Model Mathematics

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Component: Environment

Component: adjustable_parameters

X_HK = \{\begin{matrix} 0.191 if ExpType = 1 \land StateType = 3 \\ 0 otherwise \end{matrix}

Component: fixed_parameters

RT = \{\begin{matrix} 2.5037 if ExpType = 1 \\ 2.57858 otherwise \end{matrix} W_c = \{\begin{matrix} 80 if ExpType = 1 \\ 800 if ExpType = 2 \\ 0.842508 if ExpType = 3 \lor ExpType = 4 \\ 80 otherwise \end{matrix} V_mito = \{\begin{matrix} 0.2882 if ExpType = 3 \\ 0.056 if ExpType = 4 \\ 1 otherwise \end{matrix} V_cyto = \{\begin{matrix} 0.6801 if ExpType = 3 \\ 0.894 if ExpType = 4 \\ 1 otherwise \end{matrix}

Component: J_C1

J_C1 = X_C1 (k_eqC1 NADH_x COQ_x - (NAD_x QH2_x))

Component: k_eqC1

k_eqC1_nought = ⅇ^{\frac{- (deltaG_C1 + 4 F deltaPsi)}{RT}} k_eqC1 = \frac{\frac{k_eqC1_nought {H_x}^{5}}{{H_i}^{4}}}{1}

Component: J_C3

J_C3 = \frac{X_C3 (1 + \frac{PI_x}{k_PI_1})}{1 + \frac{PI_x}{k_PI_2}} ({k_eqC3}^{0.5} Cox_i {QH2_x}^{0.5} - (Cred_i {COQ_x}^{0.5}))

Component: k_eqC3

k_eqC3_nought = ⅇ^{\frac{- (deltaG_C3 + 2 F deltaPsi)}{RT}} k_eqC3 = \frac{1 1 k_eqC3_nought {H_x}^{2}}{{H_i}^{4}}

Component: J_C4

J_C4 = \frac{\frac{X_C4 O2_x}{O2_x + k_O2} ⅇ^{\frac{F deltaPsi}{RT}} Cred_i}{cytC_tot} ({k_eqC4}^{\frac{1}{2}} Cred_i {O2_x}^{\frac{1}{4}} - Cox_i)

Component: k_eqC4

k_eqC4_nought = ⅇ^{\frac{- (deltaG_C4 + 4 F deltaPsi)}{RT}} k_eqC4 = \frac{\frac{k_eqC4_nought {H_x}^{4}}{{H_i}^{2}}}{1 1}

Component: J_F1

J_F1 = X_F1 (k_eqF1 ADP_x PI_x - ATP_x)

Component: k_eqF1

k_eqF1_nought = ⅇ^{\frac{- (deltaG_F1 - (n_A F deltaPsi))}{RT}} k_eqF1 = \frac{k_eqF1_nought {H_i}^{n_A} P_ATP_x}{{H_x}^{n_A - 1} P_ADP_x P_PI_x 1}

Component: J_pdh

K_eq_pdh = \frac{K0_eq_pdh P_CO2_tot_x}{H_x P_PYR_x P_COASH_x} alpha_i1 = 1 + \frac{ACCOA_x}{K_iACCOA} alpha_i2 = 1 + \frac{NADH_x}{K_iNADH} J_pdh = \{\begin{matrix} \frac{V_mf (PYR_x COASH_x NAD_x - (\frac{CO2_tot_x ACCOA_x NADH_x}{K_eq_pdh}))}{K_mC alpha_i2 PYR_x COASH_x + K_mB alpha_i1 PYR_x NAD_x + K_mA COASH_x NAD_x + PYR_x COASH_x NAD_x} if PYR_x > minCon \land COASH_x > minCon \land NAD_x > minCon \\ 0 otherwise \end{matrix}

Component: J_cits

K_eq_cits = \frac{K0_eq_cits P_CIT_x}{H_x H_x P_OAA_x} alpha_i1 = 1 + \frac{uCIT_x}{K_iCIT} alpha_i2 = 1 + \frac{fATP_x}{K_iATP} + \frac{fADP_x}{K_iADP} + \frac{fAMP_x}{K_iAMP} + \frac{COASH_x}{K_iCOASH} + \frac{SCOA_x}{K_iSCOA} J_cits = \frac{V_mf (ACCOA_x OAA_x - (\frac{COASH_x CIT_x}{K_eq_cits}))}{K_ia K_mB alpha_i1 + K_mA alpha_i1 ACCOA_x + K_mB alpha_i2 OAA_x + OAA_x ACCOA_x}

Component: J_acon

K_eq_acon = \frac{K0_eq_acon P_ICIT_x}{P_CIT_x} V_mr = \frac{V_mf K_mP}{K_mA K_eq_acon} J_acon = \frac{V_mf V_mr (CIT_x - (\frac{ICIT_x}{K_eq_acon}))}{K_mA V_mr + V_mr CIT_x + \frac{V_mf ICIT_x}{K_eq_acon}}

Component: J_isod

K_eq_isod = \frac{K0_eq_isod P_CO2_tot_x}{H_x H_x P_ICIT_x} alpha_i = 1 + \frac{K_aADP}{fADP_x} (1 + \frac{fATP_x}{K_aATP}) J_isod = \{\begin{matrix} \frac{V_mf (1 - (\frac{CO2_tot_x AKG_x NADH_x}{K_eq_isod NAD_x ICIT_x}))}{1 + {(\frac{K_mB}{ICIT_x})}^{n_H} alpha_i + \frac{K_mA}{NAD_x} (1 + {(\frac{K_ib}{ICIT_x})}^{n_H} alpha_i + \frac{NADH_x alpha_i}{K_iq})} if NAD_x > minCon \land ICIT_x > minCon \\ 0 otherwise \end{matrix}

Component: J_akgd

K_eq_akgd = \frac{K0_eq_akgd P_CO2_tot_x P_SCOA_x}{H_x P_COASH_x} alpha_i = 1 + \frac{K_aADP}{fADP_x} (1 + \frac{fATP_x}{K_iATP}) J_akgd = \{\begin{matrix} \frac{\frac{V_mf (1 - (\frac{CO2_tot_x SCOA_x NADH_x}{K_eq_akgd AKG_x COASH_x NAD_x}))}{1 + \frac{K_mA}{AKG_x} alpha_i + \frac{K_mB}{COASH_x} (1 + \frac{SCOA_x}{K_iq}) + \frac{K_mC}{NAD_x} (1 + \frac{NADH_x}{K_ir})}}{1 + \frac{NADH_x}{K_ir2}} if AKG_x > minCon \land COASH_x > minCon \land NAD_x > minCon \\ 0 otherwise \end{matrix}

Component: J_scoas

K_eq_scoas = \frac{K0_eq_scoas P_COASH_x P_SUC_x P_GTP_x}{H_x P_GDP_x P_SCOA_x P_PI_x} V_mr = \frac{V_mf K_mCOASH K_iSUC K_iGTP}{K_eq_scoas K_iGDP K_iSCOA K_mPI} J_scoas = \frac{V_mf V_mr (GDP_x SCOA_x PI_x - (\frac{COASH_x SUC_x GTP_x}{K_eq_scoas}))}{V_mr K_iGDP K_iSCOA K_mCOASH + V_mr K_iSCOA K_mCOASH GDP_x + V_mr K_iGDP K_mSCOA PI_x + V_mr K_mCOASH GDP_x SCOA_x + V_mr K_mSCOA GDP_x PI_x + V_mr K_mGDP SCOA_x PI_x + V_mr GDP_x SCOA_x PI_x + \frac{V_mf K_iGTP K_mSUC COASH_x}{K_eq_scoas} + \frac{V_mf K_iSUC K_mCOASH GTP_x}{K_eq_scoas} + \frac{V_mf K_mGTP COASH_x SUC_x}{K_eq_scoas} + \frac{V_mf K_mSUC COASH_x GTP_x}{K_eq_scoas} + \frac{V_mf K_mCOASH SUC_x GTP_x}{K_eq_scoas} + \frac{V_mf COASH_x SUC_x GTP_x}{K_eq_scoas} + \frac{V_mf K_mSUC K_iGTP GDP_x COASH_x}{K_iGDP K_eq_scoas} + \frac{V_mr K_iGDP K_mSCOA PI_x GTP_x}{K_iGTP} + \frac{V_mf K_mSUC K_iGTP GDP_x SCOA_x SUC_x}{K_iGDP K_iSCOA K_eq_scoas} + \frac{V_mr K_mGDP SCOA_x PI_x GTP_x}{K_iGTP} + \frac{V_mf K_mGTP GDP_x COASH_x SUC_x}{K_iGDP K_eq_scoas} + \frac{V_mr K_iGDP K_mSCOA PI_x SUC_x GTP_x}{K_iSUC K_iGTP} + \frac{V_mf K_iGTP K_mSUC GDP_x SCOA_x PI_x COASH_x}{K_iGDP K_iSCOA K_iPI K_eq_scoas} + \frac{V_mf K_iCOASH K_mGTP GDP_x SCOA_x PI_x SUC_x}{K_iGDP K_iSCOA K_iCOASH K_eq_scoas} + \frac{V_mf K_mGTP GDP_x SCOA_x COASH_x SUC_x}{K_iGDP K_iSCOA K_eq_scoas} + \frac{V_mf K_mGDP SCOA_x PI_x SUC_x GTP_x}{K_iSUC K_iGTP} + \frac{V_mr K_mGDP K_iCOASH SCOA_x COASH_x SUC_x GTP_x}{K_iCOASH K_iSUC K_iGTP} + \frac{V_mr K_iGDP K_mSCOA PI_x COASH_x SUC_x GTP_x}{K_iCOASH K_iSUC K_iGTP} + \frac{V_mf K_mGTP GDP_x SCOA_x PI_x COASH_x SUC_x}{K_iGDP K_iSCOA K_iCOASH K_eq_scoas} + \frac{V_mf K_mGDP SCOA_x PI_x COASH_x SUC_x GTP_x}{K_iCOASH K_iSUC K_iGTP}}

Component: J_sdh

K_eq_sdh = \frac{K0_eq_sdh P_FUM_x}{P_SUC_x} V_mr = \frac{V_mf K_mQH2 K_iq}{K_eq_sdh K_ia K_mCOQ} alpha_i = \frac{1 + \frac{OAA_x}{K_iOAA} + \frac{SUC_x}{K_aSUC} + \frac{FUM_x}{K_aFUM}}{1 + \frac{SUC_x}{K_aSUC} + \frac{FUM_x}{K_aFUM}} J_sdh = \frac{V_mf V_mr (SUC_x COQ_x - (\frac{QH2_x FUM_x}{K_eq_sdh}))}{V_mr K_ia K_mCOQ alpha_i + V_mr K_mCOQ SUC_x + V_mr K_mSUC alpha_i COQ_x + \frac{V_mf K_mFUM alpha_i QH2_x}{K_eq_sdh} + \frac{V_mf K_mQH2 FUM_x}{K_eq_sdh} + V_mr SUC_x COQ_x + \frac{V_mf K_mFUM SUC_x QH2_x}{K_eq_sdh K_ia} + \frac{V_mr K_mSUC COQ_x FUM_x}{K_iq} + \frac{V_mf QH2_x FUM_x}{K_eq_sdh}}

