Model Mathematics

Component: environment

Component: membrane

V_cell=πRadius_cell2Length_cell V_myo=0.65V_cell V_sr=0.035V_cell V_sl=0.02V_cell V_junc=5.39 e -4V_cell FoRT=FrdyRT F_sl=1-F_junc F_sl_Ca_L=1-F_junc_Ca_L I_Stim=I_Stim_AmplitudeiftI_Stim_StarttI_Stim_Endt-I_Stim_Start-t-I_Stim_StartI_Stim_PeriodI_Stim_PeriodI_Stim_PulseDuration0otherwise I_Na_tot=I_Na_tot_junc+I_Na_tot_sl I_Cl_tot=I_ClCa+I_Cl_Bk I_Ca_tot=I_Ca_tot_junc+I_Ca_tot_sl I_tot=I_Na_tot+I_Cl_tot+I_Ca_tot+I_K_tot ddtV=-I_tot-I_Stim

Component: Fast_Na_Current

m_ss=11+-56.86+V9.032 tau_m=0.1292-V+45.7915.542+0.06487-V-4.82351.122 a_h=0ifV-400.057-V+806.8otherwise b_h=5.92311+-V+10.6611.1ifV-402.70.079V+3.1 e 50.3485Votherwise a_j=0ifV-40-2.5428 e 40.2444V-6.948 e -6-0.04391VV+37.781+0.311V+79.23otherwise b_j=0.60.057V1+-0.1V+32ifV-400.02424-0.01052V1+-0.1378V+40.14otherwise tau_h=1a_h+b_h h_ss=11+V+71.557.432 tau_j=1a_j+b_j j_ss=11+V+71.557.432 ddtm=m_ss-mtau_m ddth=h_ss-htau_h ddtj=j_ss-jtau_j I_Na_junc=F_juncG_Nam3hjV-E_Na_junc I_Na_sl=F_slG_Nam3hjV-E_Na_sl I_Na=I_Na_junc+I_Na_sl

Component: Background_Na_Current

I_Na_Bk_junc=F_juncG_Na_BV-E_Na_junc I_Na_Bk_sl=F_slG_Na_BV-E_Na_sl I_Na_Bk=I_Na_Bk_junc+I_Na_Bk_sl

Component: Na_K_Pump_Current

sigma=Na_o67.3-17 f_NaK=11+0.1245-0.1VFoRT+0.0365sigma-VFoRT I_NaK_junc=F_juncIbar_NaKf_NaKK_o1+Km_NaipNa_j4K_o+Km_Ko I_NaK_sl=F_slIbar_NaKf_NaKK_o1+Km_NaipNa_sl4K_o+Km_Ko I_NaK=I_NaK_junc+I_NaK_sl

Component: Rapidly_Activating_K_Current

x_r_ss=11+-V+105 tau_xr=33001+-22-V91+V+119+2301+V+4020 ddtx_Kr=x_r_ss-x_Krtau_xr r_Kr=11+V+7424 I_Kr=G_KrK_o5.4x_Krr_KrV-E_K

Component: Slowly_Activating_K_Current

x_s_ss=11+-V+3.814.25 tau_xs=990.11+-V+2.43614.12 ddtx_Ks=x_s_ss-x_Kstau_xs I_Ks_junc=F_juncG_Ks_juncx_Ks2V-E_Ks I_Ks_sl=F_slG_Ks_slx_Ks2V-E_Ks I_Ks=I_Ks_junc+I_Ks_sl

Component: Plateau_K_Current

kp_Kp=11+7.488-V5.98 I_Kp=G_Kpkp_KpV-E_K

Component: Transient_Outward_K_Current

x_to_ss=11+-V-1913 y_to_ss=11+V+19.55 tau_x_tos=91+V+315+0.5 tau_y_tos=8001+V+6010+30 ddtx_to_s=x_to_ss-x_to_stau_x_tos ddty_to_s=y_to_ss-y_to_stau_y_tos tau_x_tof=8.5-V+45502+0.5 tau_y_tof=85-V+402220+7 ddtx_to_f=x_to_ss-x_to_ftau_x_tof ddty_to_f=y_to_ss-y_to_ftau_y_tof I_to_s=G_to_sx_to_sy_to_sV-E_K I_to_f=G_to_fx_to_fy_to_fV-E_K I_to=I_to_s+I_to_f

