Model Mathematics

Component: environment

Component: Membrane

i_tot=i_f+i_Kr+i_Ks+i_to+i_NaK+i_NaCa+i_Na+i_CaL+i_CaT+i_KACh ddtimeV_ode=-i_totC RTONF=RTF V=V_clampifclamp_mode1V_odeotherwise

Component: Voltage_clamp

V_clamp=V_testiftime>t_holdingtime<t_holding+t_testV_holdingotherwise

Component: Rate_modulation_experiments

Component: Ionic_values

E_Na=RTONFlnNaoNai E_K=RTONFlnKoKi E_Ca=0.5RTONFlnCaoCa_sub

Component: Nai_concentration

ddtimeNai_=-1i_Na+i_fNa+i_siNa+3i_NaK+3i_NaCa1V_i+V_subF Nai=7.5ifBAPTA_10_mM>0Nai_otherwise

Component: i_f

g_f_Na=0.031-0.66ifIva_3_uM10.03otherwise g_f_K=0.031-0.66ifIva_3_uM10.03otherwise ICs_on_Icontrol=10.6015510.60155+-0.71V25ifCs_5_mM11otherwise i_fNa=y2KcKc+Km_fg_f_NaV-E_NaICs_on_Icontrol i_fK=y2KcKc+Km_fg_f_KV-E_KICs_on_Icontrol i_f=i_fNa+i_fK

Component: i_f_y_gate

ACh_shift=-1-9.8981ACh0.6181ACh0.618+0.00122423ifACh>00otherwise Iso_shift=7.5ifIso_1_uM>00otherwise tau_y=0.71665290.0708-V+5-ACh_shift-Iso_shift20.2791+10.6V-ACh_shift-Iso_shift18 y_infinity=11+V+52.5-ACh_shift-Iso_shift9 ddtimey=y_infinity-ytau_y

Component: i_NaK

Iso_increase=1.2ifIso_1_uM>01otherwise i_NaK=Iso_increasei_NaK_max1+Km_KpKc1.2-11+Km_NapNai1.3-11+-V-E_Na+11020-1

Component: i_NaCa

i_NaCa=K_NaCax2k21-x1k12x1+x2+x3+x4 x1=k41k34k23+k21+k21k32k43+k41 x2=k32k43k14+k12+k41k12k34+k32 x3=k14k43k23+k21+k12k23k43+k41 x4=k23k34k14+k12+k14k21k34+k32 k43=NaiK3ni+Nai k12=Ca_subKci-QciVRTONFdi k14=NaiK1niNaiK2ni1+NaiK3niQnV2RTONFdi k41=-QnV2RTONF di=1+Ca_subKci1+-QciVRTONF+NaiKcni+NaiK1ni1+NaiK2ni1+NaiK3ni k34=NaoK3no+Nao k21=CaoKcoQcoVRTONFdo k23=NaoK1noNaoK2no1+NaoK3no-QnV2RTONFdo k32=QnV2RTONF do=1+CaoKco1+QcoVRTONF+NaoK1no1+NaoK2no1+NaoK3no

Component: i_Na

E_mh=RTONFlnNao+0.12KcNai+0.12Ki i_Na=g_Nam3hV-E_mh

Component: i_Na_m_gate

E0_m=V+41 alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwise beta_m=8000-0.056V+66 ddtimem=alpha_m1-m-beta_mm

Component: i_Na_h_gate

alpha_h=20-0.125V+75 beta_h=2000320-0.1V+75+1 ddtimeh=alpha_h1-h-beta_hh

Component: i_CaL

Iso_increase=1.23ifIso_1_uM>01otherwise i_siCa=2P_CaLV-0RTONF1--1V-02RTONFCa_sub-Cao-2V-0RTONFdLfLfCa i_siK=0.000365P_CaLV-0RTONF1--1V-0RTONFKi-Kc-1V-0RTONFdLfLfCa i_siNa=0.0000185P_CaLV-0RTONF1--1V-0RTONFNai-Nao-1V-0RTONFdLfLfCa ACh_block=0.31AChACh+0.00009 i_CaL=i_siCa+i_siK+i_siNa1-ACh_block1Iso_increase

Component: i_CaL_dL_gate

Iso_shift=-8ifIso_1_uM>00otherwise Iso_slope=0.69ifIso_1_uM>01otherwise dL_infinity=11+-V+20.3-Iso_shiftIso_slope4.2 tau_dL=0.001alpha_dL+beta_dL alpha_dL=-0.02839adVm+41.8-Iso_shift-adVm+41.8-Iso_shift2.5-1-0.0849adVm+6.8-Iso_shift-adVm+6.8-Iso_shift4.8-1 adVm=-41.80001ifV=-41.80ifV=0-6.80001ifV=-6.8Votherwise beta_dL=0.01143bdVm+1.8-Iso_shiftbdVm+1.8-Iso_shift2.5-1 bdVm=-1.80001ifV=-1.8Votherwise ddtimedL=dL_infinity-dLtau_dL

Component: i_CaL_fL_gate

fL_infinity=11+V+37.45.3 tau_fL=0.00144.3+230-V+36102 ddtimefL=fL_infinity-fLtau_fL

Component: i_CaL_fCa_gate

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

Component: i_CaT

i_CaT=2P_CaTVRTONF1--1V2RTONFCa_sub-Cao-2VRTONFdTfT

Component: i_CaT_dT_gate

dT_infinity=11+-V+38.35.5 tau_dT=0.0011.068V+38.330+1.068-V+38.330 ddtimedT=dT_infinity-dTtau_dT

