Model Mathematics

Component: buffca

Bmax_SLhighjn=0.00165⁢VmyoVjn⁢0.1 Bmax_SLhighsl=VmyoVsl⁢0.0134 Bmax_SLlowjn=0.0046⁢VmyoVjn⁢0.1 Bmax_SLlowsl=VmyoVsl⁢0.0374 Bmax_SR=19.0⁢0.0009 ddtimeCaM=kon_cam⁢Ca_i⁢Bmax_CaM-CaM-koff_cam⁢CaM J_CaB_cytosol=ddtimeTnCL+ddtimeTnCHc+ddtimeTnCHm+ddtimeCaM+ddtimeMyoc+ddtimeMyom+ddtimeSRB J_CaB_jn=ddtimeSLL_jn+ddtimeSLH_jn J_CaB_sl=ddtimeSLL_sl+ddtimeSLH_sl ddtimeMyoc=kon_myoca⁢Ca_i⁢Bmax_myosin-Myoc-Myom-koff_myoca⁢Myoc ddtimeMyom=kon_myomg⁢Mg_i⁢Bmax_myosin-Myoc-Myom-koff_myomg⁢Myom ddtimeSLH_jn=kon_slh⁢Ca_jn⁢Bmax_SLhighjn-SLH_jn-koff_slh⁢SLH_jn ddtimeSLH_sl=kon_slh⁢Ca_sl⁢Bmax_SLhighsl-SLH_sl-koff_slh⁢SLH_sl ddtimeSLL_jn=kon_sll⁢Ca_jn⁢Bmax_SLlowjn-SLL_jn-koff_sll⁢SLL_jn ddtimeSLL_sl=kon_sll⁢Ca_sl⁢Bmax_SLlowsl-SLL_sl-koff_sll⁢SLL_sl ddtimeSRB=kon_sr⁢Ca_i⁢Bmax_SR-SRB-koff_sr⁢SRB ddtimeTnCHc=kon_tnchca⁢Ca_i⁢Bmax_TnChigh-TnCHc-TnCHm-koff_tnchca⁢TnCHc ddtimeTnCHm=kon_tnchmg⁢Mg_i⁢Bmax_TnChigh-TnCHc-TnCHm-koff_tnchmg⁢TnCHm ddtimeTnCL=kon_tncl⁢Ca_i⁢Bmax_TnClow-TnCL-koff_tncl⁢TnCL

Component: buffna

ddtimeNaB_jn=kon_na⁢Na_jn⁢Bmax_Na_jn-NaB_jn-koff_na⁢NaB_jn ddtimeNaB_sl=kon_na⁢Na_sl⁢Bmax_Na_sl-NaB_sl-koff_na⁢NaB_sl

Component: calcium

Bmax_Csqn=VmyoVsr⁢0.14 ddtimeCa_i=-J_serca⁢VsrVmyo-J_CaB_cytosol+JCa_slmyoVmyo⁢Ca_sl-Ca_i ddtimeCa_jn=-ICa_tot_jn⁢CVjn⁢2.0⁢F+JCa_jnslVjn⁢Ca_sl-Ca_jn-J_CaB_jn+J_SRCarel⁢VsrVjn+J_SRleak⁢VmyoVjn ddtimeCa_sl=-ICa_tot_sl⁢CVsl⁢2.0⁢F+JCa_jnslVsl⁢Ca_jn-Ca_sl+JCa_slmyoVsl⁢Ca_i-Ca_sl-J_CaB_sl ddtimeCa_sr=J_serca-J_SRleak⁢VmyoVsr+J_SRCarel-ddtimeCsqn ddtimeCsqn=kon_csqn⁢Ca_sr⁢Bmax_Csqn-Csqn-koff_csqn⁢Csqn ICa_tot_jn=ICaL_Ca_jn+ICaB_jn+IpCa_jn-2.0⁢INaCa_jn ICa_tot_sl=ICaL_Ca_sl+ICaB_sl+IpCa_sl-2.0⁢INaCa_sl JCa_jnsl=1.0 1.21340000000000000e+12 JCa_slmyo=1.0 2.68510000000000000e+11

Component: cell

Component: engine

Component: geom

Vcell=pi⁢cell_radius2.0⁢cell_length⁢1e-15 Vjn=0.0539⁢0.01⁢Vcell Vmyo=0.65⁢Vcell Vsl=0.02⁢Vcell Vsr=0.035⁢Vcell