Component: Inward_Rectifier_K_Current

a_K1=4.09381+0.12165V-E_K-49.9344 b_K1=15.71970.06739V-E_K-3.2571+0.06175V-E_K-594.311+-0.16285V-E_K+14.2067 K1_ss=a_K1a_K1+b_K1 I_K1=G_K1K_o5.4K1_ssV-E_K

Component: Ca_Activated_Cl_Current

I_ClCa_junc=F_juncG_ClCa1+Kd_ClCaCa_jV-E_Cl I_ClCa_sl=F_slG_ClCa1+Kd_ClCaCa_slV-E_Cl I_ClCa=I_ClCa_junc+I_ClCa_sl

Component: Background_Cl_Current

I_Cl_Bk=G_Cl_BV-E_Cl

Component: L_Type_Calcium_Current

d_ss=11+-V+56 alpha_d=1.41+-35-V13+0.25 beta_d=1.41+V+55 gamma_d=11+50-V20 tau_d=alpha_dbeta_d+gamma_d f_ss=11+V+207 alpha_f=1102.5-V+27152 beta_f=2001+13-V10 gamma_f=1801+V+3010+20 tau_f=alpha_f+beta_f+gamma_f f_2_ss=0.671+V+357+0.33 alpha_f_2=300-V+252170 beta_f_2=311+25-V10 gamma_f_2=161+V+3010 tau_f_2=alpha_f_2+beta_f_2+gamma_f_2 ddtd=d_ss-dtau_d ddtf=f_ss-ftau_f ddtf_2=f_2_ss-f_2tau_f_2 ddtf_Ca_B_j=1.7Ca_j1-f_Ca_B_j-11.9 e -3f_Ca_B_j ddtf_Ca_B_sl=1.7Ca_sl1-f_Ca_B_sl-11.9 e -3f_Ca_B_sl Ibar_Ca_j=p_CaVFrdyFoRTCa_j2VFoRT-Ca_o2VFoRT-1 Ibar_Ca_sl=p_CaVFrdyFoRTCa_sl2VFoRT-Ca_o2VFoRT-1 Ibar_K=p_KVFrdyFoRTK_iVFoRT-K_oVFoRT-1 Ibar_Na_j=p_NaVFrdyFoRTNa_jVFoRT-Na_oVFoRT-1 Ibar_Na_sl=p_NaVFrdyFoRTNa_slVFoRT-Na_oVFoRT-1 I_Ca_junc=F_junc_Ca_LIbar_Ca_jdff_21-f_Ca_B_j I_Ca_sl=F_sl_Ca_LIbar_Ca_sldff_21-f_Ca_B_sl I_Ca=I_Ca_junc+I_Ca_sl I_Ca_K=Ibar_Kdff_2F_junc_Ca_L1-f_Ca_B_j+F_sl_Ca_L1-f_Ca_B_sl I_Ca_Na_junc=F_junc_Ca_LIbar_Na_jdff_21-f_Ca_B_j I_Ca_Na_sl=F_sl_Ca_LIbar_Na_sldff_21-f_Ca_B_sl I_Ca_Na=I_Ca_Na_junc+I_Ca_Na_sl I_Ca_L=I_Ca+I_Ca_K+I_Ca_Na

