.00012⁢ⅇv7 Afcaf=0.3+0.61+ⅇv-1010 Afcas=1-Afcaf ddtimefcaf=fcass-fcaftfcaf ddtimefcas=fcass-fcastfcas fca=Afcaf⁢fcaf+Afcas⁢fcas tjca=75 ddtimejca=fcass-jcatjca tffp=2.5⁢tff ddtimeffp=fss-ffptffp fp=Aff⁢ffp+Afs⁢fs tfcafp=2.5⁢tfcaf ddtimefcafp=fcass-fcafptfcafp fcap=Afcaf⁢fcafp+Afcas⁢fcas km2n=jca⁢1 anca=1k2nkm2n+1+Kmncass4 ddtimenca=anca⁢k2n-nca⁢km2n PhiCaL=4⁢vffrt⁢cass⁢ⅇ2⁢vfrt-0.341⁢caoⅇ2⁢vfrt-1 PhiCaNa=1⁢vffrt⁢0.75⁢nass⁢ⅇ1⁢vfrt-0.75⁢naoⅇ1⁢vfrt-1 PhiCaK=1⁢vffrt⁢0.75⁢kss⁢ⅇ1⁢vfrt-0.75⁢koⅇ1⁢vfrt-1 PCa=PCa_b⁢1.2ifcelltype=1PCa_b⁢2.5ifcelltype=2PCa_botherwise PCap=1.1⁢PCa PCaNa=0.00125⁢PCa PCaK=3.574 e -4⁢PCa PCaNap=0.00125⁢PCap PCaKp=3.574 e -4⁢PCap fICaLp=11+KmCaMKCaMKa ICaL=1-fICaLp⁢PCa⁢PhiCaL⁢d⁢f⁢1-nca+jca⁢fca⁢nca+fICaLp⁢PCap⁢PhiCaL⁢d⁢fp⁢1-nca+jca⁢fcap⁢nca ICaNa=1-fICaLp⁢PCaNa⁢PhiCaNa⁢d⁢f⁢1-nca+jca⁢fca⁢nca+fICaLp⁢PCaNap⁢PhiCaNa⁢d⁢fp⁢1-nca+jca⁢fcap⁢nca ICaK=1-fICaLp⁢PCaK⁢PhiCaK⁢d⁢f⁢1-nca+jca⁢fca⁢nca+fICaLp⁢PCaKp⁢PhiCaK⁢d⁢fp⁢1-nca+jca⁢fcap⁢nca

Component: IKr

xrss=11+ⅇ-v+8.3376.789 txrf=12.98+10.3652⁢ⅇv-31.663.869+4.123 e -5⁢ⅇ-v-47.7820.38 txrs=1.865+10.06629⁢ⅇv-34.77.355+1.128 e -5⁢ⅇ-v-29.7425.94 Axrf=11+ⅇv+54.8138.21 Axrs=1-Axrf ddtimexrf=xrss-xrftxrf ddtimexrs=xrss-xrstxrs xr=Axrf⁢xrf+Axrs⁢xrs rkr=11+ⅇv+5575⁢11+ⅇv-1030 GKr=GKr_b⁢1.3ifcelltype=1GKr_b⁢0.8ifcelltype=2GKr_botherwise IKr=GKr⁢ko5.4⁢xr⁢rkr⁢v-EK

Component: IKs

xs1ss=11+ⅇ-v+11.68.932 txs1=817.3+12.326 e -4⁢ⅇv+48.2817.8+0.001292⁢ⅇ-v+210230 ddtimexs1=xs1ss-xs1txs1 xs2ss=xs1ss txs2=10.01⁢ⅇv-5020+0.0193⁢ⅇ-v+66.5431 ddtimexs2=xs2ss-xs2txs2 KsCa=1+0.61+3.8 e -5cai1.4 GKs=GKs_b⁢1.4ifcelltype=1GKs_botherwise IKs=GKs⁢KsCa⁢xs1⁢xs2⁢v-EKs

