Model Mathematics

Component: environment

Component: membrane

ddtimeVm=-i_totCm i_tot=i_Na+i_Ca_L+i_Ca_T+i_K1+i_Kr+i_I+i_NaK+i_NaCa+i_st+i_ha+i_KACh i_I=i_bNSC+i_Cab+i_Kpl+i_lCa+i_KATP

Component: external_ion_concentrations

Component: internal_ion_concentrations

b1=CMDN_max-Ca_Total+K_mCMDN c1=K_mCMDNCa_Total Cai=b12+4c1-b12 ddtimeNai=-i_net_NaFVi ddtimeKi=-i_net_KFVi ddtimeCa_Total=-i_net_Ca-i_SR_U-i_RyR-i_SR_L2FVi+dCaidt_NL i_net_Na=i_Na_Na+i_CaL_Na+i_st_Na+i_ha_Na+i_bNSC_Na+i_lCa_Na+3i_NaK+3i_NaCa i_net_K=i_K1+i_Kr+i_KATP+i_KACh+i_Na_K+i_CaL_K+i_st_K+i_ha_K+i_bNSC_K+i_lCa_K+i_Kpl-2i_NaK i_net_Ca=i_CaL_Ca+i_Ca_T+i_Cab-2i_NaCa

Component: constant_field_equations

CF_Na=-NaoifVm=0FVmRTNai-Nao-FVmRT1--FVmRTotherwise CF_Ca=-CaoifVm=02FVmRTCai-Cao-2FVmRT1--2FVmRTotherwise CF_K=KiifVm=0FVmRTKi-Ko-FVmRT1--FVmRTotherwise

Component: ATP_production

ddtimeATPi=ProducingRate_MaxAdenosine_Total-ATPi+dATPdt_NL-i_NaKFVi+i_SR_U4FVi

Component: sodium_current

i_Na=i_Na_Na+i_Na_K i_Na_Na=P_NaCF_Nap_AP_Nay i_Na_K=0.1P_NaCF_Kp_AP_Nay

Component: sodium_current_voltage_dependent_gate

ddtimep_RP_Na=p_AP_Nak_AP_RP+p_RI_Nak_RI_RP-p_RP_Nak_RP_RI+k_RP_AP ddtimep_AP_Na=p_RP_Nak_RP_AP+p_AI_Nak_AI_AP-p_AP_Nak_AP_RP+k_AP_AI ddtimep_AI_Na=p_RI_Nak_RI_AI+p_AP_Nak_AP_AI-p_AI_Nak_AI_RI+k_AI_AP p_RI_Na=1-p_RP_Na-p_AP_Na-p_AI_Na k_RP_AP=10.1027-Vm8+0.25-Vm50 k_AP_RP=126Vm17+0.02Vm800 k_AP_AI=10.8-Vm400 k_AI_RI=11300Vm20+0.04Vm800 k_RI_AI=10.0001027-Vm8+5-Vm400 k_RP_RI=0.011+k_AI_APk_AP_RPk_RI_AIk_AP_AIk_RP_APk_AI_RI k_RI_RP=0.01-k_RP_RI

Component: sodium_current_ultra_slow_gate

alpha_y=19000000000Vm5+8000Vm100 beta_y=10.014-Vm5+4000-Vm100 ddtimey=alpha_y1-y-beta_yy

Component: L_type_Ca_channel

i_Ca_L=i_CaL_Na+i_CaL_Ca+i_CaL_K i_CaL_Ca=P_CaLCF_Cap_open_CaL i_CaL_Na=0.0000185P_CaLCF_Nap_open_CaL i_CaL_K=0.000365P_CaLCF_Kp_open_CaL p_open_CaL=p_AP_CaLp_U+p_UCay1+1.4ATPi3

Component: L_type_Ca_channel_voltage_dependent_gate

ddtimep_RP_CaL=p_AP_CaLk_AP_RP+p_RI_CaLk_RI_RP-p_RP_CaLk_RP_RI+k_RP_AP ddtimep_AP_CaL=p_RP_CaLk_RP_AP+p_AI_CaLk_AI_AP-p_AP_CaLk_AP_RP+k_AP_AI ddtimep_AI_CaL=p_RI_CaLk_RI_AI+p_AP_CaLk_AP_AI-p_AI_CaLk_AI_RI+k_AI_AP p_RI_CaL=1-p_AP_CaL-p_RP_CaL-p_AI_CaL k_RP_AP=10.27-Vm5.9+1.5-Vm65 k_AP_RP=1480Vm7+2.2Vm65 k_RI_AI=10.0018-Vm7.4+2-Vm100 k_AI_RI=12200000Vm7.4+11Vm100 k_RP_RI=0.041+k_AI_APk_AP_RPk_RI_AIk_AP_AIk_RP_APk_AI_RI k_RI_RP=0.04-k_RP_RI

