Model Mathematics

Component: environment

Component: membrane

I_st=stim_amplitudeiftimestim_starttimestim_endtime-stim_start-time-stim_startstim_periodstim_periodstim_duration0otherwise ddtimeV=-1Cmi_Na+i_Ca_L+i_Ca_T+i_Kr+i_Ks+i_K_Na+i_K_ATP+i_to+i_K1+i_Kp+i_NaCa+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_ns_Ca+I_st dVdt=-1Cmi_Na+i_Ca_L+i_Ca_T+i_Kr+i_Ks+i_K_Na+i_K_ATP+i_to+i_K1+i_Kp+i_NaCa+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_ns_Ca+I_st

Component: fast_sodium_current

i_Na=g_NaP_UO_Na+P_LO_NaV-E_Na E_Na=RTFlnNaoNai

Component: Na_channel_states

ddtimeP_UC3=beta_11P_UC2+mu_2P_LC3-alpha_11+mu_1P_UC3 ddtimeP_LC3=beta_11P_LC2+mu_1P_UC3-alpha_11+mu_2P_LC3 ddtimeP_UC2=-beta_11+alpha_12+mu_1P_UC2+alpha_11P_UC3+beta_12P_UC1+mu_2P_LC2 ddtimeP_LC2=-beta_11+alpha_12+mu_2P_LC2+alpha_11P_LC3+beta_12P_LC1+mu_1P_UC2 ddtimeP_UC1=-beta_12+alpha_13+beta_3+mu_1P_UC1+alpha_12P_UC2+beta_13P_UO_Na+alpha_3P_IF+mu_2P_LC1 ddtimeP_LC1=-beta_12+alpha_13+mu_2P_LC1+alpha_12P_LC2+beta_13P_LO_Na+mu_1P_UC1 ddtimeP_UO_Na=-alpha_2+beta_13+mu_1P_UO_Na+beta_2P_IF+alpha_13P_UC1+mu_2P_LO_Na ddtimeP_LO_Na=alpha_13P_LC1+mu_1P_UO_Na-beta_13+mu_2P_LO_Na ddtimeP_IF=-beta_2+alpha_3+alpha_4P_IF+beta_3P_UC1+beta_4P_IS+alpha_2P_UO_Na ddtimeP_IS=alpha_4P_IF-beta_4P_IS alpha_11=1.2538020.1027-V17+0.2-V150 alpha_12=1.2538020.1027-V15+0.23-V150 alpha_13=1.2538020.1027-V12+0.25-V150 beta_11=191.7-V20.3 beta_12=200-V-520.3 beta_13=220-V-1020.3 alpha_2=9178V100 beta_2=alpha_13alpha_2alpha_3beta_13beta_3 alpha_3=200.00000037933-V5.2 beta_3=28.4+0.02V alpha_4=alpha_2100 beta_4=alpha_3

Component: L_type_Ca_channel

I_CaCa=P_Ca22VF2RTgamma_CaiCai2VFRT-gamma_CaoCao2VFRT-1 I_CaNa=P_Na12VF2RTgamma_NaiNai1VFRT-gamma_NaoNao1VFRT-1 I_CaK=P_K12VF2RTgamma_KiKi1VFRT-gamma_KoKo1VFRT-1 i_CaCa=dff_CaI_CaCa i_CaNa=dff_CaI_CaNa i_CaK=dff_CaI_CaK i_Ca_L=i_CaCa+i_CaK+i_CaNa

Component: L_type_Ca_channel_d_gate

E0_d=V+10 d_infinity=11+-E0_d6.24 tau_d=0.0010.0356.24if|E0_d|<1e-50.001d_infinity1--E0_d6.240.035E0_dotherwise alpha_d=d_infinitytau_d beta_d=1-d_infinitytau_d ddtimed=alpha_d1-d-beta_dd

Component: L_type_Ca_channel_f_gate

f_infinity=11+V+328+0.61+50-V20 tau_f=0.0010.0197-0.0337V+102+0.02 alpha_f=f_infinitytau_f beta_f=1-f_infinitytau_f ddtimef=alpha_f1-f-beta_ff

