Model Mathematics

Component: environment

vol_cyt=fr_cytvol_pmu vol_pmu=πdia361 e 9111 V_tau=RTF

Component: Membrane

SVR_pmu=svrdia C_m=C_spA_pmu VD=VV_tau V=Fvol_cytC_spA_pmuK_i-K_o+2Ca_i-Ca_o+Na_i-Na_o+anoff anoff=-52.31C_spA_pmuFvol_cyt-21.5 e -4-Ca_o-6-Na_o-140-K_o A_pmu=SVR_pmuvol_pmu1 e -31 e -31 e -31 V_Ca=0.5lnCa_oCa_i V_Na=lnNa_oNa_i V_K=lnK_oK_i

Component: Cytosol

ddtCa_i=J_Ca ddtNa_i=J_Na ddtK_i=J_K

Component: calcium_dynamics

J_Ca=J_ca-J_calb+4J_cam J_ca=-12Fvol_cytI_CaL+I_CaT+I_CaHVA+2I_pmca-2I_xm

Component: sodium_dynamics

J_Na=-1Fvol_cyt3I_nk+3I_xm+I_Na+I_Nalk+I_NaHCN

Component: potassium_dynamics

I_K=I_Ksk+I_KHCN+I_Ka+I_Kdr+I_Kir J_K=-1Fvol_cytI_K-2I_nk

Component: calcium_buffer_dynamics

J_calb=kcal_1CalbCa_i-kcal_2CaCalb J_cam=alpha_camCam-beta_camCaCam kcam_cb=12000Ca_i2 kcam_nb=3.7 e 6Ca_i2 alpha_cam=kcam_cbkcam_nb1kcam_cb+kcam_nd+1kcam_cd+kcam_nd beta_cam=kcam_cdkcam_nd1kcam_cb+kcam_nd+1kcam_cd+kcam_nd CaCalb=Calbtot-Calb CaCam=Camtot-Cam ddtCalb=-J_calb ddtCam=-J_cam

Component: L_type_Ca_channel

I_CaL=g_calm_calh_calCa_iCa_osinhVD-V_CasinhVDVD ddtm_cal=11+-V+157-m_cal10-V+86.423.22+0.943 h_cal=0.000450.00045+Ca_i

Component: T_type_Ca_channel

I_CaT=g_catm_cath_catCa_iCa_osinhVD-V_CasinhVDVD ddtm_cat=11+-V+631.5-m_cat65-V+6862+12 ddth_cat=11+V+76.23-h_cat50-V+72102+10

Component: HVA_Ca_channel

I_CaHVA=g_cahm_cahh_cahCa_iCa_osinhVD-V_CasinhVDVD ddtm_cah=11+-V+1010-m_cah0.1-V+62132+0.05 ddth_cah=11+V+485-h_cah0.5-V+55.6182+0.5

Component: transient_Na_channel

O_na=m_na3h_na ddtm_na=A_mnaza_mnaVD1-m_na-B_mna-zb_mnaVDm_na ddth_na=A_hnaza_hnaVD1-h_na-B_hna-zb_hnaVDh_na I_Na=g_naO_naNa_iNa_osinh0.5VD-V_Nasinh0.5VD0.5VD

Component: Leak_Na_channel

I_Nalk=g_nalkNa_iNa_osinh0.5VD-V_Nasinh0.5VD0.5VD

Component: HCN_channel

ddtO_hcn=kf_hcn1-O_hcn-kr_hcnO_hcn kf_hcn=kf_freeP_c+kf_bnd1-P_c kr_hcn=kr_freeP_o+kr_bnd1-P_o kf_free=0.0061+V+87.76.45 kr_free=0.081+-V+51.77 kf_bnd=0.02681+V+94.213.3 kr_bnd=0.081+-V+35.57 P_c=11+cAMP1.163 e -3 P_o=11+cAMP1.45 e -5 I_NaHCN=g_nahcnO_hcnNa_iNa_osinh0.5VD-V_Nasinh0.5VD0.5VD I_KHCN=g_khcnO_hcnK_iK_osinh0.5VD-V_Ksinh0.5VD0.5VD

Component: SK_K_channel

O_sk=Ca_i4.20.35 e -34.2+Ca_i4.2 I_Ksk=g_kskO_skK_iK_osinh0.5VD-V_Ksinh0.5VD0.5VD

Component: DR_K_channel

I_Kdr=g_kdrO_kdrV-V_KV_tau O_kdr=m_kdr3 ddtm_kdr=11+-V+2512-m_kdr181+V+398+1

Component: Atype_K_channel

I_Ka=g_kaO_kaV-V_KV_tau O_ka=p_ka3q_ka ddtp_ka=11+-V+4324-p_ka2-V+5023.452+1.1 ddtq_ka=11+V+568-q_ka20

Component: IR_K_channel

I_Kir=g_kirO_kirV-V_KV_tau O_kir=11+V+9012.1

Component: sodium_pump

I_nk=k_nkk_1nkP_E1Snky_nk-k_2nkP_E2Snk1-y_nk1 k_1nk=0.371+0.094atp Na_eff=Na_o-0.82VD ddty_nk=beta_nk1-y_nk-alpha_nky_nk beta_nk=k_2nkP_E2Snk+k_4nkP_E2Dnk alpha_nk=k_1nkP_E1Snk+k_3nkP_E1Dnk P_E1Snk=11+K_nknaiNa_i1+K_iK_nkki P_E1Dnk=11+K_nkkiK_i1+Na_iK_nknai P_E2Snk=11+K_nknaoNa_eff1+K_oK_nkko P_E2Dnk=11+K_nkkoK_o1+Na_effK_nknao

Component: PMCA

I_pmca=K_pmcak_1pcP_E1Spcy_pc-k_2pcP_E2Spc1-y_pc1 K_pmca=k_pmca10.56CaCamCaCam+0.00005+1.2 ddty_pc=beta_pc1-y_pc-alpha_pcy_pc k_1pc=11+0.1atp P_E1Spc=11+K_pciCa_i P_E1pc=1-P_E1Spc P_E2Spc=11+K_pcoCa_o P_E2pc=1-P_E2Spc beta_pc=k_2pcP_E2Spc+k_4pcP_E2pc alpha_pc=k_1pcP_E1Spc+k_3pcP_E1pc K_pci=173.61+CaCam0.00005+6.41 e -5

Component: Membrane_NaCa

I_xm=k_xmk_3xmP_E1Dxmy_xm-k_4xmP_E2Dxm1-y_xm ddty_xm=beta_xm1-y_xm-alpha_xmy_xm beta_xm=k_2xmP_E2Sxm+k_4xmP_E2Dxm alpha_xm=k_1xmP_E1Sxm+k_3xmP_E1Dxm P_E1Sxm=11+K_xmcaiCa_i1+Na_iK_xmnai3 P_E1Dxm=11+K_xmnaiNa_i31+Ca_iK_xmcai P_E2Sxm=11+K_xmcaoCa_o1+Na_oK_xmnao3 P_E2Dxm=11+K_xmnaoNa_o31+Ca_oK_xmcao k_1xm=1-delta_xmcaVD k_2xm=11-delta_xmcaVD k_3xm=11-delta_xmnaVD k_4xm=1-delta_xmnaVD