Component: L_type_Ca_channel_Ca_dependent_gate

iCaL=0.0676CF_Ca CaDiadic=iCaLp_open_CaL Cacm=Cai-0.3iCaL CaEffC=Cacmp_AP_CaL CaEffU=CaEffC+Cai1-p_AP_CaL k_UUCa_Ca=k_U_UCaCaEffU k_CCCa_Ca=k_C_CCaCaEffC ddtimep_U=p_Ck_C_U+p_UCak_UCa_U-p_Uk_UUCa_Ca+k_U_C ddtimep_UCa=p_Uk_UUCa_Ca+p_CCak_CCa_UCa-p_UCak_UCa_CCa+k_UCa_U ddtimep_C=p_CCak_CCa_C+p_Uk_U_C-p_Ck_C_U+k_C_CCaCacmp_AP_CaL p_CCa=1-p_C-p_U-p_UCa k_UCa_U=k_CCa_Ck_C_Uk_U_UCak_UCa_CCak_U_Ck_C_CCak_CCa_UCa

Component: L_type_Ca_channel_ultra_slow_gate

alpha_y=1250000Vm9+58Vm65 beta_y=11800-Vm14+66-Vm65 ddtimey=alpha_y1-y-beta_yy

Component: T_type_Ca_channel

i_Ca_T=P_CaTCF_Cay1y2

Component: T_type_Ca_channel_y1_gate

alpha_y1=10.019-Vm5.6+0.82-Vm250 beta_y1=140Vm6.3+1.5Vm10000 ddtimey1=alpha_y11-y1-beta_y1y1

Component: T_type_Ca_channel_y2_gate

alpha_y2=162000Vm10.1+30Vm3000 beta_y2=10.0006-Vm6.7+1.2-Vm25 ddtimey2=alpha_y21-y2-beta_y2y2

Component: st_channel

i_st=i_st_Na+i_st_K i_st_Na=P_st_NaCF_Nay1y2y3 i_st_K=P_st_KCF_Ky1y2y3

Component: st_channel_y1_gate

alpha_y1=10.15-Vm11+0.2-Vm700 beta_y1=116Vm8+15Vm50 ddtimey1=alpha_y11-y1-beta_y1y1

Component: st_channel_y2_gate

alpha_y2=13100Vm13+700Vm70 beta_y2=195-Vm10+50-Vm700+Cai2.51+-Vm5 ddtimey2=alpha_y21-y2-beta_y2y2

Component: st_channel_y3_gate

alpha_y3=1400000Vm9+60Vm65 beta_y3=1700-Vm14+60-Vm65 ddtimey3=alpha_y31-y3-beta_y3y3

Component: ha_channel

i_ha=i_ha_Na+i_ha_K i_ha_Na=P_ha_NaCF_Na1-C1-C2 i_ha_K=P_ha_KCF_K1-C1-C2

Component: ha_channel_voltage_dependent_gate

ddtimeO1=alphaC2+betaO2-alpha+betaO1 ddtimeO2=alphaO1+betaO3-alpha+betaO2 ddtimeC1=lambdaC2-muC1 ddtimeC2=muC1+betaO1-alpha+lambdaC2 O3=1-C1-C2-O1-O2 alpha=13500Vm16.8+0.3Vm400 beta=14-Vm14+2-Vm400 mu=145000000Vm8+500Vm200 lambda=110.5-Vm16.4+0.4-Vm400

Component: time_independent_potassium_current

i_K1=g_K1Vm-E_KfO4+fO3+fO2y E_K=RTFlnKoKi g_K1=P_K1_0CmKo5.40.4 fB=mumu+lambda fO=lambdamu+lambda fO2=2fO2fB2 fO3=83fO3fB fO4=fO4 mu=0.750.035Vm-E_K-101+0.015Vm-E_K-140 lambda=3-0.048Vm-E_K-101+0.064Vm-E_K-381+0.03Vm-E_K-70

Component: time_independent_potassium_current_y_gate

alpha_y=18000Vm-E_K-978.5+7Vm-E_K-97300 beta_y=fO410.00014-Vm-E_K-979.1+0.2-Vm-E_K-97500 ddtimey=alpha_y1-y-beta_yy

Component: rapid_time_dependent_potassium_current

i_Kr=g_KrVm-E_K0.6y1+0.4y2y3 g_Kr=P_KrCmKo5.40.2

Component: rapid_time_dependent_potassium_current_y1_gate

alpha_y1=120-Vm11.5+5-Vm300 beta_y1=1160Vm28+200Vm1000+12500Vm20 ddtimey1=alpha_y11-y1-beta_y1y1

Component: rapid_time_dependent_potassium_current_y2_gate

alpha_y2=1200-Vm13+20-Vm300 beta_y2=11600Vm28+2000Vm1000+110000Vm20 ddtimey2=alpha_y21-y2-beta_y2y2

Component: rapid_time_dependent_potassium_current_y3_gate

alpha_y3=110Vm17+2.5Vm300 beta_y3=10.35-Vm17+2-Vm150 ddtimey3=alpha_y31-y3-beta_y3y3