Component: Na_Ca_Exchanger_Current

Ka_junc=11+Kd_actCa_j2 Ka_sl=11+Kd_actCa_sl2 s1_junc=nuVFoRTNa_j3Ca_o s1_sl=nuVFoRTNa_sl3Ca_o s2_junc=nu-1VFoRTNa_o3Ca_j s2_sl=nu-1VFoRTNa_o3Ca_sl s3_junc=Km_Ca_iNa_o31+Na_jKm_Na_i3+Km_Na_o3Ca_j1+Ca_jKm_Ca_i+Km_Ca_oNa_j3+Na_j3Ca_o+Na_o3Ca_j s3_sl=Km_Ca_iNa_o31+Na_slKm_Na_i3+Km_Na_o3Ca_sl1+Ca_slKm_Ca_i+Km_Ca_oNa_sl3+Na_sl3Ca_o+Na_o3Ca_sl I_ncx_junc=F_juncIbar_NCXKa_juncs1_junc-s2_juncs3_junc1+k_satnu-1VFoRT I_ncx_sl=F_slIbar_NCXKa_sls1_sl-s2_sls3_sl1+k_satnu-1VFoRT I_ncx=I_ncx_junc+I_ncx_sl

Component: Sarcolemmal_Ca_Pump_Current

I_pCa_junc=F_juncIbar_PMCACa_j1.6Km_P_Ca1.6+Ca_j1.6 I_pCa_sl=F_slIbar_PMCACa_sl1.6Km_P_Ca1.6+Ca_sl1.6 I_pCa=I_pCa_junc+I_pCa_sl

Component: Background_Ca_Current

I_Ca_Bk_junc=F_juncG_Ca_BV-E_Ca_junc I_Ca_Bk_sl=F_slG_Ca_BV-E_Ca_sl I_Ca_Bk=I_Ca_Bk_junc+I_Ca_Bk_sl

Component: SR_Fluxes

k_Ca_SR=Max_SR-Max_SR-Min_SR1+ec50_SRCa_SR2.5 ko_SR_Ca=ko_Cak_Ca_SR ki_SR_Ca=ki_Cak_Ca_SR RI=1-Ry_Rr-Ry_Ro-Ry_Ri ddtRy_Rr=ki_mRI-ki_SR_CaCa_jRy_Rr-ko_SR_CaCa_j2Ry_Rr-ko_mRy_Ro ddtRy_Ro=ko_SR_CaCa_j2Ry_Rr-ko_mRy_Ro-ki_SR_CaCa_jRy_Ro-ki_mRy_Ri ddtRy_Ri=ki_SR_CaCa_jRy_Ro-ki_mRy_Ri-ko_mRy_Ri-ko_SR_CaCa_j2RI J_SR_Ca_rel=ksRy_RoCa_SR-Ca_j J_ser_Ca=V_max_SR_CaPCa_iKm_fhill_SR_CaP-Ca_SRKm_rhill_SR_CaP1+Ca_iKm_fhill_SR_CaP+Ca_SRKm_rhill_SR_CaP J_SR_leak=5.348 e -6Ca_SR-Ca_j

Component: Cytosolic_Ca_Buffers

ddtTnC_l=k_on_TnC_lCa_iB_max_TnC_low-TnC_l-k_off_TnC_lTnC_l ddtTnC_h_c=k_on_TnC_h_CaCa_iB_max_TnC_high-TnC_h_c-TnC_h_m-k_off_TnC_h_CaTnC_h_c ddtTnC_h_m=k_on_TnC_h_MgMg_iB_max_TnC_high-TnC_h_c-TnC_h_m-k_off_TnC_h_MgTnC_h_m ddtCaM=k_on_CaMCa_iB_max_CaM-CaM-k_off_CaMCaM ddtMyo_c=k_on_myo_CaCa_iB_max_myosin-Myo_c-Myo_m-k_off_myo_CaMyo_c ddtMyo_m=k_on_myo_MgMg_iB_max_myosin-Myo_c-Myo_m-k_off_myo_MgMyo_m ddtSRB=k_on_SRCa_iB_max_SR-SRB-k_off_SRSRB J_Ca_B_cytosol=ddtTnC_l+ddtTnC_h_c+ddtTnC_h_m+ddtCaM+ddtMyo_c+ddtMyo_m+ddtSRB

