Model Mathematics

Component: environment

Component: model_parameters

Component: cell_geometry

vcell=1000πaal ageo=2πaa+2πal Acap=ageo2 AF=11AcapF1 Vmyo=vcell0.678 Vsr=vcell0.06 Vnsr=vcell0.0552 Vjsr=vcell0.0048 Vss_sr=vcell0.02 Vss_CaL=vcell0.002

Component: membrane

past=timestim_periodstim_period i_Stim=stim_amplitudeiftime-paststim_offsettime-paststim_offset+stim_duration0otherwise caiont=ICaL+ICab+IpCa-2INaCa+INaCa_ss_sr naiont=INa+3INaCa+INaCa_ss_sr+3INaK+INaL+INab kiont=IKr+IKs+IK1+IKp+-2INaK+Ito1+i_Stim clont=IClb+Ito2 ddtimeVm=-naiont+kiont+caiont+clont

Component: IKs

IKs=gKsOKsVm-EKs gKs=gKs_max1+0.61+3.8 e -5Ca_i1.4 O2=1-C1+C2+C3+C4+C5+C6+C7+C8+C9+C10+C11+C12+C13+C14+C15+O1 OKs=O1+O2 ddtimeC1=-4alphaC1+betaC2 ddtimeC2=-3alpha+beta+gammaC2+4alphaC1+2betaC3+deltaC6 ddtimeC3=-2alpha+2beta+2gammaC3+3alphaC2+3betaC4+deltaC7 ddtimeC4=-alpha+3beta+3gammaC4+2alphaC3+4betaC5+deltaC8 ddtimeC5=-4beta+4gammaC5+alphaC4+deltaC9 ddtimeC6=-3alpha+deltaC6+betaC7+gammaC2 ddtimeC7=-2alpha+beta+gamma+deltaC7+3alphaC6+2betaC8+2gammaC3+2deltaC10 ddtimeC8=-alpha+2beta+2gamma+deltaC8+2alphaC7+3betaC9+3gammaC4+2deltaC11 ddtimeC9=-3beta+3gamma+deltaC9+alphaC8+4gammaC5+2deltaC12 ddtimeC10=-2alpha+2deltaC10+betaC11+gammaC7 ddtimeC11=-alpha+beta+gamma+2deltaC11+2alphaC10+2betaC12+2gammaC8+3deltaC13 ddtimeC12=-2beta+2gamma+2deltaC12+alphaC11+3gammaC9+3deltaC14 ddtimeC13=-alpha+3deltaC13+betaC14+gammaC11 ddtimeC14=-beta+gamma+3deltaC14+alphaC13+2gammaC12+4deltaC15 ddtimeC15=-4delta+thetaC15+gammaC14+etaO1 ddtimeO1=-eta+psiO1+omegaO2+thetaC15 alpha=0.014864597980860.02987730123588VmFRT beta=0.08398631219983-0.05546105712664VmFRT gamma=0.014600661183160.24464953099645VmFRT delta=0.0031173268874-0.42625451944376VmFRT eta=0.07731990097331-0.06472612248871VmFRT theta=0.08953830641102 omega=0.7940545995864-0.08017378192977VmFRT psi=0.586382286630140.28205554331496VmFRT

Component: ICaL

OI_star=1-C+O+C_star+O_star+CI+OI+CI_star ICaL=ICaL_maxO+O_star ICaL_max=PCa4VmF2RTgamma_CaiCa_ss_CaL2VmFRT-gamma_CaoCa_o2VmFRT-1 ddtimeC=-alpha+delta+yC+betaO+thetaC_star+xCI ddtimeO=-beta+delta+yO+alphaC+thetaO_star+xOI ddtimeC_star=-alpha+theta+y_starC_star+deltaC+betaO_star+x_starCI_star ddtimeO_star=-beta+theta+y_starO_star+deltaO+alphaC_star+x_starOI_star ddtimeCI=-alpha+delta_I+xCI+yC+theta_ICI_star+betaOI ddtimeOI=-beta+delta_I+xOI+yO+theta_IOI_star+alphaCI ddtimeCI_star=-alpha+theta_I+x_starCI_star+delta_ICI+y_starC_star+betaOI_star ACT_tau=0.59+0.80.052Vm+131+0.132Vm+13 ACT_infinity=11+-Vm-13.569.45 alpha=ACT_infinityACT_tau beta=1-ACT_infinityACT_tau IV_infinity=11+Vm+17.53+0.251.25 IV_tau=1124.8281+Vm+49.110.349+130.5531+-Vm+0.21310.807 x=IV_infinityIV_tau y=1-IV_infinityIV_tau IV_infinity_star=11+Vm+17.53+0.00011.0001 IV_tau_star=1124.8281+Vm+49.110.349+IV_beta_star IV_beta_star=1IV_beta_infinity_star1+-Vm+0.21310.807 IV_beta_infinity_star=25-17.51+0.003Ca_ss_CaL4 x_star=IV_infinity_starIV_tau_star y_star=1-IV_infinity_starIV_tau_star delta=31+0.003Ca_ss_CaL4 delta_I=theta_Ixy_stardeltayx_startheta

