Model Mathematics

Component: environment

Component: b1_AR_Gs_parameters

Component: cAMP_parameters

Component: PKA_parameters

Component: PLB_parameters

Component: LCC_parameters

Component: EC_Coupling_Parameters

Component: b1_AR_module

LR=LRKl LRG=LRGsKr RG=RGsKc BARK_DESENS=k_bar_kpLR+LRG BARK_RESENS=k_bar_kmb1_AR_d PKA_DESENS=k_p_kapPKAC_Ib1_AR_tot PKA_RESENS=k_p_kamb1_AR_p G_ACT=k_g_actRG+LRG HYD=k_hydGs_agtp_tot REASSOC=k_reassocGs_agdpGs_bg L=L_totmax-LR-LRG R=b1_AR_tot-LR-LRG-RG Gs=Gs_tot-LRG-RG ddtimeb1_AR_tot=BARK_RESENS-BARK_DESENS+PKA_RESENS-PKA_DESENS ddtimeb1_AR_d=BARK_DESENS-BARK_RESENS ddtimeb1_AR_p=PKA_DESENS-PKA_RESENS ddtimeGs_agtp_tot=G_ACT-HYD ddtimeGs_agdp=HYD-REASSOC ddtimeGs_bg=G_ACT-REASSOC

Component: cAMP_module

Gsa_GTP_AC=Gsa_GTPACK_gsa Fsk_AC=FskACK_fsk AC_ACT_BASAL=k_ac_basalACATPKm_basal+ATP AC_ACT_GSA=k_ac_gsaGsa_GTP_ACATPKm_gsa+ATP AC_ACT_FSK=k_ac_fskFsk_ACATPKm_fsk+ATP PDE_ACT=k_pdePDEcAMPKm_pde+cAMP PDE_IBMX=PDEIBMXKi_ibmx Gsa_GTP=Gs_agtp_tot-Gsa_GTP_AC Fsk=Fsk_tot-Fsk_AC AC=AC_tot-Gsa_GTP_AC PDE=PDE_tot-PDE_IBMX IBMX=IBMX_tot-PDE_IBMX ddtimecAMP_tot=AC_ACT_BASAL+AC_ACT_GSA+AC_ACT_FSK-PDE_ACT

Component: PKA_module

PKI=PKI_totKi_pkiKi_pki+PKAC_I+PKAC_II A2RC_I=PKAC_IK_dPKAC_I1+PKIKi_pki A2R_I=PKAC_I1+PKIKi_pki A2RC_II=PKAC_IIK_dPKAC_II1+PKIKi_pki A2R_II=PKAC_II1+PKIKi_pki ARC_I=K_acAMPA2RC_I ARC_II=K_acAMPA2RC_II PKA_temp=K_aK_bK_d+K_acAMPK_d+cAMP2K_d cAMP=cAMP_tot-ARC_I+2A2RC_I+2A2R_I-ARC_II+2A2RC_II+2A2R_II 0=2PKAI_totcAMP2-PKAC_I1+PKIKi_pkiPKA_tempPKAC_I+cAMP2 0=2PKAII_totcAMP2-PKAC_II1+PKIKi_pkiPKA_tempPKAC_II+cAMP2

Component: PLB_module

PLB=PLB_tot-PLB_p PLB_PHOSPH=k_pka_plbPKAC_IPLBKm_pka_plb+PLB PLB_DEPHOSPH=k_pp1_plbPP1PLB_pKm_pp1_plb+PLB_p Inhib1=Inhib1_tot-Inhib1p_tot Inhib1p_PP1=Inhib1pPP1Ki_inhib1 Inhib1_PHOSPH=k_pka_i1PKAC_IInhib1Km_pka_i1+Inhib1 Inhib1_DEPHOSPH=Vmax_pp2a_i1Inhib1p_totKm_pp2a_i1+Inhib1p_tot ddtimePLB_p=PLB_PHOSPH-PLB_DEPHOSPH ddtimeInhib1p_tot=Inhib1_PHOSPH-Inhib1_DEPHOSPH Inhib1p=Inhib1p_tot-Inhib1p_PP1 PP1=PP1_tot-Inhib1p_PP1 frac_PLB_p=PLB_pPLB_tot frac_PLB=PLBPLB_tot frac_PLB_o=0.9613

