Reaction formula Rate law Turnover rates ${k}_{±}^{cat}$ Irreversible
A ↔ B $\frac{{k}_{+}^{cat}\stackrel{˜}{a}-{k}_{-}^{cat}\stackrel{˜}{b}}{1+\stackrel{˜}{a}+\stackrel{˜}{b}}$ ${k}^{V}{\left(\frac{{\stackrel{˜}{k}}_{A}^{M}}{{\stackrel{˜}{k}}_{B}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{cat}\stackrel{˜}{a}}{1+\stackrel{˜}{a}}$
A + X ↔ B $\frac{{k}_{+}^{cat}\stackrel{˜}{a}\stackrel{˜}{x}-{k}_{-}^{cat}\stackrel{˜}{b}}{1+\stackrel{˜}{a}+\stackrel{˜}{x}+\stackrel{˜}{a}\stackrel{˜}{x}+\stackrel{˜}{b}}$ ${k}^{V}{\left(\frac{{\stackrel{˜}{k}}_{A}^{M}{\stackrel{˜}{k}}_{X}^{M}}{{\stackrel{˜}{k}}_{B}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{cat}\stackrel{˜}{a}\stackrel{˜}{x}}{1+\stackrel{˜}{a}+\stackrel{˜}{x}+\stackrel{˜}{a}\stackrel{˜}{x}}$
A + X ↔ B + Y $\frac{{k}_{+}^{cat}\stackrel{˜}{a}\stackrel{˜}{x}-{k}_{-}^{cat}\stackrel{˜}{b}\stackrel{˜}{y}}{1+\stackrel{˜}{a}+\stackrel{˜}{x}+\stackrel{˜}{a}\stackrel{˜}{x}+\stackrel{˜}{b}+\stackrel{˜}{y}+\stackrel{˜}{b}\stackrel{˜}{y}}$ ${k}^{V}{\left(\frac{{\stackrel{˜}{k}}_{A}^{M}{\stackrel{˜}{k}}_{X}^{M}}{{\stackrel{˜}{k}}_{B}^{M}{\stackrel{˜}{k}}_{Y}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{cat}\stackrel{˜}{a}\stackrel{˜}{x}}{1+\stackrel{˜}{a}+\stackrel{˜}{x}+\stackrel{˜}{a}\stackrel{˜}{x}}$
2 A ↔ B $\frac{{k}_{+}^{cat}{\stackrel{˜}{a}}^{2}-{k}_{-}^{cat}\stackrel{˜}{b}}{1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}+\stackrel{˜}{b}}$ ${k}^{V}{\left(\frac{{\left({\stackrel{˜}{k}}_{A}^{M}\right)}^{2}}{{\stackrel{˜}{k}}_{B}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{\text{cat}}{\stackrel{˜}{a}}^{2}}{1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}}$
2 A ↔ B + Y $\frac{{k}_{+}^{cat}{\stackrel{˜}{a}}^{2}-{k}_{-}^{cat}\stackrel{˜}{b}\stackrel{˜}{y}}{1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}+\stackrel{˜}{b}+\stackrel{˜}{y}+\stackrel{˜}{b}\stackrel{˜}{y}}$ ${k}^{V}{\left(\frac{{\left({\stackrel{˜}{k}}_{A}^{M}\right)}^{2}}{{\stackrel{˜}{k}}_{B}^{M}{\stackrel{˜}{k}}_{Y}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{\text{cat}}{\stackrel{˜}{a}}^{2}}{1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}}$
2 A + X ↔ B $\frac{{k}_{+}^{cat}{\stackrel{˜}{a}}^{2}\stackrel{˜}{x}-{k}_{-}^{cat}\stackrel{˜}{b}}{\left(1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}\right)\left(1+\stackrel{˜}{x}\right)+\stackrel{˜}{b}}$ ${k}^{V}{\left(\frac{{\left({\stackrel{˜}{k}}_{A}^{M}\right)}^{2}{\stackrel{˜}{k}}_{X}^{M}}{{\stackrel{˜}{k}}_{B}^{M}}\right)}^{±1/2}$ $\frac{{k}_{+}^{\text{cat}}{\stackrel{˜}{a}}^{2}\stackrel{˜}{x}}{\left(1+\stackrel{˜}{a}+{\stackrel{˜}{a}}^{2}\right)\left(1+\stackrel{˜}{x}\right)}$
1. 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 $\stackrel{˜}{a}=a/{k}_{\text{A}}^{\text{M}}$ and ${\stackrel{˜}{k}}_{A}^{M}={k}_{A}^{G}{k}_{A}^{M}$ for metabolite A and analogous shortcuts for the other metabolites. For brevity, the prefactors for enzyme concentration and enzyme regulation are not shown.