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Activities are fitted to the steady-state activities in the Morroti model.

fPKACI=PKACI0+PKACIact1+PKACIKMISOfPKACII=PKACII0+PKACIIact1+PKACIIKMISOfPP1=PP10+PP1act1+ISOPP1KIfPLBp=PLBp0+PLBpact1+(PLBpKMISO)PLBpnfPLMp=PLMp0+PLMpact1+(PLMpKMISO)PLMpnTnIPKAp=TnIp0+TnIpact1+(TnIpKMISO)TnIpnLCCaPKAp=LCCap0+LCCapact1+LCCapKMISOLCCbPKAp=LCCbp0+LCCbpact1+LCCbpKMISOKURPKAp=KURp0+KURpact1+KURpKMISORyRPKAp=RyRp0+RyRpact1+RyRpKMISO\begin{align} f_{PKACI} &= PKACI_0 + \frac{PKACI_{act}}{1 + \frac{PKACI_{KM}}{ISO}} \\ f_{PKACII} &= PKACII_0 + \frac{PKACII_{act}}{1 + \frac{PKACII_{KM}}{ISO}} \\ f_{PP1} &= PP1_0 + \frac{PP1_{act}}{ 1 + \frac{ISO}{PP1_{KI}}} \\ f_{PLBp} &= PLBp_0 + \frac{PLBp_{act}}{1 + (\frac{PLBp_{KM}}{ISO})^{PLBp_{n}}} \\ f_{PLMp} &= PLMp_0 + \frac{PLMp_{act}}{1 + (\frac{PLMp_{KM}}{ISO})^{PLMp_{n}}} \\ TnI_{PKAp} &= TnIp_0 + \frac{TnIp_{act}}{1 + (\frac{TnIp_{KM}}{ISO})^{TnIp_{n}}} \\ LCCa_{PKAp} &= LCCap_0 + \frac{LCCap_{act}}{1 + \frac{LCCap_{KM}}{ISO}} \\ LCCb_{PKAp} &= LCCbp_0 + \frac{LCCbp_{act}}{1 + \frac{LCCbp_{KM}}{ISO}} \\ KUR_{PKAp} &= KURp_0 + \frac{KURp_{act}}{1 + \frac{KURp_{KM}}{ISO}} \\ RyR_{PKAp} &= RyRp_0 + \frac{RyRp_{act}}{1 + \frac{RyRp_{KM}}{ISO}} \\ \end{align}
(1)

Full model

v1=kfLR⋅ISO⋅b1AR−krLRLRv2=kfLRG⋅LR⋅Gs−krLRGLRGv3=kfRG⋅b1AR⋅Gs−krRGRGv4=kG,act⋅RGv5=kG,act⋅LRGv6=kG,hyd⋅GsaGTPv7=kG,reassoc⋅GsaGDP⋅Gsbyv8=kfbARK⋅LR−krbARK⋅b1ARS464v9=kfbARK⋅LRGv10=kfPKA⋅PKACI⋅b1AR−krPKA⋅b1ARS301v11=kfPKA⋅PKACI⋅LRv12=kfPKA⋅PKACI⋅LRGv13=kfAC,Gsa⋅AC⋅GsaGTP−krAC,Gsa⋅ACGsaGTPv14=kG,hyd⋅ACGsaGTPv15=kPKA,PDE⋅PKACII⋅PDE−kPP,PDE⋅PDEpv16f=kAC,Gsa⋅ACGsaGTP⋅ATPATP+KmAC,Gsa+kAC,basal⋅AC⋅ATPATP+KmAC,basalv16r=(kcAMP,PDE⋅PDE+kcAMP,PDEp⋅PDEp)cAMPcAMP+KmPDE,cAMPv17=kfRC,cAMP⋅RCI⋅cAMP−krRC,cAMP⋅RCcAMPIv18=kfRC,cAMP⋅RCII⋅cAMP−krRC,cAMP⋅RCcAMPIIv19=kfRCcAMP,cAMP⋅RCcAMPI⋅cAMP−krRCcAMP,cAMP⋅RCcAMPcAMPIv20=kfRCcAMP,cAMP⋅RCcAMPII⋅cAMP−krRCcAMP,cAMP⋅RCcAMPcAMPIIv21=kfRcAMPcAMP,C⋅RCcAMPcAMPI−krRcAMPcAMP,C⋅RcAMPcAMPI⋅PKACIv22=kfRcAMPcAMP,C⋅RCcAMPcAMPII−krRcAMPcAMP,C⋅RcAMPcAMPII⋅