Component: icab

ICaB=ICaB_jn+ICaB_sl ICaB_jn=Fjn⁢gCaB⁢V-ECa_jn ICaB_sl=Fsl⁢gCaB⁢V-ECa_sl

Component: ical

ICaL=ICaL_Ca+ICaL_Na+ICaL_K ICaL_Ca=ICaL_Ca_jn+ICaL_Ca_sl ICaL_Ca_jn=Fjn_CaL⁢ibarca_jn⁢d⁢f⁢1.0-fCaB_jn+fcaCaj⁢Q10CaLQ⁢0.45 ICaL_Ca_sl=Fsl_CaL⁢ibarca_sl⁢d⁢f⁢1.0-fCaB_sl+fcaCaMSL⁢Q10CaLQ⁢0.45 ICaL_K=ibark⁢d⁢f⁢Fjn_CaL⁢fcaCaj+1.0-fCaB_jn+Fsl_CaL⁢fcaCaMSL+1.0-fCaB_sl⁢Q10CaLQ⁢0.45 ICaL_Na=ICaL_Na_jn+ICaL_Na_sl ICaL_Na_jn=Fjn_CaL⁢ibarna_jn⁢d⁢f⁢1.0-fCaB_jn+fcaCaj⁢Q10CaLQ⁢0.45 ICaL_Na_sl=Fsl_CaL⁢ibarna_sl⁢d⁢f⁢1.0-fCaB_sl+fcaCaMSL⁢Q10CaLQ⁢0.45 ddtimed=ical_d_inf-dical_d_tau ddtimef=ical_f_inf-fical_f_tau ddtimefCaB_jn=1.7⁢Ca_jn⁢1.0-fCaB_jn-0.0119⁢fCaB_jn⁢1.0 ddtimefCaB_sl=1.7⁢Ca_sl⁢1.0-fCaB_sl-0.0119⁢fCaB_sl⁢1.0 ibarca_jn=pCa⁢4.0⁢V⁢F⁢FRT⁢0.341⁢Ca_jn⁢ⅇ2.0⁢V⁢FRT-0.341⁢Ca_oⅇ2.0⁢V⁢FRT-1.0 ibarca_sl=pCa⁢4.0⁢V⁢F⁢FRT⁢0.341⁢Ca_sl⁢ⅇ2.0⁢V⁢FRT-0.341⁢Ca_oⅇ2.0⁢V⁢FRT-1.0 ibark=pK⁢V⁢F⁢FRT⁢0.75⁢K_i⁢ⅇV⁢FRT-0.75⁢K_oⅇV⁢FRT-1.0 ibarna_jn=pNa⁢V⁢F⁢FRT⁢0.75⁢Na_jn⁢ⅇV⁢FRT-0.75⁢Na_oⅇV⁢FRT-1.0 ibarna_sl=pNa⁢V⁢F⁢FRT⁢0.75⁢Na_sl⁢ⅇV⁢FRT-0.75⁢Na_oⅇV⁢FRT-1.0 ical_d_inf=1.01.0+ⅇ-V+9.06.0 ical_d_tau=ical_d_inf⁢1.0-ⅇ-V+9.06.00.035⁢V+9.0 ical_f_inf=1.01.0+ⅇV+30.07.0+0.21.0+ⅇ50.0-V20.0 ical_f_tau=1.00.0197⁢ⅇ-0.0337⁢V+25.02.0+0.02 pCa=1.0-0.5⁢AF⁢0.00027 pK=1.0-0.5⁢AF⁢1.35e-07 pNa=1.0-0.5⁢AF⁢7.5e-09

Component: iclb

IClB=gClB⁢V-ECl

Component: iclca

IClCa=IClCa_jn+IClCa_sl IClCa_jn=Fjn⁢gClCa1.0+KdClCaCa_jn⁢V-ECl IClCa_sl=Fsl⁢gClCa1.0+KdClCaCa_sl⁢V-ECl

