Model Mathematics

Component: environment

Component: membrane

FVRT=FVRT FVRT_Ca=2FVRT i_Stim=stim_amplitudeiftime-timestim_periodstim_period0time-timestim_periodstim_periodstim_duration0otherwise ddtimeV=-i_Na+i_t+i_ss+i_f+i_K1+i_B_Na+i_B_K+i_NaK+i_CaB2+i_Ncx2+i_pCa2+i_LCC2+i_StimCm

Component: cell_geometry

Component: sodium_current

E_Na=RTFlnNa_oNa_i i_Na=g_Nam3hjV-E_Na

Component: sodium_current_m_gate

m_infinity=11+V+45-6.5 tau_m=1.360.32V+47.131--0.1V+47.13+0.08-V11 ddtimem=m_infinity-mtau_m

Component: sodium_current_h_gate

h_infinity=11+V+76.16.07 tau_h=0.45371+-V+10.6611.1ifV-403.490.135-V+806.8+3.560.079V+3100000.35Votherwise ddtimeh=h_infinity-htau_h

Component: sodium_current_j_gate

j_infinity=11+V+76.16.07 tau_j=11.631+-0.1V+32-0.0000002535VifV-403.49V+37.781+0.311V+79.23-1271400.2444V-0.00003474-0.04391V+0.1212-0.01052V1+-0.1378V+40.14otherwise ddtimej=j_infinity-jtau_j

Component: Ca_independent_transient_outward_K_current

E_K=RTFlnK_oK_i i_t=g_tras+bs_slowV-E_K

Component: Ca_independent_transient_outward_K_current_r_gate

r_infinity=11+V+10.6-11.42 tau_r=10045.160.03577V+50+98.9-0.1V+38 ddtimer=r_infinity-rtau_r

Component: Ca_independent_transient_outward_K_current_s_gate

s_infinity=11+V+45.36.8841 tau_s=20-V+70252+35 ddtimes=s_infinity-stau_s

Component: Ca_independent_transient_outward_K_current_s_slow_gate

s_slow_infinity=11+V+45.36.8841 tau_s_slow=1300-V+70302+35 ddtimes_slow=s_slow_infinity-s_slowtau_s_slow

Component: steady_state_outward_K_current

i_ss=g_ssr_sss_ssV-E_K

Component: steady_state_outward_K_current_r_ss_gate

r_ss_infinity=11+V+11.5-11.82 tau_r_ss=1000045.160.03577V+50+98.9-0.1V+38 ddtimer_ss=r_ss_infinity-r_sstau_r_ss

Component: steady_state_outward_K_current_s_ss_gate

s_ss_infinity=11+V+87.510.3 tau_s_ss=2100 ddtimes_ss=s_ss_infinity-s_sstau_s_ss

Component: inward_rectifier

i_K1=0.048V+3725+V+37-25+0.010.0011+V-E_K+76.77-17+g_K1V-E_K+1.731+1.613FV-E_K+1.73RT1+K_o-0.9988-0.124

Component: hyperpolarisation_activated_current

f_K=1-f_Na i_f_Na=g_fyf_NaV-E_Na i_f_K=g_fyf_KV-E_K i_f=i_f_Na+i_f_K

Component: hyperpolarisation_activated_current_y_gate

y_infinity=11+V+138.610.48 tau_y=10000.11885V+8028.37+0.5623V+80-14.19 ddtimey=y_infinity-ytau_y

Component: background_currents

i_B_Na=g_B_NaV-E_Na i_B_K=g_B_KV-E_K i_B=i_B_Na+i_B_K

Component: sodium_potassium_pump

nu_1=gamma11+KdNaioNa_i21+KdNaisNa_i-DeltaFVRT+1+alphaK_o21+Na_oKdNaes-1-DeltaFVRT i_NaK=i_NaK_maxgamma1+1nu_1

Component: extracellular_ion_concentrations

Component: CaRU

Component: CaRU_Transitions

expVL=V-V_Ldel_VL alpha_p=expVLt_LexpVL+1 alpha_m=phi_Lt_L beta_poc=C_oc2t_RC_oc2+K_RyR2 beta_pcc=Ca_i2t_RCa_i2+K_RyR2 beta_m=phi_Rt_R epsilon_pco=C_coexpVL+a1tau_LK_LexpVL+1 epsilon_pcc=Ca_iexpVL+a1tau_LK_LexpVL+1 epsilon_m=b1expVL+a1tau_Lb1expVL+a1 mu_poc=C_oc2+cK_RyR2tau_RC_oc2+K_RyR2 mu_pcc=Ca_i2+cK_RyR2tau_RCa_i2+K_RyR2 mu_moc=theta_RdC_oc2+cK_RyR2tau_RdC_oc2+cK_RyR2 mu_mcc=theta_RdCa_i2+cK_RyR2tau_RdCa_i2+cK_RyR2

Component: DS_Calcium_Concentrations

C_cc=Ca_i C_co=Ca_i+J_Rg_DCa_SR1+J_Rg_D C_oc=Ca_i+J_Lg_DCa_oFVRT_Ca-FVRT_Ca1--FVRT_Ca1+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.000000001Ca_i+J_Lg_DCa_o1+J_Lg_Dotherwise

