Model Mathematics

Component: Environment

Component: fixed_parameters

H_c=110-pH_C k_dHPI=110-6.75 k_dHatp=110-6.48 k_dHadp=110-6.29 W_m=0.6641.09 W_x=0.9W_m W_i=0.1W_m W_c=0.8071.044 H_i=H_c K_i=K_c Rm_cyto=V_mitoV_cyto Rm_cell=V_mito Rc_cell=V_cyto dG_H=FdeltaPsi+RTlnH_iH_x dG_C1op=dG_C1o-1RTlnH_x1 e -7 dG_C3op=dG_C3o+2RTlnH_x1 e -7 dG_C4op=dG_C4o-2RTlnH_x1 e -7

Component: adjustable_parameters

Component: dNAD_x_dt

NAD_x=NAD_tot-NADH_x

Component: dQH2_x_dt

QH2_x=Q_tot-Q_x

Component: dCred_x_dt

Cred_x=C_tot-Cox_x

Component: dATP_fx_dt

ATP_fx=ATP_x-ATP_mx

Component: dADP_fx_dt

ADP_fx=ADP_x-ADP_mx

Component: dH_x_dt

H_x=110-pH_x ddtimepH_x=-12.303x_buffJ_DH-5J_C1-2J_C3-4J_C4+n_A-1J_F1+2J_PI1-J_KH+J_HleW_x

