Model Mathematics

Component: environment

Component: membrane

i_Stim=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-i_Na+i_Ca_L+i_t+i_ss+i_f+i_K1+i_B+i_NaK+i_NaCa+i_Ca_P+i_Stim+I_interCm

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=0.001360.32V+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=0.00045371+-V+10.6611.1ifV-400.003490.135-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=0.011631+-0.1V+32-0.0000002535VifV-400.00349V+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: L_type_Ca_channel

i_Ca_L=g_Ca_Ld0.9+Ca_inact10f_11+0.1-Ca_inact10f_12V-E_Ca_L

Component: L_type_Ca_channel_d_gate

d_infinity=11+V+15.3-5 tau_d=0.00305-0.0045V+72+0.00105-0.002V-182+0.00025 ddtimed=d_infinity-dtau_d

Component: L_type_Ca_channel_f_11_gate

f_11_infinity=11+V+26.75.4 tau_f_11=0.105-V+45122+0.041+-V+2525+0.0151+V+7525+0.0017 ddtimef_11=f_11_infinity-f_11tau_f_11

Component: L_type_Ca_channel_f_12_gate

f_12_infinity=11+V+26.75.4 tau_f_12=0.041-V+47122+0.081+V+55-5+0.0151+V+7525+0.0017 ddtimef_12=f_12_infinity-f_12tau_f_12

Component: L_type_Ca_channel_Ca_inact_gate

Ca_inact_infinity=11+Ca_ss0.01 ddtimeCa_inact=Ca_inact_infinity-Ca_inacttau_Ca_inact

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=145.160.03577V+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=0.35-V+70152+0.035 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=3.7-V+70302+0.035 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=1045.160.03577V+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=2.1 ddtimes_ss=s_ss_infinity-s_sstau_s_ss

Component: inward_rectifier

i_K1=48V+3725+V+37-25+100.0011+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=10.11885V+8028.37+0.5623V+80-14.19 ddtimey=y_infinity-ytau_y

Component: background_currents

E_Ca=0.5RTFlnCa_oCa_i i_B_Na=g_B_NaV-E_Na i_B_Ca=g_B_CaV-E_Ca i_B_K=g_B_KV-E_K i_B=i_B_Na+i_B_Ca+i_B_K

Component: sodium_potassium_pump

sigma=Na_o67.3-17 i_NaK=i_NaK_max11+0.1245-0.1VFRT+0.0365sigma-VFRTK_oK_o+K_m_K11+K_m_NaNa_i1.5

Component: sarcolemmal_calcium_pump_current

i_Ca_P=i_Ca_P_maxCa_iCa_i+0.0004

Component: Na_Ca_ion_exchanger_current

i_NaCa=K_NaCaNa_i3Ca_o0.03743Vgamma_NaCa-Na_o3Ca_i0.03743Vgamma_NaCa-11+d_NaCaCa_iNa_o3+Ca_oNa_i3

Component: SR_Ca_release_channel

ddtimeP_C1=-k_a_plusCa_ss1nP_C1+k_a_minusP_O1 ddtimeP_O1=k_a_plusCa_ss1nP_C1-k_a_minusP_O1+k_b_plusCa_ss1mP_O1+k_c_plusP_O1+k_b_minusP_O2+k_c_minusP_C2 ddtimeP_O2=k_b_plusCa_ss1mP_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=Ca_iK_fbN_fb rb=Ca_NSRK_rbN_rb J_up=K_SRVmaxffb-Vmaxrrb1+fb+rb

Component: intracellular_and_SR_Ca_fluxes

J_tr=Ca_NSR-Ca_JSRtau_tr J_xfer=Ca_ss-Ca_itau_xfer J_HTRPNCa=k_htrpn_plusCa_iHTRPN_tot-HTRPNCa-k_htrpn_minusHTRPNCa J_LTRPNCa=k_ltrpn_plusCa_iLTRPN_tot-LTRPNCa-k_ltrpn_minusLTRPNCa J_trpn=J_HTRPNCa+J_LTRPNCa

Component: intracellular_ion_concentrations

beta_i=11+CMDN_totK_mCMDNK_mCMDN+Ca_i2+EGTA_totK_mEGTAK_mEGTA+Ca_i2 beta_SS=11+CMDN_totK_mCMDNK_mCMDN+Ca_ss2 beta_JSR=11+CSQN_totK_mCSQNK_mCSQN+Ca_JSR2 ddtimeCa_i=beta_iJ_xfer-J_up+J_trpn+i_B_Ca-2i_NaCa+i_Ca_P12V_myoF ddtimeNa_i=-i_Na+i_B_Na+i_NaCa3+i_NaK3+i_f_Na1V_myoF ddtimeK_i=-i_ss+i_B_K+i_t+i_K1+i_f_K+i_NaK-21V_myoF ddtimeCa_ss=beta_SSJ_relV_JSRV_SS-J_xferV_myoV_SS-i_Ca_L12V_SSF ddtimeCa_JSR=beta_JSRJ_tr-J_rel ddtimeCa_NSR=J_upV_myoV_NSR-J_trV_JSRV_NSR

Component: standard_ionic_concentrations

Component: eqn1

V_fibro=1e-7if|VmReal|<1e-7VmRealotherwise ddtimeVmReal=-I_Kir+I_Shkr+I_b+I_interCm

Component: eqn2

I_Kir=GKirOKirKo1e-3V_fibro-EK OKir=1aKir+bKirV_fibro-EKFRT EK=RTFlnKoKi

Component: eqn4

I_Shkr=PShkrOShkrV_fibroF2RTKi-Ko-V_fibroFRT1--V_fibroFRT C0Shkr=0ifC0ShkrReal<01ifC0ShkrReal>1C0ShkrRealotherwise C1Shkr=0ifC1ShkrReal<01ifC1ShkrReal>1C1ShkrRealotherwise C2Shkr=0ifC2ShkrReal<01ifC2ShkrReal>1C2ShkrRealotherwise C3Shkr=0ifC3ShkrReal<01ifC3ShkrReal>1C3ShkrRealotherwise C4Shkr=0ifC4ShkrReal<01ifC4ShkrReal>1C4ShkrRealotherwise OShkr=0ifOShkrReal<01ifOShkrReal>1OShkrRealotherwise kv=kv0V_fibrozvFRT k_v=k_v0V_fibroz_vFRT ddtimeC0ShkrReal=k_vC1Shkr-4kvC0Shkr ddtimeC1ShkrReal=2k_vC2Shkr+4kvC0Shkr-3kv+k_vC1Shkr ddtimeC2ShkrReal=3k_vC3Shkr+3kvC1Shkr-2kv+2k_vC2Shkr ddtimeC3ShkrReal=4k_vC4Shkr+2kvC2Shkr-kv+3k_vC3Shkr ddtimeC4ShkrReal=k_oOShkr+kvC3Shkr-ko+4k_vC4Shkr ddtimeOShkrReal=koC4Shkr-k_oOShkr

Component: eqn14

I_b=GbV_fibro-Eb

Component: I_inter

I_inter_fibro=1e+06V_fibro-VR_mf I_inter_myo=-1I_inter_fibronumber_of_fibroblasts