Model Mathematics

Component: environment

Component: cell_geometry

Component: membrane

FVRT=FVRT FVRT_Ca=2FVRT V=0iftime0time200-80otherwise

Component: CaRU

Component: CaRU_Transitions

expVL=V-V_Ldel_VL t_R=1.17t_L alpha_p=expVLt_LexpVL+1 alpha_m=phi_Lt_L beta_poc=C_oc2t_RC_oc2+K_RyR2 beta_pcc=Ca_i2t_RCa_i2+K_RyR2 beta_m=phi_Rt_R epsilon_pco=C_coexpVL+atau_LK_LexpVL+1 epsilon_pcc=Ca_iexpVL+atau_LK_LexpVL+1 epsilon_m=bexpVL+atau_LbexpVL+a mu_poc=C_oc2+cK_RyR2tau_RC_oc2+K_RyR2 mu_pcc=Ca_i2+cK_RyR2tau_RCa_i2+K_RyR2 mu_moc=theta_RdC_oc2+cK_RyR2tau_RdC_oc2+cK_RyR2 mu_mcc=theta_RdCa_i2+cK_RyR2tau_RdCa_i2+cK_RyR2

Component: DS_Calcium_Concentrations

C_cc=Ca_i C_co=Ca_i+J_Rg_DCa_SR1+J_Rg_D C_oc=Ca_i+J_Lg_DCa_oFVRT_Ca-FVRT_Ca1--FVRT_Ca1+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.000000001Ca_i+J_Lg_DCa_o1+J_Lg_Dotherwise C_oo=Ca_i+J_Rg_DCa_SR+J_Lg_DCa_oFVRT_Ca-FVRT_Ca1--FVRT_Ca1+J_Rg_D+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.000000001Ca_i+J_Rg_DCa_SR+J_Lg_DCa_o1+J_Rg_D+J_Lg_Dotherwise

Component: LCC_and_RyR_fluxes

J_Rco=J_RCa_SR-Ca_i1+J_Rg_D J_Roo=J_RCa_SR-Ca_i+J_Lg_DFVRT_Ca1--FVRT_CaCa_SR-Ca_o-FVRT_Ca1+J_Rg_D+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.00001J_RCa_SR-Ca_i+J_Lg_D0.000011--0.00001Ca_SR-Ca_o-0.000011+J_Rg_D+J_Lg_D0.000011--0.00001otherwise J_Loc=J_LFVRT_Ca1--FVRT_CaCa_o-FVRT_Ca-Ca_i1+J_Lg_DFVRT_Ca1--FVRT_Caif|FVRT_Ca|>0.00001J_L0.000011--0.00001Ca_o-0.00001-Ca_i1+J_Lg_D0.000011--0.00001otherwise J_Loo=J_LFVRT_Ca1--FVRT_CaCa_o-FVRT_Ca-Ca_i+J_Rg_DCa_o-FVRT_Ca-Ca_SR1+J_Rg_D+J_Lg_DFVRT_Ca1-FVRT_Caif|FVRT_Ca|>0.00001J_L0.000011--0.00001Ca_o-0.00001-Ca_i+J_Rg_DCa_o-0.00001-Ca_SR1+J_Rg_D+J_Lg_D0.000011--0.00001otherwise

Component: CaRU_states

denom=alpha_p+alpha_malpha_m+beta_m+beta_pocbeta_m+beta_pcc+alpha_pbeta_m+beta_poc y_oc=alpha_pbeta_malpha_p+alpha_m+beta_m+beta_pccdenom y_co=alpha_mbeta_pccalpha_m+beta_m+beta_poc+beta_pocalpha_pdenom y_oo=alpha_pbeta_pocalpha_p+beta_m+beta_pcc+beta_pccalpha_mdenom y_cc=alpha_mbeta_malpha_m+alpha_p+beta_m+beta_pocdenom y_ci=alpha_malpha_p+alpha_m y_oi=alpha_palpha_p+alpha_m y_ic=beta_mbeta_pcc+beta_m y_io=beta_pccbeta_pcc+beta_m y_ii=1-y_oc-y_co-y_oo-y_cc-y_ci-y_ic-y_oi-y_io

Component: CaRU_reduced_states

r_1=y_ocmu_poc+y_ccmu_pcc r_2=alpha_pmu_moc+alpha_mmu_mccalpha_p+alpha_m r_3=beta_mmu_pccbeta_m+beta_pcc r_4=mu_mcc r_5=y_coepsilon_pco+y_ccepsilon_pcc r_6=epsilon_m r_7=alpha_mepsilon_pccalpha_p+alpha_m r_8=epsilon_m z_4=1-z_1-z_2-z_3 ddtimez_1=-r_1+r_5z_1+r_2z_2+r_6z_3 ddtimez_2=r_1z_1-r_2+r_7z_2+r_8z_4 ddtimez_3=r_5z_1-r_6+r_3z_3+r_4z_4

Component: RyR_current

J_R1=y_ooJ_Roo+J_Rcoy_co J_R3=J_Rcobeta_pccbeta_m+beta_pcc I_RyR=z_1J_R1+z_3J_R3NV_myo

Component: LCC_current

J_L1=J_Looy_oo+J_Locy_oc J_L2=J_Localpha_palpha_p+alpha_m I_LCC=z_1J_L1+z_2J_L2NV_myo

Component: Na_Ca_Exchanger

I_NaCa=g_NCXetaFVRTNa_i3Ca_o-eta-1FVRTNa_o3Ca_iNa_o3+K_mNa3Ca_o+K_mCa1+k_sateta-1FVRT

Component: SERCA

I_SERCA=g_SERCACa_i2K_SERCA2+Ca_i2

Component: Sarcolemmal_Ca_pump

I_pCa=g_pCaCa_iK_mpCa+Ca_i

Component: Background_Ca_current

E_Ca=RT2FlnCa_oCa_i I_CaB=g_CaBE_Ca-V

Component: SR_Ca_leak_current

I_SR=g_SRlCa_SR-Ca_i

Component: troponin_Ca_buffer

I_TRPN=k_m_TRPNB_TRPN-TRPN-k_p_TRPNTRPNCa_i

Component: calmodulin_Ca_buffer

beta_CMDN=1+k_CMDNB_CMDNk_CMDN+Ca_i2-1

Component: intracellular_ion_concentrations

ddtimeTRPN=I_TRPN ddtimeCa_i=beta_CMDNI_LCC+I_RyR-I_SERCA+I_SR+I_NaCa-I_pCa+I_CaB+I_TRPN ddtimeCa_SR=V_myoV_SR-I_RyR+I_SERCA-I_SR CaSR_plot=Ca_SRV_SRV_myo

Component: extracellular_ion_concentrations