Analysis of Reaction Rates

Abstract

In Chapter 2, expressions were derived for the rates of the reactions given by the general stoichiometric equations, Eqs. (2.19)–(2.21). Intracellular representatives for substrates and metabolic products were introduced in order to emphasize the central role of the cell as the chemical reactor wherein the reactions take place. Thus Eq. (2.17) or Eq. (2.20) describes J reactions with N+L+M reactants and products, which coexist inside the cell envelope. Substrate uptake and product excretion reactions can also lead to changes in the cell composition X, as shown in Examples 2.3 and 2.12 and continued in Example 2.14, whereas the simple membrane transport mechanism illustrated in Example 2.13 effectively removes any difference between external and internal substrates. The coupling between internal reactions and membrane transport reactions will be further treated in Chapter 4, but at the present stage of our development it is convenient to condense the general stoichiometry in Eqs. (2.19)–(2.21) to

$$ As + Bp + \Gamma X = (AB\Gamma ) \cdot (\begin{array}{*{20}{c}} s \\ p \\ X \end{array}) = T(\begin{array}{*{20}{c}} s \\ p \\ X \end{array}) = 0 $$

(3.1)

where T is the total stoichiometric matrix. Equation (3.1) is formally the same as Eq. (2.20), expressing the stoichiometry of J reactions, but the extracellular substrates and products appear in place of their intracellular representatives. Matrices A and B have the same dimension as in Eq. (2.20), but otherwise they are different from the corresponding matrices of Eq. (2.20), and the internal composition vector may also be different from that considered in Eq. (2.20)—some of the S _i or P _i in the general formulation may for example be included in X in the condensed stoichiometry.