Component: INa

INa=g_Nam3hjVm-ENa

Component: INa_m_gate

am=0.32Vm+47.131--0.1Vm+47.13 bm=0.08-Vm11 ddtimem=am1-m-bmm

Component: INa_h_gate

ah=0ifVm-400.13580+Vm-6.8otherwise bh=10.131+Vm+10.66-11.1ifVm-403.560.079Vm+3.1 e 50.35Vmotherwise ddtimeh=ah1-h-bhh

Component: INa_j_gate

aj=0ifVm-40-1.2714 e 50.2444Vm-6.948 e -5-0.04391VmVm+37.781+0.311Vm+79.23otherwise bj=0.3-2.535 e -7Vm1+-0.1Vm+32ifVm-400.1212-0.01052Vm1+-0.1378Vm+40.14otherwise ddtimej=aj1-j-bjj

Component: INaK

INaK=ibarnakfvPKPNa phi=sigmaVm-V_halfFRT fv=11+-phi PK=K_oK_o+kmko PNa=Na_iNa_i+kmnai3

Component: INaCa

numerator=0.8VmaxNa_i3Ca_oetaVmFRT-Na_o3Ca_ieta-1VmFRT denom_1=1+KmCa_actCa_i2 denom_2=1+ksateta-1VmFRT denom_3=KmCaoNa_i3+KmNao3Ca_i+KmNai3Ca_o1+Ca_iKmCai denom_4=KmCaiNa_o31+Na_iKmNai3+Na_i3Ca_o+Na_o3Ca_i num_ss=0.2VmaxNa_ss_sr3Ca_oetaVmFRT-Na_o3Ca_ss_sreta-1VmFRT denom_ss_1=1+KmCa_actCa_ss_sr2 denom_ss_2=1+ksateta-1VmFRT denom_ss_3=KmCaoNa_ss_sr3+KmNao3Ca_ss_sr+KmNai3Ca_o1+Ca_ss_srKmCai denom_ss_4=KmCaiNa_o31+Na_ss_srKmNai3+Na_ss_sr3Ca_o+Na_o3Ca_ss_sr INaCa_ss_sr=num_ssdenom_ss_1denom_ss_2denom_ss_3+denom_ss_4 INaCa_cai=numeratordenom_1denom_2denom_3+denom_4 INaCa=INaCa_cai+INaCa_ss_sr

Component: IKp

IKp=gKpKpVm-EK Kp=11+7.488-Vm5.98

Component: IpCa

IpCa=gpCaCa_iKmpCa+Ca_i

Component: ICab

ICab=PCab4VmF2RTgamma_Ca_iCa_i2VmFRT-gamma_Ca_oCa_o2VmFRT-1

Component: INab

phi=FVmRT INab=FPNabphiNa_iphi-Na_ophi-1

Component: IClb

IClb=gClbVm-ECl

Component: INaL

INaL=gNaLmL3hLVm-ENa

Component: INaL_mL_gate

amL=0.32Vm+47.131--0.1Vm+47.13 bmL=0.08-Vm11 ddtimemL=amL1-mL-bmLmL

Component: INaL_hL_gate

hL_infinity=11+Vm+916.1 ddtimehL=hL_infinity-hLtau_hL

Component: reversal_potentials

ENa=RTFlnNa_oNa_i EK=RTFlnK_oK_i EKs=RTFlnK_o+prnakNa_oK_i+prnakNa_i ECl=-RTFlnCl_oCl_i

Component: IK1

IK1=gK1K1Vm-EK gK1=g_K1_maxK_o5.4

Component: IK1_K1_gate

alpha_k1=1.021+0.2385Vm-EK-59.215 beta_k1=0.491240.08032Vm-EK+5.476+0.06175Vm-EK-594.311+-0.5143Vm-EK+4.753 K1=alpha_k1alpha_k1+beta_k1

Component: CT_Na_Cl

CT_Na_Cl=CT_Na_Cl_maxENa-ECl4ENa-ECl4+87.82514

Component: CT_K_Cl

CT_K_Cl=CT_K_Cl_maxEK-EClEK+87.8251-ECl

Component: IKr

gKr=gKr_maxK_o5.4 IKr=gKrxrrVm-EK

Component: IKr_xr_gate

xr_infinity=11+-Vm+10.0854.25 tau_xr=10.0006Vm-1.73841--0.136Vm-1.7384+0.0003Vm+38.36080.1522Vm+38.3608-1 ddtimexr=xr_infinity-xrtau_xr

