Model Mathematics

Component: environment

Component: membrane

i_stim=stim_amplitudeiftimestim_starttimestim_end0otherwise ddtimeV=-i_tot+i_stim i_tot=i_Na+i_Na_L+i_Ca_L+i_Ca_T+i_to_1+i_to_2+i_Kr+i_Ks+i_K1+i_NaCa+i_NaK+i_Na_b+i_K_b+i_Ca_b+i_Cl_b+i_Ca_p+i_K_p

Component: equilibrium_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ca=RT2FlnCa_oCa_i E_Cl=-RTFlnCl_oCl_i E_Ks=RTFlnK_o+r_NaKNa_oK_i+r_NaKNa_i

Component: i_Na

i_Na=g_Nam30.8h+0.2jV-E_Na

Component: i_Na_m_gate

alpha_m=0.32V+47.131--0.1V+47.13 beta_m=0.08-V11 m_infinity=alpha_malpha_m+beta_m tau_m=1alpha_m+beta_m ddtimem=m_infinity-mtau_m

Component: i_Na_h_gate

alpha_h=0.135V+80-6.8ifV<-400otherwise beta_h=3.560.079V+3100000.35VifV<-4010.131+V+10.66-11.1otherwise h_infinity=alpha_halpha_h+beta_h tau_h=1alpha_h+beta_h ddtimeh=h_infinity-htau_h

Component: i_Na_j_gate

alpha_j=-1271400.2444V-0.00003474-0.04391VV+37.781+0.311V+79.23ifV<-400otherwise beta_j=0.1212-0.01052V1+-0.1378V+40.14ifV<-400.3-0.0000002535V1+-0.1V+32otherwise j_infinity=0.1alpha_jalpha_j+beta_j tau_j=0.1alpha_j+beta_j ddtimej=j_infinity-jtau_j

Component: i_Na_L

i_Na_L=g_Na_Lm_L3h_LV-E_Na

Component: i_Na_L_m_L_gate

alpha_m_L=0.32V+47.131--0.1V+47.13 beta_m_L=0.08-V11 m_L_infinity=alpha_m_Lalpha_m_L+beta_m_L tau_m_L=1alpha_m_L+beta_m_L ddtimem_L=m_L_infinity-m_Ltau_m_L

Component: i_Na_L_h_L_gate

h_L_infinity=11+V+696.1 tau_h_L=175+1251+-V+256 ddtimeh_L=h_L_infinity-h_Ltau_h_L

Component: i_Ca_L

i_Ca_L=g_Ca_Ldff2f_Caf_Ca2i_Ca_L_max i_Ca_L_max=1p_CaCmz_Ca2V-15F2RTgamma_CaiCa_rz_CaFV-15RT-gamma_CaoCa_oz_CaFV-15RT-1

Component: i_Ca_L_d_gate

ddtimed=d_infinity-dtau_d d_infinity=11+-V-46.74 tau_d=0.59+0.80.052V+131+0.132V+13

Component: i_Ca_L_f_gate

ddtimef=f_infinity-ftau_f f_infinity=11+V+1810 tau_f=4+0.005V-2.52

Component: i_Ca_L_f2_gate

ddtimef2=f2_infinity-f2tau_f2 f2_infinity=11+V+1810 tau_f2=38+0.07V-18.62

Component: i_Ca_L_f_Ca_gate

ddtimef_Ca=f_Ca_infinity-f_Catau_f_Ca f_Ca_infinity=0.31-i_Ca_L0.05+0.551+Ca_r0.003+0.15 tau_f_Ca=0.5+101Ca_MK_act1Ca_MK_act+km_Ca_MK+11+Ca_r0.003

Component: i_Ca_L_f_Ca2_gate

ddtimef_Ca2=f_Ca2_infinity-f_Ca2tau_f_Ca2 f_Ca2_infinity=11-i_Ca_L0.01 tau_f_Ca2=125+3001+-i_Ca_L-0.1750.04

Component: i_Ca_T

i_Ca_T=g_Ca_TbgV-50

Component: i_Ca_T_b_gate

alpha_b=1.068V+16.330 beta_b=1.068-V+16.330 b_infinity=11+-V+336.1 tau_b=1alpha_b+beta_b ddtimeb=b_infinity-btau_b

