Model Mathematics

Component: environment

Component: model_parameters

Vc=Smtot7850 Vmyo=Vc0.585 VSRup=Vc0.0315 VSRrel=Vc0.0035 Vd=Vc0.000075 Sms=Smtot-0.44e4Vc Smt=Smtot-Sms pt=ptcmSms Lt=Smt23.14159radiustpt Vt=3.14159radiust2Ltpt Cmt=Smt1 Cms=Sms1 Rst=RotLt23.14159radiust2pt

Component: common_current

i_circ=1000Vm_s-Vm_tR_st

Component: SR_Ca_release_channel

ddtimeF1=-kapCa_ss4F1+kamF2 ddtimeF2=kapCa_ss4F1-kamF2+kbpCa_ss3F2+kcpF2+kbmF3+kcmF4 ddtimeF3=kbpCa_ss3F2-kbmF3 ddtimeF4=kcpF2-kcmF4 J_CaSRrel=1800F2+F3CaSRrel-Ca_ss

Component: SERCA2a_pump

fb=Ca_iK_fbN_fb rb=CaSRupK_rbN_rb J_CaSRup=K_SRVmaxffb-Vmaxrrb1+fb+rb

Component: intracellular_and_SR_Ca_fluxes

J_tr=CaSRup-CaSRreltau_tr J_xfer=Ca_ss-Ca_itau_xfer J_BTRH=k_htrpn_plusCa_i1-BTRH-k_htrpn_minusBTRH ddtimeBTRH=J_BTRH J_BTRL=k_ltrpn_plusCa_i1-BTRL-k_ltrpn_minusBTRL ddtimeBTRL=J_BTRL J_trpn=J_BTRH+J_BTRL

Component: ion_concentrations

ddtimeNa_i=-i_Na_s+i_Na_t+i_BNa_s+i_BNa_t+i_NaCa_s3+i_NaCa_t3+i_NaK_s3+i_NaK_t3VmyoF ddtimeNa_t=i_Na_t+i_BNa_t+i_NaCa_t3+i_NaK_t3F-Jte_NaVt i_Kext=52Sms+SmtifSTIMULATION=1time-time0<0.0010otherwise ddtimeK_i=--i_Kext+i_fK_s+i_fK_t+i_Kss_s+i_Kss_t+i_K1_s+i_K1_t+i_BK_s+i_BK_t+i_NaK_s-2+i_NaK_t-2+i_Kto_s+i_Kto_tVmyoF ddtimeK_t=i_fK_t+i_Kss_t+i_K1_t+i_BK_t+i_NaK_t-2+i_Kto_tF-Jte_KVt ddtimeCa_i=11+CMDN_totK_mCMDNK_mCMDN+Ca_i2-2i_NaCa_s+i_NaCa_t+i_BCa_s+i_BCa_t+i_CaP_s+i_CaP_t-2VmyoF+Ca_ss-Ca_iVmyotau_d+J_CaSRrel-J_CaSRupVmyo-J_BTRHBTRHmax+J_BTRLBTRLmax ddtimeCa_t=i_Ca_t+i_CaP_t+i_BCa_t+i_NaCa_t-22F-Jte_CaVt ddtimeCa_ss=11+CMDN_totK_mCMDNK_mCMDN+Ca_ss2-i_Ca_s+i_Ca_t2VdF+J_CaSRrelVd-Ca_ss-Ca_iVmyotau_dVd ddtimeCaSRrel=11+CSQN_totK_mCSQNK_mCSQN+CaSRrel2J_tr-J_CaSRrel ddtimeCaSRup=J_CaSRup-J_tr

Component: t_tubular_ion_fluxes

Jte_Na=1Vttau_NaNa_t-Na_e Jte_Ca=1Vttau_CaCa_t-Ca_e Jte_K=1Vttau_KK_t-K_e

Component: surface_membrane

Component: membrane

ddtimeVm_s=1000i_Kext+i_circ-i_Na_s+i_Ca_s+i_Kto_s+i_Kss_s+i_f_s+i_K1_s+i_B_s+i_NaK_s+i_NaCa_s+i_CaP_sCms

Component: sodium_current

E_Na=RTFlnNa_eNa_i i_Na_s=g_Nasm3hVm_s-log10Na_e+0.12K_eNa_i+0.12K_iRTF g_Nas=g_NaSms+Smt1-fNat

Component: sodium_current_m_gate

alpha_m=117.26Vm_s+59.31--0.55Vm_s+59.3 beta_m=3800-0.072Vm_s+61 ddtimem=alpha_m1-m-beta_mm

Component: sodium_current_h_gate

alpha_h=284.41+0.0812Vm_s+115.9 beta_h=18.77Vm_s+64.41--0.22Vm_s+64.4 ddtimeh=alpha_h1-h-beta_hh

