# Model Mathematics

### Component: cell

$i_Stim=-stim_amplitudeiftime-⌊timestim_period⌋⁢stim_period≥stim_start∧time-⌊timestim_period⌋⁢stim_period≦stim_start+stim_duration0otherwiseddtimeV=-i_Na+i_Nab+i_NaK+i_Kr+i_Ks+i_tos+i_tof+i_K1+i_NaCa+i_Cl_Ca+i_Clb+i_CaL+i_Cab+i_Cap+i_Kp+i_Stim$

### Component: model_parameters

$Vol_Cell=3.141592654⁢cell_radius10002⁢cell_length10003Vol_SR=0.035⁢Vol_CellVol_SL=0.02⁢Vol_CellVol_jct=0.0539⁢0.01⁢Vol_CellVol_myo=0.65⁢Vol_Cell$

### Component: reversal_potentials

$E_Na_jct=R⁢TF⁢ln⁡NaoNa_jctE_Na_SL=R⁢TF⁢ln⁡NaoNa_SLE_Ca_jct=R⁢T2⁢F⁢ln⁡CaoCa_jctE_Ca_SL=R⁢T2⁢F⁢ln⁡CaoCa_SLE_K=R⁢TF⁢ln⁡KoKiE_Cl=R⁢TF⁢ln⁡CliClo$

### Component: INa

$openProb=m3⁢h⁢ji_Na_jct=Fx_Na_jct⁢G_INa⁢openProb⁢V-E_Na_jcti_Na_SL=Fx_Na_SL⁢G_INa⁢openProb⁢V-E_Na_SLi_Na=i_Na_jct+i_Na_SL$

### Component: INa_h_gate

$alpha_h=0.135⁢ⅇ80+V-6.8ifV<-400otherwisebeta_h=3.56⁢ⅇ0.079⁢V+3.1 e 5⁢ⅇ0.35⁢VifV<-4010.13⁢1+ⅇV+10.66-11.1otherwiseddtimeh=alpha_h⁢1-h-beta_h⁢h$

### Component: INa_j_gate

$alpha_j=-1.2714 e 5⁢ⅇ0.2444⁢V-3.474 e -5⁢ⅇ-0.04391⁢V⁢V+37.7811+ⅇ0.311⁢V+79.23ifV<-400otherwisebeta_j=0.1212⁢ⅇ-0.01052⁢V1+ⅇ-0.1378⁢V+40.14ifV<-400.3⁢ⅇ-2.535 e -7⁢V1+ⅇ-0.1⁢V+32otherwiseddtimej=alpha_j⁢1-j-beta_j⁢j$

### Component: INa_m_gate

$alpha_m=0.32⁢V+47.1311-ⅇ-0.1⁢V+47.13beta_m=0.08⁢ⅇ-V11ddtimem=alpha_m⁢1-m-beta_m⁢m$

### Component: INab

$i_Nab_jct=Fx_NaBk_jct⁢G_NaBk⁢V-E_Na_jcti_Nab_SL=Fx_NaBk_SL⁢G_NaBk⁢V-E_Na_SLi_Nab=i_Nab_jct+i_Nab_SL$

### Component: INaK

$sigma=ⅇNao67.3-17f_NaK=11+0.1245⁢ⅇ-0.1⁢V⁢FR⁢T+0.0365⁢sigma⁢ⅇ-V⁢FR⁢Ti_NaK_jct=Fx_NaK_jct⁢I_NaK_max⁢f_NaK1+Km_NaiNa_jctH_NaK⁢KoKo+Km_Koi_NaK_SL=Fx_NaK_SL⁢I_NaK_max⁢f_NaK1+Km_NaiNa_SLH_NaK⁢KoKo+Km_Koi_NaK=i_NaK_jct+i_NaK_SL$

### Component: IKr

$G_IKr=0.03⁢Ko5.4i_Kr=G_IKr⁢Xr⁢Rr⁢V-E_K$

### Component: IKr_Xr_gate

$ddtimeXr=Xr_infinity-Xrtau_XrXr_infinity=11+ⅇ-50+V7.5tau_Xr=10.00138⁢V+71-ⅇ-0.123⁢V+7+0.00061⁢V+10ⅇ0.145⁢V+10-1$