Component: J_fum

K_eq_fum = \frac{K0_eq_fum P_MAL_x}{P_FUM_x} V_mr = \frac{V_mf K_mMAL}{K_eq_fum K_mFUM} alpha_i = 1 + \frac{CIT_x}{K_iCIT} + \frac{fATP_x}{K_iATP} + \frac{fADP_x}{K_iADP} + \frac{fGTP_x}{K_iGTP} + \frac{fGDP_x}{K_iGDP} J_fum = \frac{V_mr V_mf (FUM_x - (\frac{MAL_x}{K_eq_fum}))}{K_mFUM V_mr alpha_i + V_mr FUM_x + \frac{V_mf MAL_x}{K_eq_fum}}

Component: J_mdh

K_eq_mdh = \frac{K0_eq_mdh P_OAA_x}{H_x P_MAL_x} V_mr = \frac{V_mf K_iq K_mOAA}{K_eq_mdh K_ia K_mMAL} alpha_i = 1 + \frac{fATP_x}{K_iATP} + \frac{fADP_x}{K_iADP} + \frac{fAMP_x}{K_iAMP} J_mdh = \frac{V_mf V_mr (NAD_x MAL_x - (\frac{OAA_x NADH_x}{K_eq_mdh}))}{V_mr K_ia K_mMAL alpha_i + V_mr K_mMAL NAD_x + V_mr K_mNAD alpha_i MAL_x + \frac{V_mf K_mNADH alpha_i OAA_x}{K_eq_mdh} + \frac{V_mf K_mOAA NADH_x}{K_eq_mdh} + V_mr NAD_x MAL_x + \frac{V_mf K_mNADH NAD_x OAA_x}{K_eq_mdh K_ia} + \frac{V_mf OAA_x NADH_x}{K_eq_mdh} + \frac{V_mr K_mNAD MAL_x NADH_x}{K_iq} + \frac{V_mr NAD_x MAL_x OAA_x}{K_ip} + \frac{V_mf MAL_x OAA_x NADH_x}{K_ib K_eq_mdh}}

Component: J_ndk

V_mr = \frac{V_mf K_mQ K_ip}{K_eq_ndk K_ia K_mB} alpha_i = 1 + \frac{fAMP_x}{K_iAMP} J_ndk_f = \{\begin{matrix} \frac{\frac{V_mf V_mr}{alpha_i} GTP_x ADP_x}{V_mr K_mB GTP_x + V_mr K_mA ADP_x + \frac{V_mf K_mQ GDP_x}{K_eq_ndk} + \frac{V_mf K_mP ATP_x}{K_eq_ndk} + V_mr GTP_x ADP_x + \frac{V_mf K_mQ GTP_x GDP_x}{K_eq_ndk K_ia} + \frac{V_mf GDP_x ATP_x}{K_eq_ndk} + \frac{V_mr K_mA ADP_x ATP_x}{K_iq}} if GTP_x > minCon \land ADP_x > minCon \\ 0 otherwise \end{matrix} J_ndk = \{\begin{matrix} J_ndk_f - (\frac{\frac{\frac{V_mf V_mr}{alpha_i} GDP_x ATP_x}{K_eq_ndk}}{V_mr K_mB GTP_x + V_mr K_mA ADP_x + \frac{V_mf K_mQ GDP_x}{K_eq_ndk} + \frac{V_mf K_mP ATP_x}{K_eq_ndk} + V_mr GTP_x ADP_x + \frac{V_mf K_mQ GTP_x GDP_x}{K_eq_ndk K_ia} + \frac{V_mf GDP_x ATP_x}{K_eq_ndk} + \frac{V_mr K_mA ADP_x ATP_x}{K_iq}}) if GDP_x > minCon \land ATP_x > minCon \\ J_ndk_f otherwise \end{matrix}

Component: J_got

K_eq_got = \frac{K0_eq_got P_GLU_x P_OAA_x}{P_ASP_x} V_mr = \frac{V_mf K_mQ K_ip}{K_eq_got K_ia K_mB} alpha_i = 1 + \frac{AKG_x}{K_iAKG} J_got_f = \{\begin{matrix} \frac{V_mf V_mr ASP_x AKG_x}{V_mr K_mB ASP_x + V_mr K_mA alpha_i AKG_x + \frac{V_mf K_mQ alpha_i OAA_x}{K_eq_got} + \frac{V_mf K_mP GLU_x}{K_eq_got} + V_mr ASP_x AKG_x + \frac{V_mf K_mQ ASP_x OAA_x}{K_eq_got K_ia} + \frac{V_mf OAA_x GLU_x}{K_eq_got} + \frac{V_mr K_mA AKG_x GLU_x}{K_iq}} if ASP_x > minCon \land AKG_x > minCon \\ 0 otherwise \end{matrix} J_got = \{\begin{matrix} J_got_f - (\frac{\frac{V_mf V_mr OAA_x GLU_x}{K_eq_got}}{V_mr K_mB ASP_x + V_mr K_mA alpha_i AKG_x + \frac{V_mf K_mQ alpha_i OAA_x}{K_eq_got} + \frac{V_mf K_mP GLU_x}{K_eq_got} + V_mr ASP_x AKG_x + \frac{V_mf K_mQ ASP_x OAA_x}{K_eq_got K_ia} + \frac{V_mf OAA_x GLU_x}{K_eq_got} + \frac{V_mr K_mA AKG_x GLU_x}{K_iq}}) if OAA_x > minCon \land GLU_x > minCon \\ J_got_f otherwise \end{matrix}

Component: J_PYRH

J_PYRH = X_PYRH (\frac{PYR_i}{P_PYR_i} H_i - (\frac{PYR_x}{P_PYR_x} H_x))

Component: J_GLUH

J_GLUH = X_GLUH (\frac{GLU_i}{P_GLU_i} H_i - (\frac{GLU_x}{P_GLU_x} H_x))

Component: J_CITMAL

J_CITMAL = X_CITMAL (\frac{hCIT_i MAL_x}{P_MAL_x} - (\frac{hCIT_x MAL_i}{P_MAL_i}))

Component: J_AKGMAL

J_AKGMAL = \frac{X_AKGMAL (AKG_i MAL_x - (AKG_x MAL_i))}{K_mAKGi K_mMALx (2 + \frac{MAL_i}{K_mMALi} + \frac{MAL_x}{K_mMALx} + \frac{AKG_i}{K_mAKGi} + \frac{AKG_x}{K_mAKGx} + \frac{MAL_i AKG_x}{K_mMALi K_mAKGx} + \frac{MAL_x AKG_i}{K_mMALx K_mAKGi})}

Component: J_MALPI

J_MALPI = X_MALPI (\frac{\frac{MAL_i}{P_MAL_i} PI_x}{P_PI_x} - (\frac{\frac{MAL_x}{P_MAL_x} PI_i}{P_PI_i}))

Component: J_ASPGLU

K_eqASPGLU = \frac{ⅇ^{\frac{(- F) deltaPsi}{RT}} P_ASP_x P_GLU_i}{P_ASP_i P_GLU_x} K_hASPGLU = 1 10^{- 6.5} J_ASPGLU = \frac{X_ASPGLU (K_eqASPGLU ASP_i GLU_x H_x - (ASP_x GLU_i H_i))}{K_eqASPGLU K_iASPi K_iGLUx K_hASPGLU (2 m + \frac{m ASP_i}{K_iASPi} + \frac{ASP_i GLU_x H_x}{K_iASPi K_iGLUx K_hASPGLU} + \frac{m ASP_x H_i}{K_iASPx K_hASPGLU} + \frac{ASP_x GLU_i H_i}{K_iASPx K_iGLUi K_hASPGLU} + \frac{m ASP_x}{K_iASPx} + \frac{m ASP_i H_x}{K_iASPi K_hASPGLU} + \frac{m H_x}{K_hASPGLU} + \frac{m GLU_i H_i}{K_iGLUi K_hASPGLU} + \frac{m H_i}{K_hASPGLU} + \frac{m GLU_x H_x}{K_iGLUx K_hASPGLU})}

Component: J_SUCMAL

J_SUCMAL = X_SUCMAL (\frac{\frac{SUC_i}{P_SUC_i} MAL_x}{P_MAL_x} - (\frac{\frac{SUC_x}{P_SUC_x} MAL_i}{P_MAL_i}))

Component: J_ATPt

J_ATPt = gamma p_A (ATP_c - ATP_i)

Component: J_ADPt

J_ADPt = gamma p_A (ADP_c - ADP_i)

Component: J_AMPt

J_AMPt = gamma p_A (AMP_c - AMP_i)

Component: J_PIt

J_PIt = gamma p_PI (PI_c - PI_i)

Component: J_PYRt

J_PYRt = gamma p_TI (PYR_c - PYR_i)

Component: J_CITt

J_CITt = gamma p_TI (CIT_c - CIT_i)

Component: J_ICITt

J_ICITt = gamma p_TI (ICIT_c - ICIT_i)

Component: J_MALt

J_MALt = gamma p_TI (MAL_c - MAL_i)

Component: J_AKGt

J_AKGt = gamma p_TI (AKG_c - AKG_i)

Component: J_SUCt

J_SUCt = gamma p_TI (SUC_c - SUC_i)

Component: J_GLUt

J_GLUt = gamma p_TI (GLU_c - GLU_i)

Component: J_ASPt

J_ASPt = gamma p_TI (ASP_c - ASP_i)

Component: J_FUMt

J_FUMt = gamma p_TI (FUM_c - FUM_i)

Component: J_ANT

J_ANT = \{\begin{matrix} \frac{X_ANT}{1 + \frac{\frac{k_mADP}{ADP_i}}{P_ADP_i}} (\frac{\frac{ADP_i}{P_ADP_i}}{\frac{ADP_i}{P_ADP_i} + \frac{ATP_i}{P_ATP_i} ⅇ^{\frac{(theta - 1) F deltaPsi}{RT}}} + \frac{\frac{ADP_x}{P_ADP_x}}{\frac{ADP_x}{P_ADP_x} + \frac{ATP_x}{P_ATP_x} ⅇ^{\frac{theta F deltaPsi}{RT}}}) if ADP_i > minCond \land ATP_x > minCond \\ 0 otherwise \end{matrix}

Component: J_PIHt

J_PIHt = \frac{X_PIHt (hPI_i H_i - (hPI_x H_x))}{k_PIHt (1 + \frac{hPI_i}{k_PIHt}) (1 + \frac{hPI_x}{k_PIHt})}

