Table 3.

Convenience rate laws for common reaction stoichiometries

Reaction formula	Rate law	Turnover rates $k_{\pm }^{cat}$	Irreversible
A ↔ B	$\frac{k_{+}^{cat}\tilde{a}-k_{-}^{cat}\tilde{b}}{1+\tilde{a}+\tilde{b}}$	$k^V{(\frac{{\tilde{k}}_A^M}{{\tilde{k}}_B^M})}^{\pm 1/2}$	$\frac{k_{+}^{cat}\tilde{a}}{1+\tilde{a}}$
A + X ↔ B	$\frac{k_{+}^{cat}\tilde{a}\tilde{x}-k_{-}^{cat}\tilde{b}}{1+\tilde{a}+\tilde{x}+\tilde{a}\tilde{x}+\tilde{b}}$	$k^V{(\frac{{\tilde{k}}_A^M{\tilde{k}}_X^M}{{\tilde{k}}_B^M})}^{\pm 1/2}$	$\frac{k_{+}^{cat}\tilde{a}\tilde{x}}{1+\tilde{a}+\tilde{x}+\tilde{a}\tilde{x}}$
A + X ↔ B + Y	$\frac{k_{+}^{cat}\tilde{a}\tilde{x}-k_{-}^{cat}\tilde{b}\tilde{y}}{1+\tilde{a}+\tilde{x}+\tilde{a}\tilde{x}+\tilde{b}+\tilde{y}+\tilde{b}\tilde{y}}$	$k^V{(\frac{{\tilde{k}}_A^M{\tilde{k}}_X^M}{{\tilde{k}}_B^M{\tilde{k}}_Y^M})}^{\pm 1/2}$	$\frac{k_{+}^{cat}\tilde{a}\tilde{x}}{1+\tilde{a}+\tilde{x}+\tilde{a}\tilde{x}}$
2 A ↔ B	$\frac{k_{+}^{cat}{\tilde{a}}^2-k_{-}^{cat}\tilde{b}}{1+\tilde{a}+{\tilde{a}}^2+\tilde{b}}$	$k^V{(\frac{{({\tilde{k}}_A^M)}^2}{{\tilde{k}}_B^M})}^{\pm 1/2}$	$\frac{k_{+}^{\text{cat}}{\tilde{a}}^2}{1+\tilde{a}+{\tilde{a}}^2}$
2 A ↔ B + Y	$\frac{k_{+}^{cat}{\tilde{a}}^2-k_{-}^{cat}\tilde{b}\tilde{y}}{1+\tilde{a}+{\tilde{a}}^2+\tilde{b}+\tilde{y}+\tilde{b}\tilde{y}}$	$k^V{(\frac{{({\tilde{k}}_A^M)}^2}{{\tilde{k}}_B^M{\tilde{k}}_Y^M})}^{\pm 1/2}$	$\frac{k_{+}^{\text{cat}}{\tilde{a}}^2}{1+\tilde{a}+{\tilde{a}}^2}$
2 A + X ↔ B	$\frac{k_{+}^{cat}{\tilde{a}}^2\tilde{x}-k_{-}^{cat}\tilde{b}}{(1+\tilde{a}+{\tilde{a}}^2)(1+\tilde{x})+\tilde{b}}$	$k^V{(\frac{{({\tilde{k}}_A^M)}^2{\tilde{k}}_X^M}{{\tilde{k}}_B^M})}^{\pm 1/2}$	$\frac{k_{+}^{\text{cat}}{\tilde{a}}^2\tilde{x}}{(1+\tilde{a}+{\tilde{a}}^2)(1+\tilde{x})}$

The rate laws follow from the enzyme mechanism and reflect the reaction stoichiometry; for each case, the thermodynamically independent expression of the turnover rates and the irreversible form are also shown. We use the shortcuts $\tilde{a}=a/k_{\text{A}}^{\text{M}}$ and ${\tilde{k}}_A^M=k_A^G{k}_A^M$ for metabolite A and analogous shortcuts for the other metabolites. For brevity, the prefactors for enzyme concentration and enzyme regulation are not shown.