Component: calcium_current

Co_inf=11+Vm_s+15.3-5 tauCo=0.00305-0.0045Vm_s+72+0.00105-0.002Vm_s-182+0.00025 ddtimeCo=Co_inf-CotauCo C1_inf=11+Vm_s+26.75.4 tauC1=0.105-Vm_s+45122+0.041+-Vm_s+2525+0.0151+Vm_s+7525+0.0017 ddtimeC1=C1_inf-C1tauC1 C2_inf=11+Vm_s+26.75.4 tauC2=0.041-Vm_s+47122+0.081+Vm_s+55-5+0.0151+Vm_s+7525+0.0017 ddtimeC2=C2_inf-C2tauC2 C_cast_inf=11+Ca_ss0.01 ddtimeC_cast=C_cast_inf-C_casttauC_cast g_Cas=g_CaSms+Smt1-fCat i_Ca_s=g_Cas4Vm_sF2RTCa_ss2Vm_sF2RT-0.341Ca_e2Vm_sF2RT-1Co0.9+C_cast10.0C1+0.1+C_cast10.0C2

Component: Ca_independent_transient_outward_K_current

E_K=RTFlnK_eK_i i_Kto_s=g_Ktosras+bs_slowVm_s-E_K g_Ktos=g_KtoSms+Smt1-fKtot

Component: Ca_independent_transient_outward_K_current_r_gate

r_max=11+Vm_s+10.6-11.42 tau_r=145.160.03577Vm_s+50+98.9-0.1Vm_s+38 ddtimer=r_max-rtau_r

Component: Ca_independent_transient_outward_K_current_s_gate

s_max=11+Vm_s+45.36.8841 tau_s=0.35-0.0666Vm_s+702+0.035 ddtimes=s_max-stau_s

Component: Ca_independent_transient_outward_K_current_s_slow_gate

s_slow_max=11+Vm_s+45.36.8841 tau_s_slow=3.7-0.0333Vm_s+702+0.035 ddtimes_slow=s_slow_max-s_slowtau_s_slow

Component: steady_state_outward_K_current

i_Kss_s=g_Ksssr_sss_ssVm_s-E_K g_Ksss=g_KssSms+Smt1-fKsst

Component: steady_state_outward_K_current_r_ss_gate

r_ss_max=11+-Vm_s+11.511.82 tau_r_ss=1045.160.03577Vm_s+50+98.9-0.1Vm_s+38 ddtimer_ss=r_ss_max-r_sstau_r_ss

Component: steady_state_outward_K_current_s_ss_gate

s_ss_max=11+Vm_s+87.510.3 tau_s_ss=2.1 ddtimes_ss=s_ss_max-s_sstau_s_ss

Component: inward_rectifier

i_K1_s=g_K1sVm_s-E_K+1.731+1.613FRTVm_s-E_K+1.731+-K_e-0.99880.124 g_K1s=g_K1Sms+Smt1-fK1t

Component: hyperpolarisation_activated_current

f_K=1-f_Na i_fNa_s=g_fsyf_NaVm_s-E_Na i_fK_s=g_fsyf_KVm_s-E_K i_f_s=g_fsy0.2Vm_s-E_Na+0.8Vm_s-E_K g_fs=g_fSms+Smt1-fft

Component: hyperpolarisation_activated_current_y_gate

y_infinity=11+Vm_s+138.610.48 tau_y=10.11885Vm_s+8028.37+0.5623Vm_s+80-14.19 ddtimey=y_infinity-ytau_y

Component: background_currents

i_BNa_s=g_B_NasVm_s-E_Na i_BCa_s=g_B_CasVm_s-E_Ca i_BK_s=g_B_KsVm_s-E_K i_B_s=i_BNa_s+i_BCa_s+i_BK_s g_B_Cas=g_B_CaSms+Smt1-fCabt g_B_Nas=g_B_NaSms+Smt1-fNabt g_B_Ks=g_B_KSms+Smt1-fKbt

Component: sodium_potassium_pump

sigma=Na_e67.3-17 i_NaK_s=i_NaK_max_s1+0.1245-0.1Vm_sFRT+0.0365sigma-Vm_sFRTK_eK_e+K_m_K1+K_m_NaNa_i1.5 i_NaK_max_s=i_NaK_maxSms+Smt1-fNaKt

Component: sarcolemmal_calcium_pump_current

i_CaP_s=i_CaP_max_sCa_iCa_i+0.0004 i_CaP_max_s=i_CaP_maxSms+Smt1-fCaPt

Component: Na_Ca_ion_exchanger_current

i_NaCa_s=i_NaCa_max_s0.0187Vm_sNa_i3Ca_e--0.0187Vm_sNa_e3Ca_i1+0.0001Ca_iNa_e3+Ca_eNa_i3 i_NaCa_max_s=i_NaCa_maxSms+Smt1-fNaCat

Component: tubular_membrane

Component: membrane

ddtimeVm_t=1000-i_circ+i_Na_t+i_Ca_t+i_Kto_t+i_Kss_t+i_f_t+i_K1_t+i_B_t+i_NaK_t+i_NaCa_t+i_CaP_tCmt

Component: sodium_current

E_Na=RTFlnNa_tNa_i i_Na_t=g_Natm3hVm_t-log10Na_t+0.12K_tNa_i+0.12K_iRTF g_Nat=g_NaSms+SmtfNat