Component: J_Hle

J_Hle = \{\begin{matrix} \frac{X_Hle deltaPsi (H_i ⅇ^{\frac{F deltaPsi}{RT}} - H_x)}{ⅇ^{\frac{F deltaPsi}{RT}} - 1} if | deltaPsi | > minCond \\ \frac{X_Hle RT (H_i - H_x)}{F} otherwise \end{matrix}

Component: J_KH

J_KH = X_KH (K_i H_x - (K_x H_i))

Component: J_AKi

K_AKi = \frac{K0_AKi P_ATP_i P_AMP_i}{P_ADP_i P_ADP_i} J_AKi = \{\begin{matrix} 0 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \\ X_AK (K_AKi ADP_i ADP_i - (AMP_i ATP_i)) otherwise \end{matrix}

Component: J_AKc

K_AKc = \frac{K0_AKc P_ATP_c P_AMP_c}{P_ADP_c P_ADP_c} J_AKc = \{\begin{matrix} 0 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \\ X_AK (K_AKc ADP_c ADP_c - (AMP_c ATP_c)) otherwise \end{matrix}

Component: J_CKc

K_CK = \frac{ⅇ^{\frac{50.7}{RT}}}{1} J_CKc = \{\begin{matrix} 0 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \\ X_CK (\frac{K_CK ADP_c}{P_ADP_c} PCr_c H_c - (\frac{ATP_c}{P_ATP_c} Cr_c)) otherwise \end{matrix}

Component: J_HK

Keq_HK = ⅇ^{\frac{- 15.38}{RT}} 1 Kapp_HK = \frac{Keq_HK P_G6P_c P_ADP_c}{H_c P_ATP_c} Kapp_HK_m = \frac{Kapp_HK KMg_ATP P_ATP_c}{KMg_ADP P_ADP_c} J_HK = \frac{\frac{X_HK}{K_ib K_mA} (mATP_c GLC_c - (\frac{G6P_c mADP_c}{Kapp_HK_m}))}{1 + \frac{mATP_c}{K_ia} + \frac{GLC_c}{K_ib} + \frac{mATP_c GLC_c}{K_ib K_mA} + \frac{G6P_c}{K_ip} + \frac{mADP_c}{K_iq} + \frac{G6P_c mADP_c}{K_iq K_mP} + \frac{G6P_c GLC_c}{Ki_G6P K_ib}}

Component: P_ATP_x

K_H = 1 10^{- 6.59} K_Mg = 1 10^{- 3.82} K_K = 1 10^{- 1.87} P_ATP_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K} ATP_xref = \frac{ATP_x}{P_ATP_x} fATP_x = \frac{ATP_x (1 + \frac{H_x}{K_H})}{P_ATP_x}

Component: P_ADP_x

K_H = 1 10^{- 6.42} K_Mg = 1 10^{- 2.79} K_K = 1 10^{- 1.53} P_ADP_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K} ADP_xref = \frac{ADP_x}{P_ADP_x} fADP_x = \frac{ADP_x (1 + \frac{H_x}{K_H})}{P_ADP_x}

Component: P_AMP_x

K_H = 1 10^{- 6.22} K_Mg = 1 10^{- 1.86} K_K = 1 10^{- 1.05} P_AMP_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K} AMP_xref = \frac{AMP_x}{P_AMP_x} fAMP_x = \frac{AMP_x (1 + \frac{H_x}{K_H})}{P_AMP_x}

Component: P_ATP_i

P_ATP_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K} ATP_iref = \frac{ATP_i}{P_ATP_i} fATP_i = \frac{ATP_i (1 + \frac{H_i}{K_H})}{P_ATP_i}

Component: P_ADP_i

P_ADP_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K} ADP_iref = \frac{ADP_i}{P_ADP_i} fADP_i = \frac{ADP_i (1 + \frac{H_i}{K_H})}{P_ADP_i}

Component: P_AMP_i

P_AMP_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K} AMP_iref = \frac{AMP_i}{P_AMP_i} fAMP_i = \frac{AMP_i (1 + \frac{H_i}{K_H})}{P_AMP_i}

Component: P_ATP_c

P_ATP_c = 1 + \frac{H_c}{K_H} + \frac{Mg_c}{K_Mg} + \frac{K_c}{K_K} mATP_c = \frac{\frac{ATP_c Mg_c}{K_Mg}}{P_ATP_c}

Component: P_ADP_c

P_ADP_c = 1 + \frac{H_c}{K_H} + \frac{Mg_c}{K_Mg} + \frac{K_c}{K_K} mADP_c = \frac{\frac{ADP_c Mg_c}{K_Mg}}{P_ADP_c}

Component: P_AMP_c

P_AMP_c = 1 + \frac{H_c}{K_H} + \frac{Mg_c}{K_Mg} + \frac{K_c}{K_K}

Component: P_GTP_x

P_GTP_x = P_ATP_x fGTP_x = fATP_x

Component: P_GDP_x

P_GDP_x = P_ADP_x fGDP_x = fADP_x

Component: P_PI_x

K_H = 1 10^{- 6.71} K_Mg = 1 10^{- 1.69} K_K = 1 10^{0.0074} P_PI_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K} hPI_x = \frac{\frac{PI_x H_x}{K_H}}{P_PI_x}

Component: P_PI_i

P_PI_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K} hPI_i = \frac{\frac{PI_i H_i}{K_H}}{P_PI_i}

Component: P_COASH_x

K_H = 1 10^{- 8.13} P_COASH_x = 1 + \frac{H_x}{K_H}

Component: P_OAA_x

K_Mg = 1 10^{- 0.0051} P_OAA_x = 1 + \frac{Mg_x}{K_Mg}

Component: P_CIT_x

K_H = 1 10^{- 5.63} K_Mg = 1 10^{- 3.37} K_K = 1 10^{- 0.339} P_CIT_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K} uCIT_x = \frac{CIT_x (1 + \frac{H_x}{K_H})}{P_CIT_x} hCIT_x = \frac{\frac{CIT_x H_x}{K_H}}{P_CIT_x}

Component: P_CIT_i

P_CIT_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K} uCIT_i = \frac{CIT_i (1 + \frac{H_i}{K_H})}{P_CIT_i} hCIT_i = \frac{\frac{CIT_i H_i}{K_H}}{P_CIT_i}

Component: P_ICIT_x

K_H = 1 10^{- 5.64} K_Mg = 1 10^{- 2.46} P_ICIT_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg}

Component: P_SCOA_x

K_H = 1 10^{- 3.96} P_SCOA_x = 1 + \frac{H_x}{K_H}

Component: P_SUC_x

K_H = 1 10^{- 5.13} K_Mg = 1 10^{- 1.17} K_K = 1 10^{- 0.503} P_SUC_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K}

Component: P_SUC_i

P_SUC_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K}

Component: P_FUM_x

K_H = 1 10^{- 4.1} P_FUM_x = 1 + \frac{H_x}{K_H}

Component: P_MAL_x

K_H = 1 10^{- 4.75} K_Mg = 1 10^{- 1.55} K_K = 1 10^{0.17} P_MAL_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg} + \frac{K_x}{K_K}

Component: P_MAL_i

P_MAL_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg} + \frac{K_i}{K_K}

Component: P_CO2_tot_x

K_H = 1 10^{- 9.82} P_CO2_tot_x = 1 + \frac{H_x}{K_H}

Component: P_PYR_x

K_Mg = 1 10^{- 1.02} P_PYR_x = 1 + \frac{Mg_x}{K_Mg}

Component: P_PYR_i

P_PYR_i = 1 + \frac{Mg_i}{K_Mg}

Component: P_GLU_x

K_H = 1 10^{- 4.06} K_Mg = 1 10^{- 1.82} P_GLU_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg}

Component: P_GLU_i

P_GLU_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg}

Component: P_ASP_x

K_H = 1 10^{- 3.65} K_Mg = 1 10^{- 2.32} P_ASP_x = 1 + \frac{H_x}{K_H} + \frac{Mg_x}{K_Mg}

Component: P_ASP_i

P_ASP_i = 1 + \frac{H_i}{K_H} + \frac{Mg_i}{K_Mg}

Component: P_NAD_x

P_NAD_x = 1

Component: P_NADH_x

P_NADH_x = 1

Component: P_QH2_x

P_QH2_x = 1

Component: P_COQ_x

P_COQ_x = 1

Component: P_ACCOA_x

P_ACCOA_x = 1

Component: P_AKG_x

P_AKG_x = 1

Component: P_O2_x

P_O2_x = 1

Component: P_FADH2_x

P_FADH2_x = 1

Component: P_FAD_x

P_FAD_x = 1

Component: P_H_x

P_H_x = 1

Component: P_Mg_x

P_Mg_x = 1

Component: P_K_x

P_K_x = 1

Component: P_G6P_c

K_H = 1 10^{- 5.91} P_G6P_c = 1 + \frac{H_c}{K_H}

Component: ddeltaPsi_dt

\frac{d}{d time} (deltaPsi) = \frac{(4 J_C1 + 2 J_C3 + 4 J_C4 - (n_A J_F1) - J_ANT - J_Hle) + J_ASPGLU}{C_IM}

Component: dATP_x_dt

\frac{d}{d time} (ATP_x) = \frac{J_ndk + J_F1 - J_ANT}{W_x} dATP_x_dt = \frac{J_ndk + J_F1 - J_ANT}{W_x}

Component: dADP_x_dt

\frac{d}{d time} (ADP_x) = \frac{(- J_ndk - J_F1) + J_ANT}{W_x} dADP_x_dt = \frac{(- J_ndk - J_F1) + J_ANT}{W_x}

Component: dAMP_x_dt

\frac{d}{d time} (AMP_x) = 0

Component: dGTP_x_dt

\frac{d}{d time} (GTP_x) = \frac{J_SCOAS - J_ndk}{W_x} dGTP_x_dt = \frac{J_SCOAS - J_ndk}{W_x}

Component: dGDP_x_dt

\frac{d}{d time} (GDP_x) = \frac{(- J_SCOAS) + J_ndk}{W_x} dGDP_x_dt = \frac{(- J_SCOAS) + J_ndk}{W_x}

Component: dPI_x_dt

\frac{d}{d time} (PI_x) = \frac{(- J_SCOAS - J_F1) + J_PIHt - J_MALPI}{W_x} dPI_x_dt = \frac{(- J_SCOAS - J_F1) + J_PIHt - J_MALPI}{W_x}

Component: dNADH_x_dt

\frac{d}{d time} (NADH_x) = \frac{J_pdh + J_isod + J_akgd + J_mdh - J_C1}{W_x} dNADH_x_dt = \frac{J_pdh + J_isod + J_akgd + J_mdh - J_C1}{W_x}

Component: dQH2_x_dt

\frac{d}{d time} (QH2_x) = \frac{J_sdh + J_C1 - J_C3}{W_x} dQH2_x_dt = \frac{J_sdh + J_C1 - J_C3}{W_x}