Component: i_Ca_T_g_gate

alpha_g=0.015-V+71.783.3 beta_g=0.015V+71.715.4 g_infinity=11+V+606.6 tau_g=1alpha_g+beta_g ddtimeg=g_infinity-gtau_g

Component: i_to_1

i_to_1=g_to_1a0.8i+0.2i2V-E_K

Component: i_to_1_a_gate

ddtimea=a_infinity-atau_a alpha_a=25V-76201+V-7620 beta_a=25-V+54201+-V+5420 tau_a=1alpha_a+beta_a a_infinity=alpha_aalpha_a+beta_a

Component: i_to_1_i_gate

ddtimei=i_infinity-itau_i alpha_i=0.031+V+2515 beta_i=0.1V-40151+V-4015 tau_i=6+51+V-16.510 i_infinity=alpha_ialpha_i+beta_i

Component: i_to_1_i2_gate

ddtimei2=i2_infinity-i2tau_i2 alpha_i2=0.004421+V+2615 beta_i2=0.05V-10151+V-1015 tau_i2=21.5+301+V-2510 i2_infinity=alpha_i2alpha_i2+beta_i2

Component: i_Kr

i_Kr=g_Krxrrr_infinityV-E_K g_Kr=0.040008488K_o5.4 rr_infinity=11+V-5.420.4

Component: i_Kr_xr_gate

ddtimexr=xr_infinity-xrtau_xr tau_xr=9001+V5+100 xr_infinity=11+-V+0.08512.25

Component: i_Ks

i_Ks=g_Ksxs1xs2V-E_Ks g_Ks=0.0525813291+0.61+0.000038Ca_i1.4

Component: i_Ks_xs1_gate

ddtimexs1=xs1_infinity-xs1tau_xs1 tau_xs1=10.0000761V+44.61--9.97V+44.6+0.00036V-0.550.128V-0.55-1 xs1_infinity=11+-V-913.7

Component: i_Ks_xs2_gate

ddtimexs2=xs2_infinity-xs2tau_xs2 tau_xs2=210.0000761V+44.61--9.97V+44.6+0.00036V-0.550.128V-0.55-1 xs2_infinity=11+-V-913.7

Component: i_K1

i_K1=g_K1xK1+0.004V-E_K g_K1=0.25K_o5.4

Component: i_K1_xK1_gate

xK1=alpha_xK1alpha_xK1+beta_xK1 beta_xK1=0.491240.08032V+5.476-E_K+0.06175V-594.31+E_K1+-0.5143V+4.753-E_K alpha_xK1=1.021+0.2385V-E_K+59.215

Component: i_K_p

i_K_p=g_K_pkpV-E_K kp=11+7.488-V5.98

Component: i_to_2

i_to_2=20i_to_2_maxa i_to_2_max=1p_ClCmz_Cl2VF2RTCl_i-Cl_o-z_ClVFRT1--z_ClVFRT

Component: i_to_2_a_gate

ddtimea=a_infinity-atau_a a_infinity=11+km_to_2Ca_r tau_a=1

Component: i_NaCa

i_NaCa=X_NaCai_NaCa_maxNa_i3Ca_o0.35FVRT-1.5Na_o3Ca_i-0.65FVRT1+km_Ca_act1.5Ca_i21+k_sat-0.65VFRTdNaCa_1+dNaCa_2 dNaCa_1=km_Ca_oNa_i3+1.5km_Na_o3Ca_i+km_Na_i_13Ca_o1+1.5Ca_ikm_Ca_i dNaCa_2=km_Ca_iNa_o31+Na_ikm_Na_i_1+Na_i3Ca_o+1.5Na_o3Ca_i

Component: i_NaK

i_NaK=g_NaKf_NaK11+km_Na_i_2Na_i2K_oK_o+km_K_o f_NaK=11+0.1245-0.1FVRT+0.0365sigma-FVRT sigma=17Na_o67.3-1

Component: i_Ca_p

i_Ca_p=i_Ca_p_maxCa_ikm_Ca_p+Ca_i

Component: CT_K_Cl

CT_K_Cl=CT_K_Cl_maxE_K-E_ClE_K+87.8251-E_Cl

Component: CT_Na_Cl

CT_Na_Cl=CT_Na_Cl_maxE_Na-E_Cl4E_Na-E_Cl4+87.82514

Component: background_currents

i_Na_b=g_Na_bV-E_Na i_K_b=g_K_bV-E_K i_Cl_b=g_Cl_bV-E_Cl i_Ca_b=1p_Ca_bCmz_Ca2VF2RTgamma_CaiCa_iz_CaVFRT-gamma_CaoCa_oz_CaVFRT-1

