Model Mathematics

Component: calcium

ddtimeCaSR1=calcium_CaSR1_betaDCaSRCaSR2-2.0CaSR1+CaSR1dx2.0+CaSR2-CaSR12.01.0dx2.0+JSRCa1VSR1calcium_CaSR1_beta ddtimeCaSR2=calcium_CaSR2_betaDCaSRCaSR3-2.0CaSR2+CaSR1dx2.0+CaSR3-CaSR12.02.0dx2.0+JSRCa2VSR2calcium_CaSR2_beta ddtimeCaSR3=calcium_CaSR3_betaDCaSRCaSR4-2.0CaSR3+CaSR2dx2.0+CaSR4-CaSR22.03.0dx2.0+JSRCa3VSR3calcium_CaSR3_beta ddtimeCaSR4=calcium_CaSR4_betaDCaSRCaSR4-2.0CaSR4+CaSR3dx2.0+CaSR4-CaSR32.04.0dx2.0+JSRCa4VSR4calcium_CaSR4_beta ddtimeCai1=calcium_Cai1_betaDCa+calcium_Cai1_gammaDCaBmCai2-2.0Cai1+Cai1dx2.0+Cai2-Cai12.01.0dx2.0-2.0calcium_Cai1_betacalcium_Cai1_gammaDCaBmKdBCa+Cai1Cai2-Cai12.0dx2.0+JCa1Vnonjunct1calcium_Cai1_beta ddtimeCai2=calcium_Cai2_betaDCa+calcium_Cai2_gammaDCaBmCai3-2.0Cai2+Cai1dx2.0+Cai3-Cai12.02.0dx2.0-2.0calcium_Cai2_betacalcium_Cai2_gammaDCaBmKdBCa+Cai2Cai3-Cai12.0dx2.0+JCa2Vnonjunct2calcium_Cai2_beta ddtimeCai3=calcium_Cai3_betaDCa+calcium_Cai3_gammaDCaBmCai4-2.0Cai3+Cai2dx2.0+Cai4-Cai22.03.0dx2.0-2.0calcium_Cai3_betacalcium_Cai3_gammaDCaBmKdBCa+Cai3Cai4-Cai22.0dx2.0+JCa3Vnonjunct3calcium_Cai3_beta ddtimeCai4=calcium_Cai4_betaDCa+calcium_Cai4_gammaDCaBmCai4-2.0Cai4+Cai3dx2.0+Cai4-Cai32.04.0dx2.0-2.0calcium_Cai4_betacalcium_Cai4_gammaDCaBmKdBCa+Cai4Cai4-Cai32.0dx2.0+JCa4Vnonjunct4calcium_Cai4_beta ddtimeCass=calcium_Cass_betaJCassVss+calcium_Cass_i_tot2.0VssF JCa1=-J_bulkSERCA1+JSRCaleak1+Jrel1 JCa2=-J_bulkSERCA2+JSRCaleak2+Jrel2 JCa3=-J_bulkSERCA3+JSRCaleak3+Jrel3 JCa4=Jj_nj JCass=-Jj_nj+JSRCaleakss-J_bulkSERCAss+Jrelss JSRCa1=J_SERCASR1-JSRCaleak1-Jrel1 JSRCa2=J_SERCASR2-JSRCaleak2-Jrel2 JSRCa3=J_SERCASR3-JSRCaleak3-Jrel3 JSRCa4=J_SERCASRss-JSRCaleakss-Jrelss JSRCaleak1=kSRleakCaSR1-Cai1Vnonjunct1 JSRCaleak2=kSRleakCaSR2-Cai2Vnonjunct2 JSRCaleak3=kSRleakCaSR3-Cai3Vnonjunct3 JSRCaleakss=kSRleakCaSR4-CassVss Jj_nj=DCaAj_njxj_njCass-Cai41e-06 calcium_CaSR1_beta=1.01.0+CSQNKdCSQNCaSR1+KdCSQN2.0 calcium_CaSR2_beta=1.01.0+CSQNKdCSQNCaSR2+KdCSQN2.0 calcium_CaSR3_beta=1.01.0+CSQNKdCSQNCaSR3+KdCSQN2.0 calcium_CaSR4_beta=1.01.0+CSQNKdCSQNCaSR4+KdCSQN2.0 calcium_Cai1_beta=1.01.0+calcium_Cai1_gamma calcium_Cai1_gamma=BCaKdBCaCai1+KdBCa2.0 calcium_Cai2_beta=1.01.0+calcium_Cai2_gamma calcium_Cai2_gamma=BCaKdBCaCai2+KdBCa2.0 calcium_Cai3_beta=1.01.0+calcium_Cai3_gamma calcium_Cai3_gamma=BCaKdBCaCai3+KdBCa2.0 calcium_Cai4_beta=1.01.0+calcium_Cai4_gamma calcium_Cai4_gamma=BCaKdBCaCai4+KdBCa2.0 calcium_Cass_beta=1.01.0+SLlowKdSLlowCass+KdSLlow2.0+SLhighKdSLhighCass+KdSLhigh2.0+BCaKdBCaCass+KdBCa2.0 calcium_Cass_i_tot=-ICaL-ICab-ICaP+2.0INaCa

