Differential equations for TCA cycle reaction network

The next step in building a biochemical network model for the TCA cycle is determining the governing differential equations. Since we are not treating transport of material into or out of the mitochondrion, the reactants of the overall reaction of Equation (6.31) are held clamped in this model. In addition, ASP and GLU are held fixed because there are no sources or sinks for the metabolites other than the aspartate aminotransferase reaction built into the model at this stage. Since the electron transport system is not modeled, proton transport is not included and pH is held fixed. 

The fixed concentrations are set at [PYR] = 0.076 mM, [CoQ] = 0.97 mM, [CoQH2] = 0.38 mM, [PI] = 1.8 mM, [ASP] = 0.06 nM, [GLU] = 0.06 mM, [ECO2] = 21.4 mM, and [H+] = 10-7 2M, which are physiologically reasonable values. (In Chapter 7 this model is integrated with a detailed model of oxidative phosphorylation and mitochondrial substrate and ion transport in which none of these species or reactants are held at fixed concentrations.) The concentrations of NAD, NADH, ATP, and ADP are varied in order to examine the biochemical mechanisms regulation flux of the TCA cycle. 

For the remaining (non-clamped) reactants, we have the following differential equations that arise from the stoichiometry of the reference reactions  

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