Component: intracellular_ion_concentrations

ddtimeNa_i=-Cmi_Na+i_Na_L+i_Na_b+3i_NaK+3i_NaCaa_capVol_myoF+CT_Na_Cl ddtimeK_i=-Cmi_to_1+i_K1+i_Kr+i_Ks+i_K_p+i_K_b-2i_NaKa_capVol_myoF+CT_K_Cl ddtimeCl_i=-Cmi_to_2+i_Cl_ba_capVol_myoF+CT_Na_Cl+CT_K_Cl

Component: Ca_i

ddtimeCa_i=-b_myoCmi_Ca_b+i_Ca_p-2i_NaCaa_cap2Vol_myoF+q_up-q_leakVol_nsrVol_myo-q_diffVol_ssVol_myo CMDN=2CMDN_maxCa_iCa_i+km_CMDN2 TRPN=2TRPN_maxCa_iCa_i+km_TRPN2 b_myo=11+TRPN+CMDN

Component: Ca_MK_act

Ca_MK_act=Ca_MK_bound+Ca_MK_trap ddtimeCa_MK_trap=alpha_Ca_MKCa_MK_boundCa_MK_bound+Ca_MK_trap-beta_Ca_MKCa_MK_trap Ca_MK_bound=Ca_MK_01-Ca_MK_trap1+km_Ca_MKCa_r

Component: Ca_NSR

ddtimeCa_NSR=q_up-q_leak+q_trVol_jsrVol_nsr

Component: Ca_JSR

ddtimeCa_JSR=q_tr-q_rel1+CSQN_maxkm_CSQNkm_CSQN+Ca_JSR2

Component: Ca_r

ddtimeCa_r=Ca_r_tot-Cmi_Ca_La_capVol_ssz_CaF+q_relVol_jsrVol_ss-q_diff q_diff=Ca_r-Ca_itau_ss b_SL=2b_SL_maxCa_rCa_r+km_b_SL2 b_SR=2b_SR_maxCa_rCa_r+km_b_SR2 Ca_r_tot=11+b_SR+b_SL

Component: q_rel

q_rel=g_relroriCa_JSR-Ca_r g_rel=3000vg vg=11+g_Ca_Li_Ca_L_max+135

Component: q_rel_ri_gate

ddtimeri=ri_infinity-ritau_ri tau_ri=350-tau_Ca_MK1+Ca_r-0.003+0.003Ca_fac0.0002+3+tau_Ca_MK ri_infinity=11+Ca_r-0.0004+0.002Ca_fac0.000025 Ca_fac=11+i_Ca_L+0.050.015 tau_Ca_MK=tau_Ca_MK_max1Ca_MK_actkm_Ca_MK+1Ca_MK_act

Component: q_rel_ro_gate

ddtimero=ro_infinity-rotau_ro ro_infinity=ro_infinity_JSRi_Ca_L2i_Ca_L2+1 ro_infinity_JSR=Ca_JSR1.9Ca_JSR1.9+49.28Ca_rCa_r+0.00281.9

Component: q_leak

q_leak=q_leak_maxCa_NSRNSR_max

Component: q_up

q_up=X_q_updq_up_Ca_MK+1q_up_maxCa_iCa_i+km_up-dkm_plb dq_up_Ca_MK=dq_up_Ca_MK_maxCa_MK_act1km_Ca_MK+Ca_MK_act1 dkm_plb=dkm_plb_maxCa_MK_act1km_Ca_MK+Ca_MK_act1

Component: q_tr

q_tr=Ca_NSR-Ca_JSRtau_tr

Component: model_parameters

a_geo=23.14radius2+23.14radiuslength a_cap=rcga_geo Vol_myo=Vol_cell0.68 Vol_nsr=Vol_cell0.0552 Vol_jsr=Vol_cell0.0048 Vol_ss=Vol_cell0.02
Source
Derived from workspace Aslanidi 2009 at changeset 794b3900e6b2.
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