Model Mathematics

Component: environment

Component: membrane

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-11i_Na+i_Ca+i_Ca_K+i_Kr+i_Ks+i_to1+i_K1+i_Kp+i_NaCa+i_NaK+i_p_Ca+i_Na_b+i_Ca_b+i_StimC_sc

Component: fast_sodium_current

E_Na=RTFlnNaoNai i_Na=g_Nam3hjV-E_Na

Component: fast_sodium_current_m_gate

E0_m=V+47.13 alpha_m=10000.1-0.005E0_mif|E0_m|<0.00001320E0_m1--0.1E0_motherwise beta_m=80-V11 ddtimem=alpha_m1-m-beta_mmifV-900otherwise

Component: fast_sodium_current_h_gate

alpha_h=13580+V-6.8ifV<-400otherwise beta_h=35600.079V+3100000.35VifV<-4010000.131+V+10.66-11.1otherwise ddtimeh=alpha_h1-h-beta_hh

Component: fast_sodium_current_j_gate

alpha_j=1000-1271400.2444V+0.00003474-0.04391VV+37.781+0.311V+79.23ifV<-400otherwise beta_j=121.2-0.01052V1+-0.1378V+40.14ifV<-40300-0.0000002535V1+-0.1V+32otherwise ddtimej=alpha_j1-j-beta_jj

Component: rapid_activating_delayed_rectifiyer_K_current

E_K=RTFlnKoKi f_Ko=Ko4 R_V=11+1.49450.0446V i_Kr=g_Krf_KoR_VX_krV-E_K

Component: rapid_activating_delayed_rectifiyer_K_current_X_kr_gate

K12=-5.495+0.1691V K21=-7.677-0.0128V X_kr_inf=K12K12+K21 tau_X_kr=0.001K12+K21+tau_factor0.027 ddtimeX_kr=X_kr_inf-X_krtau_X_kr

Component: slow_activating_delayed_rectifiyer_K_current

E_Ks=RTFlnKo+0.01833NaoKi+0.01833Nai i_Ks=g_KsX_ks2V-E_Ks

Component: slow_activating_delayed_rectifiyer_K_current_X_ks_gate

X_ks_infinity=11+-V-24.713.6 tau_X_ks=0.0010.0000719V-101--0.148V-10+0.000131V-100.0687V-10-1 ddtimeX_ks=X_ks_infinity-X_kstau_X_ks

Component: transient_outward_potassium_current

i_to1=g_to1X_to1Y_to1V-E_K

Component: transient_outward_potassium_current_X_to1_gate

alpha_X_to1=45.160.03577V beta_X_to1=98.9-0.06237V ddtimeX_to1=alpha_X_to11-X_to1-beta_X_to1X_to1

Component: transient_outward_potassium_current_Y_to1_gate

alpha_Y_to1=5.415-V+33.551+0.051335-V+33.55 beta_Y_to1=5.415V+33.551+0.051335V+33.55 ddtimeY_to1=alpha_Y_to11-Y_to1-beta_Y_to1Y_to1

Component: time_independent_potassium_current

i_K1=g_K1K1_infinity_VKoKo+K_mK1V-E_K

Component: time_independent_potassium_current_K1_gate

K1_infinity_V=12+1.5FRTV-E_K

Component: plateau_potassium_current

i_Kp=g_KpKp_VV-E_K

Component: plateau_potassium_current_Kp_gate

Kp_V=11+7.488-V5.98

Component: Na_Ca_exchanger

i_NaCa=K_NaCa5000K_mNa3+Nao3K_mCa+Cao1+K_sateta-1VFRTetaVFRTNai3Cao-eta-1VFRTNao3Cai

Component: sodium_potassium_pump

f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT sigma=17Nao67.3-1 i_NaK=I_NaKf_NaK1+K_mNaiNai1.5KoKo+K_mKo

