Model Mathematics

Component: environment

Component: membrane

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwiseddtimeV=-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=RTFlnNa_oNa_ii_Na=g_Nam3hjV-E_Na

Component: fast_sodium_current_m_gate

E0_m=V+47.13alpha_m=3200.1-0.005E0_mif|E0_m|<0.00001320E0_m1--0.1E0_motherwisebeta_m=80-V11ddtimem=alpha_m1-m-beta_mmifV-900otherwise

Component: fast_sodium_current_h_gate

alpha_h=13580+V-6.8ifV<-400otherwisebeta_h=35600.079V+3100000.35VifV<-4010000.131+V+10.66-11.1otherwiseddtimeh=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<-400otherwisebeta_j=121.2-0.01052V1+-0.1378V+40.14ifV<-40300-0.0000002535V1+-0.1V+32otherwiseddtimej=alpha_j1-j-beta_jj

Component: rapid_activating_delayed_rectifiyer_K_current

E_K=RTFlnK_oK_if_K_o=K_o4R_V=11+1.49450.0446Vi_Kr=g_Krf_K_oR_VX_krV-E_K

Component: rapid_activating_delayed_rectifiyer_K_current_X_kr_gate

K12=-5.495+0.1691VK21=-7.677-0.0128VX_kr_inf=K12K12+K21tau_X_kr=0.001K12+K21+tau_factor0.027ddtimeX_kr=X_kr_inf-X_krtau_X_kr

Component: slow_activating_delayed_rectifiyer_K_current

E_Ks=RTFlnK_o+0.01833Na_oK_i+0.01833Na_ii_Ks=g_KsX_ks2V-E_Ks

Component: slow_activating_delayed_rectifiyer_K_current_X_ks_gate

X_ks_infinity=11+-V-24.713.6tau_X_ks=0.0010.0000719V-101--0.148V-10+0.000131V-100.0687V-10-1ddtimeX_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=45.160.03577Vbeta_X_to1=98.9-0.06237VddtimeX_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+33.55beta_Y_to1=5.415V+33.551+0.051335V+33.55ddtimeY_to1=alpha_Y_to11-Y_to1-beta_Y_to1Y_to1

Component: time_independent_potassium_current

i_K1=g_K1K1_infinity_VK_oK_o+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+Na_o3K_mCa+Ca_o1+K_sateta-1VFRTetaVFRTNa_i3Ca_o-eta-1VFRTNa_o3Ca_i

Component: sodium_potassium_pump

f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRTsigma=17Na_o67.3-1i_NaK=MgATP_iMgATP_i0i_NaK_winslowi_NaK_winslow=I_NaKf_NaK1+K_mNa_iNa_i1.5K_oK_o+K_mK_o

Component: sarcolemmal_calcium_pump

i_p_Ca=MgATP_iMgATP_i0i_p_Ca_winslowi_p_Ca_winslow=I_pCaCa_iK_mpCa+Ca_i

Component: calcium_background_current

E_Ca=RT2FlnCa_oCa_ii_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_Cai_Ca_K=p_prime_k11yO+O_CaVF2RTK_iVFRT-K_oVFRT-1p_prime_k=P_K1+i_Ca_maxi_Ca_halfi_Ca_max=P_Ca114VF21000RT0.0012VFRT-0.341Ca_o2VFRT-1alpha=400V+210beta=50-V+213alpha_a=alphaabeta_b=betabgamma=103.75Ca_ss1ddtimeC0=betaC1+omegaC_Ca0-4alpha+gammaC0ddtimeC1=4alphaC0+2betaC2+omegabC_Ca1-beta+3alpha+gammaaC1ddtimeC2=3alphaC1+3betaC3+omegab2C_Ca2-beta2+2alpha+gammaa2C2ddtimeC3=2alphaC2+4betaC4+omegab3C_Ca3-beta3+alpha+gammaa3C3ddtimeC4=alphaC3+gO+omegab4C_Ca4-beta4+f+gammaa4C4ddtimeO=fC4-gOddtimeC_Ca0=beta_bC_Ca1+gammaC0-4alpha_a+omegaC_Ca0ddtimeC_Ca1=4alpha_aC_Ca0+2beta_bC_Ca2+gammaaC1-beta_b+3alpha_a+omegabC_Ca1ddtimeC_Ca2=3alpha_aC_Ca1+3beta_bC_Ca3+gammaa2C2-beta_b2+2alpha_a+omegab2C_Ca2ddtimeC_Ca3=2alpha_aC_Ca2+4beta_bC_Ca4+gammaa3C3-beta_b3+alpha_a+omegab3C_Ca3ddtimeC_Ca4=alpha_aC_Ca3+gprimeO_Ca+gammaa4C4-beta_b4+fprime+omegab4C_Ca4ddtimeO_Ca=fprimeC_Ca4-gprimeO_Ca

Component: L_type_Ca_current_y_gate

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

Component: RyR_channel

ddtimeP_C1=-k_a_plusCa_ssnP_C1+k_a_minusP_O1ddtimeP_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_C2ddtimeP_O2=k_b_plusCa_ssmP_O1-k_b_minusP_O2ddtimeP_C2=k_c_plusP_O1-k_c_minusP_C2J_rel=v1P_O1+P_O2Ca_JSR-Ca_ss