Component: IK1

xk1ss=11+ⅇ-v+2.5538⁢ko+144.591.5692⁢ko+3.8115 txk1=122.2ⅇ-v+127.220.36+ⅇv+236.869.33 ddtimexk1=xk1ss-xk1txk1 rk1=11+ⅇv+105.8-2.6⁢ko9.493 GK1=GK1_b⁢1.2ifcelltype=1GK1_b⁢1.3ifcelltype=2GK1_botherwise IK1=GK1⁢ko⁢rk1⁢xk1⁢v-EK

Component: INaCa_i

hca=ⅇqca⁢v⁢FR⁢T hna=ⅇqna⁢v⁢FR⁢T h1_i=1+naikna3⁢1+hna h2_i=nai⁢hnakna3⁢h1_i h3_i=1h1_i h4_i=1+naikna1⁢1+naikna2 h5_i=nai⁢naih4_i⁢kna1⁢kna2 h6_i=1h4_i h7_i=1+naokna3⁢1+1hna h8_i=naokna3⁢hna⁢h7_i h9_i=1h7_i h10_i=kasymm+1+naokna1⁢1+naokna2 h11_i=nao⁢naoh10_i⁢kna1⁢kna2 h12_i=1h10_i k1_i=h12_i⁢cao⁢kcaon k2_i=kcaoff k3p_i=h9_i⁢wca k3pp_i=h8_i⁢wnaca k3_i=k3p_i+k3pp_i k4p_i=h3_i⁢wcahca k4pp_i=h2_i⁢wnaca k4_i=k4p_i+k4pp_i k5_i=kcaoff k6_i=h6_i⁢cai⁢kcaon k7_i=h5_i⁢h2_i⁢wna k8_i=h8_i⁢h11_i⁢wna x1_i=k2_i⁢k4_i⁢k7_i+k6_i+k5_i⁢k7_i⁢k2_i+k3_i x2_i=k1_i⁢k7_i⁢k4_i+k5_i+k4_i⁢k6_i⁢k1_i+k8_i x3_i=k1_i⁢k3_i⁢k7_i+k6_i+k8_i⁢k6_i⁢k2_i+k3_i x4_i=k2_i⁢k8_i⁢k4_i+k5_i+k3_i⁢k5_i⁢k1_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⁢E4_i⁢k7_i-E1_i⁢k8_i+E3_i⁢k4pp_i-E2_i⁢k3pp_i JncxCa_i=E2_i⁢k2_i-E1_i⁢k1_i Gncx=Gncx_b⁢1.1ifcelltype=1Gncx_b⁢1.4ifcelltype=2Gncx_botherwise INaCa_i=0.8⁢Gncx⁢allo_i⁢zna⁢JncxNa_i+zca⁢JncxCa_i h1_ss=1+nasskna3⁢1+hna h2_ss=nass⁢hnakna3⁢h1_ss h3_ss=1h1_ss h4_ss=1+nasskna1⁢1+nasskna2 h5_ss=nass⁢nassh4_ss⁢kna1⁢kna2 h6_ss=1h4_ss h7_ss=1+naokna3⁢1+1hna h8_ss=naokna3⁢hna⁢h7_ss h9_ss=1h7_ss h10_ss=kasymm+1+naokna1⁢1+naokna2 h11_ss=nao⁢naoh10_ss⁢kna1⁢kna2 h12_ss=1h10_ss k1_ss=h12_ss⁢cao⁢kcaon k2_ss=kcaoff k3p_ss=h9_ss⁢wca k3pp_ss=h8_ss⁢wnaca k3_ss=k3p_ss+k3pp_ss k4p_ss=h3_ss⁢wcahca k4pp_ss=h2_ss⁢wnaca k4_ss=k4p_ss+k4pp_ss k5_ss=kcaoff k6_ss=h6_ss⁢cass⁢kcaon k7_ss=h5_ss⁢h2_ss⁢wna k8_ss=h8_ss⁢h11_ss⁢wna x1_ss=k2_ss⁢k4_ss⁢k7_ss+k6_ss+k5_ss⁢k7_ss⁢k2_ss+k3_ss x2_ss=k1_ss⁢k7_ss⁢k4_ss+k5_ss+k4_ss⁢k6_ss⁢k1_ss+k8_ss x3_ss=k1_ss⁢k3_ss⁢k7_ss+k6_ss+k8_ss⁢k6_ss⁢k2_ss+k3_ss x4_ss=k2_ss⁢k8_ss⁢k4_ss+k5_ss+k3_ss⁢k5_ss⁢k1_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=3⁢E4_ss⁢k7_ss-E1_ss⁢k8_ss+E3_ss⁢k4pp_ss-E2_ss⁢k3pp_ss JncxCa_ss=E2_ss⁢k2_ss-E1_ss⁢k1_ss INaCa_ss=0.2⁢Gncx⁢allo_ss⁢zna⁢JncxNa_ss+zca⁢JncxCa_ss

