Model Mathematics

Component: environment

Component: membrane

past=timestim_periodstim_period i_Stim=stim_amplitudeiftime-paststim_offsettime-paststim_offset+stim_duration0otherwise ddtimeV=-i_CaL+i_pCa+i_NaCa+i_Cab+i_Na+i_Nab+i_NaK+i_Kto_f+i_Kto_s+i_K1+i_Ks+i_Kur+i_Kss+i_Kr+i_ClCa+i_Stim

Component: calcium_concentration

ddtimeCai=BiJ_leak+J_xfer-i_Cab+i_pCa-2i_NaCaAcapCm2VmyoF-J_serca ddtimeCass=BssJ_relVJSRVss-J_xferVmyoVss+i_CaLAcapCm2VssF ddtimeCaJSR=BJSRJ_tr-J_rel ddtimeCaNSR=J_serca-J_leakVmyoVNSR-J_trVJSRVNSR Bi=1+BmaxKdKd+Cai2-1 Bss=1+BmaxKdKd+Cass2-1 BJSR=1+CSQN_totKm_CSQNKm_CSQN+CaJSR2-1

Component: calcium_fluxes

J_rel=v1P_O1+P_O2CaJSR-CassP_RyR J_tr=CaNSR-CaJSRtau_tr J_xfer=Cass-Caitau_xfer J_leak=v2CaNSR-Cai CaMKb=0.051-CaMKt11+0.7Cass ddtimeCaMKt=on_rateCaMKbCaMKb+CaMKt-off_rateCaMKt CaMKa=CaMKb+CaMKt vmup=3.1512CaMKa2.20620.15882.2062+CaMKa2.2062+1vmup_init J_serca=vmupCai2Km_up2+Cai2 ddtimeP_RyR=P_ryr_const1P_RyR+P_ryr_const2i_CaLi_CaL_max-V-52648

Component: ryanodine_receptors

ddtimeP_O1=k_plus_aCassnP_C1+k_minus_bP_O2+k_minus_cP_C2-k_minus_aP_O1+k_plus_bCassmP_O1+k_plus_cP_O1 P_C1=1-P_C2+P_O1+P_O2 ddtimeP_O2=k_plus_bCassmP_O1-k_minus_bP_O2 ddtimeP_C2=k_plus_cP_O1-k_minus_cP_C2

Component: L_type_calcium_current

FVRT=FVRT FVRT_Ca=2FVRT expVL=V-V_Ldelta_V_L alpha_p=expVLt_LexpVL+1 alpha_m=phi_Lt_L epsilon_p=expVL+atau_LK_LexpVL+1 epsilon_m=bexpVL+atau_LbexpVL+a y_gate_inf=11+V+16.6577const5+0.11+-V+406 y_gate_tau=20+6001+V+309.6 C=1-O-I ddtimeO=alpha_pC-alpha_mO ddtimeI=epsilon_pCassC-epsilon_mI ddtimey_gate=y_gate_inf-y_gatey_gate_tau i_CaL=-P_CaL2VssFAcapCmOy_gateFVRT_Ca1--FVRT_CaCao-FVRT_Ca-Cassif|FVRT_Ca|>0.00001-P_CaL2VssFAcapCmOy_gate0.000011--0.00001Cao-0.00001-Cassotherwise

Component: calcium_pump_current

i_pCa=i_pCa_maxCai2Km_pCa2+Cai2 J_pCa=-i_pCaAcapCm2VmyoF

Component: sodium_calcium_exchange_current

i_NaCa=k_NaCa1K_mNa3+Nao31K_mCa+Cao11+k_sateta-1VFRTetaVFRTNai3Cao-eta-1VFRTNao3Cai J_ncx=i_NaCaAcapCmVmyoF