Component: ik1

IK1=IK1_Fact⁢gK1⁢inf⁢V-EK Na_observed=Na_sl a_fact=0.1+0.91.0+Na_observed7.02.0 gK1=1.0+AF⁢K_o5.4⁢0.0525 ik1_inf_a=a_fact⁢1.01.0+ⅇ0.2385⁢V-EK-59.215 ik1_inf_b=1.0⁢0.49124⁢ⅇ0.08032⁢V-EK+5.476+ⅇ0.06175⁢V-EK-594.311.0+ⅇ-0.5143⁢V-EK+4.753 inf=ik1_inf_aik1_inf_a+ik1_inf_b

Component: ikach

Act=Constitutive_Frac+1.0-Constitutive_Frac⁢CChCCh+0.125 IKACh=gKACh⁢Na_dep⁢Act⁢0.055+0.41.0+ⅇV-EK+9.5317.18⁢V-EK⁢K_o5.4 Na_dep=1.0+1.51.0+9.0Na_observed4.0ifAF<1.01.0otherwise Na_observed=Na_sl gKACh=0.1-0.05⁢AF

Component: ikp

IKp=IKp_jn+IKp_sl IKp_jn=Fjn⁢gKp⁢kp⁢V-EK IKp_sl=Fsl⁢gKp⁢kp⁢V-EK kp=1.01.0+ⅇ7.488-V5.98

Component: ikr

IKr=gKr⁢x⁢r⁢V-EK gKr=0.035⁢K_o5.4 ikr_x_inf=1.01.0+ⅇ-V+10.05.0 ikr_x_tau=+550.01.0+ⅇ-22.0-V9.0⁢6.01.0+ⅇV+11.09.0+230.01.0+ⅇV+40.020.0 r=1.01.0+ⅇV+74.024.0 ddtimex=ikr_x_inf-xikr_x_tau

Component: iks

EKs=1.0FRT⁢ln⁡K_o+pNaK⁢Na_oK_i+pNaK⁢Na_i IKs=IKs_jn+IKs_sl IKs_jn=Fjn⁢gKs_jn⁢x2.0⁢V-EKs IKs_sl=Fsl⁢gKs_sl⁢x2.0⁢V-EKs gKs_jn=1.0+AF⁢0.0035 gKs_sl=1.0+AF⁢0.0035 iks_x_inf=1.01.0+ⅇ-V+3.814.25 iks_x_tau=990.11.0+ⅇ-V+2.43614.12 ddtimex=iks_x_inf-xiks_x_tau

Component: ikur

IKur=gKur⁢r⁢s⁢V-EK gKur=1.0-0.5⁢AF⁢0.045 ikur_r_inf=1.01.0+ⅇV+6.0-8.6 ikur_r_tau=9.01.0+ⅇV+5.012.0+0.5 ikur_s_inf=1.01.0+ⅇV+7.510.0 ikur_s_tau=590.01.0+ⅇV+60.010.0+3050.0 ddtimer=ikur_r_inf-rikur_r_tau ddtimes=ikur_s_inf-sikur_s_tau

Component: ina

INa=INa_jn+INa_sl INa_jn=Fjn⁢gNa⁢m3.0⁢h⁢j⁢V-ENa_jn INa_sl=Fsl⁢gNa⁢m3.0⁢h⁢j⁢V-ENa_sl ddtimeh=ina_h_inf-hina_h_tau ina_h_alpha=0.135⁢ⅇV+80.0-6.8ifV<-40.00.0otherwise ina_h_beta=3.56⁢ⅇ0.079⁢V+310000.0⁢ⅇ0.35⁢VifV<-40.01.00.13⁢1.0+ⅇV+10.66-11.1otherwise ina_h_inf=ina_h_alphaina_h_alpha+ina_h_beta ina_h_tau=1.0ina_h_alpha+ina_h_beta ina_j_alpha=-127140.0⁢ⅇ0.2444⁢V-3.474e-05⁢ⅇ-0.04391⁢V⁢V+37.781.0+ⅇ0.311⁢V+79.23ifV<-40.00.0otherwise ina_j_beta=0.1212⁢ⅇ-0.01052⁢V1.0+ⅇ-0.1378⁢V+40.14ifV<-40.00.3⁢ⅇ-2.535e-07⁢V1.0+ⅇ-0.1⁢V+32.0otherwise ina_j_inf=ina_j_alphaina_j_alpha+ina_j_beta ina_j_tau=1.0ina_j_alpha+ina_j_beta ina_m_alpha=3.2ifV=-47.130.32⁢V+47.131.0-ⅇ-0.1⁢V+47.13otherwise ina_m_beta=0.08⁢ⅇ-V11.0 ina_m_inf=ina_m_alphaina_m_alpha+ina_m_beta ina_m_tau=1.0ina_m_alpha+ina_m_beta ddtimej=ina_j_inf-jina_j_tau ddtimem=ina_m_inf-mina_m_tau