### Component: IKr_Rr_gate

$Rr=11+ⅇ33+V22.4$

### Component: IKs

$pCa_jct=-log10⁡Ca_jct1+3pCa_SL=-log10⁡Ca_SL1+3G_Ks_jct=0.07⁢0.057+0.191+ⅇ-7.2+pCa_jct0.6G_Ks_SL=0.07⁢0.057+0.191+ⅇ-7.2+pCa_SL0.6E_Ks=R⁢TF⁢ln⁡Ko+pKNa⁢NaoKi+pKNa⁢Naii_Ks_jct=Fx_Ks_jct⁢G_Ks_jct⁢Xs2⁢V-E_Ksi_Ks_SL=Fx_Ks_SL⁢G_Ks_SL⁢Xs2⁢V-E_Ksi_Ks=i_Ks_jct+i_Ks_SL$

### Component: IKs_Xs_gate

$ddtimeXs=Xs_infinity-Xstau_XsXs_infinity=11+ⅇ-V-1.516.7tau_Xs=17.19 e -5⁢V+301-ⅇ-0.148⁢V+30+1.31 e -4⁢V+30-1+ⅇ0.0687⁢V+30$

### Component: IKp

$i_Kp=g_Kp⁢V-E_K1+ⅇ7.488-V5.98$

### Component: Itos

$i_tos=G_tos⁢X_tos⁢Y_tos+0.5⁢R_tos⁢V-E_K$

### Component: Itos_X_gate

$ddtimeX_tos=X_tos_infinity-X_tostau_X_tosX_tos_infinity=11+ⅇ-V+315tau_X_tos=91+ⅇV+315+0.5$

### Component: Itos_Y_gate

$ddtimeY_tos=Y_tos_infinity-Y_tostau_Y_tosY_tos_infinity=11+ⅇV+33.510tau_Y_tos=30001+ⅇV+6010+30$

### Component: Itos_R_gate

$R_tos_infinity=11+ⅇV+33.510tau_R_tos=2.8 e 31+ⅇV+6010+220ddtimeR_tos=R_tos_infinity-R_tostau_R_tos$

### Component: Itof

$i_tof=G_tof⁢X_tof⁢Y_tof⁢V-E_K$

### Component: Itof_X_gate

$ddtimeX_tof=X_tof_infinity-X_toftau_X_tofX_tof_infinity=11+ⅇ-V+315tau_X_tof=3.5⁢ⅇ-V302+1.5$

### Component: Itof_Y_gate

$ddtimeY_tof=Y_tof_infinity-Y_toftau_Y_tofY_tof_infinity=11+ⅇV+33.510tau_Y_tof=201+ⅇV+33.510+20$

### Component: IK1

$G_K1=0.9⁢Ko5.4i_K1=G_K1⁢K1_infinity⁢V-E_K$

### Component: IK1_K1_gate

$K1_infinity=alpha_K1alpha_K1+beta_K1alpha_K1=1.021+ⅇ0.2385⁢V-E_K+59.215beta_K1=0.49124⁢ⅇ0.08032⁢V-E_K+5.476+1⁢ⅇ0.06175⁢V-E_K+594.311+ⅇ-0.5143⁢V-E_K+4.753$

