Model Mathematics

Component: membrane

$I_st=stim_amplitudeiftime≥stim_start∧time≦stim_end∧time-stim_start-⌊time-stim_startstim_period⌋⁢stim_period≦stim_duration0otherwiseddtimeV=-1Cm⁢i_Na+i_Ca_L+i_Ca_T+i_Kr+i_Ks+i_K_Na+i_K_ATP+i_to+i_K1+i_Kp+i_NaCa+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_ns_Ca+I_stdVdt=-1Cm⁢i_Na+i_Ca_L+i_Ca_T+i_Kr+i_Ks+i_K_Na+i_K_ATP+i_to+i_K1+i_Kp+i_NaCa+i_p_Ca+i_Na_b+i_Ca_b+i_NaK+i_ns_Ca+I_st$

Component: fast_sodium_current

$i_Na=g_Na⁢P_O_Na⁢V-E_NaE_Na=R⁢TF⁢ln⁡NaoNai$

Component: Na_channel_states

$ddtimeP_C3=beta_11⁢P_C2-alpha_11⁢P_C3ddtimeP_C2=-beta_11+alpha_12⁢P_C2+alpha_11⁢P_C3+beta_12⁢P_C1ddtimeP_C1=-beta_12+alpha_13+beta_3⁢P_C1+alpha_12⁢P_C2+beta_13⁢P_O_Na+alpha_3⁢P_IFddtimeP_O_Na=-alpha_2+beta_13⁢P_O_Na+beta_2⁢P_IF+alpha_13⁢P_C1ddtimeP_IF=-beta_2+alpha_3+alpha_4⁢P_IF+beta_3⁢P_C1+beta_4⁢P_IS+alpha_2⁢P_O_NaddtimeP_IS=alpha_4⁢P_IF-beta_4⁢P_ISalpha_11=38020.1027⁢ⅇ-V17+0.2⁢ⅇ-V150alpha_12=38020.1027⁢ⅇ-V15+0.23⁢ⅇ-V150alpha_13=38020.1027⁢ⅇ-V12+0.25⁢ⅇ-V150beta_11=191.7⁢ⅇ-V20.3beta_12=200⁢ⅇ-V-520.3beta_13=220⁢ⅇ-V-1020.3alpha_2=9178⁢ⅇV29.68beta_2=alpha_13⁢alpha_2⁢alpha_3beta_13⁢beta_3alpha_3=0.00000037933⁢ⅇ-V5.2beta_3=8.4+0.02⁢Valpha_4=alpha_2100beta_4=alpha_3$

Component: L_type_Ca_channel

$I_CaCa=P_Ca⁢22⁢V⁢F2R⁢T⁢gamma_Cai⁢Cai⁢ⅇ2⁢V⁢FR⁢T-gamma_Cao⁢Caoⅇ2⁢V⁢FR⁢T-1I_CaNa=P_Na⁢12⁢V⁢F2R⁢T⁢gamma_Nai⁢Nai⁢ⅇ1⁢V⁢FR⁢T-gamma_Nao⁢Naoⅇ1⁢V⁢FR⁢T-1I_CaK=P_K⁢12⁢V⁢F2R⁢T⁢gamma_Ki⁢Ki⁢ⅇ1⁢V⁢FR⁢T-gamma_Ko⁢Koⅇ1⁢V⁢FR⁢T-1i_CaCa=d⁢f⁢f_Ca⁢I_CaCai_CaNa=d⁢f⁢f_Ca⁢I_CaNai_CaK=d⁢f⁢f_Ca⁢I_CaKi_Ca_L=i_CaCa+i_CaK+i_CaNa$

Component: L_type_Ca_channel_d_gate

$E0_d=V+10d_infinity=11+ⅇ-E0_d6.24tau_d=0.0010.035⁢6.24if|E0_d|<1e-50.001⁢d_infinity⁢1-ⅇ-E0_d6.240.035⁢E0_dotherwisealpha_d=d_infinitytau_dbeta_d=1-d_infinitytau_dddtimed=alpha_d⁢1-d-beta_d⁢d$

Component: L_type_Ca_channel_f_gate

$f_infinity=11+ⅇV+328+0.61+ⅇ50-V20tau_f=0.0010.0197⁢ⅇ-0.0337⁢V+102+0.02alpha_f=f_infinitytau_fbeta_f=1-f_infinitytau_fddtimef=alpha_f⁢1-f-beta_f⁢f$

Component: L_type_Ca_channel_f_Ca_gate

$f_Ca=11+CaiKm_Ca$

Component: T_type_Ca_channel

$i_Ca_T=g_CaT⁢b⁢b⁢g⁢V-E_Ca$

Component: T_type_Ca_channel_b_gate

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

Component: T_type_Ca_channel_g_gate

$g_inf=11+ⅇV+605.6tau_g=-0.000875⁢V+0.012ifV≦00.012otherwiseddtimeg=g_inf-gtau_g$