Component: inab

INaB=INaB_jn+INaB_sl INaB_jn=Fjn⁢gNaB⁢V-ENa_jn INaB_sl=Fsl⁢gNaB⁢V-ENa_sl

Component: inaca

INaCa=INaCa_jn+INaCa_sl INaCa_jn=Fjn⁢IbarNCX⁢Q10NCXQ⁢Ka_jn⁢inaca_INaCa_jn_s1-inaca_INaCa_jn_s2inaca_INaCa_jn_s31.0+ksat⁢ⅇnu-1.0⁢V⁢FRT INaCa_sl=Fsl⁢IbarNCX⁢Q10NCXQ⁢Ka_sl⁢inaca_INaCa_sl_s1-inaca_INaCa_sl_s2inaca_INaCa_sl_s31.0+ksat⁢ⅇnu-1.0⁢V⁢FRT IbarNCX=1.0+0.4⁢AF⁢3.15 Ka_jn=1.01.0+KdactCa_jn2.0 Ka_sl=1.01.0+KdactCa_sl2.0 inaca_INaCa_jn_s1=ⅇnu⁢V⁢FRT⁢Na_jn3.0⁢Ca_o inaca_INaCa_jn_s2=ⅇnu-1.0⁢V⁢FRT⁢Na_o3.0⁢Ca_jn inaca_INaCa_jn_s3=KmCai⁢Na_o3.0⁢1.0+Na_jnKmNai3.0+KmNao3.0⁢Ca_jn⁢1.0+Ca_jnKmCai+KmCao⁢Na_jn3.0+Na_jn3.0⁢Ca_o+Na_o3.0⁢Ca_jn inaca_INaCa_sl_s1=ⅇnu⁢V⁢FRT⁢Na_sl3.0⁢Ca_o inaca_INaCa_sl_s2=ⅇnu-1.0⁢V⁢FRT⁢Na_o3.0⁢Ca_sl inaca_INaCa_sl_s3=KmCai⁢Na_o3.0⁢1.0+Na_slKmNai3.0+KmNao3.0⁢Ca_sl⁢1.0+Ca_slKmCai+KmCao⁢Na_sl3.0+Na_sl3.0⁢Ca_o+Na_o3.0⁢Ca_sl

Component: inak

INaK=INaK_jn+INaK_sl INaK_jn=Fjn⁢IbarNaK⁢fnak⁢K_o1.0+KmNaipNa_jn4.0K_o+KmKo INaK_sl=Fsl⁢IbarNaK⁢fnak⁢K_o1.0+KmNaipNa_sl4.0K_o+KmKo fnak=1.01.0+0.1245⁢ⅇ-0.1⁢V⁢FRT+0.0365⁢sigma⁢ⅇ-V⁢FRT sigma=ⅇNa_o67.3-1.07.0

Component: inal

INaL=INaL_jn+INaL_sl INaL_jn=Fjn⁢gNaL⁢ml3.0⁢hl⁢V-ENa_jn INaL_sl=Fsl⁢gNaL⁢ml3.0⁢hl⁢V-ENa_sl gNaL=0.0025⁢AF ddtimehl=inal_hl_inf-hlinal_hl_tau inal_hl_inf=1.01.0+ⅇV+91.06.1 inal_ml_a=0.32⁢V+47.131.0-ⅇ-0.1⁢V+47.13 inal_ml_b=0.08⁢ⅇ-V11.0 ddtimeml=inal_ml_a⁢1.0-ml-inal_ml_b⁢ml

Component: ion

Component: ipca

IpCa=IpCa_jn+IpCa_sl IpCa_jn=Fjn⁢Q10SLCaPQ⁢IbarSLCaP⁢ipca_IpCa_jn_aipca_IpCa_jn_a+b IpCa_sl=Fsl⁢Q10SLCaPQ⁢IbarSLCaP⁢ipca_IpCa_sl_aipca_IpCa_sl_a+b b=KmPCa⁢1.01.6 ipca_IpCa_jn_a=Ca_jn⁢1.01.6 ipca_IpCa_sl_a=Ca_sl⁢1.01.6