Component: LCC_module

LCCa=LCC_tot-LCCa_p LCCa_PHOSPH=epsilonk_pka_lccPKAC_IILCCaKm_pka_lcc+epsilonLCCa LCCa_DEPHOSPH=epsilonk_pp2a_lccPP2A_lcc_totLCCa_pKm_pp2a_lcc+epsilonLCCa_p LCCb=LCC_tot-LCCb_p LCCb_PHOSPH=epsilonk_pka_lccPKAC_IILCCbKm_pka_lcc+epsilonLCCb LCCb_DEPHOSPH=epsilonk_pp1_lccPP1_lcc_totLCCb_pKm_pp1_lcc+epsilonLCCb_p ddtimeLCCa_p=LCCa_PHOSPH-LCCa_DEPHOSPH ddtimeLCCb_p=LCCb_PHOSPH-LCCb_DEPHOSPH frac_LCCa_p=LCCa_pLCC_tot frac_LCCa_po=0.2041 frac_LCCb_p=LCCb_pLCC_tot frac_LCCb_po=0.2336

Component: Nernst_Potentials

FoRT=FrdyRTemp E_Na=1FoRTz_NalnNa_extNa_i E_K=1FoRTz_KlnK_extK_i E_Ca=1FoRTz_CalnCa_extCa_i E_Cl=-40

Component: Fast_Na_Current

am=0.32V_m+47.131--0.1V_m+47.13 bm=0.08-V_m11 ah=0ifV_m-400.13580+V_m-6.8otherwise aj=0ifV_m-40-1.2714 e 50.2444V_m-3.474 e -5-0.04391V_mV_m+37.781+0.311V_m+79.23otherwise bh=10.131+-V_m+10.6611.1ifV_m-403.560.079V_m+3.1 e 50.35V_motherwise bj=0.3-2.575 e -7V_m1+-0.1V_m+32ifV_m-400.1212-0.01052V_m1+-0.1378V_m+40.14otherwise ddtimem=1 e 3am1-m-bmm ddtimeh=1 e 3ah1-h-bhh ddtimej=1 e 3aj1-j-bjj I_Na=G_Nam3hjV_m-E_Na

Component: L_Type_Calcium_Current

a_lcc=400V_m+210 b_lcc=50-1V_m+213 f_lcc=f0.375frac_LCCa_pfrac_LCCa_po+0.625 y_lcc_inf=11+V_m+557.5+0.11+-V_m+216 tau_y_lcc=0.02+0.31+V_m+309.5 gamma=gamma_oCa_i v_gamma=gamma1-v4+2v1-v3+4v21-v2+8v31-v+16v41-f_lccg v_omega=omega1-w4+0.5w1-w3+0.25w21-w2+0.125w31-w+0.0625w4 ddtimev=a_lcc1-v-b_lccv ddtimew=2a_lcc1-w-b_lcc2w ddtimex=f_lcc1-x-gx ddtimey=y_lcc_inf-ytau_y_lcc ddtimez=v_omega1-z-v_gammaz i_bar_Ca=p_Ca4V_mFrdyFoRT1 e -32V_mFoRT-0.341Ca_ext2V_mFoRT-1 i_bar_K=p_KV_mFrdyFoRTK_iV_mFoRT-K_extV_mFoRT-1 f_avail=0.50.4frac_LCCb_pfrac_LCCb_po+0.6 I_Ca=i_bar_CaN_lccf_availv4xyz I_CaK=i_bar_K1+I_CaI_Ca05N_lccf_availv4xyz I_Ca_tot=I_Ca+I_CaK

Component: Transient_Outward_K_Current

r_toss=11+V_m+10.6-11.42 s_toss=11+V_m+43.56.8841 tau_r_to=145.160.03577V_m+50+98.9-0.1V_m+38 tau_s_to=0.35-1V_m+70152+0.035 tau_ss_to=3.7-1V_m+70302+0.035 ddtimer_to=r_toss-r_totau_r_to ddtimes_to=s_toss-s_totau_s_to ddtimess_to=s_toss-ss_totau_ss_to I_to=G_tor_to0.886s_to+0.114ss_toV_m-E_K