Component: INaK

Knai=Knai0⁢ⅇdelta⁢v⁢F3⁢R⁢T Knao=Knao0⁢ⅇ1-delta⁢v⁢F3⁢R⁢T P=eP1+HKhp+naiKnap+kiKxkur a1=k1p⁢naiKnai31+naiKnai3+1+kiKki2-1 b1=k1m⁢MgADP a2=k2p b2=k2m⁢naoKnao31+naoKnao3+1+koKko2-1 a3=k3p⁢koKko21+naoKnao3+1+koKko2-1 b3=k3m⁢P⁢H1+MgATPKmgatp a4=k4p⁢MgATPKmgatp1+MgATPKmgatp b4=k4m⁢kiKki21+naiKnai3+1+kiKki2-1 x1=a4⁢a1⁢a2+b2⁢b4⁢b3+a2⁢b4⁢b3+b3⁢a1⁢a2 x2=b2⁢b1⁢b4+a1⁢a2⁢a3+a3⁢b1⁢b4+a2⁢a3⁢b4 x3=a2⁢a3⁢a4+b3⁢b2⁢b1+b2⁢b1⁢a4+a3⁢a4⁢b1 x4=b4⁢b3⁢b2+a3⁢a4⁢a1+b2⁢a4⁢a1+b3⁢b2⁢a1 E1=x1x1+x2+x3+x4 E2=x2x1+x2+x3+x4 E3=x3x1+x2+x3+x4 E4=x4x1+x2+x3+x4 JnakNa=3⁢E1⁢a3-E2⁢b3 JnakK=2⁢E4⁢b1-E3⁢a1 Pnak=Pnak_b⁢0.9ifcelltype=1Pnak_b⁢0.7ifcelltype=2Pnak_botherwise INaK=Pnak⁢zna⁢JnakNa+zk⁢JnakK

Component: IKb

xkb=11+ⅇ-v-14.4818.34 GKb=GKb_b⁢0.6ifcelltype=1GKb_botherwise IKb=GKb⁢xkb⁢v-EK

Component: INab

INab=PNab⁢vffrt⁢nai⁢ⅇvfrt-naoⅇvfrt-1

Component: ICab

ICab=PCab⁢4⁢vffrt⁢cai⁢ⅇ2⁢vfrt-0.341⁢caoⅇ2⁢vfrt-1

Component: IpCa

IpCa=GpCa⁢caiKmCap+cai

Component: diff

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

Component: ryr

a_rel=0.5⁢bt Jrel_inf_temp=a_rel⁢-ICaL1+1⁢1.5cajsr8 Jrel_inf=Jrel_inf_temp⁢1.7ifcelltype=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=1.25⁢bt a_relp=0.5⁢btp Jrel_temp=a_relp⁢-ICaL1+1.5cajsr8 Jrel_infp=Jrel_temp⁢1.7ifcelltype=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-fJrelp⁢Jrelnp+fJrelp⁢Jrelp

Component: SERCA

upScale=1.3ifcelltype=11otherwise Jupnp=upScale⁢0.004375⁢caicai+0.00092 Jupp=upScale⁢2.75⁢0.004375⁢caicai+0.00092-0.00017 fJupp=11+KmCaMKCaMKa Jleak=0.0039375⁢cansr15 Jup=1-fJupp⁢Jupnp+fJupp⁢Jupp-Jleak

Component: trans_flux

Jtr=cansr-cajsr100