Component: SERCA2a_pump

fb=Ca_iK_fbN_fbrb=Ca_NSRK_rbN_rbJ_up=MgATP_iMgATP_i0J_up_winslowJ_up_winslow=K_SRVmaxffb-Vmaxrrb1+fb+rb

Component: intracellular_Ca_fluxes

J_tr=Ca_NSR-Ca_JSRtau_trJ_xfer=Ca_ss-Ca_itau_xferJ_trpn=HTRPN_totJ_HTRPNCa+LTRPN_totJ_LTRPNCaJ_HTRPNCa=ddtimeHTRPNCaddtimeHTRPNCa=k_htrpn_plusCa_i1-HTRPNCa-k_htrpn_minusHTRPNCaJ_LTRPNCa=ddtimeLTRPNCaddtimeLTRPNCa=k_ltrpn_plusCa_i1-LTRPNCa-k_ltrpn_minusLTRPNCa

Component: intracellular_ion_concentrations

ddtimeCa_i=beta_iJ_xfer-J_up+J_trpn+-i_p_Ca+i_Ca_b-2i_NaCaA_capC_sc2V_myoF+ k_minus_CaATP CaATP_i + k_minus_CaADP CaADP_i - k_plus_CaATP Ca_i ATP_i + k_plus_CaADP Ca_i ADP_i ddtimeNa_i=-0i_Na+i_Na_b+i_NaCa3+i_NaK3A_cap1V_myoFddtimeK_i=-0i_Ca_K+i_Kr+i_Ks+i_K1+i_Kp+i_to1+i_NaK-2A_cap1V_myoFbeta_i=11+CMDN_totK_mCMDNK_mCMDN+Ca_i2+EGTA_totK_mEGTAK_mEGTA+Ca_i2beta_SS=11+CMDN_totK_mCMDNK_mCMDN+Ca_ss2+EGTA_totK_mEGTAK_mEGTA+Ca_ss2beta_JSR=11+CSQN_totK_mCSQNK_mCSQN+Ca_JSR2ddtimeCa_ss=beta_SSJ_relV_JSRV_ss+k_minus_CaATPCaATP_ss+k_minus_CaADPCaADP_ss-J_xferV_myoV_ss+i_CaA_cap12V_ssF+k_plus_CaATPCa_ssATP_ss+k_plus_CaADPCa_ssADP_ssddtimeCa_JSR=beta_JSRJ_tr-J_relddtimeCa_NSR=J_upV_myoV_NSR-J_trV_JSRV_NSR

Component: Ca_and_Mg_buffering_by_ATP

ATP_ss = ATP_tot - CaATP_ss + MgATP_ss dd time CaATP_ss = k_plus_CaATP Ca_ss ATP_ss - Jxfer_CaATP V_myo V_ss + k_minus_CaATP CaATP_ss dd time MgATP_ss = k_plus_MgATP Mg_ss ATP_ss - Jxfer_MgATP V_myo V_ss + k_minus_MgATP MgATP_ss ATP_i = ATP_tot - CaATP_i + MgATP_i dd time CaATP_i = Jxfer_CaATP + k_plus_CaATP Ca_i ATP_i - k_minus_CaATP CaATP_i dd time MgATP_i = Jxfer_MgATP + k_plus_MgATP Mg_i ATP_i - k_minus_MgATP MgATP_i Jxfer_CaATP = CaATP_ss - CaATP_i tau_xfer_CaATP Jxfer_MgATP = MgATP_ss - MgATP_i tau_xfer_MgATP ADP_ss = ADP_tot - CaADP_ss + MgADP_ss dd time CaADP_ss = k_plus_CaADP Ca_ss ADP_ss - Jxfer_CaADP V_myo V_ss + k_minus_CaADP CaADP_ss dd time MgADP_ss = k_plus_MgADP Mg_ss ADP_ss - Jxfer_MgADP V_myo V_ss + k_minus_MgADP MgADP_ss ADP_i = ADP_tot - CaADP_i + MgADP_i dd time CaADP_i = Jxfer_CaADP + k_plus_CaADP Ca_i ADP_i - k_minus_CaADP CaADP_i dd time MgADP_i = Jxfer_MgADP + k_plus_MgADP Mg_i ADP_i - k_minus_MgADP MgADP_i Jxfer_CaADP = CaADP_ss - CaADP_i tau_xfer_CaADP Jxfer_MgADP = MgADP_ss - MgADP_i tau_xfer_MgADP dd time Mg_ss = k_minus_MgATP MgATP_ss + k_minus_MgADP MgADP_ss - k_plus_MgATP Mg_ss ATP_ss + k_plus_MgADP Mg_ss ADP_ss + Jxfer_Mg V_myo V_ss dd time Mg_i = Jxfer_Mg + k_minus_MgATP MgATP_i + k_minus_MgADP MgADP_i - k_plus_MgATP Mg_i ATP_i + k_plus_MgADP Mg_i ADP_i Jxfer_Mg = Mg_ss - Mg_i tau_xfer_Mg

Component: extracellular_ion_concentrations

Component: model_parameters

Model Curation
  • Curation Status c2
  • JSim c0
  • COR c2
  • OpenCell c2
Source
Derived from workspace Michailova, Mcculloch, 2001 at changeset 8e192508749c.
Collaboration
To begin collaborating on this work, please use your mercurial client and issue this command:
License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.