Component: cell

Aj_nj=pirjunct2.0lcell0.5 VSR1=0.05Vnonjunct12.00.9 VSR2=0.05Vnonjunct22.00.9 VSR3=0.05Vnonjunct32.00.9 VSR4=0.05Vnonjunct42.00.9 Vcytosol=Vnonjunct_Nai+Vss Vnonjunct1=1.0dx2.0-0.0dx2.0pilcell0.51e-06 Vnonjunct2=2.0dx2.0-1.0dx2.0pilcell0.51e-06 Vnonjunct3=3.0dx2.0-2.0dx2.0pilcell0.51e-06 Vnonjunct4=4.0dx2.0-3.0dx2.0pilcell0.51e-06 Vnonjunct_Nai=Vnonjunct1+Vnonjunct2+Vnonjunct3+Vnonjunct4 xj_nj=0.022.0+dx2.0 xj_nj_Nai=0.022.0+2.0dx

Component: engine

Component: extra

Component: icab

ICab=gCabV-ECa

Component: ical

ICaL=gCaLdfcaf1f2V-ECa_app ddtimed=ical_d_inf-dical_d_tau ddtimef1=f_inf-f1ical_f1_tau ddtimef2=f_inf-f2ical_f2_tau f_inf=1.01.0+V+27.47.1 ddtimefca=ical_fca_inf-fcaical_fca_tau ical_d_inf=1.01.0+V+9.0-5.8 ical_d_tau=0.0027-V+35.030.02.0+0.002 ical_f1_tau=0.98698-V+30.160477.093962.0+0.042751.0+V-51.61555-80.61331+0.035761.0+V+29.5727213.21758-0.00821 ical_f2_tau=1.3323-V+40.014.22.0+0.0626 ical_fca_inf=1.0-1.01.0+kCaCasskCan

Component: icap

ICaP=ICaPmaxCasskCaP+Cass

Component: if

If=IfK+IfNa IfK=gIfy1.0-0.2677V-EK IfNa=gIfy0.2677V-ENa if_y_inf=1.01.0+V+97.8287412.48025 if_y_tau=1.00.00332-V16.54103+23.71839V16.54103 ddtimey=if_y_inf-yif_y_tau

Component: ik1

IK1=gK1Ko1.00.4457V-EK1.0+1.5V-EK+3.6FRT gK1=3.8250.9

Component: ikr

IKr=gKrpapiV-EK ikr_pa_inf=1.01.0+V+15.0-6.0 ikr_pa_tau=0.21718-V+20.137622.19962.0+0.03118 ddtimepa=ikr_pa_inf-paikr_pa_tau pi=1.01.0+V+55.024.0

Component: iks

IKs=gKsnV-EK iks_n_inf=1.01.0+V-19.9-12.7 iks_n_tau=0.4-V-20.020.02.0+0.7 ddtimen=iks_n_inf-niks_n_tau

Component: ikur

IKur=gKurrsV-EK gKur=0.892.75 ikur_r_inf=1.01.0+V+6.0-8.6 ikur_r_tau=0.0091.0+V+5.012.0+0.0005 ikur_s_inf=1.01.0+V+7.510.0 ikur_s_tau=0.591.0+V+60.010.0+3.05 ddtimer=ikur_r_inf-rikur_r_tau ddtimes=ikur_s_inf-sikur_s_tau

Component: ina

INa=PNam3.00.9h1+0.1h2NaoVFFRTV-ENaFRT-1.0VFRT-1.0 ddtimeh1=h_inf-h1ina_h1_tau ddtimeh2=h_inf-h2ina_h2_tau h_inf=1.01.0+V+63.65.3 ina_h1_tau=0.031.0+V+35.13.2+0.0003 ina_h2_tau=0.121.0+V+35.13.2+0.003 ina_m_inf=1.01.0+V+27.12-8.21 ina_m_tau=4.2e-05-V+25.5728.82.0+2.4e-05 ddtimem=ina_m_inf-mina_m_tau

Component: inab

INab=gNabV-ENa

Component: inaca

INaCa=kNaCagamVFRTNass3.0Cao-gam-1.0VFRTNao3.0CassfCaNCX1.0+dNaCaNao3.0CassfCaNCX+Nass3.0Cao

Component: inak

INaK=INaKmaxKoKo+kNaKKNass15Nass15+kNaKNa1.5V+150.0V+200.0 Nass15=Nass1.01.5

Component: it

It=gtrsV-EK gt=1.097.5 it_r_inf=1.01.0+V-1.0-11.0 it_r_tau=0.0035-V+0.030.02.0+0.0015 it_s_inf=1.01.0+V+40.511.5 it_s_tau=0.025635-V+52.4515.88272.0+0.01414 ddtimer=it_r_inf-rit_r_tau ddtimes=it_s_inf-sit_s_tau

