Model Mathematics

Component: Protocol

V_clamp=-20iftimemod100001000time+9000-t_delaymod100001000-80otherwiseI_app=V_clamp-V_mR_clampt_delay=10iftime<100001if20000timetime<300005if30000timetime<4000080otherwise

Component: interface

Component: environment

Component: parameters

epi=1 R=8314 Frdy=96485 Temp=310 FoRT=FrdyRTemp Cmem=1.381 e -10 Qpow=Temp-31010 cellLength=100 cellRadius=10.25 junctionLength=160 e -3 junctionRadius=15 e -3 distSLcyto=0.45 distJuncSL=0.5 DcaJuncSL=1.64 e -6 DcaSLcyto=1.22 e -6 DnaJuncSL=1.09 e -5 DnaSLcyto=1.79 e -5 Vcell=πcellRadius2cellLength1 e -15 Vmyo=0.65Vcell Vsr=0.035Vcell Vsl=0.02Vcell Vjunc=0.05390.01Vcell SAjunc=20150π2junctionLengthjunctionRadius SAsl=π2cellRadiuscellLength J_ca_juncsl=8.2413 e -13 J_ca_slmyo=3.2743 e -12 J_na_juncsl=1.8313 e -14 J_na_slmyo=1.6386 e -12 Fjunc=0.11 Fsl=1-Fjunc Fjunc_CaL=0.9 Fsl_CaL=1-Fjunc_CaL Cli=15 Clo=150 Ko=5.4 Nao=140 Cao=1.8 Mgi=1 ena_junc=1FoRTlnNaoNa_j ena_sl=1FoRTlnNaoNa_sl ek=1FoRTlnKoK_i eca_junc=1FoRT2lnCaoCa_j eca_sl=1FoRT2lnCaoCa_sl ecl=1FoRTlnCliClo GNa=23 GNaB=0.597 e -3 IbarNaK=11.8 KmNaip=11 KmKo=1.5 Q10NaK=1.63 Q10KmNai=1.39 pNaK=0.01833 gkp=20.001 GClCa=0.50.109625 GClB=19 e -3 KdClCa=100 e -3 pNa=0.51.5 e -8 pCa=0.55.4 e -4 pK=0.52.7 e -7 Q10CaL=1.8 IbarNCX=14.5 KmCai=3.59 e -3 KmCao=1.3 KmNai=12.29 KmNao=87.5 ksat=0.32 nu=0.27 Kdact=0.15 e -3 Q10NCX=1.57 IbarSLCaP=0.0673 KmPCa=0.5 e -3 GCaB=5.513 e -4 Q10SLCaP=2.35 Q10SRCaP=2.6 Vmax_SRCaP=5.3114 e -3 Kmf=0.246 e -3 Kmr=1.7 hillSRCaP=1.787 ks=25 koCa=10 kom=0.06 kiCa=0.5 kim=0.005 ec50SR=0.45 Bmax_Naj=7.561 Bmax_Nasl=1.65 koff_na=1 e -3 kon_na=0.1 e -3 Bmax_TnClow=70 e -3 koff_tncl=19.6 e -3 kon_tncl=32.7 Bmax_TnChigh=140 e -3 koff_tnchca=0.032 e -3 kon_tnchca=2.37 koff_tnchmg=3.33 e -3 kon_tnchmg=3 e -3 Bmax_CaM=24 e -3 koff_cam=238 e -3 kon_cam=34 Bmax_myosin=140 e -3 koff_myoca=0.46 e -3 kon_myoca=13.8 koff_myomg=0.057 e -3 kon_myomg=0.0157 Bmax_SR=190.9 e -3 koff_sr=60 e -3 kon_sr=100 Bmax_SLlowsl=37.4 e -3VmyoVsl Bmax_SLlowj=4.6 e -3VmyoVjunc0.1 koff_sll=1300 e -3 kon_sll=100 Bmax_SLhighsl=13.4 e -3VmyoVsl Bmax_SLhighj=1.65 e -3VmyoVjunc0.1 koff_slh=30 e -3 kon_slh=100 Bmax_Csqn=140 e -3VmyoVsr koff_csqn=65 kon_csqn=100

Component: I_Na

mss=11+-56.86+V_m9.032 taum=0.1292-V_m+45.7915.542+0.06487-V_m-4.82351.122 ah=0ifV_m-400.057-V_m+806.8otherwise bh=0.770.131+-V_m+10.6611.1ifV_m-402.70.079V_m+3.1 e 50.3485V_motherwise tauh=1ah+bh hss=11+V_m+71.557.432 aj=0ifV_m-40-2.5428 e 40.2444V_m-6.948 e -6-0.04391V_mV_m+37.781+0.311V_m+79.23otherwise bj=0.60.057V_m1+-0.1V_m+32ifV_m-400.02424-0.01052V_m1+-0.1378V_m+40.14otherwise tauj=1aj+bj jss=11+V_m+71.557.432 ddtimem=mss-mtaum ddtimeh=hss-htauh ddtimej=jss-jtauj I_Na_junc=FjuncGNam3hjV_m-ena_junc I_Na_sl=FslGNam3hjV_m-ena_sl I_Na=I_Na_junc+I_Na_sl