Component: Junctional_and_SL_Ca_Buffers

B_max_SL_low_sl=37.4 e -3V_myoV_sl B_max_SL_low_j=4.6 e -4V_myoV_junc B_max_SL_high_sl=13.4 e -3V_myoV_sl B_max_SL_high_j=1.65 e -4V_myoV_junc ddtSLL_j=k_on_sl_lCa_jB_max_SL_low_j-SLL_j-k_off_sl_lSLL_j ddtSLL_sl=k_on_sl_lCa_slB_max_SL_low_sl-SLL_sl-k_off_sl_lSLL_sl ddtSLH_j=k_on_sl_hCa_jB_max_SL_high_j-SLH_j-k_off_sl_hSLH_j ddtSLH_sl=k_on_sl_hCa_slB_max_SL_high_sl-SLH_sl-k_off_sl_hSLH_sl J_Ca_B_junction=ddtSLL_j+ddtSLH_j J_Ca_B_sl=ddtSLL_sl+ddtSLH_sl

Component: Sodium_Concentrations

I_Na_tot_junc=I_Na_junc+I_Na_Bk_junc+3I_ncx_junc+3I_NaK_junc+I_Ca_Na_junc I_Na_tot_sl=I_Na_sl+I_Na_Bk_sl+3I_ncx_sl+3I_NaK_sl+I_Ca_Na_sl ddtNa_j=-I_Na_tot_juncC_memV_juncFrdy+J_Na_juncslV_juncNa_sl-Na_j-ddtNa_B_j ddtNa_sl=-I_Na_tot_slC_memV_slFrdy+J_Na_juncslV_slNa_j-Na_sl+J_Na_slmyoV_slNa_i-Na_sl-ddtNa_B_sl ddtNa_i=J_Na_slmyoV_myoNa_sl-Na_i ddtNa_B_j=k_on_NaNa_jB_max_Na_j-Na_B_j-k_off_NaNa_B_j ddtNa_B_sl=k_on_NaNa_slB_max_Na_sl-Na_B_sl-k_off_NaNa_B_sl

Component: Potassium_Concentrations

I_K_tot=I_to+I_Kr+I_Ks+I_K1-2I_NaK+I_Ca_K+I_Kp

Component: Calcium_Concentrations

I_Ca_tot_junc=I_Ca_junc+I_Ca_Bk_junc+I_pCa_junc-2I_ncx_junc I_Ca_tot_sl=I_Ca_sl+I_Ca_Bk_sl+I_pCa_sl-2I_ncx_sl B_max_csqn=140 e -3V_myoV_sr ddtCsqn_b=k_on_csqnCa_SRB_max_csqn-Csqn_b-k_off_csqnCsqn_b ddtCa_j=-I_Ca_tot_juncC_memV_junc2Frdy+J_Ca_juncslV_juncCa_sl-Ca_j-J_Ca_B_junction+J_SR_Ca_relV_srV_junc+J_SR_leakV_myoV_junc ddtCa_sl=-I_Ca_tot_slC_memV_sl2Frdy+J_Ca_juncslV_slCa_j-Ca_sl+J_Ca_slmyoV_slCa_i-Ca_sl-J_Ca_B_sl ddtCa_i=-J_ser_CaV_srV_myo-J_Ca_B_cytosol+J_Ca_slmyoV_myoCa_sl-Ca_i ddtCa_SR=J_ser_Ca-J_SR_leakV_myoV_sr+J_SR_Ca_rel-ddtCsqn_b

Component: Magnesium_Concentrations

Component: Chlorine_Concentrations

Component: Nerst_Potentials

E_Na_junc=1FoRTlnNa_oNa_j E_Na_sl=1FoRTlnNa_oNa_sl E_Ks=1FoRTlnK_o+p_Na_KNa_oK_i+p_Na_KNa_i E_K=1FoRTlnK_oK_i E_Ca_junc=12FoRTlnCa_oCa_j E_Ca_sl=12FoRTlnCa_oCa_sl E_Cl=1FoRTlnCl_iCl_o