Component: ito

Ito=gto⁢x⁢y⁢V-EK gto=1.0-0.7⁢AF⁢0.165 ito_x_inf=1.01.0+ⅇ-V+1.011.0 ito_x_tau=3.5⁢ⅇ-V30.02.0+1.5 ito_y_inf=1.01.0+ⅇV+40.511.5 ito_y_tau=25.635⁢ⅇ-V+52.4515.88272.0+24.14 ddtimex=ito_x_inf-xito_x_tau ddtimey=ito_y_inf-yito_y_tau

Component: junc

Fsl=1.0-Fjn Fsl_CaL=1.0-Fjn_CaL

Component: membrane

ICa_tot=ICa_tot_jn+ICa_tot_sl ICl_tot=IClCa+IClB INa_tot=INa_tot_jn+INa_tot_sl I_tot=INa_tot+ICl_tot+ICa_tot+IK_tot ddtimeV=-I_tot+I_stim

Component: nernst

ECa_jn=1.0FRT2.0⁢ln⁡Ca_oCa_jn ECa_sl=1.0FRT2.0⁢ln⁡Ca_oCa_sl ECl=1.0FRT⁢ln⁡Cl_iCl_o EK=1.0FRT⁢ln⁡K_oK_i ENa_jn=1.0FRT⁢ln⁡Na_oNa_jn ENa_sl=1.0FRT⁢ln⁡Na_oNa_sl

Component: phys

FRT=FRT Q=T-310.010.0

Component: potassium

IK_tot=Ito+IKr+IKs+IK1-2.0⁢INaK+ICaL_K+IKp+IKur+IKACh ddtimeK_i=0.0

Component: ryr

J_SRCarel=ks⁢o⁢Ca_sr-Ca_jn J_SRleak=1.0+0.25⁢AF⁢Ca_sr-Ca_jn⁢5.348e-06 J_serca=Q10SRCaPQ⁢Vmax_SRCaP⁢Ca_iKmfhillSRCaP-Ca_srKmrhillSRCaP1.0+Ca_iKmfhillSRCaP+Ca_srKmrhillSRCaP Kmf=2.5⁢0.000246 RI=1.0-r-o-i ddtimei=kiSRCa⁢Ca_jn⁢o-kim⁢i-kom⁢i-koSRCa⁢Ca_jn2.0⁢RI kCaSR=MaxSR-MaxSR-MinSR1.0+ec50SRCa_sr2.5 kiSRCa=kiCa⁢kCaSR koCa=10.0+20.0⁢AF⁢1.0 koSRCa=koCakCaSR ddtimeo=koSRCa⁢Ca_jn2.0⁢r-kom⁢o-kiSRCa⁢Ca_jn⁢o-kim⁢i ddtimer=kim⁢RI-kiSRCa⁢Ca_jn⁢r-koSRCa⁢Ca_jn2.0⁢r-kom⁢o

Component: sodium

INa_tot_jn=INa_jn+INaB_jn+3.0⁢INaCa_jn+3.0⁢INaK_jn+ICaL_Na_jn+INaL_jn INa_tot_sl=INa_sl+INaB_sl+3.0⁢INaCa_sl+3.0⁢INaK_sl+ICaL_Na_sl+INaL_sl JNa_jnsl=1.0 1.63820000000000000e+123.0⁢100.0 JNa_slmyo=1.0 1.83080000000000000e+103.0⁢100.0 ddtimeNa_i=JNa_slmyoVmyo⁢Na_sl-Na_i ddtimeNa_jn=-INa_tot_jn⁢CVjn⁢F+JNa_jnslVjn⁢Na_sl-Na_jn-ddtimeNaB_jn ddtimeNa_sl=-INa_tot_sl⁢CVsl⁢F+JNa_jnslVsl⁢Na_jn-Na_sl+JNa_slmyoVsl⁢Na_i-Na_sl-ddtimeNaB_sl

Component: stimulus

I_stim=1.0iftime-offset-period⁢⌊time-offsetperiod⌋<duration0.0otherwise⁢amplitude amplitude=-90.0