Component: rapid_delayed_rectifier_potassium_current

$i_Kr=g_Kr⁢P_O⁢V-E_Krg_Kr=0.0135⁢Ko0.59E_Kr=R⁢TF⁢ln⁡KoKi$

Component: Kr_channel_states

$ddtimeP_C3=beta⁢P_C2-alpha⁢P_C3ddtimeP_C2=-beta+alpha_in⁢P_C2+alpha⁢P_C3+beta_in⁢P_C1ddtimeP_C1=-beta_in+alpha_alpha+alpha_alpha⁢P_C1+alpha_in⁢P_C2+beta_beta⁢P_O+mu⁢P_IddtimeP_O=-beta_beta+beta_i⁢P_O+alpha_alpha⁢P_C1+alpha_i⁢P_IddtimeP_I=-mu+alpha_i⁢P_I+alpha_alpha⁢P_C1+beta_i⁢P_Oalpha=55.5⁢ⅇ0.05547153⁢V+6beta=2.357⁢ⅇ-0.036588⁢Valpha_alpha=65.5⁢ⅇ0.05547153⁢V+25beta_beta=2.9357⁢ⅇ-0.02158⁢Valpha_i=439⁢ⅇ-0.02352⁢V+25⁢4.5Kobeta_i=656⁢ⅇ0.000942⁢V⁢4.5Ko0.3mu=alpha_i⁢beta_beta⁢alpha_alphaalpha_alpha⁢beta_i$

Component: slow_delayed_rectifier_potassium_current

$E_Ks=R⁢TF⁢ln⁡Ko+PNaK⁢NaoKi+PNaK⁢Naig_Ks=0.433⁢1+0.61+3.8e-5Cai1.4i_Ks=g_Ks⁢xs1⁢xs2⁢V-E_Ks$

Component: slow_delayed_rectifier_potassium_current_xs1_gate

$xs1_infinity=11+ⅇ-V-1.516.7tau_xs1=0.0017.19e-5⁢V+301-ⅇ-0.148⁢V+30+0.000131⁢V+30ⅇ0.0687⁢V+30-1ddtimexs1=xs1_infinity-xs1tau_xs1$

Component: slow_delayed_rectifier_potassium_current_xs2_gate

$xs2_infinity=11+ⅇ-V-1.516.7tau_xs2=4⁢0.0017.19e-5⁢V+301-ⅇ-0.148⁢V+30+0.000131⁢V+30ⅇ0.0687⁢V+30-1ddtimexs2=xs2_infinity-xs2tau_xs2$

Component: time_independent_potassium_current

$g_K1=0.75⁢Ko5.4E_K=R⁢TF⁢ln⁡KoKii_K1=g_K1⁢K1_infinity⁢V-E_K$

Component: time_independent_potassium_current_K1_gate

$alpha_K1=10201+ⅇ0.2385⁢V-E_K-59.215beta_K1=1000⁢0.49124⁢ⅇ0.08032⁢V-E_K+5.476+ⅇ0.06175⁢V-E_K-594.311+ⅇ-0.5143⁢V-E_K+4.753K1_infinity=alpha_K1alpha_K1+beta_K1$

Component: plateau_potassium_current

$Kp=11+ⅇ7.488-V5.98i_Kp=g_Kp⁢Kp⁢V-E_K$

Component: sodium_activated_potassium_current

$g_K_Na=0⁢0.12848pona=0.851+kdKNaNainKNapov=0.8-0.651+ⅇV+12515i_K_Na=g_K_Na⁢pona⁢pov⁢V-E_K$

Component: ATP_sensitive_potassium_current

$g_K_ATP=i_K_ATP_on⁢0.000193nicholsareapATP=11+ATPikATPhATPGKbaraATP=g_K_ATP⁢pATP⁢Ko4nATPi_K_ATP=GKbaraATP⁢V-E_K$

Component: transient_outward_current

$g_to=0⁢0.5rvdv=ⅇV100i_to=g_to⁢zdv3⁢ydv⁢rvdv⁢V-E_K$

Component: transient_outward_current_zdv_gate

$alpha_zdv=10000⁢ⅇV-40251+ⅇV-4025beta_zdv=10000⁢ⅇ-V+90251+ⅇ-V+9025tau_zdv=1alpha_zdv+beta_zdvzdv_ss=alpha_zdvalpha_zdv+beta_zdvddtimezdv=zdv_ss-zdvtau_zdv$

Component: transient_outward_current_ydv_gate

$alpha_ydv=151+ⅇV+605beta_ydv=100⁢ⅇV+2551+ⅇV+255tau_ydv=1alpha_ydv+beta_ydvydv_ss=alpha_ydvalpha_ydv+beta_ydvddtimeydv=ydv_ss-ydvtau_ydv$

