Model Mathematics

Component: environment

Component: membrane

ddtimeV=i_Na+i_Ca_L_Ca+i_Ca_L_K+i_K+i_NaCa+i_K1+i_Kp+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_ns_Ca+I_stimCm I_stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise

Component: fast_sodium_current

i_Na=g_Nam3hjV-E_Na E_Na=RTFlnNaoNai

Component: fast_sodium_current_m_gate

alpha_m=0.32V+47.131--0.1V+47.13 beta_m=0.08-V11 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=0.13580+V-6.8ifV<-400otherwise beta_h=3.560.079V+3100000.35VifV<-4010.131+V+10.66-11.1otherwise ddtimeh=alpha_h1-h-beta_hh

Component: fast_sodium_current_j_gate

alpha_j=-1271400.2444V-0.00003474-0.04391VV+37.781+0.311V+79.23ifV<-400otherwise beta_j=0.1212-0.01052V1+-0.1378V+40.14ifV<-400.3-0.0000002535V1+-0.1V+32otherwise ddtimej=alpha_j1-j-beta_jj

Component: L_type_Ca_channel

i_Ca_L_Ca=i_Ca_L_Ca_maxyO+O_Ca i_Ca_L_K=p_kyO+O_CaVF2RTKiVFRT-KoVFRT-1 p_k=P_K1+i_Ca_L_Ca_maxi_Ca_L_Ca_half i_Ca_L_Ca_max=P_Ca4VF2RT0.0012VFRT-0.341Cao2VFRT-1 alpha=0.4V+1210 beta=0.05V+12-13 alpha_a=alphaa beta_b=betab gamma=0.1875Ca_SS 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+gammaC_Ca0-4alpha_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+g_O_Ca+gammaa4C4-beta_b4+f_+omegab4C_Ca4 ddtimeO_Ca=f_C_Ca4-g_O_Ca

Component: L_type_Ca_channel_y_gate

ddtimey=y_infinity-ytau_y y_infinity=11+V+557.5+0.11+-V+216 tau_y=20+6001+V+309.5

Component: time_dependent_potassium_current

g_K=g_K_maxKo5.4 E_K=RTFlnKo+P_NaKNaoKi+P_NaKNai i_K=g_KXiX2V-E_K

Component: time_dependent_potassium_current_X_gate

alpha_X=0.0000719V+301--0.148V+30 beta_X=0.000131V+30-1+0.0687V+30 ddtimeX=alpha_X1-X-beta_XX

Component: time_dependent_potassium_current_Xi_gate

Xi=11+V-56.2632.1

Component: time_independent_potassium_current

g_K1=g_K1_maxKo5.4 E_K1=RTFlnKoKi i_K1=g_K1K1_infinityV-E_K1

Component: time_independent_potassium_current_K1_gate

alpha_K1=1.021+0.2385V-E_K1-59.215 beta_K1=0.491240.08032V+5.476-E_K1+0.06175V-E_K1+594.311+-0.5143V-E_K1+4.753 K1_infinity=alpha_K1alpha_K1+beta_K1

Component: plateau_potassium_current

E_Kp=E_K1 Kp=11+7.488-V5.98 i_Kp=g_KpKpV-E_Kp

Component: Na_Ca_exchanger

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

Component: sarcolemmal_calcium_pump

i_p_Ca=I_pCaCaiK_mpCa+Cai

Component: sodium_background_current

E_NaN=E_Na i_Na_b=g_NabV-E_NaN

Component: calcium_background_current

E_CaN=RT2FlnCaoCai i_Ca_b=g_CabV-E_CaN

Component: sodium_potassium_pump

f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT sigma=17Nao67.3-1 i_NaK=I_NaKf_NaK11+K_mNaiNai1.5KoKo+K_mKo