Component: calcium_background_current

i_Cab=g_CabV-E_CaN E_CaN=RT2FlnCaoCai J_Cab=-i_CabAcapCm2VmyoF

Component: sodium_concentration

ddtimeNai=-i_Na+i_Nab+3i_NaK+3i_NaCaAcapCmVmyoF

Component: fast_sodium_current

i_Na=g_NaO_NaV-E_Na E_Na=RTFln0.9Nao+0.1Ko0.9Nai+0.1Ki C_Na3=1-O_Na+C_Na1+C_Na2+IF_Na+I1_Na+I2_Na+IC_Na2+IC_Na3 ddtimeC_Na2=alpha_Na11C_Na3+beta_Na12C_Na1+alpha_Na3IC_Na2-beta_Na11C_Na2+alpha_Na12C_Na2+beta_Na3C_Na2 ddtimeC_Na1=alpha_Na12C_Na2+beta_Na13O_Na+alpha_Na3IF_Na-beta_Na12C_Na1+alpha_Na13C_Na1+beta_Na3C_Na1 ddtimeO_Na=alpha_Na13C_Na1+beta_Na2IF_Na-beta_Na13O_Na+alpha_Na2O_Na ddtimeIF_Na=alpha_Na2O_Na+beta_Na3C_Na1+beta_Na4I1_Na+alpha_Na12IC_Na2-beta_Na2IF_Na+alpha_Na3IF_Na+alpha_Na4IF_Na+beta_Na12IF_Na ddtimeI1_Na=alpha_Na4IF_Na+beta_Na5I2_Na-beta_Na4I1_Na+alpha_Na5I1_Na ddtimeI2_Na=alpha_Na5I1_Na-beta_Na5I2_Na ddtimeIC_Na2=alpha_Na11IC_Na3+beta_Na12IF_Na+beta_Na3IC_Na2-beta_Na11IC_Na2+alpha_Na12IC_Na2+alpha_Na3IC_Na2 ddtimeIC_Na3=beta_Na11IC_Na2+beta_Na3C_Na3-alpha_Na11IC_Na3+alpha_Na3IC_Na3 alpha_Na11=3.8020.1027-V+2.517+0.2-V+2.5150 alpha_Na12=3.8020.1027-V+2.515+0.23-V+2.5150 alpha_Na13=3.8020.1027-V+2.512+0.25-V+2.5150 beta_Na11=0.1917-V+2.520.3 beta_Na12=0.2-V-2.520.3 beta_Na13=0.22-V-7.520.3 alpha_Na3=7e-7-V+77.7 beta_Na3=0.0084+0.00002V+7 alpha_Na2=10.188495-V+716.6+0.393956 beta_Na2=alpha_Na13alpha_Na2alpha_Na3beta_Na13beta_Na3 alpha_Na4=alpha_Na21000 beta_Na4=alpha_Na3 alpha_Na5=alpha_Na295000 beta_Na5=alpha_Na350

Component: sodium_background_current

i_Nab=g_NabV-E_Na

Component: potassium_concentration

ddtimeKi=-i_Stim+i_Kto_f+i_Kto_s+i_K1+i_Ks+i_Kss+i_Kur+i_Kr-2i_NaKAcapCmVmyoF

Component: fast_transient_outward_K_I

i_Kto_f=g_Kto_fato_f3ito_fV-E_K E_K=RTFlnKoKi ddtimeato_f=alpha_a1-ato_f-beta_aato_f ddtimeito_f=alpha_i1-ito_f-beta_iito_f alpha_a=0.180640.03577V+30 beta_a=0.3956-0.06237V+30 alpha_i=0.000152-V+13.570.0067083-V+33.57+1 beta_i=0.00095V+33.570.051335V+33.57+1

Component: slow_transient_outward_K_I

i_Kto_s=g_Kto_sato_sito_sV-E_K ddtimeato_s=ass-ato_stau_ta_s ddtimeito_s=iss-ito_stau_ti_s ass=11+-V+22.57.7 iss=11+V+45.25.7 tau_ta_s=0.493-0.0629V+2.058 tau_ti_s=270+10501+V+45.25.7

Component: time_independent_K_I

i_K1=g_K1KoKo+210V-E_K1+0.0896V-E_K

Component: slow_delayed_rectifier_K_I

i_Ks=g_KsnKs2V-E_K ddtimenKs=alpha_n1-nKs-beta_nnKs alpha_n=0.00000481333V+26.51--0.128V+26.5 beta_n=0.0000953333-0.038V+26.5

Component: ultra_rapidly_activating_delayed_rectifier_K_I

i_Kur=g_KurauriurV-E_K ddtimeaur=ass-aurtau_aur ddtimeiur=iss-iurtau_iur tau_aur=0.493-0.0629V+2.058 tau_iur=1200-1701+V+45.25.7

Component: non_inactivating_steady_state_K_I

i_Kss=g_KssaKssiKssV-E_K ddtimeaKss=ass-aKsstau_Kss ddtimeiKss=0 tau_Kss=39.3-0.0862V+13.17

Component: rapid_delayed_rectifier_K_I

i_Kr=g_KrO_KV-RTFln0.98Ko+0.02Nao0.98Ki+0.02Nai C_K0=1-C_K1+C_K2+O_K+I_K ddtimeC_K2=kfC_K1+beta_a1O_K-kbC_K2+alpha_a1C_K2 ddtimeC_K1=alpha_a0C_K0+kbC_K2-beta_a0C_K1+kfC_K1 ddtimeO_K=alpha_a1C_K2+beta_iI_K-beta_a1O_K+alpha_iO_K ddtimeI_K=alpha_iO_K-beta_iI_K alpha_a0=0.0223480.01176V beta_a0=0.047002-0.0631V alpha_a1=0.0137330.038198V beta_a1=0.0000689-0.04178V alpha_i=0.0908210.023391V+5 beta_i=0.006497-0.03268V+5

Component: sodium_potassium_pump_current

i_NaK=i_NaK_maxf_NaK11+Km_NaiNai1.5KoKo+Km_Ko f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT sigma=17Nao67300-1

Component: calcium_activated_chloride_current

i_ClCa=g_ClCaO_ClCaCaiCai+Km_ClV-E_Cl O_ClCa=0.21+-V-46.77.8

Component: transmembrane_currents

Component: intracellular_currents

Component: Ions_n_reversal_potentials

Source
Derived from workspace Li, Smith, 2009 at changeset b4c2308e064c.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.