Model Mathematics

Component: environment

Component: membrane

ddtimeV=-i_Na+i_Ca_T+i_Ca_L+i_K+i_f+i_B+i_NaK+i_NaCa+i_Ca_P+i_K_AChCm

Component: sodium_current

F_ACh_Na=1-AChACh+1e-3 i_Na=F_ACh_NaP_Nam3h1h2Na_cVF2RTV-E_NaFRT-1VFRT-1

Component: sodium_current_m_gate

alpha_m=-824V+51.9V+51.9-8.9-1 beta_m=32960V+51.9-8.9 m_infinity=alpha_malpha_m+beta_m tau_m=1alpha_m+beta_m+0.000015 ddtimem=m_infinity-mtau_m

Component: sodium_current_h_gate

alpha_h1=165V+101.3-12.6 beta_h1=12360320V+101.3-12.6+1 h1_infinity=alpha_h1alpha_h1+beta_h1 tau_h1=1alpha_h1+beta_h1 h2_infinity=h1_infinity tau_h2=20tau_h1 ddtimeh1=h1_infinity-h1tau_h1 ddtimeh2=h2_infinity-h2tau_h2

Component: L_type_Ca_channel

F_cAMP_CaL=0.41+4.5cAMPcAMP+6.5e-3+0.03157 g_Ca_L=g_Ca_L_contF_cAMP_CaL i_Ca_L=g_Ca_Lf_Ld_L+0.095d_L_infinityV-E_Ca_L

Component: L_type_Ca_channel_d_gate

alpha_d_L=-28.39V+35V+35-2.5-1+-84.9V-0.208V-1 beta_d_L=11.43V-50.4V-5-1 tau_d_L=1alpha_d_L+beta_d_L d_L_infinity=11+V+14.1-6 ddtimed_L=d_L_infinity-d_Ltau_d_L

Component: L_type_Ca_channel_f_gate

alpha_f_L=3.75V+28V+284-1 beta_f_L=301+V+28-4 tau_f_L=1alpha_f_L+beta_f_L f_L_infinity=11+V+305 ddtimef_L=f_L_infinity-f_Ltau_f_L

Component: T_type_Ca_channel

i_Ca_T=g_Ca_Td_Tf_TV-E_Ca_T

Component: T_type_Ca_channel_d_gate

alpha_d_T=1068V+26.330 beta_d_T=1068V+26.3-30 tau_d_T=1alpha_d_T+beta_d_T d_T_infinity=11+V+26.3-6 ddtimed_T=d_T_infinity-d_Ttau_d_T

Component: T_type_Ca_channel_f_gate

alpha_f_T=15.3V+61.7-83.3 beta_f_T=15V+61.715.38 tau_f_T=1alpha_f_T+beta_f_T f_T_infinity=11+V+61.75.6 ddtimef_T=f_T_infinity-f_Ttau_f_T

Component: delayed_rectifying_potassium_current

F_cAMP_K=0.621+2.6129cAMPcAMP+9e-3-0.025 g_K=F_cAMP_K0.00693K_b10.59 i_K=g_KP_aP_iV-E_K

Component: delayed_rectifying_potassium_current_P_a_gate

P_a_infinity=11+V+5.1-7.4 tau_P_a=1170.0398V+2.11-0.051V ddtimeP_a=P_a_infinity-P_atau_P_a

Component: delayed_rectifying_potassium_current_P_i_gate

alpha_P_i=100-0.0183V beta_P_i=6560.00942V ddtimeP_i=alpha_P_i1-P_i-beta_P_iP_i

Component: linear_background_current

F_ACh_bNa=1-AChACh+5e-1 i_B_Na=F_ACh_bNag_B_NaV-E_Na i_B_Ca=g_B_CaV-E_Ca i_B_K=g_B_KV-E_K i_B=i_B_Na+i_B_Ca+i_B_K

Component: hyperpolarisation_activated_current

i_f_Na=g_f_Nay2V-75 i_f_K=g_f_Ky2V+85 i_f=i_f_Na+i_f_K

Component: hyperpolarisation_activated_current_y_gate

V_half=20.51+cAMP-3.4e-3-5e-4-78.56 y_infinity=11+V-V_half9 tau_y=11.6483V+54.06-24.33+14.010550.7+V+60-5.5 ddtimey=y_infinity-ytau_y