Component: non_specific_calcium_activated_current

EnsCa=RTFlnKo+NaoKi+Nai VnsCa=V-EnsCa i_ns_Na=I_ns_Na11+K_m_ns_CaCai3 i_ns_K=I_ns_K11+K_m_ns_CaCai3 i_ns_Ca=i_ns_Na+i_ns_K I_ns_Na=P_ns_Ca12VnsCaF2RT0.75NaiVnsCaFRT-0.75NaoVnsCaFRT-1 I_ns_K=P_ns_Ca12VnsCaF2RT0.75KiVnsCaFRT-0.75KoVnsCaFRT-1

Component: calcium_subsystem

V_SS=5.828e-5V_myo V_NSR=0.081V_myo V_JSR=0.00464V_myo J_rel=v1RyR_openCa_JSR-Ca_SS RyR_open=P_O1+P_O2 ddtimeP_C1=-k_a_plusCa_SSnCaP_C1+k_a_minusP_O1 ddtimeP_O1=k_a_plusCa_SSnCaP_C1-k_a_minusP_O1+k_b_plusCa_SSmCaP_O1+k_c_plusP_O1+k_b_minusP_O2+k_c_minusP_C2 ddtimeP_O2=k_b_plusCa_SSmCaP_O1-k_b_minusP_O2 ddtimeP_C2=k_c_plusP_O1-k_c_minusP_C2 J_leak=v2Ca_NSR-Cai J_up=v3Cai2K_mup2+Cai2 J_tr=Ca_NSR-Ca_JSRtau_tr J_xfer=Ca_SS-Caitau_xfer J_htrpn=k_htrpn_plusCaiHTRPN_tot-HTRPNCa-k_htrpn_minusHTRPNCa J_ltrpn=k_ltrpn_plusCaiLTRPN_tot-LTRPNCa-k_ltrpn_minusLTRPNCa J_trpn=J_htrpn+J_ltrpn ddtimeHTRPNCa=J_htrpn ddtimeLTRPNCa=J_ltrpn Bi=11+CMDN_totK_mCMDNK_mCMDN+Cai2 B_SS=11+CMDN_totK_mCMDNK_mCMDN+Ca_SS2 B_JSR=11+CSQN_totK_mCSQNK_mCSQN+Ca_JSR2 ddtimeCai=BiJ_leak+J_xfer-J_up+J_trpn+i_Ca_b-2i_NaCa+i_p_CaAm2V_myoF ddtimeCa_SS=B_SSJ_relV_JSRV_SS-J_xferV_myoV_SS-i_Ca_L_CaAm2V_SSF ddtimeCa_JSR=B_JSRJ_tr-J_rel ddtimeCa_NSR=J_up-J_leakV_myoV_NSR-J_trV_JSRV_NSR

Component: ionic_concentrations

ddtimeNai=-i_Na+i_Na_b+i_ns_Na+i_NaCa3+i_NaK3AmV_myoF ddtimeKi=-i_Ca_L_K+i_K+i_K1+i_Kp+i_ns_K+-i_NaK2AmV_myoF ddtimeKo=i_Ca_L_K+i_K+i_K1+i_Kp+i_ns_K+-i_NaK2AmV_myoF

Component: Myofilaments

ddtimeCab=konCaiTRPN_tot-Cab-koff1-Tensiongamma_trpnTrefCab K_2=alphar2zpnRelzpnRel+KznRel1-nRelKznRelzpnRel+KznRel K_1=alphar2zpnRel-1nRelKznRelzpnRel+KznRel2 z_max=alpha0CaTRPN50TRPN_totnHill-K_2alphar1+K_1+alpha0CaTRPN50TRPN_totnHill Ca50=Ca50ref1+beta1lambda-1 CaTRPN50=Ca50TRPN_totCa50+koffkon1-1+beta0lambda-10.5gamma_trpn ddtimez=alpha0CabCaTRPN50nHill1-z+-zalphar1+-alphar2znRelznRel+KznRel T0max=Tref1+beta0lambda-1 T0=T0maxzz_max Tension=T0aQ+11-QifQ<0T01-a+2Q1+Qotherwise ddtimeQ1=A1dlambdadt-alpha1Q1 ddtimeQ2=A2dlambdadt-alpha2Q2 ddtimeQ3=A3dlambdadt-alpha3Q3 Q=Q1+Q2+Q3