Component: sarcolemmal_calcium_pump

i_p_Ca=I_pCaCaiK_mpCa+Cai

Component: calcium_background_current

E_Ca=RT2FlnCaoCai i_Ca_b=g_CabV-E_Ca

Component: sodium_background_current

i_Na_b=g_NabV-E_Na

Component: L_type_Ca_current

i_Ca=i_Ca_maxyO+O_Ca i_Ca_K=p_prime_k11yO+O_CaVF2RTKiVFRT-KoVFRT-1 p_prime_k=P_K1+i_Ca_maxi_Ca_half i_Ca_max=P_Ca114VF21000RT0.0012VFRT-0.341Cao2VFRT-1 alpha=400V+210 beta=50-V+213 alpha_a=alphaa beta_b=betab gamma=103.75Ca_ss1 ddtimeC0=betaC1+omegaC_Ca0-4alpha+gammaC0 ddtimeC1=4alphaC0+2betaC2+omegabC_Ca1-beta+3alpha+gammaaC1 ddtimeC2=3alphaC1+3betaC3+omegab2C_Ca2-beta2+2alpha+gammaa2C2 ddtimeC3=2alphaC2+4betaC4+omegab3C_Ca3-beta3+alpha+gammaa3C3 ddtimeC4=alphaC3+gO+omegab4C_Ca4-beta4+f+gammaa4C4 ddtimeO=fC4-gO ddtimeC_Ca0=beta_bC_Ca1+gammaC0-4alpha_a+omegaC_Ca0 ddtimeC_Ca1=4alpha_aC_Ca0+2beta_bC_Ca2+gammaaC1-beta_b+3alpha_a+omegabC_Ca1 ddtimeC_Ca2=3alpha_aC_Ca1+3beta_bC_Ca3+gammaa2C2-beta_b2+2alpha_a+omegab2C_Ca2 ddtimeC_Ca3=2alpha_aC_Ca2+4beta_bC_Ca4+gammaa3C3-beta_b3+alpha_a+omegab3C_Ca3 ddtimeC_Ca4=alpha_aC_Ca3+gprimeO_Ca+gammaa4C4-beta_b4+fprime+omegab4C_Ca4 ddtimeO_Ca=fprimeC_Ca4-gprimeO_Ca

Component: L_type_Ca_current_y_gate

y_infinity=0.81+V+12.55+0.2 tau_y=20+6001+V+209.51000 ddtimey=y_infinity-ytau_y

Component: RyR_channel

ddtimeP_C1=-k_a_plusCa_ssnP_C1+k_a_minusP_O1 ddtimeP_O1=k_a_plusCa_ssnP_C1-k_a_minusP_O1+k_b_plusCa_ssmP_O1+k_c_plusP_O1+k_b_minusP_O2+k_c_minusP_C2 ddtimeP_O2=k_b_plusCa_ssmP_O1-k_b_minusP_O2 ddtimeP_C2=k_c_plusP_O1-k_c_minusP_C2 J_rel=v1P_O1+P_O2Ca_JSR-Ca_ss

Component: SERCA2a_pump

fb=CaiK_fbN_fb rb=Ca_NSRK_rbN_rb J_up=K_SRVmaxffb-Vmaxrrb1+fb+rb

Component: intracellular_Ca_fluxes

J_tr=Ca_NSR-Ca_JSRtau_tr J_xfer=Ca_ss-Caitau_xfer J_trpn=HTRPN_totJ_HTRPNCa+LTRPN_totJ_LTRPNCa J_HTRPNCa=ddtimeHTRPNCa ddtimeHTRPNCa=k_htrpn_plusCai1-HTRPNCa-k_htrpn_minusHTRPNCa J_LTRPNCa=ddtimeLTRPNCa ddtimeLTRPNCa=k_ltrpn_plusCai1-LTRPNCa-k_ltrpn_minusLTRPNCa

Component: intracellular_ion_concentrations

ddtimeCai=beta_iJ_xfer-J_up+J_trpn+2i_NaCa-i_p_Ca+i_Ca_bA_cap12V_myoF ddtimeNai=-0i_Na+i_Na_b+i_NaCa3+i_NaK3A_cap1V_myoF ddtimeKi=-0i_Ca_K+i_Kr+i_Ks+i_K1+i_Kp+i_to1+i_NaK-2A_cap1V_myoF beta_i=11+CMDN_totK_mCMDNK_mCMDN+Cai2+EGTA_totK_mEGTAK_mEGTA+Cai2 beta_SS=11+CMDN_totK_mCMDNK_mCMDN+Ca_ss2+EGTA_totK_mEGTAK_mEGTA+Ca_ss2 beta_JSR=11+CSQN_totK_mCSQNK_mCSQN+Ca_JSR2 ddtimeCa_ss=beta_SSJ_relV_JSRV_SS-J_xferV_myoV_SS-i_CaA_cap12V_SSF ddtimeCa_JSR=beta_JSRJ_tr-J_rel ddtimeCa_NSR=J_upV_myoV_NSR-J_trV_JSRV_NSR

Component: standard_ionic_concentrations