### Component: ICl_Ca

$i_Cl_Ca=G_Cl⁢V-E_Cl⁢Fx_Cl_jct1+Kd_ClCaCa_jct+Fx_Cl_SL1+Kd_ClCaCa_SL$

### Component: IClb

$i_Clb=G_ClBk⁢V-E_Cl$

### Component: ICaL

$Q_CaL=Q10_CaLT-31010temp=0.45⁢d⁢f⁢Q_CaL⁢V⁢F2R⁢Ti_CaL_Ca_jct=temp⁢fCa_jct⁢Fx_ICaL_jct⁢PCa⁢4⁢gamma_Cai⁢Ca_jct⁢ⅇ2⁢V⁢FR⁢T-gamma_Cao⁢Caoⅇ2⁢V⁢FR⁢T-1i_CaL_Na_jct=temp⁢fCa_jct⁢Fx_ICaL_jct⁢PNa⁢gamma_Nai⁢Na_jct⁢ⅇV⁢FR⁢T-gamma_Nao⁢NaoⅇV⁢FR⁢T-1i_CaL_Ca_SL=temp⁢fCa_SL⁢Fx_ICaL_SL⁢PCa⁢4⁢gamma_Cai⁢Ca_SL⁢ⅇ2⁢V⁢FR⁢T-gamma_Cao⁢Caoⅇ2⁢V⁢FR⁢T-1i_CaL_Na_SL=temp⁢fCa_SL⁢Fx_ICaL_SL⁢PNa⁢gamma_Nai⁢Na_SL⁢ⅇV⁢FR⁢T-gamma_Nao⁢NaoⅇV⁢FR⁢T-1i_CaL_K=temp⁢fCa_SL⁢Fx_ICaL_SL+fCa_jct⁢Fx_ICaL_jct⁢PK⁢gamma_Ki⁢Ki⁢ⅇV⁢FR⁢T-gamma_Ko⁢KoⅇV⁢FR⁢T-1i_CaL=i_CaL_Ca_SL+i_CaL_Ca_jct+i_CaL_Na_SL+i_CaL_Na_jct+i_CaL_K$

### Component: ICaL_d_gate

$d_infinity=11+ⅇ-V+14.56tau_d=1⁢d_infinity⁢1-ⅇ-V+14.560.035⁢V+14.5ddtimed=d_infinity-dtau_d$

### Component: ICaL_f_gate

$f_infinity=11+ⅇV+35.063.6+0.61+ⅇ50-V20tau_f=10.0197⁢ⅇ-0.0337⁢V+14.52+0.02ddtimef=f_infinity-ftau_f$

### Component: ICaL_fCa_gate

$fCa_SL=1-fCaB_SLfCa_jct=1-fCaB_jctddtimefCaB_SL=1.7⁢Ca_SL⁢1-fCaB_SL-11.9 e -3⁢fCaB_SLddtimefCaB_jct=1.7⁢Ca_jct⁢1-fCaB_jct-11.9 e -3⁢fCaB_jct$

### Component: INaCa

$temp_jct=ⅇeta⁢V⁢FR⁢T⁢Na_jctHNa⁢Cao-ⅇeta-1⁢V⁢FR⁢T⁢NaoHNa⁢Ca_jct1+ksat⁢ⅇeta-1⁢V⁢FR⁢Ttemp_SL=ⅇeta⁢V⁢FR⁢T⁢Na_SLHNa⁢Cao-ⅇeta-1⁢V⁢FR⁢T⁢NaoHNa⁢Ca_SL1+ksat⁢ⅇeta-1⁢V⁢FR⁢TQ_NCX=Q10_NCXT-31010Ka_SL=11+Kd_actCa_SL3Ka_jct=11+Kd_actCa_jct3i_NaCa_jct=Fx_NCX_jct⁢V_max⁢Ka_jct⁢Q_NCX⁢temp_jctK_mCai⁢NaoHNa⁢1+Na_jctK_mNaiHNa+K_mNaoHNa⁢Ca_jct⁢1+Ca_jctK_mCai+K_mCao⁢Na_jctHNa+Na_jctHNa⁢Cao+NaoHNa⁢Ca_jcti_NaCa_SL=Fx_NCX_SL⁢V_max⁢Ka_SL⁢Q_NCX⁢temp_SLK_mCai⁢NaoHNa⁢1+Na_SLK_mNaiHNa+K_mNaoHNa⁢Ca_SL⁢1+Ca_SLK_mCai+K_mCao⁢Na_SLHNa+Na_SLHNa⁢Cao+NaoHNa⁢Ca_SLi_NaCa=i_NaCa_jct+i_NaCa_SL$

### Component: ICap

$Q_SLCaP=Q10_SLCaPT-31010i_Cap_jct=Q_SLCaP⁢V_maxAF⁢Fx_SLCaP_jct1+KmCa_jctHi_Cap_SL=Q_SLCaP⁢V_maxAF⁢Fx_SLCaP_SL1+KmCa_SLHi_Cap=i_Cap_jct+i_Cap_SL$