Component: dPYR_x_dt

\frac{d}{d time} (PYR_x) = \frac{(- J_pdh) + J_PYRH}{W_x} dPYR_x_dt = \frac{(- J_pdh) + J_PYRH}{W_x}

Component: dACCOA_x_dt

\frac{d}{d time} (ACCOA_x) = \frac{J_pdh - J_cits}{W_x} dACCOA_x_dt = \frac{J_pdh - J_cits}{W_x}

Component: dCIT_x_dt

\frac{d}{d time} (CIT_x) = \frac{(- J_acon) + J_CITMAL + J_cits}{W_x} dCIT_x_dt = \frac{(- J_acon) + J_CITMAL + J_cits}{W_x}

Component: dICIT_x_dt

\frac{d}{d time} (ICIT_x) = \frac{J_acon - J_isod}{W_x} dICIT_x_dt = \frac{J_acon - J_isod}{W_x}

Component: dAKG_x_dt

\frac{d}{d time} (AKG_x) = \frac{(J_isod - J_akgd - J_got) + J_AKGMAL}{W_x} dAKG_x_dt = \frac{(J_isod - J_akgd - J_got) + J_AKGMAL}{W_x}

Component: dSCOA_x_dt

\frac{d}{d time} (SCOA_x) = \frac{J_akgd - J_scoas}{W_x} dSCOA_x_dt = \frac{J_akgd - J_scoas}{W_x}

Component: dCOASH_x_dt

\frac{d}{d time} (COASH_x) = \frac{(- J_pdh - J_akgd) + J_scoas + J_cits}{W_x} dCOASH_x_dt = \frac{(- J_pdh - J_akgd) + J_scoas + J_cits}{W_x}

Component: dSUC_x_dt

\frac{d}{d time} (SUC_x) = \frac{(J_scoas - J_sdh) + J_SUCMAL}{W_x} dSUC_x_dt = \frac{(J_scoas - J_sdh) + J_SUCMAL}{W_x}

Component: dFUM_x_dt

\frac{d}{d time} (FUM_x) = \frac{J_sdh - J_fum}{W_x} dFUM_x_dt = \frac{J_sdh - J_fum}{W_x}

Component: dMAL_x_dt

\frac{d}{d time} (MAL_x) = \frac{(J_fum - J_mdh) + J_MALPI - J_AKGMAL - J_CITMAL - J_SUCMAL}{W_x} dMAL_x_dt = \frac{(J_fum - J_mdh) + J_MALPI - J_AKGMAL - J_CITMAL - J_SUCMAL}{W_x}

Component: dOAA_x_dt

\frac{d}{d time} (OAA_x) = \frac{(- J_cits) + J_mdh + J_got}{W_x} dOAA_x_dt = \frac{(- J_cits) + J_mdh + J_got}{W_x}

Component: dGLU_x_dt

\frac{d}{d time} (GLU_x) = \frac{J_got + J_GLUH - J_ASPGLU}{W_x} dGLU_x_dt = \frac{J_got + J_GLUH - J_ASPGLU}{W_x}

Component: dASP_x_dt

\frac{d}{d time} (ASP_x) = \frac{(- J_got) + J_ASPGLU}{W_x} dASP_x_dt = \frac{(- J_got) + J_ASPGLU}{W_x}

Component: dO2_x_dt

\frac{d}{d time} (O2_x) = 0

Component: dCO2_tot_x_dt

\frac{d}{d time} (CO2_tot_x) = 0

Component: dNAD_x_dt

NAD_x = \{\begin{matrix} 0 if NADH_x > NAD_tot \\ NAD_tot - NADH_x otherwise \end{matrix} dNAD_x_dt = - dNADH_x_dt

Component: dCOQ_x_dt

COQ_x = Q_tot - QH2_x dCOQ_x_dt = - dQH2_x_dt

Component: dFAD_x_dt

FAD_x = \frac{FAD_tot}{2} FADH2_x = FAD_x

Component: dH_x_dt

dH_x_dt = 0 \frac{d}{d time} (H_x) = \frac{(dKB_dMg dMgB_dK - (alpha_Mg alpha_K)) phi_H + (alpha_K dHB_dMg - (dHB_dK dKB_dMg)) phi_Mg + (alpha_Mg dHB_dK - (dHB_dMg dMgB_dK)) phi_K}{D}

Component: dMg_x_dt

\frac{d}{d time} (Mg_x) = \frac{(alpha_K dMgB_dH - (dKB_dH dMgB_dK)) phi_H + (dKB_dH dHB_dK - (alpha_H alpha_K)) phi_Mg + (alpha_H dMgB_dK - (dHB_dK dMgB_dH)) phi_K}{D} dMg_x_dt = 0

Component: dK_x_dt

\frac{d}{d time} (K_x) = \frac{(alpha_Mg dKB_dH - (dKB_dMg dMgB_dH)) phi_H + (alpha_H dKB_dMg - (dKB_dH dHB_dMg)) phi_Mg + (dMgB_dH dHB_dMg - (alpha_H alpha_Mg)) phi_K}{D} dK_x_dt = 0

Component: dH_i_dt

\frac{d}{d time} (H_i) = 0

Component: dMg_i_dt

\frac{d}{d time} (Mg_i) = 0

Component: dK_i_dt

\frac{d}{d time} (K_i) = 0

Component: dCox_i_dt

Cox_i = cytC_tot - Cred_i

Component: dCred_i_dt

\frac{d}{d time} (Cred_i) = \frac{2 J_C3 - (2 J_C4)}{W_i}

Component: dATP_i_dt

\frac{d}{d time} (ATP_i) = \frac{J_ATPt + J_ANT + J_AKi}{W_i}

Component: dADP_i_dt

\frac{d}{d time} (ADP_i) = \frac{J_ADPt - J_ANT - (2 J_AKi)}{W_i}

Component: dAMP_i_dt

\frac{d}{d time} (AMP_i) = \frac{J_AMPt + J_AKi}{W_i}

Component: dPI_i_dt

\frac{d}{d time} (PI_i) = \frac{(- J_PIHt) + J_PIt + J_MALPI}{W_i}

Component: dPYR_i_dt

\frac{d}{d time} (PYR_i) = \frac{(- J_PYRH) + J_PYRt}{W_i}

Component: dCIT_i_dt

\frac{d}{d time} (CIT_i) = \frac{(- J_CITMAL) + J_CITt}{W_i}

Component: dICIT_i_dt

\frac{d}{d time} (ICIT_i) = \frac{J_ICITt}{W_i}

Component: dAKG_i_dt

\frac{d}{d time} (AKG_i) = \frac{(- J_AKGMAL) + J_AKGt}{W_i}

Component: dSUC_i_dt

\frac{d}{d time} (SUC_i) = \frac{J_SUCt - J_SUCMAL}{W_i}

Component: dFUM_i_dt

\frac{d}{d time} (FUM_i) = \frac{J_FUMt}{W_i}

Component: dMAL_i_dt

\frac{d}{d time} (MAL_i) = \frac{(- J_MALPI) + J_MALt + J_AKGMAL + J_CITMAL + J_SUCMAL}{W_i}

Component: dGLU_i_dt

\frac{d}{d time} (GLU_i) = \frac{(- J_GLUH) + J_ASPGLU + J_GLUt}{W_i}

Component: dASP_i_dt

\frac{d}{d time} (ASP_i) = \frac{(- J_ASPGLU) + J_ASPt}{W_i}

Component: dH_c_dt

H_c = H_i

Component: dMg_c_dt

Mg_c = Mg_i

Component: dK_c_dt

K_c = K_i

Component: dATP_c_dt

Rm_cyto = \{\begin{matrix} 1 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (ATP_c) = \{\begin{matrix} \frac{(- (1 + \frac{1}{W_c})) J_HK - (Rm_cyto J_ATPt)}{W_c} if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{(- Rm_cyto) J_ATPt + J_CKc + J_AKc - J_AtC}{W_c} otherwise \end{matrix}

Component: dADP_c_dt

Rm_cyto = \{\begin{matrix} 1 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (ADP_c) = \{\begin{matrix} \frac{(1 + \frac{1}{W_c}) J_HK - (Rm_cyto J_ADPt)}{W_c} if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{((- Rm_cyto) J_ADPt - J_CKc - J_AKc) + J_AtC}{W_c} otherwise \end{matrix}

Component: dAMP_c_dt

\frac{d}{d time} (AMP_c) = \{\begin{matrix} 0 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{\frac{- V_mito}{V_cyto} J_AMPt + J_AKc}{W_c} otherwise \end{matrix}

Component: dPI_c_dt

Rm_cyto = \{\begin{matrix} 1 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (PI_c) = \{\begin{matrix} \frac{(- Rm_cyto) J_PIt}{W_c} if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{\frac{- V_mito}{V_cyto} J_PIt + J_AtC}{W_c} otherwise \end{matrix}

Component: dPYR_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 3 \lor ExpType = 4 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (PYR_c) = \frac{(- Rm_cyto) J_PYRt}{W_c}

Component: dCIT_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (CIT_c) = \frac{(- Rm_cyto) J_CITt}{W_c}

Component: dICIT_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (ICIT_c) = \frac{(- Rm_cyto) J_ICITt}{W_c}

Component: dAKG_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (AKG_c) = \frac{(- Rm_cyto) J_AKGt}{W_c}

Component: dSUC_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (SUC_c) = \frac{(- Rm_cyto) J_SUCt}{W_c}

Component: dFUM_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (FUM_c) = \frac{(- Rm_cyto) J_FUMt}{W_c}

Component: dMAL_c_dt

Rm_cyto = \{\begin{matrix} 0 if StateType = 0 \lor ExpType = 5 \\ 1 if ExpType = 1 \land StateType \neq 0 \lor ExpType = 2 \land StateType \neq 0 \lor ExpType = 6 \land StateType \neq 0 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (MAL_c) = \frac{(- Rm_cyto) J_MALt}{W_c}

Component: dGLU_c_dt

Rm_cyto = \{\begin{matrix} 1 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (GLU_c) = \frac{(- Rm_cyto) J_GLUt}{W_c}

Component: dASP_c_dt

Rm_cyto = \{\begin{matrix} 1 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ \frac{V_mito}{V_cyto} otherwise \end{matrix} \frac{d}{d time} (ASP_c) = \frac{(- Rm_cyto) J_ASPt}{W_c}

Component: dPCr_c_dt

multiplier = \{\begin{matrix} 0 if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ 1 otherwise \end{matrix} \frac{d}{d time} (PCr_c) = \frac{(- multiplier) J_CKc}{W_c}

Component: dCr_c_dt

Cr_c = CR_tot - PCr_c

Component: dGLC_c_dt

multiplier = \{\begin{matrix} 1 + \frac{1}{W_c} if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ 0 otherwise \end{matrix} \frac{d}{d time} (GLC_c) = \frac{(- multiplier) J_HK}{W_c}

