Model Mathematics

Component: Ca_SR_release

ddtimeI=kiSRCaCa_subO-kimI-komI-koSRCaCa_sub2.0RI ddtimeO=koSRCaCa_sub2.0R-komO-kiSRCaCa_subO-kimI ddtimeR=kimRI-kiSRCaCa_subR-koSRCaCa_sub2.0R-komO ddtimeRI=komI-koSRCaCa_sub2.0RI-kimRI-kiSRCaCa_subR j_SRCarel=ksOCa_jsr-Ca_sub kCaSR=MaxSR-MaxSR-MinSR1.0+EC50_SRCa_jsrHSR kiSRCa=kiCakCaSR koSRCa=koCakCaSR

Component: Ca_buffering

delta_fCMi=kf_CMCai1.0-fCMi-kb_CMfCMi delta_fCMs=kf_CMCa_sub1.0-fCMs-kb_CMfCMs delta_fCQ=kf_CQCa_jsr1.0-fCQ-kb_CQfCQ delta_fTC=kf_TCCai1.0-fTC-kb_TCfTC delta_fTMC=kf_TMCCai1.0-fTMC+fTMM-kb_TMCfTMC delta_fTMM=kf_TMMMgi1.0-fTMC+fTMM-kb_TMMfTMM ddtimefCMi=delta_fCMi ddtimefCMs=delta_fCMs ddtimefCQ=delta_fCQ ddtimefTC=delta_fTC ddtimefTMC=delta_fTMC ddtimefTMM=delta_fTMM

Component: Ca_dynamics

ddtimeCa_jsr=j_tr-j_SRCarel+CQ_totdelta_fCQ ddtimeCa_nsr=j_up-j_trV_jsrV_nsr ddtimeCa_sub=j_SRCarelV_jsrV_sub-i_siCa+i_CaT_i_CaT-2.0i_NaCa_i_NaCa2.0FV_sub+j_Ca_dif+CM_totdelta_fCMs ddtimeCai=1.0j_Ca_difV_sub-j_upV_nsrV_i-CM_totdelta_fCMi+TC_totdelta_fTC+TMC_totdelta_fTMC

Component: Ca_intracellular_fluxes

P_up=P_up_basal1.0-b_up b_up=-0.25ifIso_1_uM>0.00.7ACh9e-05+AChifACh>0.00.0otherwise j_Ca_dif=Ca_sub-Caitau_dif_Ca j_tr=Ca_nsr-Ca_jsrtau_tr j_up=P_up1.0+-Cai+K_upslope_up

Component: Cell_parameters

V_cell=1e-09 3.14159265358979312e+00R_cell2.0L_cell V_i=V_i_partV_cell-V_sub V_jsr=V_jsr_partV_cell V_nsr=V_nsr_partV_cell V_sub=1e-092.0 3.14159265358979312e+00L_subR_cell-L_sub2.0L_cell

Component: Ionic_values

E_K=RTONFlnKoKi E_Na=RTONFlnNaoNai

Component: Ki_concentration

ddtimeKi=-1.0i_Kur_i_Kur+i_to_i_to+i_Kr_i_Kr+i_Ks_i_Ks+i_fK+i_siK+i_SK_i_SK-2.0i_NaK_i_NaK1.0V_i+V_subF

Component: Membrane

RTONF=RTF V=V_ode ddtimeV_ode=-i_totC i_tot=i_f_i_f+i_Kr_i_Kr+i_Ks_i_Ks+i_to_i_to+i_NaK_i_NaK+i_NaCa_i_NaCa+i_Na_i_Na+i_CaL_i_CaL+i_CaT_i_CaT+i_KACh_i_KACh+i_Kur_i_Kur+i_SK_i_SK

Component: Nai_concentration

ddtimeNai=-1.0i_Na_i_Na+i_fNa+i_siNa+3.0i_NaK_i_NaK+3.0i_NaCa_i_NaCa1.0V_i+V_subF

Component: Rate_modulation_experiments

Component: environment

Component: i_CaL

ACh_block=0.31AChACh+9e-05 Iso_increase=1.23ifIso_1_uM>0.01.0otherwise i_CaL=i_siCa+i_siK+i_siNa1.0-ACh_block1.0Iso_increase i_siCa=2.0P_CaLV-0.0RTONF1.0--1.0V-0.02.0RTONFCa_sub-Cao-2.0V-0.0RTONFdLfLfCa i_siK=0.000365P_CaLV-0.0RTONF1.0--1.0V-0.0RTONFKi-Ko-1.0V-0.0RTONFdLfLfCa i_siNa=1.85e-05P_CaLV-0.0RTONF1.0--1.0V-0.0RTONFNai-Nao-1.0V-0.0RTONFdLfLfCa