Component: I_NaBK

I_nabk_junc=FjuncGNaBV_m-ena_junc I_nabk_sl=FslGNaBV_m-ena_sl I_nabk=I_nabk_junc+I_nabk_sl

Component: I_NaK

sigma=Nao67.3-17 fnak=11+0.1245-0.1V_mFoRT+0.0365sigma-V_mFoRT I_nak_junc=FjuncIbarNaKfnakKo1+KmNaipNa_j4Ko+KmKo I_nak_sl=FslIbarNaKfnakKo1+KmNaipNa_sl4Ko+KmKo I_nak=I_nak_junc+I_nak_sl

Component: I_Kr

gkr=0.035Ko5.4 xrss=11+-V_m+105 tauxr=5501+-22-V_m961+V_m--119+2301+V_m--4020 ddtimex_kr=xrss-x_krtauxr rkr=11+V_m+7424 I_kr=gkrx_krrkrV_m-ek

Component: I_Kp

kp_kp=11+7.488-V_m5.98 I_kp_junc=Fjuncgkpkp_kpV_m-ek I_kp_sl=Fslgkpkp_kpV_m-ek I_kp=I_kp_junc+I_kp_sl

Component: I_Ks

eks=1FoRTlnKo+pNaKNaoK_i+pNaKNa_i gks_junc=0.0035 gks_sl=0.0035 xsss=11+-V_m+3.814.25 tauxs=990.11+-V_m+2.43614.12 ddtimex_ks=xsss-x_kstauxs I_ks_junc=Fjuncgks_juncx_ks2V_m-eks I_ks_sl=Fslgks_slx_ks2V_m-eks I_ks=I_ks_junc+I_ks_sl

Component: I_to

GtoSlow=10.130.12ifepi=10.130.30.964otherwise GtoFast=10.130.88ifepi=10.130.30.036otherwise xtoss=11+-V_m-1913 ytoss=11+V_m+19.55 tauxtos=91+V_m+315+0.5 tauytos=8001+V_m+6010+30 ddtimex_to_s=xtoss-x_to_stauxtos ddtimey_to_s=ytoss-y_to_stauytos I_tos=GtoSlowx_to_sy_to_sV_m-ek tauxtof=8.5-V_m+45502+0.5 tauytof=85-V_m+402220+7 ddtimex_to_f=xtoss-x_to_ftauxtof ddtimey_to_f=ytoss-y_to_ftauytof I_tof=GtoFastx_to_fy_to_fV_m-ek I_to=I_tos+I_tof

Component: I_Ki

aki=1.021+0.2385V_m-ek-59.215 bki=0.491240.08032V_m+5.476-ek+0.06175V_m-ek-594.311+-0.5143V_m-ek+4.753 kiss=akiaki+bki I_ki=10.35Ko5.4kissV_m-ek

Component: I_ClCa

I_ClCa_junc=FjuncGClCa1+KdClCaCa_jV_m-ecl I_ClCa_sl=FslGClCa1+KdClCaCa_slV_m-ecl I_ClCa=I_ClCa_junc+I_ClCa_sl I_Clbk=GClBV_m-ecl