Component: IKr_r_gate

r=11+Vm+1015.4

Component: Ito1

Ito1=gto1a3i1fi1srto1Vm-EK rto1=Vm550

Component: Ito1_a_gate

alpha_a=11.20891+Vm-18.4099-29.3814 beta_a=3.51+Vm+10029.3814 tau_a=1alpha_a+beta_a a_infinity=11+Vm+9.437-7.133 ddtimea=a_infinity-atau_a

Component: Ito1_i1f_gate

beta_i1f=19.79531+Vm+19-9 alpha_i1f=0.0251+Vm+585 ddtimei1f=alpha_i1f1-i1f-beta_i1fi1f

Component: Ito1_i1s_gate

beta_i1s=19.79531+Vm+19-9 alpha_i1s=12501+Vm+605 ddtimei1s=alpha_i1s1-i1s-beta_i1si1s

Component: Ito2

Ito2=Ito2_maxIto2_max_scaling_factori2fKCa_ito2 Ito2_max=PClzCl2VmF2RTCl_i-Cl_oVmFRT1-VmFRT KCa_ito2=1-11+IrelkCa_ito22

Component: Ito2_i2f_gate

ddtimei2f=i2f_infinity-i2ftau_i2f i2f_infinity=alpha_i2falpha_i2f+beta_i2f beta_i2f=151+Vm+19-9 alpha_i2f=0.0251+Vm+585

Component: Irel

alpha_rel=beta_taukappa beta_tau=beta_01+delta_beta_CaMK delta_beta_CaMK=delta_beta_01+K_beta1CaMK_activeh_beta tau_rel=beta_tau1+Krel_tauCa_JSR rel_infinity=ICaLalpha_rel1+Krel_infinityCa_JSRh_rel ddtimeIrel=-rel_infinity+Ireltau_rel

Component: Iup

Iup=delta_iupCaMK+1iupbarCa_iCa_i+kmup-delta_kmPLB delta_iupCaMK=delta_iupCaMK_barCaMK_active1kmCaMK+CaMK_active1 delta_kmPLB=delta_kmPLB_barCaMK_active1kmCaMK+CaMK_active1

Component: Ileak

Ileak=0.004375nsrbarCa_NSR

Component: Itr

Itr=Ca_NSR-Ca_JSRtautr

Component: Ca

Idiff=Ca_ss_sr-Ca_itau_diff Idiff_ss=Ca_ss_sr-Ca_ss_CaLtau_diff_ss bmyo=11+cmdn_barkm_cmdnCa_i+km_cmdn2+km_trpntrpn_barCa_i+km_trpn2 ddtimeCa_i=bmyo-ICab+IpCa-2INaCaAFVmyo2+Ileak-IupVnsrVmyo+IdiffVss_srVmyo ddtimeCa_ss_sr=-bss_srIdiff+Idiff_ss-2INaCa_ss_srAF2Vss_sr+IrelVjsrVss_sr bss_sr=11+BSRmaxKmBSRKmBSR+Ca_ss_sr2+BSLmaxKmBSLKmBSL+Ca_ss_sr2 ddtimeCa_ss_CaL=-bss_calICaLAF2Vss_CaL-Idiff_ssVss_srVss_CaL bss_cal=11+BSRmaxKmBSRKmBSR+Ca_ss_CaL2+BSLmaxKmBSLKmBSL+Ca_ss_CaL2 ddtimeCa_NSR=Iup-Ileak+ItrVjsrVnsr bcsqn=11+kmcsqncsqnbarCa_JSR+kmcsqn2 ddtimeCa_JSR=bcsqnItr-Irel

Component: Na

Idiff_Na=Na_ss_sr-Na_itau_diff ddtimeNa_i=-3INaCa+3INaK+INa+INaL+INabAFVmyo-CT_Na_Cl+Idiff_NaVss_srVmyo ddtimeNa_ss_sr=-3INaCa_ss_srAFVss_sr+Idiff_Na

Component: Cl

Idiff_Cl=Cl_ss-Cl_itau_diff ddtimeCl_i=-IClbAF-1Vmyo-CT_Na_Cl+CT_K_Cl+Idiff_ClVss_srVmyo ddtimeCl_ss=-Ito2AF-1Vss_sr+Idiff_Cl

Component: K

ddtimeK_i=-IKs+IKr+IK1+Ito1+IKp+I_stim-2INaKAFVmyo-CT_K_Cl

Component: CaMK_active

ddtimeCaMK_trap=alpha_CaMKCaMK_activeCaMK_active-CaMK_trap-beta_CaMKCaMK_trap CaMK_active=CaMK_01-CaMK_trap1+KmCa_ss_sr+CaMK_trap