Component: i_CaL_dL_gate

Iso_shift_dL=-8.0ifIso_1_uM>0.00.0otherwise Iso_slope_dL=-27.0ifIso_1_uM>0.00.0otherwise V_dL=-7.7713 adVm=-41.80001ifV=-41.80.0ifV=0.0-6.80001ifV=-6.8Votherwise alpha_dL=-0.02839adVm+41.8-adVm+41.82.5-1.0-0.0849adVm+6.8-adVm+6.84.8-1.0 bdVm=-1.80001ifV=-1.8Votherwise beta_dL=0.01143bdVm+1.8bdVm+1.82.5-1.0 ddtimedL=dL_infinity-dLtau_dL dL_infinity=1.01.0+-V-V_dL-Iso_shift_dLk_dL1.0+Iso_slope_dL100.0 tau_dL=0.001alpha_dL+beta_dL

Component: i_CaL_fCa_gate

ddtimefCa=fCa_infinity-fCatau_fCa fCa_infinity=Km_fCaKm_fCa+Ca_sub tau_fCa=0.001fCa_infinityalpha_fCa

Component: i_CaL_fL_gate

ddtimefL=fL_infinity-fLtau_fL fL_infinity=1.01.0+V+12.1847+shift_fL tau_fL=0.00144.3+230.0-V+36.010.02.0

Component: i_CaT

i_CaT=2.0P_CaTVRTONF1.0--1.0V2.0RTONFCa_sub-Cao-2.0VRTONFdTfT

Component: i_CaT_dT_gate

ddtimedT=dT_infinity-dTtau_dT dT_infinity=1.01.0+-V+38.35.5 tau_dT=0.0011.068V+38.330.0+1.068-V+38.330.0

Component: i_CaT_fT_gate

ddtimefT=fT_infinity-fTtau_fT fT_infinity=1.01.0+V+58.73.8 tau_fT=1.016.67-V+75.083.3+16.67V+75.015.38+offset_fT

Component: i_KACh

i_KACh=ACh_ong_KAChV-E_K1.0+V+20.020.0aifACh>0.00.0otherwise

Component: i_KACh_a_gate

ddtimea=a_infinity-atau_a a_infinity=alpha_aalpha_a+beta_a alpha_a=3.5988-0.0256411.0+ 1.21550000000000005e-061.0ACh1.6951+0.025641 beta_a=10.00.0133V+40.0 tau_a=1.0alpha_a+beta_a

Component: i_Kr

g_Kr= 4.98909900000000031e-03Ko5.4 i_Kr=g_KrV-E_K0.9paF+0.1paSpiy

Component: i_Kr_pa_gate

ddtimepaF=pa_infinity-paFtau_paF ddtimepaS=pa_infinity-paStau_paS pa_infinity=1.01.0+-V+10.01447.6607 tau_paF=1.030.0V10.0+-V12.0 tau_paS= 8.46553540000000049e-014.2V17.0+0.15-V21.6

Component: i_Kr_pi_gate

pi_infinity=1.01.0+V+28.617.1 ddtimepiy=pi_infinity-piytau_pi tau_pi=1.0100.0-V54.645+656.0V106.157

Component: i_Ks

E_Ks=RTONFlnKo+0.12NaoKi+0.12Nai g_Ks=1.2g_Ks_ifIso_1_uM>0.0g_Ks_otherwise i_Ks=g_KsV-E_Ksn2.0

Component: i_Ks_n_gate

Iso_shift=-14.0ifIso_1_uM>0.00.0otherwise alpha_n=28.01.0+-V-40.0-Iso_shift3.0 beta_n=1.0-V-Iso_shift-5.025.0 ddtimen=n_infinity-ntau_n n_infinity=1.01.0+-V+0.6383-Iso_shift10.7071 tau_n=1.0alpha_n+beta_n

Component: i_Kur

i_Kur=g_Kurr_Kurs_KurV-E_K

Component: i_Kur_rKur_gate

ddtimer_Kur=r_Kur_infinity-r_Kurtau_r_Kur r_Kur_infinity=1.01.0+V+6.0-8.6 tau_r_Kur=0.0091.0+V+5.012.0+0.0005