PKACIIv23=kfPKA,PKI⋅PKACI⋅PKI−krPKA,PKIPKACI_PKIv24=kfPKA,PKI⋅PKACII⋅PKI−krPKA,PKIPKACII_PKIv25=⋅kPKA,I1⋅PKACI⋅I1I1+KmPKA,I1−VmaxPP2A,I1⋅I1pI1p+KmPP2A,I1v26=kfPP1,I1⋅I1p⋅PP1−krPP1,I1⋅I1p_PP1v27=kPKA,PLB⋅PKACI⋅PLBPLB+KmPKA,PLB−kPP1,PLB⋅PP1⋅PLBpPLBp+KmPP1,PLBv28=kPKA,PLM⋅PKACI⋅PLMPLM+KmPKA,PLM−kPP1,PLM⋅PP1⋅PLMpPLMp+KmPP1,PLMv29=kPKA,TnI⋅PKACI⋅TnITnI+KmPKA,TnI−kPP2A,TnI⋅PP2A_TnI⋅TnIpTnIp+KmPP2A,TnIv30=kPKA,LCC′⋅PKACII⋅LCCa′LCCa′+KmPKA,LCC−kPP2A,LCC⋅PP2ALCC⋅LCCap′LCCap′+KmPP2A,LCCkPKA,LCC′=kPKA,LCC⋅PKACIILCCtotBA/PKAIItotLCCa′=ϵ⋅LCCaLCCap′=ϵ⋅LCCapv31=kPKA,LCC′⋅PKACII⋅LCCb′LCCb′+KmPKA,LCC−kPP1,LCC⋅PP1LCC⋅LCCbp′LCCbp′+KmPP1,LCCLCCb′=ϵ⋅LCCbLCCbp′=ϵ⋅LCCbpv32=kpka,KUR′⋅PKACII⋅KURn′KURn′+KmPKA,LCC−kpp1,KUR⋅PP1KURtot⋅KURp′KURp′+Kmpp1,KURkpka,KUR′=kpka,KUR⋅PKACIIKURtot/PKAIItotKURn′=ϵ⋅KURnKURp′=ϵ⋅KURpv33=kpka,RyR′⋅PKACII⋅RyRn′RyRn′+KmPKA,RyR−kpp1,RyR⋅PP1RyR⋅RyRp′RyRp′+Kmpp1,RyR−kpp2a,RyR⋅PP2ARyR⋅RyRp′RyRp′+Kmpp2a,RyRkpka,RyR′=kcatpka,RyR⋅PKACIIRyRtot/PKAIItotRyRn′=ϵ⋅RyRnRyRp′=ϵ⋅RyRp\begin{align} v_1 &= kf_{LR} \cdot \mathtt{ISO} \cdot \mathtt{b1AR} - kr_{LR} \mathtt{LR} \\ v_2 &= kf_{LRG} \cdot \mathtt{LR} \cdot \mathtt{Gs} - kr_{LRG} \mathtt{LRG} \\ v_3 &= kf_{RG} \cdot \mathtt{b1AR} \cdot \mathtt{Gs} - kr_{RG} \mathtt{RG} \\ v_4 &= k_{G, act} \cdot \mathtt{RG} \\ v_5 &= k_{G, act} \cdot \mathtt{LRG} \\ v_6 &= k_{G, hyd} \cdot \mathtt{GsaGTP} \\ v_7 &= k_{G, reassoc} \cdot \mathtt{GsaGDP} \cdot \mathtt{Gsby} \\ v_8 &= kf_{bARK} \cdot \mathtt{LR} - kr_{bARK} \cdot \mathtt{b1AR_{S464}} \\ v_9 &= kf_{bARK} \cdot \mathtt{LRG} \\ v_{10} &= kf_{PKA} \cdot \mathtt{PKACI} \cdot \mathtt{b1AR} - kr_{PKA} \cdot \mathtt{b1AR_{S301}} \\ v_{11} &= kf_{PKA} \cdot \mathtt{PKACI} \cdot \mathtt{LR} \\ v_{12} &= kf_{PKA} \cdot \mathtt{PKACI} \cdot \mathtt{LRG} \\ v_{13} &= kf_{AC, Gsa} \cdot \mathtt{AC} \cdot \mathtt{GsaGTP} - kr_{AC, Gsa} \cdot \mathtt{AC_GsaGTP} \\ v_{14} &= k_{G, hyd} \cdot \mathtt{AC_GsaGTP} \\ v_{15} &= k_{PKA, PDE} \cdot \mathtt{PKACII} \cdot \mathtt{PDE} - k_{PP, PDE} \cdot \mathtt{PDEp} \\ v_{16f} &= \frac{k_{AC, Gsa} \cdot \mathtt{AC_GsaGTP} \cdot ATP}{ATP + Km_{AC,Gsa}} + \frac{k_{AC, basal} \cdot \mathtt{AC} \cdot ATP}{ATP + Km_{AC,basal}} \\ v_{16r} &= \frac{(k_{cAMP, PDE} \cdot \mathtt{PDE} + k_{cAMP, PDEp} \cdot \mathtt{PDEp}) \mathtt{cAMP}}{\mathtt{cAMP} + Km_{PDE, cAMP}} \\ v_{17} &= kf_{RC, cAMP} \cdot \mathtt{RC_I} \cdot \mathtt{cAMP} - kr_{RC,cAMP} \cdot \mathtt{RCcAMP_I} \\ v_{18} &= kf_{RC, cAMP} \cdot \mathtt{RC_{II}} \cdot \mathtt{cAMP} - kr_{RC,cAMP} \cdot \mathtt{RCcAMP_{II}} \\ v_{19} &= kf_{RCcAMP, cAMP} \cdot \mathtt{RCcAMP_I} \cdot \mathtt{cAMP} - kr_{RCcAMP,cAMP} \cdot \mathtt{RCcAMPcAMP_I} \\ v_{20} &= kf_{RCcAMP, cAMP} \cdot \mathtt{RCcAMP_{II}} \cdot \mathtt{cAMP} - kr_{RCcAMP,cAMP} \cdot \mathtt{RCcAMPcAMP_{II}} \\ v_{21} &= kf_{RcAMPcAMP,C} \cdot \mathtt{RCcAMPcAMP_I} - kr_{RcAMPcAMP,C} \cdot \mathtt{RcAMPcAMP_I} \cdot \mathtt{PKACI} \\ v_{22} &= kf_{RcAMPcAMP,C} \cdot \mathtt{RCcAMPcAMP_{II}} - kr_{RcAMPcAMP,C} \cdot \mathtt{RcAMPcAMP_{II}} \cdot \mathtt{PKACII} \\ v_{23} &= kf_{PKA,PKI} \cdot \mathtt{PKACI} \cdot \mathtt{PKI} - kr_{PKA,PKI} \mathtt{PKACI\_PKI} \\ v_{24} &= kf_{PKA,PKI} \cdot \mathtt{PKACII} \cdot \mathtt{PKI} - kr_{PKA,PKI} \mathtt{PKACII\_PKI} \\ v_{25} &= \cdot \frac{k_{PKA,I1} \cdot \mathtt{PKACI} \cdot \mathtt{I1}}{\mathtt{I1} + Km_{PKA,I1}} - \frac{Vmax_{PP2A, I1} \cdot \mathtt{I1p}}{\mathtt{I1p} + Km_{PP2A,I1}} \\ v_{26} &= kf_{PP1, I1} \cdot \mathtt{I1p} \cdot \mathtt{PP1} - kr_{PP1, I1} \cdot \mathtt{I1p\_PP1} \\ v_{27} &= \frac{k_{PKA,PLB} \cdot \mathtt{PKACI} \cdot \mathtt{PLB}}{\mathtt{PLB} + Km_{PKA,PLB}} - \frac{k_{PP1,PLB} \cdot \mathtt{PP1} \cdot \mathtt{PLBp}}{\mathtt{PLBp} + Km_{PP1,PLB}} \\ v_{28} &= \frac{k_{PKA,PLM} \cdot \mathtt{PKACI} \cdot \mathtt{PLM}}{\mathtt{PLM} + Km_{PKA,PLM}} - \frac{k_{PP1,PLM} \cdot \mathtt{PP1} \cdot \mathtt{PLMp}}{\mathtt{PLMp} + Km_{PP1,PLM}} \\ v_{29} &= \frac{k_{PKA,TnI} \cdot \mathtt{PKACI} \cdot \mathtt{TnI}}{\mathtt{TnI} + Km_{PKA,TnI}} - \frac{k_{PP2A,TnI} \cdot \mathtt{PP2A\_TnI} \cdot \mathtt{TnIp}}{\mathtt{TnIp} + Km_{PP2A,TnI}} \\ v_{30} &= \frac{k_{PKA,LCC}^{\prime} \cdot \mathtt{PKACII} \cdot LCCa^{\prime}}{{LCCa}^{\prime} + Km_{PKA,LCC}} - \frac{ k_{PP2A,LCC} \cdot PP2A_{LCC} \cdot LCCap^{\prime}}{{LCCap}^{\prime} + Km_{PP2A,LCC}} \\ k_{PKA,LCC}^{\prime} &= k_{PKA,LCC} \cdot PKACII_{LCCtotBA} / PKAIItot \\ {LCCa}^{\prime} &= \epsilon \cdot \mathtt{LCCa} \\ {LCCap}^{\prime} &= \epsilon \cdot \mathtt{LCCap} \\ v_{31} &= \frac{k_{PKA,LCC}^{\prime} \cdot \mathtt{PKACII} \cdot LCCb^{\prime}}{{LCCb}^{\prime} + Km_{PKA,LCC}} - \frac{k_{PP1,LCC} \cdot PP1_{LCC} \cdot LCCbp^{\prime}}{{LCCbp}^{\prime} + Km_{PP1,LCC}} \\ {LCCb}^{\prime} &= \epsilon \cdot \mathtt{LCCb} \\ {LCCbp}^{\prime} &= \epsilon \cdot \mathtt{LCCbp} \\ v_{32} &= \frac{k_{pka,KUR}^{\prime} \cdot \mathtt{PKACII} \cdot KURn^{\prime}}{{KURn}^{\prime} + Km_{PKA,LCC}} - \frac{k_{pp1,KUR} \cdot PP1_{KURtot} \cdot {KURp}^{\prime}}{{KURp}^{\prime} + Km_{pp1,KUR}} \\ k_{pka,KUR}^{\prime} &= k_{pka,KUR} \cdot PKACII_{KURtot} / PKAIItot \\ {KURn}^{\prime} &= \epsilon \cdot \mathtt{KURn} \\ {KURp}^{\prime} &= \epsilon \cdot \mathtt{KURp} \\ v_{33} &= \frac{k_{pka,RyR}^{\prime} \cdot \mathtt{PKACII} \cdot RyRn^{\prime}}{{RyRn}^{\prime} + Km_{PKA,RyR}} - \frac{k_{pp1,RyR} \cdot PP1_{RyR} \cdot {RyRp}^{\prime}}{{RyRp}^{\prime} + Km_{pp1,RyR}} - \frac{k_{pp2a,RyR} \cdot PP2A_{RyR} \cdot {RyRp}^{\prime}}{{RyRp}^{\prime} + Km_{pp2a,RyR}} \\ k_{pka,RyR}^{\prime} &= kcat_{pka,RyR} \cdot PKACII_{RyRtot} / PKAIItot \\ {RyRn}^{\prime} &= \epsilon \cdot \mathtt{RyRn} \\ {RyRp}^{\prime} &= \epsilon \cdot \mathtt{RyRp} \\ \end{align}
(2)
ddtLR=v1−v2−v8−v11ddtLRG=v2−v5−v9−v12ddtRG=v3−v4ddtGsaGTP=v4+v5−v6−v13ddtGsaGDP=v6−v7+v14ddtb1AR_S464=v8+v9ddtb1AR_S301=v10+v11+v12ddtAC_GsaGTP=v13−v14ddtPDEp=v15ddtcAMP=v16f−v16r−v17−v18−v19−v20ddtRCcAMPI=v17−v19ddtRCcAMPII=v18−v20ddtRCcAMPcAMPI=v19−v21ddtRCcAMPcAMPII=v20−v22ddtPKACI=v21−v23ddtPKACII=v22−v24ddtPKACI_PKI=v23ddtPKACII_PKI=v24ddtI1p=v25−v26ddtI1p_PP1=v26ddtPLBp=v27ddtPLMp=v28ddtTnIp=v29ddtLCCap=v30ddtLCCbp=v31ddtKURp=v32ddtRyRp=v33b1ARtot=LR+RG+b1AR_S464+b1AR+