Component: LCC_and_RyR_fluxes

J_Rco=J_RCa_SR-Ca_i1+J_Rg_D J_Roo=J_RCa_SR-Ca_i+J_Lg_DFVRT_Ca1--FVRT_CaCa_SR-Ca_o-FVRT_Ca1+J_Rg_D+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.00001J_RCa_SR-Ca_i+J_Lg_D0.000011--0.00001Ca_SR-Ca_o-0.000011+J_Rg_D+J_Lg_D0.000011--0.00001otherwise J_Loc=J_LFVRT_Ca1--FVRT_CaCa_o-FVRT_Ca-Ca_i1+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.00001J_L0.000011--0.00001Ca_o-0.00001-Ca_i1+J_Lg_D0.000011--0.00001otherwise J_Loo=J_LFVRT_Ca1--FVRT_CaCa_o-FVRT_Ca-Ca_i+J_Rg_DCa_o-FVRT_Ca-Ca_SR1+J_Rg_D+J_Lg_DFVRT_Ca1-FVRT_Caif|FVRT_Ca|>0.00001J_L0.000011--0.00001Ca_o-0.00001-Ca_i+J_Rg_DCa_o-0.00001-Ca_SR1+J_Rg_D+J_Lg_D0.000011--0.00001otherwise

Component: CaRU_states

denom=alpha_p+alpha_malpha_m+beta_m+beta_pocbeta_m+beta_pcc+alpha_pbeta_m+beta_poc P1=alpha_pbeta_malpha_p+alpha_m+beta_m+beta_pccdenom P2=alpha_mbeta_pccalpha_m+beta_m+beta_poc+beta_pocalpha_pdenom P3=alpha_pbeta_pocalpha_p+beta_m+beta_pcc+beta_pccalpha_mdenom P4=alpha_mbeta_malpha_m+alpha_p+beta_m+beta_pocdenom

Component: CaRU_reduced_states

r_1=P1mu_poc+P4mu_pcc r_2=alpha_pmu_moc+alpha_mmu_mccalpha_p+alpha_m r_3=beta_mmu_pccbeta_m+beta_pcc r_4=mu_mcc r_5=P2epsilon_pco+P4epsilon_pcc r_6=epsilon_m r_7=alpha_mepsilon_pccalpha_p+alpha_m r_8=epsilon_m z_4=1-z_1-z_2-z_3 ddtimez_1=-r_1+r_5z_1+r_2z_2+r_6z_3 ddtimez_2=r_1z_1-r_2+r_7z_2+r_8z_4 ddtimez_3=r_5z_1-r_6+r_3z_3+r_4z_4

Component: RyR_current

J_R1=P3J_Roo+J_RcoP2 J_R3=J_Rcobeta_pccbeta_m+beta_pcc i_RyR1=z_1J_R1+z_3J_R3NVmyo i_RyR2=i_RyR1

Component: LCC_current

J_L1=J_LooP3+J_LocP1 J_L2=J_Localpha_palpha_p+alpha_m i_LCC1=z_1J_L1+z_2J_L2NVmyo i_LCC2=-i_LCC12FVmyo_uL

Component: Na_Ca_Exchanger

i_Ncx1=g_NCXetaFVRTNa_i3Ca_o-eta-1FVRTNa_o3Ca_iNa_o3+K_mNa3Ca_o+K_mCa1+k_sateta-1FVRT i_Ncx2=i_Ncx1FVmyo_uL

Component: SERCA

i_SERCA=g_SERCACa_i2K_SERCA2+Ca_i2

Component: SarcolemMal_Ca_pump

i_pCa1=g_pCaCa_iK_mpCa+Ca_i i_pCa2=i_pCa12FVmyo_uL

Component: Background_Ca_current

E_Ca=RT2FlnCa_oCa_i i_CaB1=g_CaBE_Ca-V i_CaB2=-i_CaB12FVmyo_uL

Component: SR_Ca_leak_current

i_SR=g_SRlCa_SR-Ca_i

Component: troponin_Ca_buffer

i_TRPN=k_m_TRPNB_TRPN-TRPN-k_p_TRPNTRPNCa_i

Component: calmodulin_Ca_buffer

beta_CMDN=1+k_CMDNB_CMDNk_CMDN+Ca_i2+EGTA_totKmEGTAKmEGTA+Ca_i2-1

Component: intracellular_ion_concentrations

ddtimeNa_i=-i_Na+i_B_Na+i_Ncx23+i_NaK3+i_f_Na1Vmyo_uLF ddtimeK_i=-i_Stim+i_ss+i_B_K+i_t+i_K1+i_f_K+-2i_NaK1Vmyo_uLF ddtimeTRPN=i_TRPN ddtimeCa_i=beta_CMDNi_RyR2-i_SERCA+i_SR+i_TRPN--2i_Ncx2+i_LCC2+i_pCa2+i_CaB22Vmyo_uLF ddtimeCa_SR=Vmyo_uLVSR_uL-i_RyR2+i_SERCA-i_SR
Source
Derived from workspace Gattoni 2016 at changeset 2a10a6a1fb00.
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