Component: dK_x_dt

ddtimeK_x=J_KH+J_KW_x

Component: dMg_x_dt

ddtimeMg_x=-J_MgADP_x-J_MgATP_xW_x

Component: dNADH_x_dt

ddtimeNADH_x=J_DH-J_C1W_x

Component: dQ_x_dt

ddtimeQ_x=-J_C1-J_C3W_x

Component: dCox_x_dt

ddtimeCox_x=-2J_C3-2J_C4W_x

Component: dATP_x_dt

ddtimeATP_x=J_F1-J_ANTW_x

Component: dADP_x_dt

ddtimeADP_x=-J_F1+J_ANTW_x

Component: dATP_mx_dt

ddtimeATP_mx=J_MgATP_xW_x

Component: dADP_mx_dt

ddtimeADP_mx=J_MgADP_xW_x

Component: dPI_x_dt

ddtimePI_x=-J_F1+J_PI1W_x

Component: dATP_fi_dt

ATP_fi=ATP_i-ATP_mi

Component: dADP_fi_dt

ADP_fi=ADP_i-ADP_mi

Component: dATP_i_dt

ddtimeATP_i=J_ATP+J_ANT+J_AKiW_i

Component: dADP_i_dt

ddtimeADP_i=J_ADP-J_ANT-2J_AKiW_i

Component: dAMP_i_dt

ddtimeAMP_i=J_AMP+J_AKiW_i

Component: dATP_mi_dt

ddtimeATP_mi=J_MgATP_iW_i

Component: dADP_mi_dt

ddtimeADP_mi=J_MgADP_iW_i

Component: dPI_i_dt

ddtimePI_i=-J_PI1+J_PI2W_i

Component: dMg_i_dt

ddtimeMg_i=-J_MgADP_i-J_MgATP_iW_i

Component: dATP_c_dt

ddtimeATP_c=-Rm_cytoJ_ATP+J_AKc-J_AtCRc_cell+J_CKcW_c

Component: dADP_c_dt

ddtimeADP_c=-Rm_cytoJ_ADP-2J_AKc+J_AtCRc_cell-J_CKcW_c

Component: dAMP_c_dt

ddtimeAMP_c=-Rm_cytoJ_AMP+J_AKcW_c

Component: dATP_mc_dt

ddtimeATP_mc=J_MgATP_cW_c

Component: dADP_mc_dt

ddtimeADP_mc=J_MgADP_cW_c

Component: dPI_c_dt

ddtimePI_c=-J_PI2Rm_cyto+J_AtCRc_cellW_c

Component: dMg_c_dt

ddtimeMg_c=-J_MgATP_c-J_MgADP_cW_c

Component: dPCr_c_dt

ddtimePCr_c=-J_CKcW_c

Component: dATP_fc_dt

ATP_fc=ATP_c-ATP_mc

Component: dADP_fc_dt

ADP_fc=ADP_c-ADP_mc

Component: dCr_c_dt

Cr_c=CR_tot-PCr_c

Component: ddeltaPsi_dt

ddtimedeltaPsi=4J_C1+2J_C3+4J_C4-n_AJ_F1-J_ANT-J_Hle-J_KC_IM

Component: J_DH

J_DH=X_DHrNAD_x-NADH_x1+PI_xk_PI11+PI_xk_PI2

Component: J_C1

J_C1=X_C1-dG_C1op+4dG_HRTNADH_xQ_x-NAD_xQH2_x

Component: J_C3

J_C3=X_C31+PI_xk_PI31+PI_xk_PI4-dG_C3op+4dG_H-2FdeltaPsi2RTCox_xQH2_x-Cred_xQ_x

Component: J_C4

J_C4=0ifO2_x<1 e -12X_C4O2_xO2_x+k_O2Cred_xC_tot-dG_C4op+2dG_H2RTCred_xO2_x10.25-Cox_xFdeltaPsiRTotherwise

Component: J_F1

J_F1=X_F1-dG_F1o-n_AdG_HRTK_DDK_DTADP_mxPI_x-ATP_mx1

Component: J_ANT

Psi_x=-0.65deltaPsi Psi_i=0.35deltaPsi J_ANT=X_ANTADP_fiADP_fi+ATP_fi-FPsi_iRT-ADP_fxADP_fx+ATP_fx-FPsi_xRTADP_fiADP_fi+k_mADPifADP_fi>minconATP_fi>mincon0otherwise

Component: J_PI1

H2PIi=PI_iH_iH_i+k_dHPI H2PIx=PI_xH_xH_x+k_dHPI J_PI1=X_PI1H_iH2PIi-H_xH2PIxH2PIi+k_PIH

Component: J_Hle

J_Hle=X_HledeltaPsiH_iFdeltaPsiRT-H_xFdeltaPsiRT-1if|deltaPsi|>mincondX_HleRTH_i-H_xFotherwise

Component: J_KH

J_KH=X_KHK_iH_x-K_xH_i

Component: J_K

J_K=X_KdeltaPsiK_iFdeltaPsiRT-K_xFdeltaPsiRT-1if|deltaPsi|>mincondX_KRTK_i-K_xFotherwise

Component: J_AMP

J_AMP=gammaX_AAMP_c-AMP_i

Component: J_ADP

J_ADP=gammaX_AADP_c-ADP_i

Component: J_ATP

J_ATP=gammaX_AATP_c-ATP_i

Component: J_PI2

J_PI2=gammaX_PI2PI_c-PI_i

Component: J_MgATP_x

J_MgATP_x=X_MgAATP_fxMg_x-K_DTATP_mx

Component: J_MgADP_x

J_MgADP_x=X_MgAADP_fxMg_x-K_DDADP_mx

Component: J_MgATP_i

J_MgATP_i=X_MgAATP_fiMg_i-K_DTATP_mi

Component: J_MgADP_i

J_MgADP_i=X_MgAADP_fiMg_i-K_DDADP_mi

Component: J_MgATP_c

J_MgATP_c=X_MgA1ATP_fcMg_c-K_DTATP_mc

Component: J_MgADP_c

J_MgADP_c=X_MgA1ADP_fcMg_c-K_DDADP_mc

Component: J_AKi

J_AKi=X_AKK_AKADP_iADP_i-AMP_iATP_i

Component: J_AKc

J_AKc=X_AK1K_AKADP_cADP_c-AMP_cATP_c

Component: J_AtC

J_AtC=X_AtC

Component: J_CKc

J_CKc=X_CK1K_CKADP_cPCr_cH_c-ATP_cCr_c