Model Mathematics

Component: Protocol

V_clamp=30iftime+1800mod20000-40otherwiseI_app=V_clamp-V_mR_clamp

Component: interface

Component: environment

Component: parameters

epi=1R=8314Frdy=96485Temp=310FoRT=FrdyRTempCmem=1.381 e -10Qpow=Temp-31010cellLength=100cellRadius=10.25junctionLength=160 e -3junctionRadius=15 e -3distSLcyto=0.45distJuncSL=0.5DcaJuncSL=1.64 e -6DcaSLcyto=1.22 e -6DnaJuncSL=1.09 e -5DnaSLcyto=1.79 e -5Vcell=πcellRadius2cellLength1 e -15Vmyo=0.65VcellVsr=0.035VcellVsl=0.02VcellVjunc=0.05390.01VcellSAjunc=20150π2junctionLengthjunctionRadiusSAsl=π2cellRadiuscellLengthJ_ca_juncsl=8.2413 e -13J_ca_slmyo=3.2743 e -12J_na_juncsl=1.8313 e -14J_na_slmyo=1.6386 e -12Fjunc=0.11Fsl=1-FjuncFjunc_CaL=0.9Fsl_CaL=1-Fjunc_CaLCli=15Clo=150Ko=5.4Nao=140Cao=1.8Mgi=1ena_junc=1FoRTlnNaoNa_jena_sl=1FoRTlnNaoNa_slek=1FoRTlnKoK_ieca_junc=1FoRT2lnCaoCa_jeca_sl=1FoRT2lnCaoCa_slecl=1FoRTlnCliCloGNa=23GNaB=0.597 e -3IbarNaK=11.8KmNaip=11KmKo=1.5Q10NaK=1.63Q10KmNai=1.39pNaK=0.01833gkp=20.001GClCa=0.50.109625GClB=19 e -3KdClCa=100 e -3pNa=0.51.5 e -8pCa=0.55.4 e -4pK=0.52.7 e -7Q10CaL=1.8IbarNCX=14.5KmCai=3.59 e -3KmCao=1.3KmNai=12.29KmNao=87.5ksat=0.32nu=0.27Kdact=0.15 e -3Q10NCX=1.57IbarSLCaP=0.0673KmPCa=0.5 e -3GCaB=5.513 e -4Q10SLCaP=2.35Q10SRCaP=2.6Vmax_SRCaP=5.3114 e -3Kmf=0.246 e -3Kmr=1.7hillSRCaP=1.787ks=25koCa=10kom=0.06kiCa=0.5kim=0.005ec50SR=0.45Bmax_Naj=7.561Bmax_Nasl=1.65koff_na=1 e -3kon_na=0.1 e -3Bmax_TnClow=70 e -3koff_tncl=19.6 e -3kon_tncl=32.7Bmax_TnChigh=140 e -3koff_tnchca=0.032 e -3kon_tnchca=2.37koff_tnchmg=3.33 e -3kon_tnchmg=3 e -3Bmax_CaM=24 e -3koff_cam=238 e -3kon_cam=34Bmax_myosin=140 e -3koff_myoca=0.46 e -3kon_myoca=13.8koff_myomg=0.057 e -3kon_myomg=0.0157Bmax_SR=190.9 e -3koff_sr=60 e -3kon_sr=100Bmax_SLlowsl=37.4 e -3VmyoVslBmax_SLlowj=4.6 e -3VmyoVjunc0.1koff_sll=1300 e -3kon_sll=100Bmax_SLhighsl=13.4 e -3VmyoVslBmax_SLhighj=1.65 e -3VmyoVjunc0.1koff_slh=30 e -3kon_slh=100Bmax_Csqn=140 e -3VmyoVsrkoff_csqn=65kon_csqn=100

Component: I_Na

mss=11+-56.86+V_m9.032taum=0.1292-V_m+45.7915.542+0.06487-V_m-4.82351.122ah=0ifV_m-400.057-V_m+806.8otherwisebh=0.770.131+-V_m+10.6611.1ifV_m-402.70.079V_m+3.1 e 50.3485V_motherwisetauh=1ah+bhhss=11+V_m+71.557.432aj=0ifV_m-40-2.5428 e 40.2444V_m-6.948 e -6-0.04391V_mV_m+37.781+0.311V_m+79.23otherwisebj=0.60.057V_m1+-0.1V_m+32ifV_m-400.02424-0.01052V_m1+-0.1378V_m+40.14otherwisetauj=1aj+bjjss=11+V_m+71.557.432ddtimem=mss-mtaumddtimeh=hss-htauhddtimej=jss-jtaujI_Na_junc=FjuncGNam3hjV_m-ena_juncI_Na_sl=FslGNam3hjV_m-ena_slI_Na=I_Na_junc+I_Na_sl

Component: I_NaBK

I_nabk_junc=FjuncGNaBV_m-ena_juncI_nabk_sl=FslGNaBV_m-ena_slI_nabk=I_nabk_junc+I_nabk_sl