Component: L_type_Ca_channel_f_Ca_gate

f_Ca=11+CaiKm_Ca

Component: T_type_Ca_channel

i_Ca_T=g_CaTbbgV-E_Ca

Component: T_type_Ca_channel_b_gate

b_inf=11+-V+1410.8 tau_b=0.0037+0.00611+V+254.5 ddtimeb=b_inf-btau_b

Component: T_type_Ca_channel_g_gate

g_inf=11+V+605.6 tau_g=-0.000875V+0.012ifV00.012otherwise ddtimeg=g_inf-gtau_g

Component: rapid_delayed_rectifier_potassium_current

i_Kr=g_KrP_OV-E_Kr g_Kr=0.0135Ko0.59 E_Kr=RTFlnKoKi

Component: Kr_channel_states

ddtimeP_C3=betaP_C2-alphaP_C3 ddtimeP_C2=-beta+alpha_inP_C2+alphaP_C3+beta_inP_C1 ddtimeP_C1=-beta_in+alpha_alpha+alpha_alphaP_C1+alpha_inP_C2+beta_betaP_O+muP_I ddtimeP_O=-beta_beta+beta_iP_O+alpha_alphaP_C1+alpha_iP_I ddtimeP_I=-mu+alpha_iP_I+alpha_alphaP_C1+beta_iP_O alpha=55.50.05547153V-12 beta=2.357-0.036588V alpha_alpha=65.50.05547153V-36 beta_beta=2.9357-0.02158V alpha_i=439-0.02352V+254.5Ko beta_i=6560.000942V4.5Ko0.3 mu=alpha_ibeta_betaalpha_alphaalpha_alphabeta_i

Component: slow_delayed_rectifier_potassium_current

E_Ks=RTFlnKo+PNaKNaoKi+PNaKNai g_Ks=0.4331+0.61+3.8e-5Cai1.4 i_Ks=g_Ksxs1xs2V-E_Ks

Component: slow_delayed_rectifier_potassium_current_xs1_gate

xs1_infinity=11+-V-1.516.7 tau_xs1=0.0017.19e-5V+301--0.148V+30+0.000131V+300.0687V+30-1 ddtimexs1=xs1_infinity-xs1tau_xs1

Component: slow_delayed_rectifier_potassium_current_xs2_gate

xs2_infinity=11+-V-1.516.7 tau_xs2=40.0017.19e-5V+301--0.148V+30+0.000131V+300.0687V+30-1 ddtimexs2=xs2_infinity-xs2tau_xs2

Component: time_independent_potassium_current

g_K1=0.75Ko5.4 E_K=RTFlnKoKi i_K1=g_K1K1_infinityV-E_K

Component: time_independent_potassium_current_K1_gate

alpha_K1=10201+0.2385V-E_K-59.215 beta_K1=10000.491240.08032V-E_K+5.476+0.06175V-E_K-594.311+-0.5143V-E_K+4.753 K1_infinity=alpha_K1alpha_K1+beta_K1

Component: plateau_potassium_current

Kp=11+7.488-V5.98 i_Kp=g_KpKpV-E_K

Component: sodium_activated_potassium_current

g_K_Na=00.12848 pona=0.851+kdKNaNainKNa pov=0.8-0.651+V+12515 i_K_Na=g_K_NaponapovV-E_K

Component: ATP_sensitive_potassium_current

g_K_ATP=i_K_ATP_on0.000193nicholsarea pATP=11+ATPikATPhATP GKbaraATP=g_K_ATPpATPKo4nATP i_K_ATP=GKbaraATPV-E_K

Component: transient_outward_current

g_to=00.5 rvdv=V100 i_to=g_tozdv3ydvrvdvV-E_K

Component: transient_outward_current_zdv_gate

alpha_zdv=10000V-40251+V-4025 beta_zdv=10000-V+90251+-V+9025 tau_zdv=1alpha_zdv+beta_zdv zdv_ss=alpha_zdvalpha_zdv+beta_zdv ddtimezdv=zdv_ss-zdvtau_zdv

Component: transient_outward_current_ydv_gate

alpha_ydv=151+V+605 beta_ydv=100V+2551+V+255 tau_ydv=1alpha_ydv+beta_ydv ydv_ss=alpha_ydvalpha_ydv+beta_ydv ddtimeydv=ydv_ss-ydvtau_ydv