Component: dG6P_c_dt

multiplier = \{\begin{matrix} 1 + \frac{1}{W_c} if ExpType = 1 \lor ExpType = 2 \lor ExpType = 5 \lor ExpType = 6 \\ 0 otherwise \end{matrix} \frac{d}{d time} (G6P_c) = \frac{multiplier J_HK}{W_c}

Component: BINDING_IONS

dHB_dMg = - (\frac{H_x H_x}{KH_H_x KMg_H_x {P_H_x}^{2}} + \frac{H_x ATP_x}{KH_ATP_x KMg_ATP_x {P_ATP_x}^{2}} + \frac{H_x ADP_x}{KH_ADP_x KMg_ADP_x {P_ADP_x}^{2}} + \frac{H_x AMP_x}{KH_AMP_x KMg_AMP_x {P_AMP_x}^{2}} + \frac{H_x GTP_x}{KH_GTP_x KMg_GTP_x {P_GTP_x}^{2}} + \frac{H_x GDP_x}{KH_GDP_x KMg_GDP_x {P_GDP_x}^{2}} + \frac{H_x PI_x}{KH_PI_x KMg_PI_x {P_PI_x}^{2}} + \frac{H_x NADH_x}{KH_NADH_x KMg_NADH_x {P_NADH_x}^{2}} + \frac{H_x NAD_x}{KH_NAD_x KMg_NAD_x {P_NAD_x}^{2}} + \frac{H_x QH2_x}{KH_QH2_x KMg_QH2_x {P_QH2_x}^{2}} + \frac{H_x COQ_x}{KH_COQ_x KMg_COQ_x {P_COQ_x}^{2}} + \frac{H_x PYR_x}{KH_PYR_x KMg_PYR_x {P_PYR_x}^{2}} + \frac{H_x OAA_x}{KH_OAA_x KMg_OAA_x {P_OAA_x}^{2}} + \frac{H_x ACCOA_x}{KH_ACCOA_x KMg_ACCOA_x {P_ACCOA_x}^{2}} + \frac{H_x CIT_x}{KH_CIT_x KMg_CIT_x {P_CIT_x}^{2}} + \frac{H_x ICIT_x}{KH_ICIT_x KMg_ICIT_x {P_ICIT_x}^{2}} + \frac{H_x AKG_x}{KH_AKG_x KMg_AKG_x {P_AKG_x}^{2}} + \frac{H_x SCOA_x}{KH_SCOA_x KMg_SCOA_x {P_SCOA_x}^{2}} + \frac{H_x COASH_x}{KH_COASH_x KMg_COASH_x {P_COASH_x}^{2}} + \frac{H_x SUC_x}{KH_SUC_x KMg_SUC_x {P_SUC_x}^{2}} + \frac{H_x FUM_x}{KH_FUM_x KMg_FUM_x {P_FUM_x}^{2}} + \frac{H_x MAL_x}{KH_MAL_x KMg_MAL_x {P_MAL_x}^{2}} + \frac{H_x GLU_x}{KH_GLU_x KMg_GLU_x {P_GLU_x}^{2}} + \frac{H_x ASP_x}{KH_ASP_x KMg_ASP_x {P_ASP_x}^{2}} + \frac{H_x K_x}{KH_K_x KMg_K_x {P_K_x}^{2}} + \frac{H_x Mg_x}{KH_Mg_x KMg_Mg_x {P_Mg_x}^{2}} + \frac{H_x O2_x}{KH_O2_x KMg_O2_x {P_O2_x}^{2}} + \frac{H_x FADH2_x}{KH_FADH2_x KMg_FADH2_x {P_FADH2_x}^{2}} + \frac{H_x FAD_x}{KH_FAD_x KMg_FAD_x {P_FAD_x}^{2}} + \frac{H_x CO2_tot_x}{KH_CO2_tot_x KMg_CO2_tot_x {P_CO2_tot_x}^{2}}) dHB_dK = - (\frac{H_x H_x}{KH_H_x KK_H_x {P_H_x}^{2}} + \frac{H_x ATP_x}{KH_ATP_x KK_ATP_x {P_ATP_x}^{2}} + \frac{H_x ADP_x}{KH_ADP_x KK_ADP_x {P_ADP_x}^{2}} + \frac{H_x AMP_x}{KH_AMP_x KK_AMP_x {P_AMP_x}^{2}} + \frac{H_x GTP_x}{KH_GTP_x KK_GTP_x {P_GTP_x}^{2}} + \frac{H_x GDP_x}{KH_GDP_x KK_GDP_x {P_GDP_x}^{2}} + \frac{H_x PI_x}{KH_PI_x KK_PI_x {P_PI_x}^{2}} + \frac{H_x NADH_x}{KH_NADH_x KK_NADH_x {P_NADH_x}^{2}} + \frac{H_x NAD_x}{KH_NAD_x KK_NAD_x {P_NAD_x}^{2}} + \frac{H_x QH2_x}{KH_QH2_x KK_QH2_x {P_QH2_x}^{2}} + \frac{H_x COQ_x}{KH_COQ_x KK_COQ_x {P_COQ_x}^{2}} + \frac{H_x PYR_x}{KH_PYR_x KK_PYR_x {P_PYR_x}^{2}} + \frac{H_x OAA_x}{KH_OAA_x KK_OAA_x {P_OAA_x}^{2}} + \frac{H_x ACCOA_x}{KH_ACCOA_x KK_ACCOA_x {P_ACCOA_x}^{2}} + \frac{H_x CIT_x}{KH_CIT_x KK_CIT_x {P_CIT_x}^{2}} + \frac{H_x ICIT_x}{KH_ICIT_x KK_ICIT_x {P_ICIT_x}^{2}} + \frac{H_x AKG_x}{KH_AKG_x KK_AKG_x {P_AKG_x}^{2}} + \frac{H_x SCOA_x}{KH_SCOA_x KK_SCOA_x {P_SCOA_x}^{2}} + \frac{H_x COASH_x}{KH_COASH_x KK_COASH_x {P_COASH_x}^{2}} + \frac{H_x SUC_x}{KH_SUC_x KK_SUC_x {P_SUC_x}^{2}} + \frac{H_x FUM_x}{KH_FUM_x KK_FUM_x {P_FUM_x}^{2}} + \frac{H_x MAL_x}{KH_MAL_x KK_MAL_x {P_MAL_x}^{2}} + \frac{H_x GLU_x}{KH_GLU_x KK_GLU_x {P_GLU_x}^{2}} + \frac{H_x ASP_x}{KH_ASP_x KK_ASP_x {P_ASP_x}^{2}} + \frac{H_x K_x}{KH_K_x KK_K_x {P_K_x}^{2}} + \frac{H_x Mg_x}{KH_Mg_x KK_Mg_x {P_Mg_x}^{2}} + \frac{H_x O2_x}{KH_O2_x KK_O2_x {P_O2_x}^{2}} + \frac{H_x FADH2_x}{KH_FADH2_x KK_FADH2_x {P_FADH2_x}^{2}} + \frac{H_x FAD_x}{KH_FAD_x KK_FAD_x {P_FAD_x}^{2}} + \frac{H_x CO2_tot_x}{KH_CO2_tot_x KK_CO2_tot_x {P_CO2_tot_x}^{2}}) dHB_dH = \frac{(1 + \frac{Mg_x}{KMg_H_x} + \frac{K_x}{KK_H_x}) H_x}{KH_H_x {P_H_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_ATP_x} + \frac{K_x}{KK_ATP_x}) ATP_x}{KH_ATP_x {P_ATP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_ADP_x} + \frac{K_x}{KK_ADP_x}) ADP_x}{KH_ADP_x {P_ADP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_AMP_x} + \frac{K_x}{KK_AMP_x}) AMP_x}{KH_AMP_x {P_AMP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_GTP_x} + \frac{K_x}{KK_GTP_x}) GTP_x}{KH_GTP_x {P_GTP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_GDP_x} + \frac{K_x}{KK_GDP_x}) GDP_x}{KH_GDP_x {P_GDP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_PI_x} + \frac{K_x}{KK_PI_x}) PI_x}{KH_PI_x {P_PI_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_NADH_x} + \frac{K_x}{KK_NADH_x}) NADH_x}{KH_NADH_x {P_NADH_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_NAD_x} + \frac{K_x}{KK_NAD_x}) NAD_x}{KH_NAD_x {P_NAD_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_QH2_x} + \frac{K_x}{KK_QH2_x}) QH2_x}{KH_QH2_x {P_QH2_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_COQ_x} + \frac{K_x}{KK_COQ_x}) COQ_x}{KH_COQ_x {P_COQ_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_PYR_x} + \frac{K_x}{KK_PYR_x}) PYR_x}{KH_PYR_x {P_PYR_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_OAA_x} + \frac{K_x}{KK_OAA_x}) OAA_x}{KH_OAA_x {P_OAA_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_ACCOA_x} + \frac{K_x}{KK_ACCOA_x}) ACCOA_x}{KH_ACCOA_x {P_ACCOA_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_CIT_x} + \frac{K_x}{KK_CIT_x}) CIT_x}{KH_CIT_x {P_CIT_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_ICIT_x} + \frac{K_x}{KK_ICIT_x}) ICIT_x}{KH_ICIT_x {P_ICIT_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_AKG_x} + \frac{K_x}{KK_AKG_x}) AKG_x}{KH_AKG_x {P_AKG_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_SCOA_x} + \frac{K_x}{KK_SCOA_x}) SCOA_x}{KH_SCOA_x {P_SCOA_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_COASH_x} + \frac{K_x}{KK_COASH_x}) COASH_x}{KH_COASH_x {P_COASH_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_SUC_x} + \frac{K_x}{KK_SUC_x}) SUC_x}{KH_SUC_x {P_SUC_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_FUM_x} + \frac{K_x}{KK_FUM_x}) FUM_x}{KH_FUM_x {P_FUM_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_MAL_x} + \frac{K_x}{KK_MAL_x}) MAL_x}{KH_MAL_x {P_MAL_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_GLU_x} + \frac{K_x}{KK_GLU_x}) GLU_x}{KH_GLU_x {P_GLU_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_ASP_x} + \frac{K_x}{KK_ASP_x}) ASP_x}{KH_ASP_x {P_ASP_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_K_x} + \frac{K_x}{KK_K_x}) K_x}{KH_K_x {P_K_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_Mg_x} + \frac{K_x}{KK_Mg_x}) Mg_x}{KH_Mg_x {P_Mg_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_O2_x} + \frac{K_x}{KK_O2_x}) O2_x}{KH_O2_x {P_O2_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_FADH2_x} + \frac{K_x}{KK_FADH2_x}) FADH2_x}{KH_FADH2_x {P_FADH2_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_FAD_x} + \frac{K_x}{KK_FAD_x}) FAD_x}{KH_FAD_x {P_FAD_x}^{2}} + \frac{(1 + \frac{Mg_x}{KMg_CO2_tot_x} + \frac{K_x}{KK_CO2_tot_x}) CO2_tot_x}{KH_CO2_tot_x {P_CO2_tot_x}^{2}} dMgB_dH = - (\frac{Mg_x H_x}{KMg_H_x KH_H_x {P_H_x}^{2}} + \frac{Mg_x ATP_x}{KMg_ATP_x KH_ATP_x {P_ATP_x}^{2}} + \frac{Mg_x ADP_x}{KMg_ADP_x KH_ADP_x {P_ADP_x}^{2}} + \frac{Mg_x AMP_x}{KMg_AMP_x KH_AMP_x {P_AMP_x}^{2}} + \frac{Mg_x GTP_x}{KMg_GTP_x KH_GTP_x {P_GTP_x}^{2}} + \frac{Mg_x GDP_x}{KMg_GDP_x KH_GDP_x {P_GDP_x}^{2}} + \frac{Mg_x PI_x}{KMg_PI_x KH_PI_x {P_PI_x}^{2}} + \frac{Mg_x NADH_x}{KMg_NADH_x KH_NADH_x {P_NADH_x}^{2}} + \frac{Mg_x NAD_x}{KMg_NAD_x KH_NAD_x {P_NAD_x}^{2}} + \frac{Mg_x QH2_x}{KMg_QH2_x KH_QH2_x {P_QH2_x}^{2}} + \frac{Mg_x COQ_x}{KMg_COQ_x KH_COQ_x {P_COQ_x}^{2}} + \frac{Mg_x PYR_x}{KMg_PYR_x KH_PYR_x {P_PYR_x}^{2}} + \frac{Mg_x OAA_x}{KMg_OAA_x KH_OAA_x {P_OAA_x}^{2}} + \frac{Mg_x ACCOA_x}{KMg_ACCOA_x KH_ACCOA_x {P_ACCOA_x}^{2}} + \frac{Mg_x CIT_x}{KMg_CIT_x KH_CIT_x {P_CIT_x}^{2}} + \frac{Mg_x ICIT_x}{KMg_ICIT_x KH_ICIT_x {P_ICIT_x}^{2}} + \frac{Mg_x AKG_x}{KMg_AKG_x KH_AKG_x {P_AKG_x}^{2}} + \frac{Mg_x SCOA_x}{KMg_SCOA_x KH_SCOA_x {P_SCOA_x}^{2}} + \frac{Mg_x COASH_x}{KMg_COASH_x KH_COASH_x {P_COASH_x}^{2}} + \frac{Mg_x SUC_x}{KMg_SUC_x KH_SUC_x {P_SUC_x}^{2}} + \frac{Mg_x FUM_x}{KMg_FUM_x KH_FUM_x {P_FUM_x}^{2}} + \frac{Mg_x MAL_x}{KMg_MAL_x KH_MAL_x {P_MAL_x}^{2}} + \frac{Mg_x GLU_x}{KMg_GLU_x KH_GLU_x {P_GLU_x}^{2}} + \frac{Mg_x ASP_x}{KMg_ASP_x KH_ASP_x {P_ASP_x}^{2}} + \frac{Mg_x K_x}{KMg_K_x KH_K_x {P_K_x}^{2}} + \frac{Mg_x Mg_x}{KMg_Mg_x KH_Mg_x {P_Mg_x}^{2}} + \frac{Mg_x O2_x}{KMg_O2_x KH_O2_x {P_O2_x}^{2}} + \frac{Mg_x FADH2_x}{KMg_FADH2_x KH_FADH2_x {P_FADH2_x}^{2}} + \frac{Mg_x FAD_x}{KMg_FAD_x KH_FAD_x {P_FAD_x}^{2}} + \frac{Mg_x CO2_tot_x}{KMg_CO2_tot_x KH_CO2_tot_x {P_CO2_tot_x}^{2}}) dMgB_dK = - (\frac{Mg_x H_x}{KMg_H_x KK_H_x {P_H_x}^{2}} + \frac{Mg_x ATP_x}{KMg_ATP_x KK_ATP_x {P_ATP_x}^{2}} + \frac{Mg_x ADP_x}{KMg_ADP_x KK_ADP_x {P_ADP_x}^{2}} + \frac{Mg_x AMP_x}{KMg_AMP_x KK_AMP_x {P_AMP_x}^{2}} + \frac{Mg_x GTP_x}{KMg_GTP_x KK_GTP_x {P_GTP_x}^{2}} + \frac{Mg_x GDP_x}{KMg_GDP_x KK_GDP_x {P_GDP_x}^{2}} + \frac{Mg_x PI_x}{KMg_PI_x KK_PI_x {P_PI_x}^{2}} + \frac{Mg_x NADH_x}{KMg_NADH_x KK_NADH_x {P_NADH_x}^{2}} + \frac{Mg_x NAD_x}{KMg_NAD_x KK_NAD_x {P_NAD_x}^{2}} + \frac{Mg_x QH2_x}{KMg_QH2_x KK_QH2_x {P_QH2_x}^{2}} + \frac{Mg_x COQ_x}{KMg_COQ_x KK_COQ_x {P_COQ_x}^{2}} + \frac{Mg_x PYR_x}{KMg_PYR_x KK_PYR_x {P_PYR_x}^{2}} + \frac{Mg_x OAA_x}{KMg_OAA_x KK_OAA_x {P_OAA_x}^{2}} + \frac{Mg_x ACCOA_x}{KMg_ACCOA_x KK_ACCOA_x {P_ACCOA_x}^{2}} + \frac{Mg_x CIT_x}{KMg_CIT_x KK_CIT_x {P_CIT_x}^{2}} + \frac{Mg_x ICIT_x}{KMg_ICIT_x KK_ICIT_x {P_ICIT_x}^{2}} + \frac{Mg_x AKG_x}{KMg_AKG_x KK_AKG_x {P_AKG_x}^{2}} + \frac{Mg_x SCOA_x}{KMg_SCOA_x KK_SCOA_x {P_SCOA_x}^{2}} + \frac{Mg_x COASH_x}{KMg_COASH_x KK_COASH_x {P_COASH_x}^{2}} + \frac{Mg_x SUC_x}{KMg_SUC_x KK_SUC_x {P_SUC_x}^{2}} + \frac{Mg_x FUM_x}{KMg_FUM_x KK_FUM_x {P_FUM_x}^{2}} + \frac{Mg_x MAL_x}{KMg_MAL_x KK_MAL_x {P_MAL_x}^{2}} + \frac{Mg_x GLU_x}{KMg_GLU_x KK_GLU_x {P_GLU_x}^{2}} + \frac{Mg_x ASP_x}{KMg_ASP_x KK_ASP_x {P_ASP_x}^{2}} + \frac{Mg_x K_x}{KMg_K_x KK_K_x {P_K_x}^{2}} + \frac{Mg_x Mg_x}{KMg_Mg_x KK_Mg_x {P_Mg_x}^{2}} + \frac{Mg_x O2_x}{KMg_O2_x KK_O2_x {P_O2_x}^{2}} + \frac{Mg_x FADH2_x}{KMg_FADH2_x KK_FADH2_x {P_FADH2_x}^{2}} + \frac{Mg_x FAD_x}{KMg_FAD_x KK_FAD_x {P_FAD_x}^{2}} + \frac{Mg_x CO2_tot_x}{KMg_CO2_tot_x KK_CO2_tot_x {P_CO2_tot_x}^{2}}) dMgB_dMg = \frac{(1 + \frac{H_x}{KH_H_x} + \frac{K_x}{KK_H_x}) H_x}{KMg_H_x {P_H_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ATP_x} + \frac{K_x}{KK_ATP_x}) ATP_x}{KMg_ATP_x {P_ATP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ADP_x} + \frac{K_x}{KK_ADP_x}) ADP_x}{KMg_ADP_x {P_ADP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_AMP_x} + \frac{K_x}{KK_AMP_x}) AMP_x}{KMg_AMP_x {P_AMP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GTP_x} + \frac{K_x}{KK_GTP_x}) GTP_x}{KMg_GTP_x {P_GTP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GDP_x} + \frac{K_x}{KK_GDP_x}) GDP_x}{KMg_GDP_x {P_GDP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_PI_x} + \frac{K_x}{KK_PI_x}) PI_x}{KMg_PI_x {P_PI_x}^{2}} + \frac{(1 + \frac{H_x}{KH_NADH_x} + \frac{K_x}{KK_NADH_x}) NADH_x}{KMg_NADH_x {P_NADH_x}^{2}} + \frac{(1 + \frac{H_x}{KH_NAD_x} + \frac{K_x}{KK_NAD_x}) NAD_x}{KMg_NAD_x {P_NAD_x}^{2}} + \frac{(1 + \frac{H_x}{KH_QH2_x} + \frac{K_x}{KK_QH2_x}) QH2_x}{KMg_QH2_x {P_QH2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_COQ_x} + \frac{K_x}{KK_COQ_x}) COQ_x}{KMg_COQ_x {P_COQ_x}^{2}} + \frac{(1 + \frac{H_x}{KH_PYR_x} + \frac{K_x}{KK_PYR_x}) PYR_x}{KMg_PYR_x {P_PYR_x}^{2}} + \frac{(1 + \frac{H_x}{KH_OAA_x} + \frac{K_x}{KK_OAA_x}) OAA_x}{KMg_OAA_x {P_OAA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ACCOA_x} + \frac{K_x}{KK_ACCOA_x}) ACCOA_x}{KMg_ACCOA_x {P_ACCOA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_CIT_x} + \frac{K_x}{KK_CIT_x}) CIT_x}{KMg_CIT_x {P_CIT_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ICIT_x} + \frac{K_x}{KK_ICIT_x}) ICIT_x}{KMg_ICIT_x {P_ICIT_x}^{2}} + \frac{(1 + \frac{H_x}{KH_AKG_x} + \frac{K_x}{KK_AKG_x}) AKG_x}{KMg_AKG_x {P_AKG_x}^{2}} + \frac{(1 + \frac{H_x}{KH_SCOA_x} + \frac{K_x}{KK_SCOA_x}) SCOA_x}{KMg_SCOA_x {P_SCOA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_COASH_x} + \frac{K_x}{KK_COASH_x}) COASH_x}{KMg_COASH_x {P_COASH_x}^{2}} + \frac{(1 + \frac{H_x}{KH_SUC_x} + \frac{K_x}{KK_SUC_x}) SUC_x}{KMg_SUC_x {P_SUC_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FUM_x} + \frac{K_x}{KK_FUM_x}) FUM_x}{KMg_FUM_x {P_FUM_x}^{2}} + \frac{(1 + \frac{H_x}{KH_MAL_x} + \frac{K_x}{KK_MAL_x}) MAL_x}{KMg_MAL_x {P_MAL_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GLU_x} + \frac{K_x}{KK_GLU_x}) GLU_x}{KMg_GLU_x {P_GLU_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ASP_x} + \frac{K_x}{KK_ASP_x}) ASP_x}{KMg_ASP_x {P_ASP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_K_x} + \frac{K_x}{KK_K_x}) K_x}{KMg_K_x {P_K_x}^{2}} + \frac{(1 + \frac{H_x}{KH_Mg_x} + \frac{K_x}{KK_Mg_x}) Mg_x}{KMg_Mg_x {P_Mg_x}^{2}} + \frac{(1 + \frac{H_x}{KH_O2_x} + \frac{K_x}{KK_O2_x}) O2_x}{KMg_O2_x {P_O2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FADH2_x} + \frac{K_x}{KK_FADH2_x}) FADH2_x}{KMg_FADH2_x {P_FADH2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FAD_x} + \frac{K_x}{KK_FAD_x}) FAD_x}{KMg_FAD_x {P_FAD_x}^{2}} + \frac{(1 + \frac{H_x}{KH_CO2_tot_x} + \frac{K_x}{KK_CO2_tot_x}) CO2_tot_x}{KMg_CO2_tot_x {P_CO2_tot_x}^{2}} dKB_dH = - (\frac{K_x H_x}{KK_H_x KH_H_x {P_H_x}^{2}} + \frac{K_x ATP_x}{KK_ATP_x KH_ATP_x {P_ATP_x}^{2}} + \frac{K_x ADP_x}{KK_ADP_x KH_ADP_x {P_ADP_x}^{2}} + \frac{K_x AMP_x}{KK_AMP_x KH_AMP_x {P_AMP_x}^{2}} + \frac{K_x GTP_x}{KK_GTP_x KH_GTP_x {P_GTP_x}^{2}} + \frac{K_x GDP_x}{KK_GDP_x KH_GDP_x {P_GDP_x}^{2}} + \frac{K_x PI_x}{KK_PI_x KH_PI_x {P_PI_x}^{2}} + \frac{K_x NADH_x}{KK_NADH_x KH_NADH_x {P_NADH_x}^{2}} + \frac{K_x NAD_x}{KK_NAD_x KH_NAD_x {P_NAD_x}^{2}} + \frac{K_x QH2_x}{KK_QH2_x KH_QH2_x {P_QH2_x}^{2}} + \frac{K_x COQ_x}{KK_COQ_x KH_COQ_x {P_COQ_x}^{2}} + \frac{K_x PYR_x}{KK_PYR_x KH_PYR_x {P_PYR_x}^{2}} + \frac{K_x OAA_x}{KK_OAA_x KH_OAA_x {P_OAA_x}^{2}} + \frac{K_x ACCOA_x}{KK_ACCOA_x KH_ACCOA_x {P_ACCOA_x}^{2}} + \frac{K_x CIT_x}{KK_CIT_x KH_CIT_x {P_CIT_x}^{2}} + \frac{K_x ICIT_x}{KK_ICIT_x KH_ICIT_x {P_ICIT_x}^{2}} + \frac{K_x AKG_x}{KK_AKG_x KH_AKG_x {P_AKG_x}^{2}} + \frac{K_x SCOA_x}{KK_SCOA_x KH_SCOA_x {P_SCOA_x}^{2}} + \frac{K_x COASH_x}{KK_COASH_x KH_COASH_x {P_COASH_x}^{2}} + \frac{K_x SUC_x}{KK_SUC_x KH_SUC_x {P_SUC_x}^{2}} + \frac{K_x FUM_x}{KK_FUM_x KH_FUM_x {P_FUM_x}^{2}} + \frac{K_x MAL_x}{KK_MAL_x KH_MAL_x {P_MAL_x}^{2}} + \frac{K_x GLU_x}{KK_GLU_x KH_GLU_x {P_GLU_x}^{2}} + \frac{K_x ASP_x}{KK_ASP_x KH_ASP_x {P_ASP_x}^{2}} + \frac{K_x K_x}{KK_K_x KH_K_x {P_K_x}^{2}} + \frac{K_x Mg_x}{KK_Mg_x KH_Mg_x {P_Mg_x}^{2}} + \frac{K_x O2_x}{KK_O2_x KH_O2_x {P_O2_x}^{2}} + \frac{K_x FADH2_x}{KK_FADH2_x KH_FADH2_x {P_FADH2_x}^{2}} + \frac{K_x FAD_x}{KK_FAD_x KH_FAD_x {P_FAD_x}^{2}} + \frac{K_x CO2_tot_x}{KK_CO2_tot_x KH_CO2_tot_x {P_CO2_tot_x}^{2}}) dKB_dMg = - (\frac{K_x H_x}{KK_H_x KMg_H_x {P_H_x}^{2}} + \frac{K_x ATP_x}{KK_ATP_x KMg_ATP_x {P_ATP_x}^{2}} + \frac{K_x ADP_x}{KK_ADP_x KMg_ADP_x {P_ADP_x}^{2}} + \frac{K_x AMP_x}{KK_AMP_x KMg_AMP_x {P_AMP_x}^{2}} + \frac{K_x GTP_x}{KK_GTP_x KMg_GTP_x {P_GTP_x}^{2}} + \frac{K_x GDP_x}{KK_GDP_x KMg_GDP_x {P_GDP_x}^{2}} + \frac{K_x PI_x}{KK_PI_x KMg_PI_x {P_PI_x}^{2}} + \frac{K_x NADH_x}{KK_NADH_x KMg_NADH_x {P_NADH_x}^{2}} + \frac{K_x NAD_x}{KK_NAD_x KMg_NAD_x {P_NAD_x}^{2}} + \frac{K_x QH2_x}{KK_QH2_x KMg_QH2_x {P_QH2_x}^{2}} + \frac{K_x COQ_x}{KK_COQ_x KMg_COQ_x {P_COQ_x}^{2}} + \frac{K_x PYR_x}{KK_PYR_x KMg_PYR_x {P_PYR_x}^{2}} + \frac{K_x OAA_x}{KK_OAA_x KMg_OAA_x {P_OAA_x}^{2}} + \frac{K_x ACCOA_x}{KK_ACCOA_x KMg_ACCOA_x {P_ACCOA_x}^{2}} + \frac{K_x CIT_x}{KK_CIT_x KMg_CIT_x {P_CIT_x}^{2}} + \frac{K_x ICIT_x}{KK_ICIT_x KMg_ICIT_x {P_ICIT_x}^{2}} + \frac{K_x AKG_x}{KK_AKG_x KMg_AKG_x {P_AKG_x}^{2}} + \frac{K_x SCOA_x}{KK_SCOA_x KMg_SCOA_x {P_SCOA_x}^{2}} + \frac{K_x COASH_x}{KK_COASH_x KMg_COASH_x {P_COASH_x}^{2}} + \frac{K_x SUC_x}{KK_SUC_x KMg_SUC_x {P_SUC_x}^{2}} + \frac{K_x FUM_x}{KK_FUM_x KMg_FUM_x {P_FUM_x}^{2}} + \frac{K_x MAL_x}{KK_MAL_x KMg_MAL_x {P_MAL_x}^{2}} + \frac{K_x GLU_x}{KK_GLU_x KMg_GLU_x {P_GLU_x}^{2}} + \frac{K_x ASP_x}{KK_ASP_x KMg_ASP_x {P_ASP_x}^{2}} + \frac{K_x K_x}{KK_K_x KMg_K_x {P_K_x}^{2}} + \frac{K_x Mg_x}{KK_Mg_x KMg_Mg_x {P_Mg_x}^{2}} + \frac{K_x O2_x}{KK_O2_x KMg_O2_x {P_O2_x}^{2}} + \frac{K_x FADH2_x}{KK_FADH2_x KMg_FADH2_x {P_FADH2_x}^{2}} + \frac{K_x FAD_x}{KK_FAD_x KMg_FAD_x {P_FAD_x}^{2}} + \frac{K_x CO2_tot_x}{KK_CO2_tot_x KMg_CO2_tot_x {P_CO2_tot_x}^{2}}) dKB_dK = \frac{(1 + \frac{H_x}{KH_H_x} + \frac{Mg_x}{KMg_H_x}) H_x}{KK_H_x {P_H_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ATP_x} + \frac{Mg_x}{KMg_ATP_x}) ATP_x}{KK_ATP_x {P_ATP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ADP_x} + \frac{Mg_x}{KMg_ADP_x}) ADP_x}{KK_ADP_x {P_ADP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_AMP_x} + \frac{Mg_x}{KMg_AMP_x}) AMP_x}{KK_AMP_x {P_AMP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GTP_x} + \frac{Mg_x}{KMg_GTP_x}) GTP_x}{KK_GTP_x {P_GTP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GDP_x} + \frac{Mg_x}{KMg_GDP_x}) GDP_x}{KK_GDP_x {P_GDP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_PI_x} + \frac{Mg_x}{KMg_PI_x}) PI_x}{KK_PI_x {P_PI_x}^{2}} + \frac{(1 + \frac{H_x}{KH_NADH_x} + \frac{Mg_x}{KMg_NADH_x}) NADH_x}{KK_NADH_x {P_NADH_x}^{2}} + \frac{(1 + \frac{H_x}{KH_NAD_x} + \frac{Mg_x}{KMg_NAD_x}) NAD_x}{KK_NAD_x {P_NAD_x}^{2}} + \frac{(1 + \frac{H_x}{KH_QH2_x} + \frac{Mg_x}{KMg_QH2_x}) QH2_x}{KK_QH2_x {P_QH2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_COQ_x} + \frac{Mg_x}{KMg_COQ_x}) COQ_x}{KK_COQ_x {P_COQ_x}^{2}} + \frac{(1 + \frac{H_x}{KH_PYR_x} + \frac{Mg_x}{KMg_PYR_x}) PYR_x}{KK_PYR_x {P_PYR_x}^{2}} + \frac{(1 + \frac{H_x}{KH_OAA_x} + \frac{Mg_x}{KMg_OAA_x}) OAA_x}{KK_OAA_x {P_OAA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ACCOA_x} + \frac{Mg_x}{KMg_ACCOA_x}) ACCOA_x}{KK_ACCOA_x {P_ACCOA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_CIT_x} + \frac{Mg_x}{KMg_CIT_x}) CIT_x}{KK_CIT_x {P_CIT_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ICIT_x} + \frac{Mg_x}{KMg_ICIT_x}) ICIT_x}{KK_ICIT_x {P_ICIT_x}^{2}} + \frac{(1 + \frac{H_x}{KH_AKG_x} + \frac{Mg_x}{KMg_AKG_x}) AKG_x}{KK_AKG_x {P_AKG_x}^{2}} + \frac{(1 + \frac{H_x}{KH_SCOA_x} + \frac{Mg_x}{KMg_SCOA_x}) SCOA_x}{KK_SCOA_x {P_SCOA_x}^{2}} + \frac{(1 + \frac{H_x}{KH_COASH_x} + \frac{Mg_x}{KMg_COASH_x}) COASH_x}{KK_COASH_x {P_COASH_x}^{2}} + \frac{(1 + \frac{H_x}{KH_SUC_x} + \frac{Mg_x}{KMg_SUC_x}) SUC_x}{KK_SUC_x {P_SUC_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FUM_x} + \frac{Mg_x}{KMg_FUM_x}) FUM_x}{KK_FUM_x {P_FUM_x}^{2}} + \frac{(1 + \frac{H_x}{KH_MAL_x} + \frac{Mg_x}{KMg_MAL_x}) MAL_x}{KK_MAL_x {P_MAL_x}^{2}} + \frac{(1 + \frac{H_x}{KH_GLU_x} + \frac{Mg_x}{KMg_GLU_x}) GLU_x}{KK_GLU_x {P_GLU_x}^{2}} + \frac{(1 + \frac{H_x}{KH_ASP_x} + \frac{Mg_x}{KMg_ASP_x}) ASP_x}{KK_ASP_x {P_ASP_x}^{2}} + \frac{(1 + \frac{H_x}{KH_K_x} + \frac{Mg_x}{KMg_K_x}) K_x}{KK_K_x {P_K_x}^{2}} + \frac{(1 + \frac{H_x}{KH_Mg_x} + \frac{Mg_x}{KMg_Mg_x}) Mg_x}{KK_Mg_x {P_Mg_x}^{2}} + \frac{(1 + \frac{H_x}{KH_O2_x} + \frac{Mg_x}{KMg_O2_x}) O2_x}{KK_O2_x {P_O2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FADH2_x} + \frac{Mg_x}{KMg_FADH2_x}) FADH2_x}{KK_FADH2_x {P_FADH2_x}^{2}} + \frac{(1 + \frac{H_x}{KH_FAD_x} + \frac{Mg_x}{KMg_FAD_x}) FAD_x}{KK_FAD_x {P_FAD_x}^{2}} + \frac{(1 + \frac{H_x}{KH_CO2_tot_x} + \frac{Mg_x}{KMg_CO2_tot_x}) CO2_tot_x}{KK_CO2_tot_x {P_CO2_tot_x}^{2}} nK_JK = \frac{((- J_pdh) + 2 J_cits - J_akgd) + J_scoas + J_mdh}{W_x} J_H_t = \frac{(J_PYRH + J_GLUH + J_CITMAL - J_ASPGLU - (5 J_C1) - (2 J_C3) - (4 J_C4)) + (n_A - 1) J_F1 + 2 J_PIHt + J_Hle - J_KH}{W_x} J_Mg_t = 0 J_K_t = \frac{J_KH}{W_x} phi_H = \frac{H_x dH_x_dt}{KH_H_x P_H_x} + \frac{H_x dATP_x_dt}{KH_ATP_x P_ATP_x} + \frac{H_x dADP_x_dt}{KH_ADP_x P_ADP_x} + \frac{H_x dAMP_x_dt}{KH_AMP_x P_AMP_x} + \frac{H_x dGTP_x_dt}{KH_GTP_x P_GTP_x} + \frac{H_x dGDP_x_dt}{KH_GDP_x P_GDP_x} + \frac{H_x dPI_x_dt}{KH_PI_x P_PI_x} + \frac{H_x dNADH_x_dt}{KH_NADH_x P_NADH_x} + \frac{H_x dNAD_x_dt}{KH_NAD_x P_NAD_x} + \frac{H_x dQH2_x_dt}{KH_QH2_x P_QH2_x} + \frac{H_x dCOQ_x_dt}{KH_COQ_x P_COQ_x} + \frac{H_x dPYR_x_dt}{KH_PYR_x P_PYR_x} + \frac{H_x dOAA_x_dt}{KH_OAA_x P_OAA_x} + \frac{H_x dACCOA_x_dt}{KH_ACCOA_x P_ACCOA_x} + \frac{H_x dCIT_x_dt}{KH_CIT_x P_CIT_x} + \frac{H_x dICIT_x_dt}{KH_ICIT_x P_ICIT_x} + \frac{H_x dAKG_x_dt}{KH_AKG_x P_AKG_x} + \frac{H_x dSCOA_x_dt}{KH_SCOA_x P_SCOA_x} + \frac{H_x dCOASH_x_dt}{KH_COASH_x P_COASH_x} + \frac{H_x dSUC_x_dt}{KH_SUC_x P_SUC_x} + \frac{H_x dFUM_x_dt}{KH_FUM_x P_FUM_x} + \frac{H_x dMAL_x_dt}{KH_MAL_x P_MAL_x} + \frac{H_x dGLU_x_dt}{KH_GLU_x P_GLU_x} + \frac{H_x dASP_x_dt}{KH_ASP_x P_ASP_x} + \frac{H_x dK_x_dt}{KH_K_x P_K_x} + \frac{H_x dMg_x_dt}{KH_Mg_x P_Mg_x} + \frac{H_x dO2_x_dt}{KH_O2_x P_O2_x} + \frac{H_x dFADH2_x_dt}{KH_FADH2_x P_FADH2_x} + \frac{H_x dFAD_x_dt}{KH_FAD_x P_FAD_x} + \frac{H_x dCO2_tot_x_dt}{KH_CO2_tot_x P_CO2_tot_x} + nK_JK + J_H_t phi_Mg = \frac{Mg_x dH_x_dt}{KMg_H_x P_H_x} + \frac{Mg_x dATP_x_dt}{KMg_ATP_x P_ATP_x} + \frac{Mg_x dADP_x_dt}{KMg_ADP_x P_ADP_x} + \frac{Mg_x dAMP_x_dt}{KMg_AMP_x P_AMP_x} + \frac{Mg_x dGTP_x_dt}{KMg_GTP_x P_GTP_x} + \frac{Mg_x dGDP_x_dt}{KMg_GDP_x P_GDP_x} + \frac{Mg_x dPI_x_dt}{KMg_PI_x P_PI_x} + \frac{Mg_x dNADH_x_dt}{KMg_NADH_x P_NADH_x} + \frac{Mg_x dNAD_x_dt}{KMg_NAD_x P_NAD_x} + \frac{Mg_x dQH2_x_dt}{KMg_QH2_x P_QH2_x} + \frac{Mg_x dCOQ_x_dt}{KMg_COQ_x P_COQ_x} + \frac{Mg_x dPYR_x_dt}{KMg_PYR_x P_PYR_x} + \frac{Mg_x dOAA_x_dt}{KMg_OAA_x P_OAA_x} + \frac{Mg_x dACCOA_x_dt}{KMg_ACCOA_x P_ACCOA_x} + \frac{Mg_x dCIT_x_dt}{KMg_CIT_x P_CIT_x} + \frac{Mg_x dICIT_x_dt}{KMg_ICIT_x P_ICIT_x} + \frac{Mg_x dAKG_x_dt}{KMg_AKG_x P_AKG_x} + \frac{Mg_x dSCOA_x_dt}{KMg_SCOA_x P_SCOA_x} + \frac{Mg_x dCOASH_x_dt}{KMg_COASH_x P_COASH_x} + \frac{Mg_x dSUC_x_dt}{KMg_SUC_x P_SUC_x} + \frac{Mg_x dFUM_x_dt}{KMg_FUM_x P_FUM_x} + \frac{Mg_x dMAL_x_dt}{KMg_MAL_x P_MAL_x} + \frac{Mg_x dGLU_x_dt}{KMg_GLU_x P_GLU_x} + \frac{Mg_x dASP_x_dt}{KMg_ASP_x P_ASP_x} + \frac{Mg_x dK_x_dt}{KMg_K_x P_K_x} + \frac{Mg_x dMg_x_dt}{KMg_Mg_x P_Mg_x} + \frac{Mg_x dO2_x_dt}{KMg_O2_x P_O2_x} + \frac{Mg_x dFADH2_x_dt}{KMg_FADH2_x P_FADH2_x} + \frac{Mg_x dFAD_x_dt}{KMg_FAD_x P_FAD_x} + \frac{Mg_x dCO2_tot_x_dt}{KMg_CO2_tot_x P_CO2_tot_x} + J_Mg_t phi_K = \frac{K_x dH_x_dt}{KK_H_x P_H_x} + \frac{K_x dATP_x_dt}{KK_ATP_x P_ATP_x} + \frac{K_x dADP_x_dt}{KK_ADP_x P_ADP_x} + \frac{K_x dAMP_x_dt}{KK_AMP_x P_AMP_x} + \frac{K_x dGTP_x_dt}{KK_GTP_x P_GTP_x} + \frac{K_x dGDP_x_dt}{KK_GDP_x P_GDP_x} + \frac{K_x dPI_x_dt}{KK_PI_x P_PI_x} + \frac{K_x dNADH_x_dt}{KK_NADH_x P_NADH_x} + \frac{K_x dNAD_x_dt}{KK_NAD_x P_NAD_x} + \frac{K_x dQH2_x_dt}{KK_QH2_x P_QH2_x} + \frac{K_x dCOQ_x_dt}{KK_COQ_x P_COQ_x} + \frac{K_x dPYR_x_dt}{KK_PYR_x P_PYR_x} + \frac{K_x dOAA_x_dt}{KK_OAA_x P_OAA_x} + \frac{K_x dACCOA_x_dt}{KK_ACCOA_x P_ACCOA_x} + \frac{K_x dCIT_x_dt}{KK_CIT_x P_CIT_x} + \frac{K_x dICIT_x_dt}{KK_ICIT_x P_ICIT_x} + \frac{K_x dAKG_x_dt}{KK_AKG_x P_AKG_x} + \frac{K_x dSCOA_x_dt}{KK_SCOA_x P_SCOA_x} + \frac{K_x dCOASH_x_dt}{KK_COASH_x P_COASH_x} + \frac{K_x dSUC_x_dt}{KK_SUC_x P_SUC_x} + \frac{K_x dFUM_x_dt}{KK_FUM_x P_FUM_x} + \frac{K_x dMAL_x_dt}{KK_MAL_x P_MAL_x} + \frac{K_x dGLU_x_dt}{KK_GLU_x P_GLU_x} + \frac{K_x dASP_x_dt}{KK_ASP_x P_ASP_x} + \frac{K_x dK_x_dt}{KK_K_x P_K_x} + \frac{K_x dMg_x_dt}{KK_Mg_x P_Mg_x} + \frac{K_x dO2_x_dt}{KK_O2_x P_O2_x} + \frac{K_x dFADH2_x_dt}{KK_FADH2_x P_FADH2_x} + \frac{K_x dFAD_x_dt}{KK_FAD_x P_FAD_x} + \frac{K_x dCO2_tot_x_dt}{KK_CO2_tot_x P_CO2_tot_x} + J_K_t alpha_H = 1 + dHB_dH + \frac{B_x}{K_BX {(1 + \frac{H_x}{K_BX})}^{2}} alpha_Mg = 1 + dMgB_dMg alpha_K = 1 + dKB_dK D = alpha_H dKB_dMg dMgB_dK + alpha_K dHB_dMg dMgB_dH + alpha_Mg dHB_dK dKB_dH - (alpha_Mg alpha_K alpha_H) - (dHB_dK dKB_dMg dMgB_dH) - (dHB_dMg dMgB_dK dKB_dH)