Component: ACh_dependent_potassium_current

i_KACh=g_AChVm-E_K1+Vm+2020y

Component: ACh_dependent_potassium_current_y_gate

alpha_y=0.0002475ifACh=00.012321+Km_AChACh+0.0002475otherwise beta_y=0.010.0133Vm+40 ddtimey=alpha_y1-y-beta_yy

Component: background_NSC_current

i_bNSC=i_bNSC_K+i_bNSC_Na i_bNSC_K=0.4P_bNSCCF_K i_bNSC_Na=P_bNSCCF_Na

Component: background_Kpl_current

i_Kpl=P_KplCF_K13.0077ifVm=-3P_KplCF_KVm+31--Vm+313otherwise P_Kpl=0.007Ko5.40.16

Component: background_lCa_current

i_lCa=i_lCa_K+i_lCa_Na i_lCa_K=P_lCaCF_Kp_open i_lCa_Na=P_lCaCF_Nap_open p_open=11+0.0012Cai3

Component: background_KATP_current

i_KATP=gammaVm-E_Kp_open gamma=P_KATPNKo10.24 p_open=0.81+ATPi0.12

Component: background_Cab_current

i_Cab=P_CabCF_Ca

Component: sodium_calcium_exchanger

i_NaCa=P_NaCaCm1k1p_E1Nay-k2p_E2Na1-y p_E1Na=11+Km_NaiNai31+CaiKm_Cai p_E2Na=11+Km_NaoNao31+CaoKm_Cao p_E1Ca=11+Km_CaiCai1+NaiKm_Nai3 p_E2Ca=11+Km_CaoCao1+NaoKm_Nao3 k1=1PartitionFVmRT k2=1Partition-1FVmRT

Component: sodium_calcium_exchanger_y_gate

alpha_y=k2p_E2Na+k4p_E2Ca beta_y=k1p_E1Na+k3p_E1Ca ddtimey=alpha_y1-y-beta_yy

Component: sodium_potassium_pump

i_NaK=P_NaKCm1k1p_E1Nay-k2p_E2Na1-y p_E1Na=11+Km_NaiNai1.061+KiKm_Ki1.12 p_E2Na=11+Km_NaoNao_Eff1.061+KoKm_Ko1.12 p_E1K=11+Km_KiKi1.121+NaiKm_Nai1.06 p_E2K=11+Km_KoKo1.121+Nao_EffKm_Nao1.06 k1=0.371+Km_ATPATPi Nao_Eff=Nao-0.82FVmRT

Component: sodium_potassium_pump_y_gate

alpha_y=k2p_E2Na+k4p_E2K beta_y=k1p_E1Na+k3p_E1K ddtimey=alpha_y1-y-beta_yy

Component: SR_calcium_pump

i_SR_U=i_max1k1p_E1Cay-k2p_E2Ca1-y p_E1Ca=11+Km_CaSRCaup p_E2Ca=11+Km_CaCytoCai p_E1=1-p_E1Ca p_E2=1-p_E2Ca k2=11+Km_ATPATPi

Component: SR_calcium_pump_y_gate

alpha_y=k2p_E2Ca+k4p_E2 beta_y=k1p_E1Ca+k3p_E1 ddtimey=alpha_y1-y-beta_yy

Component: RyR_channel

i_RyR=P_RyRCarel-Caip_open_RyR ddtimep_open_RyR=p_close_RyRk1-p_open_RyRk2 ddtimep_close_RyR=k31-p_open_RyR+p_close_RyR-k1+k4p_close_RyR k1=280000Cai12+Diadid_FactorCaDiadic k2=0.081+0.36Carel k3=0.000377Carel12

Component: SR_T_current

i_SR_T=P_SR_TCaup-Carel

Component: SR_L_current

i_SR_L=P_SR_LCaup-Cai

Component: Ca_concentrations_in_SR

b1=CSQN_max-Ca_Total+K_mCSQN c1=K_mCSQNCa_Total Carel=b12+4c1-b12 ddtimeCa_Total=i_SR_T-i_RyR2FV_rel ddtimeCaup=-i_SR_U-i_SR_T-i_SR_L2FV_up

Component: NL_model

h=L-X p=1-pCa-pCaCB-pCB Q_b=Y_1Caip-Z_1pCa EffFraction=-20L-L_a2 Q_a=Y_2pCaEffFraction-Z_2pCaCB Q_r=Y_3pCaCB-Z_3pCBCai Q_d=Y_4pCB Q_d1=Y_dddtimeX2pCB Q_d2=Y_dddtimeX2pCaCB ddtimepCa=Q_b-Q_a ddtimepCaCB=Q_a-Q_r-Q_d2 ddtimepCB=Q_r-Q_d-Q_d1 dCaidt=T_tQ_d2+Q_r-Q_b dATPdt=-0.4pCaCBT_t CBBound=T_tpCaCB+pCB NewCBF=ForceFactorCBBound ForceEcomp=KForceECZeroForceEL-L5+KForceLinearEcZeroForceEL-L ForceCB=NewCBFh ForceExt=-ForceEcomp+ForceCB ddtimeX=Bh-h_c

Component: internal_concentrations

Component: intracellular_currents

Component: transmembrane_currents