Component: I_Ca

fss=11+V_m+359+0.61+50-V_m20 dss=11+-V_m+56 taud=1dss1--V_m+560.035V_m+5 tauf=10.0197-0.0337V_m+14.52+0.02 ddtimed=dss-dtaud ddtimef=fss-ftauf ddtimef_Ca_Bj=1.7Ca_j11-f_Ca_Bj-11.9 e -3f_Ca_Bj ddtimef_Ca_Bsl=1.7Ca_sl11-f_Ca_Bsl-11.9 e -3f_Ca_Bsl fcaCaMSL=0 fcaCaj=0 ibarca_j=pCa4V_mFrdyFoRT0.341Ca_j2V_mFoRT-0.341Cao2V_mFoRT-1 ibarca_sl=pCa4V_mFrdyFoRT0.341Ca_sl2V_mFoRT-0.341Cao2V_mFoRT-1 ibark=pKV_mFrdyFoRT0.75K_iV_mFoRT-0.75KoV_mFoRT-1 ibarna_j=pNaV_mFrdyFoRT0.75Na_jV_mFoRT-0.75NaoV_mFoRT-1 ibarna_sl=pNaV_mFrdyFoRT0.75Na_slV_mFoRT-0.75NaoV_mFoRT-1 I_Ca_junc=Fjunc_CaLibarca_jdf1-f_Ca_Bj+fcaCajQ10CaLQpow0.451 I_Ca_sl=Fsl_CaLibarca_sldf1-f_Ca_Bsl+fcaCaMSLQ10CaLQpow0.451 I_Ca=I_Ca_junc+I_Ca_sl I_CaK=ibarkdfFjunc_CaLfcaCaj+1-f_Ca_Bj+Fsl_CaLfcaCaMSL+1-f_Ca_BslQ10CaLQpow0.451 I_CaNa_junc=Fjunc_CaLibarna_jdf1-f_Ca_Bj+fcaCajQ10CaLQpow0.451 I_CaNa_sl=Fsl_CaLibarna_sldf1-f_Ca_Bsl+fcaCaMSLQ10CaLQpow0.451 I_CaNa=I_CaNa_junc+I_CaNa_sl I_Catot=I_Ca+I_CaK+I_CaNa

Component: I_NCX

Ka_junc=11+KdactCa_j2 Ka_sl=11+KdactCa_sl2 s1_junc=nuV_mFoRTNa_j3Cao s1_sl=nuV_mFoRTNa_sl3Cao s2_junc=nu-1V_mFoRTNao3Ca_j s3_junc=KmCaiNao31+Na_jKmNai3+KmNao3Ca_j1+Ca_jKmCai+KmCaoNa_j3+Na_j3Cao+Nao3Ca_j s2_sl=nu-1V_mFoRTNao3Ca_sl s3_sl=KmCaiNao31+Na_slKmNai3+KmNao3Ca_sl1+Ca_slKmCai+KmCaoNa_sl3+Na_sl3Cao+Nao3Ca_sl I_ncx_junc=FjuncIbarNCXQ10NCXQpowKa_juncs1_junc-s2_juncs3_junc1+ksatnu-1V_mFoRT I_ncx_sl=FslIbarNCXQ10NCXQpowKa_sls1_sl-s2_sls3_sl1+ksatnu-1V_mFoRT I_ncx=I_ncx_junc+I_ncx_sl

Component: I_PCa

I_pca_junc=FjuncQ10SLCaPQpowIbarSLCaPCa_j1.6KmPCa1.6+Ca_j1.6 I_pca_sl=FslQ10SLCaPQpowIbarSLCaPCa_sl1.6KmPCa1.6+Ca_sl1.6 I_pca=I_pca_junc+I_pca_sl

Component: I_CaBK

I_cabk_junc=FjuncGCaBV_m-eca_junc I_cabk_sl=FslGCaBV_m-eca_sl I_cabk=I_cabk_junc+I_cabk_sl

Component: SR_Fluxes

MaxSR=15 MinSR=1 kCaSR=MaxSR-MaxSR-MinSR1+ec50SRCa_sr2.5 koSRCa=koCakCaSR kiSRCa=kiCakCaSR RI=1-Ry_Rr-Ry_Ro-Ry_Ri ddtimeRy_Rr=kimRI-kiSRCaCa_jRy_Rr-koSRCaCa_j2Ry_Rr-komRy_Ro ddtimeRy_Ro=koSRCaCa_j2Ry_Rr-komRy_Ro-kiSRCaCa_jRy_Ro-kimRy_Ri ddtimeRy_Ri=kiSRCaCa_jRy_Ro-kimRy_Ri-komRy_Ri-koSRCaCa_j2RI J_SRCarel=ksRy_Ro1Ca_sr-Ca_j J_serca=Q10SRCaPQpowVmax_SRCaPCa_iKmfhillSRCaP-Ca_srKmrhillSRCaP1+Ca_iKmfhillSRCaP+Ca_srKmrhillSRCaP J_SRleak=5.348 e -6Ca_sr-Ca_j

Component: Na_Buffers

ddtimeNa_Bj=dNa_Bj_dt dNa_Bj_dt=kon_naNa_jBmax_Naj-Na_Bj-koff_naNa_Bj ddtimeNa_Bsl=dNa_Bsl_dt dNa_Bsl_dt=kon_naNa_slBmax_Nasl-Na_Bsl-koff_naNa_Bsl