Component: I_NaK

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

Component: I_Kr

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

Component: I_Kp

kp_kp=11+7.488-V_m5.98I_kp_junc=Fjuncgkpkp_kpV_m-ekI_kp_sl=Fslgkpkp_kpV_m-ekI_kp=I_kp_junc+I_kp_sl

Component: I_Ks

eks=1FoRTlnKo+pNaKNaoK_i+pNaKNa_igks_junc=0.0035gks_sl=0.0035xsss=11+-V_m+3.814.25tauxs=990.11+-V_m+2.43614.12ddtimex_ks=xsss-x_kstauxsI_ks_junc=Fjuncgks_juncx_ks2V_m-eksI_ks_sl=Fslgks_slx_ks2V_m-eksI_ks=I_ks_junc+I_ks_sl

Component: I_to

GtoSlow=10.130.12ifepi=10.130.30.964otherwiseGtoFast=10.130.88ifepi=10.130.30.036otherwisextoss=11+-V_m-1913ytoss=11+V_m+19.55tauxtos=91+V_m+315+0.5tauytos=8001+V_m+6010+30ddtimex_to_s=xtoss-x_to_stauxtosddtimey_to_s=ytoss-y_to_stauytosI_tos=GtoSlowx_to_sy_to_sV_m-ektauxtof=8.5-V_m+45502+0.5tauytof=85-V_m+402220+7ddtimex_to_f=xtoss-x_to_ftauxtofddtimey_to_f=ytoss-y_to_ftauytofI_tof=GtoFastx_to_fy_to_fV_m-ekI_to=I_tos+I_tof

Component: I_Ki

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

Component: I_ClCa

I_ClCa_junc=FjuncGClCa1+KdClCaCa_jV_m-eclI_ClCa_sl=FslGClCa1+KdClCaCa_slV_m-eclI_ClCa=I_ClCa_junc+I_ClCa_slI_Clbk=GClBV_m-ecl

Component: I_Ca

fss=11+V_m+359+0.61+50-V_m20dss=11+-V_m+56taud=1dss1--V_m+560.035V_m+5tauf=10.0197-0.0337V_m+14.52+0.02ddtimed=dss-dtaudddtimef=fss-ftaufddtimef_Ca_Bj=1.7Ca_j11-f_Ca_Bj-11.9 e -3f_Ca_Bjddtimef_Ca_Bsl=1.7Ca_sl11-f_Ca_Bsl-11.9 e -3f_Ca_BslfcaCaMSL=0fcaCaj=0ibarca_j=pCa4V_mFrdyFoRT0.341Ca_j2V_mFoRT-0.341Cao2V_mFoRT-1ibarca_sl=pCa4V_mFrdyFoRT0.341Ca_sl2V_mFoRT-0.341Cao2V_mFoRT-1ibark=pKV_mFrdyFoRT0.75K_iV_mFoRT-0.75KoV_mFoRT-1ibarna_j=pNaV_mFrdyFoRT0.75Na_jV_mFoRT-0.75NaoV_mFoRT-1ibarna_sl=pNaV_mFrdyFoRT0.75Na_slV_mFoRT-0.75NaoV_mFoRT-1I_Ca_junc=Fjunc_CaLibarca_jdf1-f_Ca_Bj+fcaCajQ10CaLQpow0.451I_Ca_sl=Fsl_CaLibarca_sldf1-f_Ca_Bsl+fcaCaMSLQ10CaLQpow0.451I_Ca=I_Ca_junc+I_Ca_slI_CaK=ibarkdfFjunc_CaLfcaCaj+1-f_Ca_Bj+Fsl_CaLfcaCaMSL+1-f_Ca_BslQ10CaLQpow0.451I_CaNa_junc=Fjunc_CaLibarna_jdf1-f_Ca_Bj+fcaCajQ10CaLQpow0.451I_CaNa_sl=Fsl_CaLibarna_sldf1-f_Ca_Bsl+fcaCaMSLQ10CaLQpow0.451I_CaNa=I_CaNa_junc+I_CaNa_slI_Catot=I_Ca+I_CaK+I_CaNa

Component: I_NCX

Ka_junc=11+KdactCa_j2Ka_sl=11+KdactCa_sl2s1_junc=nuV_mFoRTNa_j3Caos1_sl=nuV_mFoRTNa_sl3Caos2_junc=nu-1V_mFoRTNao3Ca_js3_junc=KmCaiNao31+Na_jKmNai3+KmNao3Ca_j1+Ca_jKmCai+KmCaoNa_j3+Na_j3Cao+Nao3Ca_js2_sl=nu-1V_mFoRTNao3Ca_sls3_sl=KmCaiNao31+Na_slKmNai3+KmNao3Ca_sl1+Ca_slKmCai+KmCaoNa_sl3+Na_sl3Cao+Nao3Ca_slI_ncx_junc=FjuncIbarNCXQ10NCXQpowKa_juncs1_junc-s2_juncs3_junc1+ksatnu-1V_mFoRTI_ncx_sl=FslIbarNCXQ10NCXQpowKa_sls1_sl-s2_sls3_sl1+ksatnu-1V_mFoRTI_ncx=I_ncx_junc+I_ncx_sl