Component: i_CaT_fT_gate

fT_infinity=11+V+58.73.8 tau_fT=116.67-V+7583.3+16.67V+7515.38 ddtimefT=fT_infinity-fTtau_fT

Component: Ca_SR_release

j_SRCarel=ksOCa_jsr-Ca_sub kCaSR=MaxSR-MaxSR-MinSR1+EC50_SRCa_jsrHSR koSRCa=koCakCaSR kiSRCa=kiCakCaSR ddtimeR=kimRI-kiSRCaCa_subR-koSRCaCa_sub2R-komO ddtimeO=koSRCaCa_sub2R-komO-kiSRCaCa_subO-kimI ddtimeI=kiSRCaCa_subO-kimI-komI-koSRCaCa_sub2RI ddtimeRI=komI-koSRCaCa_sub2RI-kimRI-kiSRCaCa_subR

Component: Ca_intracellular_fluxes

b_up=-0.25ifIso_1_uM>00.7ACh0.00009+AChifACh>00otherwise P_up=P_up_basal1-b_up j_Ca_dif=Ca_sub-Caitau_dif_Ca j_up=P_up1+K_upCai j_tr=Ca_nsr-Ca_jsrtau_tr

Component: Ca_buffering

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

Component: Ca_dynamics

BAPTA=10ifBAPTA_10_mM>0time>T0otherwise ddtimeCai=1j_Ca_difV_sub-j_upV_nsrV_i-CM_totdelta_fCMi+TC_totdelta_fTC+TMC_totdelta_fTMC-kfBAPTACaiBAPTA-fBAPTA-kbBAPTAfBAPTA ddtimefBAPTA=kfBAPTACaiBAPTA-fBAPTA-kbBAPTAfBAPTA ddtimeCa_sub=j_SRCarelV_jsrV_sub-i_siCa+i_CaT-2i_NaCa2FV_sub+j_Ca_dif+CM_totdelta_fCMs-kfBAPTACa_subBAPTA-fBAPTA_sub-kbBAPTAfBAPTA_sub ddtimefBAPTA_sub=kfBAPTACa_subBAPTA-fBAPTA_sub-kbBAPTAfBAPTA_sub ddtimeCa_nsr=j_up-j_trV_jsrV_nsr ddtimeCa_jsr=j_tr-j_SRCarel+CQ_totdelta_fCQ

Component: Cell_parameters

V_cell=0.000000001πR_cell2L_cell V_sub=0.0000000012πL_subR_cell-L_sub2L_cell V_jsr=V_jsr_partV_cell V_i=V_i_partV_cell-V_sub V_nsr=V_nsr_partV_cell

Component: i_to

i_to=g_toV-E_Kqr

Component: i_to_q_gate

q_infinity=11+V+4913 tau_q=0.0010.665.170.57-0.08V+44+0.0650.1V+45.93+10.1 ddtimeq=q_infinity-qtau_q

Component: i_to_r_gate

r_infinity=11+-V-19.315 tau_r=0.0010.661.415.591.0370.09V+30.61+0.369-0.12V+23.84+2.98 ddtimer=r_infinity-rtau_r

Component: i_Kr

i_Kr=g_KrV-E_K0.9paF+0.1paSpiy

Component: i_Kr_pa_gate

alfapaF=11+-V+23.26.60.8465535437.2V11.9+0.96-V18.5 betapaF=437.2V15.9+0.96-V22.50.84655354-11+-V+23.210.60.8465535437.2V15.9+0.96-V22.5 pa_infinity=11+-V+14.88.5 tau_paS=0.846553544.2V17+0.15-V21.6 tau_paF=130V10+-V12 ddtimepaS=pa_infinity-paStau_paS ddtimepaF=pa_infinity-paFtau_paF

Component: i_Kr_pi_gate

tau_pi=1100-V54.645+656V106.157 pi_infinity=11+V+28.617.1 ddtimepiy=pi_infinity-piytau_pi

Component: i_Ks

g_Ks=1.20.0016576ifIso_1_uM>00.0016576otherwise E_Ks=RTONFlnKo+0NaoKi+0Nai i_Ks=g_KsV-E_Ksn2

Component: i_Ks_n_gate

Iso_shift=-14ifIso_1_uM>00otherwise n_infinity=141+-V-40-Iso_shift12141+-V-40-Iso_shift12+1-V-Iso_shift45 tau_n=1alpha_n+beta_n alpha_n=281+-V-40-Iso_shift3 beta_n=1-V-Iso_shift-shift-525 ddtimen=n_infinity-ntau_n

Component: i_KACh

i_KACh=g_KAChV-E_K1+V+2020aifACh>00otherwise

Component: i_KACh_a_gate

alpha_a=3.5988-0.0256411+0.00000121551ACh1.6951+0.025641 beta_a=100.0133V+40 a_infinity=alpha_aalpha_a+beta_a tau_a=1alpha_a+beta_a ddtimea=a_infinity-atau_a
Source
Derived from workspace severi_fantini_charawi_difrancesco_2012 at changeset 1acf719d8f4b.
This exposure was expired.
Collaboration
To begin collaborating on this work, please use your git client and issue this command:
License
The terms of use/license for this work is unspecified.