### Component: ICab

$i_Cab_jct=G_CaBk⁢Fx_CaBk_jct⁢V-E_Ca_jcti_Cab_SL=G_CaBk⁢Fx_CaBk_SL⁢V-E_Ca_SLi_Cab=i_Cab_SL+i_Cab_jct$

### Component: Jrel_SR

$kCaSR=Max_SR-Max_SR-Min_SR1+EC50_SRCa_SRHSRkoSRCa=koCakCaSRkiSRCa=kiCa⁢kCaSRRI=1-R-O-IddtimeR=kim⁢RI-kiSRCa⁢Ca_jct⁢R-koSRCa⁢Ca_jct2⁢R-kom⁢OddtimeO=koSRCa⁢Ca_jct2⁢R-kom⁢O-kiSRCa⁢Ca_jct⁢O-kim⁢IddtimeI=kiSRCa⁢Ca_jct⁢O-kim⁢I-kom⁢I-koSRCa⁢Ca_jct2⁢RIj_rel_SR=ks⁢O⁢Ca_SR-Ca_jct$

### Component: Jleak_SR

$j_leak_SR=KSRleak⁢Ca_SR-Ca_jct$

### Component: Jpump_SR

$Q_SRCaP=Q10_SRCaPT-31010j_pump_SR=Q_SRCaP⁢V_max⁢CaiKmfH-Ca_SRKmrH1+CaiKmfH+Ca_SRKmrH$

### Component: ion_diffusion

$J_Na_jct_SL=Na_jct-Na_SL⁢1.8313 e -14J_Na_SL_myo=Na_SL-Nai⁢1.6386 e -12J_Ca_jct_SL=Ca_jct-Ca_SL⁢8.2413 e -13J_Ca_SL_myo=Ca_SL-Cai⁢3.7243 e -12$

### Component: Na_buffer

$dNa_jct_buf=kon⁢Na_jct⁢Bmax_jct-Na_jct_buf-koff⁢Na_jct_bufdNa_SL_buf=kon⁢Na_SL⁢Bmax_SL-Na_SL_buf-koff⁢Na_SL_bufddtimeNa_jct_buf=dNa_jct_bufddtimeNa_SL_buf=dNa_SL_bufddtimeNa_jct=-Cm⁢i_Na_jct+3⁢i_NaCa_jct+i_Nab_jct+3⁢i_NaK_jct+i_CaL_Na_jctVol_jct⁢F-J_Na_jct_SLVol_jct-dNa_jct_bufddtimeNa_SL=-Cm⁢i_Na_SL+3⁢i_NaCa_SL+i_Nab_SL+3⁢i_NaK_SL+i_CaL_Na_SLVol_SL⁢F+J_Na_jct_SL-J_Na_SL_myoVol_SL-dNa_SL_bufddtimeNai=J_Na_SL_myoVol_myo$