LRG+b1AR_S301Gstot=RG+GsaGTP+AC_GsaGTP+Gs+GsaGDP+LRGGstot=RG+Gsby+Gs+LRGACtot=AC_GsaGTP+ACPDEtot=PDEp+PDERItot=RCcAMPcAMP_I+RCcAMP_I+RC_I+RcAMPcAMP_IRIItot=RcAMPcAMP_II+RCcAMP_II+RC_II+RCcAMPcAMP_IIRcAMPcAMP_I=PKACI_PKI+PKACIRcAMPcAMP_II=PKACII+PKACII_PKIPKItot=PKACI_PKI+PKACII_PKI+PKII1tot=I1+I1p+I1p_PP1PP1totBA=PP1+I1p_PP1PLBtotBA=PLBp+PLBPLMtotBA=PLMp+PLMTnItotBA=TnI+TnIpLCCtotBA=LCCa+LCCapLCCtotBA=LCCbp+LCCbIKurtotBA=KURn+KURpRyRtotBA=RyRn+RyRpLCCa_PKAp=LCCapLCCtotBALCCb_PKAp=LCCbpLCCtotBAfracPLBp=PLBpPLBtotBAfracPLMp=PLMpPLMtotBATnI_PKAp=TnIpTnItotBAIKUR_PKAp=KURpIKurtotBARyR_PKAp=RyRpRyRtotBAfracPKACI=PKACIRItotfracPKACII=PKACIIRIItotfracPP1=PP1PP1totBA\begin{align} \frac{d}{dt}\mathtt{LR} &= v_1 - v_2 - v_8 - v_{11} \\ \frac{d}{dt}\mathtt{LRG} &= v_2 - v_5 - v_9 - v_{12} \\ \frac{d}{dt}\mathtt{RG} &= v_3 - v_4 \\ \frac{d}{dt}\mathtt{GsaGTP} &= v_4 + v_5 - v_6 - v_{13} \\ \frac{d}{dt}\mathtt{GsaGDP} &= v_6 - v_7 + v_{14} \\ \frac{d}{dt}\mathtt{b1AR\_S464} &= v_8 + v_9 \\ \frac{d}{dt}\mathtt{b1AR\_S301} &= v_{10} + v_{11} + v_{12} \\ \frac{d}{dt}\mathtt{AC\_GsaGTP} &= v_{13} - v_{14} \\ \frac{d}{dt}\mathtt{PDEp} &= v_{15} \\ \frac{d}{dt}\mathtt{cAMP} &= v_{16f} - v_{16r} - v_{17} - v_{18} - v_{19} - v_{20} \\ \frac{d}{dt}\mathtt{RCcAMP_I} &= v_{17} - v_{19} \\ \frac{d}{dt}\mathtt{RCcAMP_{II}} &= v_{18} - v_{20} \\ \frac{d}{dt}\mathtt{RCcAMPcAMP_I} &= v_{19} - v_{21} \\ \frac{d}{dt}\mathtt{RCcAMPcAMP_{II}} &= v_{20} - v_{22} \\ \frac{d}{dt}\mathtt{PKACI} &= v_{21} - v_{23} \\ \frac{d}{dt}\mathtt{PKACII} &= v_{22} - v_{24} \\ \frac{d}{dt}\mathtt{PKACI\_PKI} &= v_{23} \\ \frac{d}{dt}\mathtt{PKACII\_PKI} &= v_{24} \\ \frac{d}{dt}\mathtt{I1p} &= v_{25} - v_{26} \\ \frac{d}{dt}\mathtt{I1p\_PP1} &= v_{26} \\ \frac{d}{dt}\mathtt{PLBp} &= v_{27} \\ \frac{d}{dt}\mathtt{PLMp} &= v_{28} \\ \frac{d}{dt}\mathtt{TnIp} &= v_{29} \\ \frac{d}{dt}\mathtt{LCCap} &= v_{30} \\ \frac{d}{dt}\mathtt{LCCbp} &= v_{31} \\ \frac{d}{dt}\mathtt{KURp} &= v_{32} \\ \frac{d}{dt}\mathtt{RyRp} &= v_{33} \\ \mathtt{b1ARtot} &= \mathtt{LR} + \mathtt{RG} + \mathtt{b1AR\_S464} + \mathtt{b1AR} + \mathtt{LRG} + \mathtt{b1AR\_S301} \\ \mathtt{Gstot} &= \mathtt{RG} + \mathtt{GsaGTP} + \mathtt{AC\_GsaGTP} + \mathtt{Gs} + \mathtt{GsaGDP} + \mathtt{LRG} \\ \mathtt{Gstot} &= \mathtt{RG} + \mathtt{Gsby} + \mathtt{Gs} + \mathtt{LRG} \\ \mathtt{ACtot} &= \mathtt{AC\_GsaGTP} + \mathtt{AC} \\ \mathtt{PDEtot} &= \mathtt{PDEp} + \mathtt{PDE} \\ \mathtt{RItot} &= \mathtt{RCcAMPcAMP\_I} + \mathtt{RCcAMP\_I} + \mathtt{RC\_I} + \mathtt{RcAMPcAMP\_I} \\ \mathtt{RIItot} &= \mathtt{RcAMPcAMP\_II} + \mathtt{RCcAMP\_II} + \mathtt{RC\_II} + \mathtt{RCcAMPcAMP\_II} \\ \mathtt{RcAMPcAMP\_I} &= \mathtt{PKACI\_PKI} + \mathtt{PKACI} \\ \mathtt{RcAMPcAMP\_II} &= \mathtt{PKACII} + \mathtt{PKACII\_PKI} \\ \mathtt{PKItot} &= \mathtt{PKACI\_PKI} + \mathtt{PKACII\_PKI} + \mathtt{PKI} \\ \mathtt{I1tot} &= \mathtt{I1} + \mathtt{I1p} + \mathtt{I1p\_PP1} \\ \mathtt{PP1totBA} &= \mathtt{PP1} + \mathtt{I1p\_PP1} \\ \mathtt{PLBtotBA} &= \mathtt{PLBp} + \mathtt{PLB} \\ \mathtt{PLMtotBA} &= \mathtt{PLMp} + \mathtt{PLM} \\ \mathtt{TnItotBA} &= \mathtt{TnI} + \mathtt{TnIp} \\ \mathtt{LCCtotBA} &= \mathtt{LCCa} + \mathtt{LCCap} \\ \mathtt{LCCtotBA} &= \mathtt{LCCbp} + \mathtt{LCCb} \\ \mathtt{IKurtotBA} &= \mathtt{KURn} + \mathtt{KURp} \\ \mathtt{RyRtotBA} &= \mathtt{RyRn} + \mathtt{RyRp} \\ \mathtt{LCCa\_PKAp} &= \frac{\mathtt{LCCap}}{\mathtt{LCCtotBA}} \\ \mathtt{LCCb\_PKAp} &= \frac{\mathtt{LCCbp}}{\mathtt{LCCtotBA}} \\ \mathtt{fracPLBp} &= \frac{\mathtt{PLBp}}{\mathtt{PLBtotBA}} \\ \mathtt{fracPLMp} &= \frac{\mathtt{PLMp}}{\mathtt{PLMtotBA}} \\ \mathtt{TnI\_PKAp} &= \frac{\mathtt{TnIp}}{\mathtt{TnItotBA}} \\ \mathtt{IKUR\_PKAp} &= \frac{\mathtt{KURp}}{\mathtt{IKurtotBA}} \\ \mathtt{RyR\_PKAp} &= \frac{\mathtt{RyRp}}{\mathtt{RyRtotBA}} \\ \mathtt{fracPKACI} &= \frac{\mathtt{PKACI}}{\mathtt{RItot}} \\ \mathtt{fracPKACII} &= \frac{\mathtt{PKACII}}{\mathtt{RIItot}} \\ \mathtt{fracPP1} &= \frac{\mathtt{PP1}}{\mathtt{PP1totBA}} \end{align}
(3)
NRVM CaMKII model
Sarcolemmal Na-K pump
NRVM CaMKII model
CaMKII system