Model Mathematics

Component: Environment

Component: Fixed_parameters

H_e=110-pH_e W_x=0.9W_m W_i=0.1W_m H_i=H_e K_i=K_e k_dHPi=110-6.75 k_dHatp=110-6.48 k_dHadp=110-6.29

Component: Adjustable_parameters

Component: Proton_motive_force

dG_H=FdPsi+RTlnH_iH_x

Component: Dehydrogenase_flux

J_DH=x_DHrNAD_x-NADH_x1+Pi_xk_Pi11+Pi_xk_Pi2

Component: Electron_flux_complex_I

dG_C1op=dG_C1o-RTlnH_x1 e -7-RTlnQQH2 J_C1=x_C1-dG_C1op+4dG_HRTNADH_x-NAD_x

Component: Electron_flux_complex_III

dG_C3op=dG_C3o+2RTlnH_x1 e -7-RTlnQH2Q J_C3=x_C31+Pi_xk_Pi31+Pi_xk_Pi4-dG_C3op+4dG_H-2FdPsi2RTCox-Cred

Component: Electron_flux_complex_IV

dG_C4op=dG_C4o-2RTlnH_x1 e -7-RT2lnO21 J_C4=x_C411+k_O2O2CredCtot-dG_C4op+2dG_H2RTCred-CoxFdPsiRT

Component: ATP_synthesis_flux

J_F1=x_F1-dG_F1o-n_AdG_HRTK_DDK_DTADP_mxPi_x-ATP_mx1

Component: ANT_flux

Psi_x=-0.65dPsi Psi_i=0.35dPsi J_ANT=x_ANTADP_fiADP_fi+ATP_fi-FPsi_iRT-ADP_fxADP_fx+ATP_fx-FPsi_xRTADP_fik_mADP+ADP_fiifADP_fi>mincondATP_fi>mincond0otherwise

Component: MgATPx_binding_flux

ATP_fx=ATP_x-ATP_mx J_MgATPx=x_MgAATP_fxMg_x-K_DTATP_mx

Component: MgADPx_binding_flux

ADP_fx=ADP_x-ADP_mx J_MgADPx=x_MgAADP_fxMg_x-K_DDADP_mx

Component: MgATPi_binding_flux

ATP_fi=ATP_i-ATP_mi J_MgATPi=x_MgAATP_fiMg_i-K_DTATP_mi

Component: MgADPi_binding_flux

ADP_fi=ADP_i-ADP_mi J_MgADPi=x_MgAADP_fiMg_i-K_DDADP_mi

Component: ATP_substrate_flux

J_ATP=gammap_AATP_e-ATP_i

Component: ADP_substrate_flux

J_ADP=gammap_AADP_e-ADP_i

Component: AMP_substrate_flux

J_AMP=gammap_AAMP_e-AMP_i

Component: Pi_substrate_flux

J_Pi2=gammax_Pi2Pi_e-Pi_i

Component: Phosphate_hydrogen_cotransporter_flux

H2PIi=Pi_iH_iH_i+k_dHPi H2PIx=Pi_xH_xH_x+k_dHPi J_Pi1=x_Pi1H_xH2PIi-H_iH2PIxH2PIi+k_PiH

Component: Adenylate_kinase_flux

J_AKi=x_AKK_AKADP_iADP_i-AMP_iATP_i

Component: Hydrogen_leak_flux

J_Hle=x_HledPsiH_iFdPsiRT-H_xFdPsiRT-1

Component: Passive_potassium_flux

J_K=x_KdPsiK_iFdPsiRT-K_xFdPsiRT-1

Component: Potassium_hydrogen_flux

J_KH=x_KHK_iH_x-K_xH_i

Component: NAD_x_concentration

NAD_x=NADtot-NADH_x

Component: Q_concentration

Q=Qtot-QH2

Component: Cox_concentration

Cox=Ctot-Cred

Component: ADP_binding

ADP_fe=ADP_e-ADP_me ADP_me=K_DD+ADP_e+Mg_tot-K_DD+ADP_e+Mg_tot2-4Mg_totADP_e2

Component: Mg_binding

Mg_e=Mg_tot-ADP_me Mg_i=Mg_e

Component: dH_x_dt

ddtH_x=x_buffH_xJ_DH-5J_C1-2J_C3-4J_C4+n_A-1J_F1+2J_Pi1+J_Hle-J_KHW_x

Component: dK_x_dt

ddtK_x=J_KH+J_KW_x

Component: dMg_x_dt

ddtMg_x=-J_MgATPx-J_MgADPxW_x

Component: dNADH_x_dt

ddtNADH_x=J_DH-J_C1W_x

Component: dQH2_dt

ddtQH2=J_C1-J_C3W_x

Component: dCred_dt

ddtCred=2J_C3-2J_C4W_i

Component: dATP_x_dt

ddtATP_x=J_F1-J_ANTW_x

Component: dADP_x_dt

ddtADP_x=-J_F1+J_ANTW_x

Component: dATP_mx_dt

ddtATP_mx=J_MgATPxW_x

Component: dADP_mx_dt

ddtADP_mx=J_MgADPxW_x

Component: dPi_x_dt

ddtPi_x=-J_F1+J_Pi1W_x

Component: dATP_i_dt

ddtATP_i=J_ATP+J_ANT+J_AKiW_i

Component: dADP_i_dt

ddtADP_i=J_ADP-J_ANT-2J_AKiW_i

Component: dAMP_i_dt

ddtAMP_i=J_AMP+J_AKiW_i

Component: dATP_mi_dt

ddtATP_mi=J_MgATPiW_i

Component: dADP_mi_dt

ddtADP_mi=J_MgADPiW_i

Component: dPi_i_dt

ddtPi_i=-J_Pi1+J_Pi2W_i

Component: dPsi_dt

ddtdPsi=4J_C1+2J_C3+4J_C4-n_AJ_F1-J_ANT-J_Hle-J_KC_im

Component: dO2_dt

ddtO2=0