Component: I_PCa

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

Component: I_CaBK

I_cabk_junc=FjuncGCaBV_m-eca_juncI_cabk_sl=FslGCaBV_m-eca_slI_cabk=I_cabk_junc+I_cabk_sl

Component: SR_Fluxes

MaxSR=15MinSR=1kCaSR=MaxSR-MaxSR-MinSR1+ec50SRCa_sr2.5koSRCa=koCakCaSRkiSRCa=kiCakCaSRRI=1-Ry_Rr-Ry_Ro-Ry_RiddtimeRy_Rr=kimRI-kiSRCaCa_jRy_Rr-koSRCaCa_j2Ry_Rr-komRy_RoddtimeRy_Ro=koSRCaCa_j2Ry_Rr-komRy_Ro-kiSRCaCa_jRy_Ro-kimRy_RiddtimeRy_Ri=kiSRCaCa_jRy_Ro-kimRy_Ri-komRy_Ri-koSRCaCa_j2RIJ_SRCarel=ksRy_Ro1Ca_sr-Ca_jJ_serca=Q10SRCaPQpowVmax_SRCaPCa_iKmfhillSRCaP-Ca_srKmrhillSRCaP1+Ca_iKmfhillSRCaP+Ca_srKmrhillSRCaPJ_SRleak=5.348 e -6Ca_sr-Ca_j

Component: Na_Buffers

ddtimeNa_Bj=dNa_Bj_dtdNa_Bj_dt=kon_naNa_jBmax_Naj-Na_Bj-koff_naNa_BjddtimeNa_Bsl=dNa_Bsl_dtdNa_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_CLddtimeTn_CHc=kon_tnchcaCa_iBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchcaTn_CHcddtimeTn_CHm=kon_tnchmgMgiBmax_TnChigh-Tn_CHc-Tn_CHm-koff_tnchmgTn_CHmddtimeCaM=kon_camCa_iBmax_CaM-CaM-koff_camCaMddtimeMyo_c=kon_myocaCa_iBmax_myosin-Myo_c-Myo_m-koff_myocaMyo_cddtimeMyo_m=kon_myomgMgiBmax_myosin-Myo_c-Myo_m-koff_myomgMyo_mddtimeSRB=kon_srCa_iBmax_SR-SRB-koff_srSRBJ_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_jddtimeSLL_sl=kon_sllCa_slBmax_SLlowsl-SLL_sl-koff_sllSLL_slddtimeSLH_j=kon_slhCa_jBmax_SLhighj-SLH_j-koff_slhSLH_jddtimeSLH_sl=kon_slhCa_slBmax_SLhighsl-SLH_sl-koff_slhSLH_slJ_CaB_junction=kon_sllCa_jBmax_SLlowj-SLL_j-koff_sllSLL_j+kon_slhCa_jBmax_SLhighj-SLH_j-koff_slhSLH_jJ_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_bddtimeCa_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_juncI_Na_tot_sl=I_Na_sl+I_nabk_sl+3I_ncx_sl+3I_nak_sl+I_CaNa_slI_Na_tot_sl2=3I_ncx_sl+3I_nak_sl+I_CaNa_slI_Na_tot_junc2=3I_ncx_junc+3I_nak_junc+I_CaNa_juncddtimeNa_j=-I_Na_tot_juncCmemVjuncFrdy+J_na_juncslVjuncNa_sl-Na_j-dNa_Bj_dtddtimeNa_sl=-I_Na_tot_slCmemVslFrdy+J_na_juncslVslNa_j-Na_sl+J_na_slmyoVslNa_i-Na_sl-dNa_Bsl_dtddtimeNa_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_kpddtimeK_i=0

Component: Ca_Concentrations

I_Ca_tot_junc=I_Ca_junc+I_cabk_junc+I_pca_junc-2I_ncx_juncI_Ca_tot_sl=I_Ca_sl+I_cabk_sl+I_pca_sl-2I_ncx_slddtimeCa_j=-I_Ca_tot_juncCmemVjunc2Frdy+J_ca_juncslVjuncCa_sl-Ca_j-J_CaB_junction+J_SRCarelVsrVjunc+J_SRleakVmyoVjuncddtimeCa_sl=-I_Ca_tot_slCmemVsl2Frdy+J_ca_juncslVslCa_j-Ca_sl+J_ca_slmyoVslCa_i-Ca_sl-J_CaB_slddtimeCa_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_slI_Cl_tot=I_ClCa+I_ClbkI_Ca_tot=I_Ca_tot_junc+I_Ca_tot_slI_tot=I_Na_tot+I_Cl_tot+I_Ca_tot+I_K_totddtimeV_m=-I_tot-I_app