Component: sarcolemmal_calcium_pump

$i_p_Ca=I_pCa⁢CaiK_mpCa+Cai$

Component: sodium_background_current

$i_Na_b=g_Nab⁢V-E_Na$

Component: calcium_background_current

$E_Ca=R⁢T2⁢F⁢ln⁡CaoCaii_Ca_b=g_Cab⁢V-E_Ca$

Component: sodium_potassium_pump

$sigma=17⁢ⅇNao67.3-1f_NaK=11+0.1245⁢ⅇ-0.1⁢V⁢FR⁢T+0.0365⁢sigma⁢ⅇ-V⁢FR⁢Ti_NaK=I_NaK⁢f_NaK⁢11+K_mNaiNai2⁢KoKo+K_mKo$

Component: non_specific_calcium_activated_current

$P_ns_Ca=0⁢1.75e-7I_ns_Na=P_ns_Ca⁢12⁢V⁢F2R⁢T⁢gamma_Nai⁢Nai⁢ⅇ1⁢V⁢FR⁢T-gamma_Nao⁢Naoⅇ1⁢V⁢FR⁢T-1I_ns_K=P_ns_Ca⁢12⁢V⁢F2R⁢T⁢gamma_Ki⁢Ki⁢ⅇ1⁢V⁢FR⁢T-gamma_Ko⁢Koⅇ1⁢V⁢FR⁢T-1i_ns_Na=I_ns_Na⁢11+K_m_ns_CaCai3i_ns_K=I_ns_K⁢11+K_m_ns_CaCai3i_ns_Ca=i_ns_Na+i_ns_K$

Component: Na_Ca_exchanger

$i_NaCa=c1⁢ⅇgamma-1⁢V⁢FR⁢T⁢ⅇV⁢FR⁢T⁢Nai3⁢Cao-Nao3⁢Cai1+c2⁢ⅇgamma-1⁢V⁢FR⁢T⁢ⅇV⁢FR⁢T⁢Nai3⁢Cao+Nao3⁢Cai$

Component: calcium_dynamics

$V_JSR=0.00480.68⁢V_myoV_NSR=0.05520.68⁢V_myoddtimeAPtrack=100000⁢1-APtrack-500⁢APtrackifdVdt>150000-500⁢APtrackotherwiseddtimeAPtrack2=100000⁢1-APtrack2-500⁢APtrack2ifAPtrack<0.2∧APtrack>0.18-500⁢APtrack2otherwiseddtimeAPtrack3=100000⁢1-APtrack3-500⁢APtrack3ifAPtrack<0.2∧APtrack>0.18-10⁢APtrack3otherwiseddtimeCainfluxtrack=-A_cap⁢i_CaCa+i_Ca_T-i_NaCa+i_p_Ca+i_Ca_b2⁢V_myo⁢FifAPtrack>0.20ifAPtrack2>0.01∧APtrack≦0.2-500⁢CainfluxtrackotherwiseddtimeOVRLDtrack=50000⁢1-OVRLDtrackif11+K_mCSQNCa_NSR>CSQNthresh∧OVRLDtrack3<0.37∧APtrack3<0.37-500⁢OVRLDtrackotherwiseddtimeOVRLDtrack2=50000⁢1-OVRLDtrack2ifOVRLDtrack>Logicthresh∧OVRLDtrack2Logicthresh∧OVRLDtrack3delta_Ca_ithG_rel_overload⁢1-OVRLDtrack2⁢OVRLDtrack2ifCainfluxtrack≦delta_Ca_ith∧OVRLDtrack2>00otherwisei_rel=G_rel⁢Ca_JSR-Caii_up=I_up⁢CaiCai+K_mupK_leak=I_upCa_NSR_maxi_leak=K_leak⁢Ca_NSRi_tr=Ca_NSR-Ca_JSRtau_trddtimeCa_JSR=11+CSQN_max⁢K_mCSQNK_mCSQN+Ca_JSR2⁢i_tr-i_relddtimeCa_NSR=-i_tr⁢V_JSRV_NSR-i_leak+i_upddtimeCai=11+CMDN_max⁢K_mCMDNK_mCMDN+Cai2+Tn_max⁢K_mTnK_mTn+Cai2⁢-A_cap⁢i_CaCa+i_Ca_T-2⁢i_NaCa+i_p_Ca+i_Ca_b2⁢V_myo⁢F+i_rel⁢V_JSRV_myo+i_leak-i_up⁢V_NSRV_myo$

Component: ionic_concentrations

$volume=π⁢preplength⁢radius2V_myo=0.68⁢volumeddtimeNai=-i_Na+i_CaNa+i_Na_b+i_ns_Na+i_NaCa⁢3+i_NaK⁢3⁢A_capV_myo⁢FddtimeKi=-i_CaK+i_Kr+i_Ks+i_K1+i_Kp+i_K_Na+i_K_ATP+i_to+i_ns_K+-i_NaK⁢2⁢A_capV_myo⁢F$
Source
Derived from workspace Clancy, Rudy, 2001 at changeset 6b827a4ab6b6.
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