Component: sodium_potassium_pump

F_cAMP_NaK=1.61+cAMP-3.75e-3-1.5e-4+0.99 i_NaK=2-F_cAMP_NaKi_NaK_maxNa_iK_m_Na+Na_i3K_cK_m_K+K_c21.61.5+V+60-40ifCa_i<0.00015F_cAMP_NaKi_NaK_maxNa_iK_m_Na+Na_i3K_cK_m_K+K_c21.61.5+V+60-40otherwise

Component: calcium_pump_current

i_Ca_P=i_Ca_P_maxCa_iCa_i+0.0004

Component: sodium_calcium_pump

i_NaCa=K_NaCaNa_i3Ca_c0.03743Vgamma-Na_c3Ca_i0.03743Vgamma-11+d_NaCaCa_iNa_c3+Ca_cNa_i3

Component: muscarinic_potassium_current

i_K_ACh=aI_K_ACh ddtimea=beta_a1-a-alpha_aa beta_a=12.321+0.0042ACh alpha_a=170.0133V+40 I_K_ACh=g_K_AChV-E_K g_K_ACh=P_M2_KAChg_K_ACh_base P_M2_KACh=1.0261+f_Vagal+11.05-7.5095-0.99iff_Vagal<100f_Vagal>250.0006otherwise

Component: intracellular_concentrations_and_buffer_equations

V_i=0.465Vol phi_C=129000Ca_i1-Ca_Calmod-307Ca_Calmod ddtimeCa_Calmod=phi_C phi_TC=50500Ca_i1-Ca_Trop-252Ca_Trop ddtimeCa_Trop=phi_TC phi_TMgC=129000Ca_i1-Ca_Mg_Trop+Mg_Mg_Trop-4.25Ca_Mg_Trop ddtimeCa_Mg_Trop=phi_TMgC phi_TMgM=1290Mg_i1-Ca_Mg_Trop+Mg_Mg_Trop-429Mg_Mg_Trop ddtimeMg_Mg_Trop=phi_TMgM F_C=0.09phi_C F_TC=0.031phi_TC F_TMgC=0.062phi_TMgC phi_B=F_C+F_TC+F_TMgC ddtimeNa_i=-3i_NaK+3i_NaCa+i_B_Na+i_f_Na+i_NaFV_i ddtimeK_i=2i_NaK-i_K+i_f_K+i_B_KFV_i ddtimeCa_i=2i_NaCa+i_rel-i_Ca_L+i_Ca_T+i_Ca_P+i_B_Ca+i_up2V_iF-phi_B

Component: cleft_space_equations

V_c=0.136Vol ddtimeNa_c=Na_b-Na_ctau_p+i_Na+3i_NaCa+3i_NaK+i_B_Na+i_f_NaFV_c ddtimeK_c=K_b-K_ctau_p+-2i_NaK+i_K+i_B_K+i_f_KFV_c ddtimeCa_c=Ca_b-Ca_ctau_p+-2i_NaCa+i_Ca_L+i_Ca_T+i_Ca_P+i_B_Ca2FV_c

Component: SR_Ca_uptake_and_release

V_up=0.01166V_i V_rel=0.001296V_i K1=k_cycak_xcsk_SRCa K2=Ca_i+Ca_upK1+k_cycak_xcs+k_cyca r_act=240V-400.08+240Ca_iCa_i+k_rel4 r_inact=40+240Ca_iCa_i+k_rel4 phi_Calse=770Ca_rel1-Ca_Calse-641Ca_Calse ddtimeCa_Calse=phi_Calse ddtimeF1=0.96F3-r_actF1 ddtimeF2=r_actF1-r_inactF2 ddtimeF3=r_inactF2-0.96F3 i_rel=alpha_relF2F2+0.252Ca_rel i_tr=Ca_up-Ca_rel2FV_up0.06418 i_up=alpha_upCa_i-beta_upCa_upK1K2 ddtimeCa_up=i_up-i_tr2V_upF ddtimeCa_rel=i_tr-i_rel2V_relF-11.48phi_Calse

Component: reversal_potentials

E_Na=RTFlnNa_cNa_i E_K=RTFlnK_cK_i E_Ca=0.5RTFlnCa_cCa_i

Component: cAMP_balance

ddtimecAMP=1K_ADC1+IsoIso+Km_Iso-P_M2_ADCAChP_M2_ADCACh+Km_ACh-V_PDEcGMPcAMPcAMP+K_PDEcGMP