Component: Cytosolic_Ca_Buffers

ddtimeTn_CL=kon_tnclCa_iBmax_TnClow-Tn_CL-koff_tnclTn_CL ddtimeTn_CHc=kon_tnchcaCa_iBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchcaTn_CHc ddtimeTn_CHm=kon_tnchmgMgiBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchmgTn_CHm ddtimeCaM=kon_camCa_iBmax_CaM-CaM-koff_camCaM ddtimeMyo_c=kon_myocaCa_iBmax_myosin-Myo_c-Myo_m-koff_myocaMyo_c ddtimeMyo_m=kon_myomgMgiBmax_myosin-Myo_c-Myo_m-koff_myomgMyo_m ddtimeSRB=kon_srCa_iBmax_SR-SRB-koff_srSRB J_CaB_cytosol=kon_tnclCa_iBmax_TnClow-Tn_CL-koff_tnclTn_CL+kon_tnchcaCa_iBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchcaTn_CHc+kon_tnchmgMgiBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchmgTn_CHm+kon_camCa_iBmax_CaM-CaM-koff_camCaM+kon_myocaCa_iBmax_myosin-Myo_c-Myo_m-koff_myocaMyo_c+kon_myomgMgiBmax_myosin-Myo_c-Myo_m-koff_myomgMyo_m+kon_srCa_iBmax_SR-SRB-koff_srSRB

Component: Junctional_and_SL_Ca_Buffers

ddtimeSLL_j=kon_sllCa_jBmax_SLlowj-SLL_j-koff_sllSLL_j ddtimeSLL_sl=kon_sllCa_slBmax_SLlowsl-SLL_sl-koff_sllSLL_sl ddtimeSLH_j=kon_slhCa_jBmax_SLhighj-SLH_j-koff_slhSLH_j ddtimeSLH_sl=kon_slhCa_slBmax_SLhighsl-SLH_sl-koff_slhSLH_sl J_CaB_junction=kon_sllCa_jBmax_SLlowj-SLL_j-koff_sllSLL_j+kon_slhCa_jBmax_SLhighj-SLH_j-koff_slhSLH_j J_CaB_sl=kon_sllCa_slBmax_SLlowsl-SLL_sl-koff_sllSLL_sl+kon_slhCa_slBmax_SLhighsl-SLH_sl-koff_slhSLH_sl

Component: SR_Ca_Concentrations

ddtimeCsqn_b=kon_csqnCa_srBmax_Csqn-Csqn_b-koff_csqnCsqn_b ddtimeCa_sr=J_serca-J_SRleakVmyoVsr+J_SRCarel-kon_csqnCa_srBmax_Csqn-Csqn_b-koff_csqnCsqn_b

Component: Na_Concentrations

I_Na_tot_junc=I_Na_junc+I_nabk_junc+3I_ncx_junc+3I_nak_junc+I_CaNa_junc I_Na_tot_sl=I_Na_sl+I_nabk_sl+3I_ncx_sl+3I_nak_sl+I_CaNa_sl I_Na_tot_sl2=3I_ncx_sl+3I_nak_sl+I_CaNa_sl I_Na_tot_junc2=3I_ncx_junc+3I_nak_junc+I_CaNa_junc ddtimeNa_j=-I_Na_tot_juncCmemVjuncFrdy+J_na_juncslVjuncNa_sl-Na_j-dNa_Bj_dt ddtimeNa_sl=-I_Na_tot_slCmemVslFrdy+J_na_juncslVslNa_j-Na_sl+J_na_slmyoVslNa_i-Na_sl-dNa_Bsl_dt ddtimeNa_i=J_na_slmyoVmyoNa_sl-Na_i

Component: K_Concentration

I_K_tot=I_to+I_kr+I_ks+I_ki-2I_nak+I_CaK+I_kp ddtimeK_i=0

Component: Ca_Concentrations

I_Ca_tot_junc=I_Ca_junc+I_cabk_junc+I_pca_junc-2I_ncx_junc I_Ca_tot_sl=I_Ca_sl+I_cabk_sl+I_pca_sl-2I_ncx_sl ddtimeCa_j=-I_Ca_tot_juncCmemVjunc2Frdy+J_ca_juncslVjuncCa_sl-Ca_j-J_CaB_junction+J_SRCarelVsrVjunc+J_SRleakVmyoVjunc ddtimeCa_sl=-I_Ca_tot_slCmemVsl2Frdy+J_ca_juncslVslCa_j-Ca_sl+J_ca_slmyoVslCa_i-Ca_sl-J_CaB_sl ddtimeCa_i=-J_sercaVsrVmyo-J_CaB_cytosol+J_ca_slmyoVmyoCa_sl-Ca_i

Component: membrane_potential

I_Na_tot=I_Na_tot_junc+I_Na_tot_sl I_Cl_tot=I_ClCa+I_Clbk I_Ca_tot=I_Ca_tot_junc+I_Ca_tot_sl I_tot=I_Na_tot+I_Cl_tot+I_Ca_tot+I_K_tot ddtimeV_m=-I_tot-I_app