Model Mathematics

Component: environment

Component: cell_parameters

Component: membrane_potential

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-1Cmi_Na+i_b_Na+i_K1+i_K+i_to+i_b_K+i_Ca_L+i_b_Ca+i_NaCa+i_NaK+i_Stim

Component: reversal_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ca=0.5RTFlnCa_oCa_i E_mh=RTFlnNa_o+0.12K_oNa_i+0.12K_i

Component: fast_sodium_current

i_Na=g_Nam3hV-E_mh

Component: fast_sodium_current_m_gate

E0_m=V+41 alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwise beta_m=8000-0.056V+66 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=20-0.125V+75-shift_h beta_h=20001+320-0.1V+75-shift_h ddtimeh=alpha_h1-h-beta_hh

Component: time_dependent_rectifier_potassium_current

i_K=i_KmaxxK_i-K_o-VFRT140

Component: time_dependent_rectifier_potassium_current_x_gate

alpha_x=0.50.0826V+501+0.057V+50 beta_x=1.3-0.06V+201+-0.04V+20 ddtimex=alpha_x1-x-beta_xx

Component: time_independent_potassium_current

i_K1=g_K1K_oK_o+K_mk1V-E_K1+2FV-E_K-10RT

Component: transient_outward_current

i_to=g_tosrV-E_K

Component: transient_outward_current_s_gate

alpha_s=0.033-V17 beta_s=331+-0.125V+10 ddtimes=alpha_s1-s-beta_ss

Component: transient_outward_current_r_gate

ddtimer=33311+-V+45-r

Component: L_type_Ca_channel

i_Ca_L_Ca=4dfP_Ca_L_CaV-50FRT1--2V-50FRTCa_i100FRT-Ca_o-2V-50FRT i_Ca_L_K=0.002dfP_Ca_L_CaV-50FRT1--V-50FRTK_i50FRT-K_o-V-50FRT i_Ca_L_Na=0.01dfP_Ca_L_CaV-50FRT1--V-50FRTNa_i50FRT-Na_o-V-50FRT i_Ca_L=i_Ca_L_Ca+i_Ca_L_K+i_Ca_L_Na

Component: L_type_Ca_channel_d_gate

E0_d=V+24-5 alpha_d=speed_d120if|E0_d|<0.00001speed_d30E0_d1--E0_d4otherwise beta_d=speed_d120if|E0_d|<0.00001speed_d-12E0_d1-E0_d10otherwise ddtimed=alpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

E0_f=V+34 alpha_f=speed_f25if|E0_f|<0.00001speed_f6.25E0_f-1+E0_f4otherwise beta_f=speed_f501+-E0_f4 ddtimef=alpha_f1-f-beta_ff

Component: sodium_calcium_exchanger

i_NaCa=i_NaCa_maxgammaVFRTNa_i3Ca_o-gamma-1VFRTNa_o3Ca_i1+Ca_i0.0069

Component: sodium_potassium_pump

i_NaK=i_NaK_maxK_oK_mK+K_oNa_iK_mNa+Na_i11+0.1245-0.1VFRT+0.0353-VFRT

Component: calcium_background_current

i_b_Ca=g_b_CaV-E_Ca

Component: potassium_background_current

i_b_K=g_b_KV-E_K

Component: sodium_background_current

i_b_Na=g_b_NaV-E_Na

Component: CaMKII_factor

Inf_CaMK=Cmdn_Ca0.00005 ddtimeF_CaMK=Inf_CaMK-F_CaMKTau_CaMK

Component: RyR

N_CaMK=F_CaMK0.72 k_1=gain_k130625000Ca_i2-245i_Ca_L k_2=gain_k24501+0.36Ca_SR k_3=gain_k31.885F_SRCa_RyR0.22N_CaMK k_4=gain_k41.8 ddtimeF_1=k_3F_3-k_4F_1-k_1F_1 ddtimeF_2=k_1F_1-k_2F_2 F_3=1-F_1+F_2 F_rel=F_2F_2+0.252 ddtimeF_SRCa_RyR=Ca_SR-F_SRCa_RyRTau_SRCa_RyR K_rel=K_rel_maxF_SRCa_RyRF_SRCa_RyR+0.2 j_rel=K_relF_rel+K_leak_rateCa_SR-Ca_i

Component: SERCA

f_b=Ca_i0.000242 r_b=Ca_SR1.642 j_up=F_CaMKV_max_ff_b-V_max_rr_b1+f_b+r_b

Component: calmodulin

dCmdn_Ca_dtime=alpha_cmdnCmdn_tot-Cmdn_CaCa_i-beta_cmdnCmdn_Ca ddtimeCmdn_Ca=alpha_cmdnCmdn_tot-Cmdn_CaCa_i-beta_cmdnCmdn_Ca

Component: troponin

dTrpn_Ca_dtime=alpha_trpnTrpn_tot-Trpn_CaCa_i-beta_trpn1+21-Force_norm3Trpn_Ca ddtimeTrpn_Ca=alpha_trpnTrpn_tot-Trpn_CaCa_i-beta_trpn1+21-Force_norm3Trpn_Ca

Component: intracellular_calcium_concentration

ddtimeCa_i=-i_Ca_L_Ca+i_b_Ca-2i_NaCa2v_iF-j_up+j_relv_SRv_i-dCmdn_Ca_dtime-dTrpn_Ca_dtime

Component: SR_calcium_concentration

ddtimeCa_SR=j_upv_iv_SR-j_rel

Component: intracellular_sodium_concentration

ddtimeNa_i=-i_Na+i_b_Na+i_Ca_L_Na+3i_NaCa+3i_NaKv_iF

Component: intracellular_potassium_concentration

ddtimeK_i=-i_K1+i_K+i_to+i_b_K+i_Ca_L_K-2i_NaKv_iF

Component: Force

f_01=3f_XB f_12=10f_XB f_23=7f_XB g_01=g_XB2-SL_norm g_12=2g_XB2-SL_norm g_23=3g_XB2-SL_norm SL_norm=SL-1.70.7 N_tm=3.5+2.5SL_norm K_tm=11+beta_trpnalpha_trpn0.0017-0.0009SL_norm alpha_tm=beta_tmTrpn_CaTrpn_totK_tmN_tm ddtimeN_0=beta_tmP_0-alpha_tmN_0+g_01N_1 ddtimeP_0=-beta_tm+f_01P_0+alpha_tmN_0+g_01P_1 ddtimeP_1=-beta_tm+f_12+g_01P_1+alpha_tmN_1+f_01P_0+g_12P_2 ddtimeP_2=-f_23+g_12P_2+f_12P_1+g_23P_3 ddtimeP_3=-g_23P_3+f_23P_2 N_1=1-N_0+P_0+P_1+P_2+P_3 sigma_paths=1g_XB2g_XB3g_XB+1f_012g_XB3g_XB+1f_011f_123g_XB+1f_011f_121f_23 P_1_max=1f_012g_XB3g_XBsigma_paths P_2_max=1f_011f_123g_XBsigma_paths P_3_max=1f_011f_121f_23sigma_paths Force_max=P_1_max+2P_2_max+3P_3_max phi_SL=SL-0.61.4ifSL1.7SL21ifSL>2SL2.23.6-SL1.4ifSL>2.2SL2.3 Force_norm=phi_SLP_1+N_1+2P_2+3P_3Force_max Force=zetaForce_norm