Component: i_Kur_sKur_gate

ddtimes_Kur=s_Kur_infinity-s_Kurtau_s_Kur s_Kur_infinity=1.01.0+V+7.510.0 tau_s_Kur=0.591.0+V+60.010.0+3.05

Component: i_Na

E_mh=RTONFlnNao+0.12KoNai+0.12Ki i_Na=i_Na_+i_Na_L i_Na_=g_Nam3.0hV-E_mh i_Na_L=g_Na_Lm3.0V-E_mh

Component: i_NaCa

di=1.0+Ca_subKci1.0+-QciVRTONF+NaiKcni+NaiK1ni1.0+NaiK2ni1.0+NaiK3ni do=1.0+CaoKco1.0+QcoVRTONF+NaoK1no1.0+NaoK2no1.0+NaoK3no i_NaCa=K_NaCax2k21-x1k12x1+x2+x3+x4 k12=Ca_subKci-QciVRTONFdi k14=NaiK1niNaiK2ni1.0+NaiK3niQnV2.0RTONFdi k21=CaoKcoQcoVRTONFdo k23=NaoK1noNaoK2no1.0+NaoK3no-QnV2.0RTONFdo k32=QnV2.0RTONF k34=NaoK3no+Nao k41=-QnV2.0RTONF k43=NaiK3ni+Nai x1=k41k34k23+k21+k21k32k43+k41 x2=k32k43k14+k12+k41k12k34+k32 x3=k14k43k23+k21+k12k23k43+k41 x4=k23k34k14+k12+k14k21k34+k32

Component: i_NaK

Iso_increase=1.2ifIso_1_uM>0.01.0otherwise i_NaK=Iso_increasei_NaK_max1.0+Km_KpKo1.2-1.01.0+Km_NapNai1.3-1.01.0+-V-E_Na+110.020.0-1.0

Component: i_Na_h_gate

alpha_h=20.0-0.125V+75.0 beta_h=2000.0320.0-0.1V+75.0+1.0 ddtimeh=h_infinity-htau_h h_infinity=1.01.0+V+69.8044.4565 tau_h=1.0alpha_h+beta_h

Component: i_Na_m_gate

E0_m=V+41.0 alpha_m=2000.0if|E0_m|<delta_m200.0E0_m1.0--0.1E0_motherwise beta_m=8000.0-0.056V+66.0 ddtimem=m_infinity-mtau_m m_infinity=1.01.0+-V+42.05048.3106 tau_m=1.0alpha_m+beta_m

Component: i_SK

i_SK=g_SKV-E_Kx

Component: i_SK_x_gate

tau_x=0.0010.0471000.0Ca_sub1.0+1.076.0 ddtimex=x_infinity-xtau_x x_infinity=0.81Ca_sub1.0n_SKCa_sub1.0n_SK+EC50_SK1.0n_SK

Component: i_f

i_f=i_fNa+i_fK i_fK=yg_f_KV-E_K i_fNa=yg_f_NaV-E_Na

Component: i_f_y_gate

ACh_shift=-1.0-9.8981.0ACh0.6181.0ACh0.618+ 1.22422999999999998e-03ifACh>0.00.0otherwise Iso_shift=7.5ifIso_1_uM>0.00.0otherwise tau_y=1.00.36V+148.8-ACh_shift-Iso_shift0.066V+148.8-ACh_shift-Iso_shift-1.0+0.1V+87.3-ACh_shift-Iso_shift1.0--0.2V+87.3-ACh_shift-Iso_shift-0.054 ddtimey=y_infinity-ytau_y y_infinity=0.01329+0.999211.0+V+97.134-ACh_shift-Iso_shift-y_shift8.1752ifV<-80.0-ACh_shift-Iso_shift-y_shift0.0002501-V-ACh_shift-Iso_shift-y_shift12.861otherwise

Component: i_to

i_to=g_toV-E_Kqr

Component: i_to_q_gate

ddtimeq=q_infinity-qtau_q q_infinity=1.01.0+V+49.013.0 tau_q=0.0010.665.170.57-0.08V+44.0+0.0650.1V+45.93+10.1

Component: i_to_r_gate

ddtimer=r_infinity-rtau_r r_infinity=1.01.0+-V-19.315.0 tau_r=0.0010.661.415.591.0370.09V+30.61+0.369-0.12V+23.84+2.98