Component: Steady_State_K_Current

r_ss_inf=11+V_m+11.5-11.82 tau_r_ss=1045.160.03577V_m+50+98.9-0.1V_m+38 s_ss_inf=11+V_m+87.510.3 tau_s_ss=2.1 ddtimer_ss=r_ss_inf-r_sstau_r_ss ddtimes_ss=s_ss_inf-s_sstau_s_ss I_ss=G_ssr_sss_ssV_m-E_K

Component: Time_Independent_K_Current

a_Ki=1.021+0.2385V_m-E_K-59.215 b_Ki=0.491240.08032V_m+5.476-E_K+0.06175V_m-E_K-594.311+-0.5143V_m-E_K+4.753 Ki_ss=a_Kia_Ki+b_Ki I_Ki=G_Ki_barK_ext5.4Ki_ssV_m-E_K

Component: Plateau_K_Current

Kp=11+7.488-V_m5.98 I_Kp=G_KpKpV_m-E_K

Component: Na_Ca_Exchanger_Current

s4=etaV_mFoRTNa_i3Ca_ext s5=eta-1V_mFoRTNa_ext3Ca_i I_NCX=k_NaCaKm_Na3+Na_ext3Km_Ca+Ca_ext1+k_sateta-1V_mFoRTs4-s5

Component: Na_K_Pump_Current

sigma=Na_ext67.3-17 f_NaK=11+0.1245-0.1V_mFoRT+0.0365sigma-V_mFoRT I_NaK=I_bar_NaKf_NaK1+Km_NaiNa_i1.5K_extK_ext+Km_Ko

Component: Sarcolemmal_Ca_Pump_Current

I_PCa=I_bar_PCaCa_iKm_PCa+Ca_i

Component: Ca_Background_Current

I_CaB=G_CaBV_m-E_Ca

Component: Na_Background_Current

I_NaB=G_NaBV_m-E_Na

Component: Total_Membrane_Currents

I_Na_tot=I_Na+I_NaB+3I_NCX+3I_NaK I_K_tot=I_to+I_ss+I_Ki+I_Kp-2I_NaK+I_CaK I_Ca_tot=I_Ca+I_CaB+I_PCa-2I_NCX

Component: Calcium_Induced_Calcium_Release

t_rel=trel+2 e -3 ryr_on=1--t_reltau_on ryr_off=-t_reltau_off g_rel=G_max_rel1+I_Ca_tot+50.9 I_rel=g_relryr_onryr_offCa_jsr-Ca_i

Component: Other_SR_Fluxes_and_Concentrations

Km_up=Km_up01+2frac_PLB1+2frac_PLB_o I_up=I_up_barCa_i2Km_up2+Ca_i2 I_leak=I_up_barCa_nsrNSR_bar I_tr=Ca_nsr-Ca_jsrtau_tr B_jsr=11+CSQN_barKm_CSQNKm_CSQN+Ca_jsr2 ddtimeCa_nsr=I_up-I_leak-I_trV_jsrV_nsr ddtimeCa_jsr=B_jsrI_tr-I_rel SR_content=1 e 3Ca_jsr+Ca_jsrB_jsrV_jsrV_myo+Ca_nsrV_nsrV_myo

Component: Cytoplasmic_Calcium_Buffering

b_trpn=TRPN_barKm_TRPNKm_TRPN+Ca_i2 b_cmdn=CMDN_barKm_CMDNKm_CMDN+Ca_i2 b_indo=INDO_barKm_INDOKm_INDO+Ca_i2 B_myo=11+b_cmdn+b_trpn+b_trpn+b_indo

Component: Ion_Concentrations_and_Membrane_Potential

V_clamp=V_testiftime>59.1time<59.5V_holdotherwise I_app=0ifprotocol=0I_paceifprotocol=1V_clamp-V_m0.02otherwise ddtimeNa_i=-1 e 3I_Na_totA_CapV_myoz_NaFrdy ddtimeK_i=-1 e 3I_K_totA_CapV_myoz_KFrdy ddtimeCa_i=-B_myo1 e 3I_Ca_totA_CapV_myoz_CaFrdy+I_up-I_leakV_nsrV_myo-I_relV_jsrV_myo ddtimeV_m=-1 e 3I_Ca_tot+I_K_tot+I_Na_tot-I_app ddtimetrel=1-1 e 4trelif-1 e 3I_Ca_tot+I_K_tot+I_Na_tot-I_app>30 e 31otherwise I_pace=10iftime+0.9mod1<0.0050otherwise