Component: membrane

ddtimeV=-i_ion+i_stimCm i_ion=+INa+ICaL+It+IKur+IK1+IKr+IKs+INab+ICab+INaK+ICaP+INaCa+If

Component: nernst

ECa=RTFlnCaoCass2.0 EK=RTFlnKoKi ENa=RTFlnNaoNass

Component: phys

FRT=1.0RTF RTF=RTF

Component: potassium

ddtimeKi=-i_totVcytosolF i_tot=+It+IKur+IK1+IKr+IKs-2.0INaK+IfK+i_stim

Component: ryr

Jrel1=nu1o1c1SRCa1CaSR1-Cai1 Jrel2=nu2o2c2SRCa2CaSR2-Cai2 Jrel3=nu3o3c3SRCa3CaSR3-Cai3 Jrelss=nussosscssSRCassCaSR4-Cass SRCa1=1.0-1.01.0+CaSR1-0.30.1 SRCa2=1.0-1.01.0+CaSR2-0.30.1 SRCa3=1.0-1.01.0+CaSR3-0.30.1 SRCass=1.0-1.01.0+CaSR4-0.30.1 ddtimea1=ainf1-a1tau_adapt ddtimea2=ainf2-a2tau_adapt ddtimea3=ainf3-a3tau_adapt ainf1=0.505-0.4271.0+Cai11000.0-0.290.082 ainf2=0.505-0.4271.0+Cai21000.0-0.290.082 ainf3=0.505-0.4271.0+Cai31000.0-0.290.082 ainfss=0.505-0.4271.0+Cass1000.0-0.290.082 ddtimeass=ainfss-asstau_adapt ddtimec1=cinf1-c1tau_inact ddtimec2=cinf2-c2tau_inact ddtimec3=cinf3-c3tau_inact cinf1=1.01.0+Cai11000.0-a1+0.020.01 cinf2=1.01.0+Cai21000.0-a2+0.020.01 cinf3=1.01.0+Cai31000.0-a3+0.020.01 cinfss=1.01.0+Cass1000.0-ass+0.020.01 ddtimecss=cinfss-csstau_inactss nu1=1.0Vnonjunct1 nu2=1.0Vnonjunct2 nu3=1.0Vnonjunct3 nuss=625.0Vss ddtimeo1=oinf1-o1tau_act ddtimeo2=oinf2-o2tau_act ddtimeo3=oinf3-o3tau_act oinf1=1.0-1.01.0+Cai11000.0-a1+0.220.03 oinf2=1.0-1.01.0+Cai21000.0-a2+0.220.03 oinf3=1.0-1.01.0+Cai31000.0-a3+0.220.03 oinfss=1.0-1.01.0+Cass1000.0-ass+0.220.03 ddtimeoss=oinfss-osstau_actss

Component: serca

J_SERCASR1=-k3CaSR12.0cpumps-a1+k4a1Vnonjunct12.0 J_SERCASR2=-k3CaSR22.0cpumps-a2+k4a2Vnonjunct22.0 J_SERCASR3=-k3CaSR32.0cpumps-a3+k4a3Vnonjunct32.0 J_SERCASRss=-k3CaSR42.0cpumps-ass+k4assVss2.0 J_bulkSERCA1=k1Cai12.0cpumps-a1-k2a1Vnonjunct12.0 J_bulkSERCA2=k1Cai22.0cpumps-a2-k2a2Vnonjunct22.0 J_bulkSERCA3=k1Cai32.0cpumps-a3-k2a3Vnonjunct32.0 J_bulkSERCAss=k1Cass2.0cpumps-ass-k2assVss2.0 ddtimea1=0.5-J_SERCASR1+J_bulkSERCA1Vnonjunct1 ddtimea2=0.5-J_SERCASR2+J_bulkSERCA2Vnonjunct2 ddtimea3=0.5-J_SERCASR3+J_bulkSERCA3Vnonjunct3 ddtimeass=0.5-J_SERCASRss+J_bulkSERCAssVss k1=1000.02.0k4 k2=k1SERCAKmf2.0 k3=k4SERCAKmr2.0

Component: sodium

BNa=0.492.31 JNa=DNaAj_njxj_nj_NaiNass-Nai1e-06 ddtimeNai=JNaVnonjunct_Nai ddtimeNass=betaNass-JNaVss-i_ssVssF betaNass=1.01.0+BNaKdBNaNass+KdBNa2.0 i_ss=+INa+INab+3.0INaK+3.0INaCa+IfNa

Component: stimulus

amplitude=-2500.0 i_stim=1.0iftime-offset-periodtime-offsetperiod<duration0.0otherwiseamplitude
Source
Derived from workspace Koivumäki, Korhonen, Tavi 2011 Atrial AP model at changeset dbf305e925d3.
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