Component: sodium_current_m_gate

alpha_m=117.26Vm_t+59.31--0.55Vm_t+59.3 beta_m=3800-0.072Vm_t+61 ddtimem=alpha_m1-m-beta_mm

Component: sodium_current_h_gate

alpha_h=284.41+0.0812Vm_t+115.9 beta_h=18.77Vm_t+64.41--0.22Vm_t+64.4 ddtimeh=alpha_h1-h-beta_hh

Component: calcium_current

Co_inf=11+Vm_t+15.3-5 tauCo=0.00305-0.0045Vm_t+72+0.00105-0.002Vm_t-182+0.00025 ddtimeCo=Co_inf-CotauCo C1_inf=11+Vm_t+26.75.4 tauC1=0.105-Vm_t+45122+0.041+-Vm_t+2525+0.0151+Vm_t+7525+0.0017 ddtimeC1=C1_inf-C1tauC1 C2_inf=11+Vm_t+26.75.4 tauC2=0.041-Vm_t+47122+0.081+Vm_t+55-5+0.0151+Vm_t+7525+0.0017 ddtimeC2=C2_inf-C2tauC2 C_cast_inf=11+Ca_ss0.01 ddtimeC_cast=C_cast_inf-C_casttauC_cast g_Cat=g_CaSms+SmtfCat i_Ca_t=g_Cat4Vm_tF2RTCa_ss2Vm_tF2RT-0.341Ca_t2Vm_tF2RT-1Co0.9+C_cast10.0C1+0.1+C_cast10.0C2

Component: Ca_independent_transient_outward_K_current

E_K=RTFlnK_tK_i i_Kto_t=g_Ktotras+bs_slowVm_t-E_K g_Ktot=g_KtoSms+SmtfKtot

Component: Ca_independent_transient_outward_K_current_r_gate

r_max=11+Vm_t+10.6-11.42 tau_r=145.160.03577Vm_t+50+98.9-0.1Vm_t+38 ddtimer=r_max-rtau_r

Component: Ca_independent_transient_outward_K_current_s_gate

s_max=11+Vm_t+45.36.8841 tau_t=0.35-0.0666Vm_t+702+0.035 ddtimes=s_max-stau_t

Component: Ca_independent_transient_outward_K_current_s_slow_gate

s_slow_max=11+Vm_t+45.36.8841 tau_s_slow=3.7-0.0333Vm_t+702+0.035 ddtimes_slow=s_slow_max-s_slowtau_s_slow

Component: steady_state_outward_K_current

i_Kss_t=g_Ksstr_sss_ssVm_t-E_K g_Ksst=g_KssSms+SmtfKsst

Component: steady_state_outward_K_current_r_ss_gate

r_ss_max=11+-Vm_t+11.511.82 tau_r_ss=1045.160.03577Vm_t+50+98.9-0.1Vm_t+38 ddtimer_ss=r_ss_max-r_sstau_r_ss

Component: steady_state_outward_K_current_s_ss_gate

s_ss_max=11+Vm_t+87.510.3 tau_s_ss=2.1 ddtimes_ss=s_ss_max-s_sstau_s_ss

Component: inward_rectifier

i_K1_t=g_K1tVm_t-E_K+1.731+1.613FRTVm_t-E_K+1.731+-K_t-0.99880.124 g_K1t=g_K1Sms+SmtfK1t

Component: hyperpolarisation_activated_current

f_K=1-f_Na i_fNa_t=g_ftyf_NaVm_t-E_Na i_fK_t=g_ftyf_KVm_t-E_K i_f_t=g_fty0.2Vm_t-E_Na+0.8Vm_t-E_K g_ft=g_fSms+Smtfft

Component: hyperpolarisation_activated_current_y_gate

y_infinity=11+Vm_t+138.610.48 tau_y=10.11885Vm_t+8028.37+0.5623Vm_t+80-14.19 ddtimey=y_infinity-ytau_y

Component: background_currents

i_BNa_t=g_B_NatVm_t-E_Na i_BCa_t=g_B_CatVm_t-E_Ca i_BK_t=g_B_KtVm_t-E_K i_B_t=i_BNa_t+i_BCa_t+i_BK_t g_B_Cat=g_B_CaSms+SmtfCabt g_B_Nat=g_B_NaSms+SmtfNabt g_B_Kt=g_B_KSms+SmtfKbt

Component: sodium_potassium_pump

sigma=Na_t67.3-17 i_NaK_t=i_NaK_max_t1+0.1245-0.1Vm_tFRT+0.0365sigma-Vm_tFRTK_tK_t+K_m_K1+K_m_NaNa_i1.5 i_NaK_max_t=i_NaK_maxSms+SmtfNaKt

Component: sarcolemmal_calcium_pump_current

i_CaP_t=i_CaP_max_tCa_iCa_i+0.0004 i_CaP_max_t=i_CaP_maxSms+SmtfCaPt

Component: Na_Ca_ion_exchanger_current

i_NaCa_t=i_NaCa_max_t0.0187Vm_tNa_i3Ca_t--0.0187Vm_tNa_t3Ca_i1+0.0001Ca_iNa_t3+Ca_tNa_i3 i_NaCa_max_t=i_NaCa_maxSms+SmtfNaCat