### Component: Ca_buffer

$dCalsequestrin=kon_Calsequestrin⁢Ca_SR⁢Bmax_Calsequestrin⁢Vol_myoVol_SR-Ca_Calsequestrin-koff_Calsequestrin⁢Ca_CalsequestrinddtimeCa_Calsequestrin=dCalsequestrindCa_SLB_SL=kon_SL⁢Ca_SL⁢Bmax_SLB_SL⁢Vol_myoVol_SL-Ca_SLB_SL-koff_SLB⁢Ca_SLB_SLdCa_SLB_jct=kon_SL⁢Ca_jct⁢Bmax_SLB_jct⁢0.1⁢Vol_myoVol_jct-Ca_SLB_jct-koff_SLB⁢Ca_SLB_jctdCa_SLHigh_SL=kon_SL⁢Ca_SL⁢Bmax_SLHigh_SL⁢Vol_myoVol_SL-Ca_SLHigh_SL-koff_SLHigh⁢Ca_SLHigh_SLdCa_SLHigh_jct=kon_SL⁢Ca_jct⁢Bmax_SLHigh_jct⁢0.1⁢Vol_myoVol_jct-Ca_SLHigh_jct-koff_SLHigh⁢Ca_SLHigh_jctddtimeCa_SLB_SL=dCa_SLB_SLddtimeCa_SLB_jct=dCa_SLB_jctddtimeCa_SLHigh_SL=dCa_SLHigh_SLddtimeCa_SLHigh_jct=dCa_SLHigh_jctdCa_jct_tot_bound=dCa_SLB_jct+dCa_SLHigh_jctdCa_SL_tot_bound=dCa_SLB_SL+dCa_SLHigh_SLi_Ca_jct_tot=i_CaL_Ca_jct-2⁢i_NaCa_jct+i_Cab_jct+i_Cap_jcti_Ca_SL_tot=i_CaL_Ca_SL-2⁢i_NaCa_SL+i_Cab_SL+i_Cap_SLddtimeCa_SR=j_pump_SR-j_leak_SR⁢Vol_myoVol_SR+j_rel_SR-dCalsequestrinddtimeCa_jct=-i_Ca_jct_tot⁢CmVol_jct⁢2⁢F-J_Ca_jct_SLVol_jct+j_rel_SR⁢Vol_SRVol_jct+j_leak_SR⁢Vol_myoVol_jct-1⁢dCa_jct_tot_boundddtimeCa_SL=-i_Ca_SL_tot⁢CmVol_SL⁢2⁢F+J_Ca_jct_SL-J_Ca_SL_myoVol_SL-1⁢dCa_SL_tot_boundddtimeCai=-j_pump_SR⁢Vol_SRVol_myo+J_Ca_SL_myoVol_myo-1⁢dCa_cytosol_tot_bound$

### Component: cytosolic_Ca_buffer

$dCa_TroponinC=kon_TroponinC⁢Cai⁢Bmax_TroponinC-Ca_TroponinC-koff_TroponinC⁢Ca_TroponinCdCa_TroponinC_Ca_Mg=kon_TroponinC_Ca_Mg_Ca⁢Cai⁢Bmax_TroponinC_Ca_Mg_Ca-Ca_TroponinC_Ca_Mg+Mg_TroponinC_Ca_Mg-koff_TroponinC_Ca_Mg_Ca⁢Ca_TroponinC_Ca_MgdMg_TroponinC_Ca_Mg=kon_TroponinC_Ca_Mg_Mg⁢Mgi⁢Bmax_TroponinC_Ca_Mg_Mg-Ca_TroponinC_Ca_Mg+Mg_TroponinC_Ca_Mg-koff_TroponinC_Ca_Mg_Mg⁢Mg_TroponinC_Ca_MgdCa_Calmodulin=kon_Calmodulin⁢Cai⁢Bmax_Calmodulin-Ca_Calmodulin-koff_Calmodulin⁢Ca_CalmodulindCa_Myosin=kon_Myosin_Ca⁢Cai⁢Bmax_Myosin_Ca-Ca_Myosin+Mg_Myosin-koff_Myosin_Ca⁢Ca_MyosindMg_Myosin=kon_Myosin_Mg⁢Mgi⁢Bmax_Myosin_Mg-Ca_Myosin+Mg_Myosin-koff_Myosin_Mg⁢Mg_MyosindCa_SRB=kon_SRB⁢Cai⁢Bmax_SRB-Ca_SRB-koff_SRB⁢Ca_SRBdCa_cytosol_tot_bound=dCa_TroponinC+dCa_TroponinC_Ca_Mg+dMg_TroponinC_Ca_Mg+dCa_Calmodulin+dCa_Myosin+dMg_Myosin+dCa_SRBddtimeCa_TroponinC=dCa_TroponinCddtimeCa_TroponinC_Ca_Mg=dCa_TroponinC_Ca_MgddtimeMg_TroponinC_Ca_Mg=dMg_TroponinC_Ca_MgddtimeCa_Calmodulin=dCa_CalmodulinddtimeCa_Myosin=dCa_MyosinddtimeMg_Myosin=dMg_MyosinddtimeCa_SRB=dCa_SRB$

### Component: intracellular_currents

Source
Derived from workspace Shannon, Wang, Puglisi, Weber, Bers, 2004 at changeset bb85ada8052b.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.