Component: sarcolemmal_calcium_pump

i_p_Ca=I_pCaCaiK_mpCa+Cai

Component: sodium_background_current

i_Na_b=g_NabV-E_Na

Component: calcium_background_current

E_Ca=RT2FlnCaoCai i_Ca_b=g_CabV-E_Ca

Component: sodium_potassium_pump

sigma=17Nao67.3-1 f_NaK=11+0.1245-0.1VFRT+0.0365sigma-VFRT i_NaK=I_NaKf_NaK11+K_mNaiNai2KoKo+K_mKo

Component: non_specific_calcium_activated_current

P_ns_Ca=01.75e-7 I_ns_Na=P_ns_Ca12VF2RTgamma_NaiNai1VFRT-gamma_NaoNao1VFRT-1 I_ns_K=P_ns_Ca12VF2RTgamma_KiKi1VFRT-gamma_KoKo1VFRT-1 i_ns_Na=I_ns_Na11+K_m_ns_CaCai3 i_ns_K=I_ns_K11+K_m_ns_CaCai3 i_ns_Ca=i_ns_Na+i_ns_K

Component: Na_Ca_exchanger

i_NaCa=c1gamma-1VFRTVFRTNai3Cao-Nao3Cai1+c2gamma-1VFRTVFRTNai3Cao+Nao3Cai

Component: calcium_dynamics

V_JSR=0.00480.68V_myo V_NSR=0.05520.68V_myo ddtimeAPtrack=1000001-APtrack-500APtrackifdVdt>150000-500APtrackotherwise ddtimeAPtrack2=1000001-APtrack2-500APtrack2ifAPtrack<0.2APtrack>0.18-500APtrack2otherwise ddtimeAPtrack3=1000001-APtrack3-500APtrack3ifAPtrack<0.2APtrack>0.18-10APtrack3otherwise ddtimeCainfluxtrack=-A_capi_CaCa+i_Ca_T-i_NaCa+i_p_Ca+i_Ca_b2V_myoFifAPtrack>0.20ifAPtrack2>0.01APtrack0.2-500Cainfluxtrackotherwise ddtimeOVRLDtrack=500001-OVRLDtrackif11+K_mCSQNCa_NSR>CSQNthreshOVRLDtrack3<0.37APtrack3<0.37-500OVRLDtrackotherwise ddtimeOVRLDtrack2=500001-OVRLDtrack2ifOVRLDtrack>LogicthreshOVRLDtrack2<Logicthresh-500OVRLDtrack2otherwise ddtimeOVRLDtrack3=500001-OVRLDtrack3ifOVRLDtrack>LogicthreshOVRLDtrack3<Logicthresh-10OVRLDtrack3otherwise G_rel=G_rel_maxCainfluxtrack-delta_Ca_ithK_mrel+Cainfluxtrack-delta_Ca_ith1-APtrack2APtrack2ifCainfluxtrack>delta_Ca_ithG_rel_overload1-OVRLDtrack2OVRLDtrack2ifCainfluxtrackdelta_Ca_ithOVRLDtrack2>00otherwise i_rel=G_relCa_JSR-Cai i_up=I_upCaiCai+K_mup K_leak=I_upCa_NSR_max i_leak=K_leakCa_NSR i_tr=Ca_NSR-Ca_JSRtau_tr ddtimeCa_JSR=11+CSQN_maxK_mCSQNK_mCSQN+Ca_JSR2i_tr-i_rel ddtimeCa_NSR=-i_trV_JSRV_NSR-i_leak+i_up ddtimeCai=11+CMDN_maxK_mCMDNK_mCMDN+Cai2+Tn_maxK_mTnK_mTn+Cai2-A_capi_CaCa+i_Ca_T-2i_NaCa+i_p_Ca+i_Ca_b2V_myoF+i_relV_JSRV_myo+i_leak-i_upV_NSRV_myo

Component: ionic_concentrations

volume=πpreplengthradius2 V_myo=0.68volume ddtimeNai=-i_Na+i_CaNa+i_Na_b+i_ns_Na+i_NaCa3+i_NaK3A_capV_myoF ddtimeKi=-i_CaK+i_Kr+i_Ks+i_K1+i_Kp+i_K_Na+i_K_ATP+i_to+i_ns_K+-i_NaK2A_capV_myoF
Source
Derived from workspace Clancy, Rudy, 2001 at changeset f40fb42adae8.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.