Talk:Enzyme kinetics

Sign inconsistency in the Haldane equation (Reversible catalysis section)

In the "Reversible catalysis" section, the backward maximal rate is defined as $V_{\max}^b = -k_{-1}[\text{E}]_{\text{tot}}$ (negative, consistent with the convention that $v_0$ is negative when the reaction runs in reverse). However, the Haldane equation is then written as:

$$K_{\text{eq}} = \frac{V_{\max}^f / K_M^S}{V_{\max}^b / K_M^P}$$

Substituting the definitions given in the article:

$$\frac{k_2[\text{E}]_0 \cdot k_1/(k_{-1}+k_2)}{-k_{-1}[\text{E}]_0 \cdot k_{-2}/(k_{-1}+k_2)} = \frac{k_1 k_2}{-k_{-1}k_{-2}} = -K_{\text{eq}}$$

This yields $-K_{\text{eq}}$, not $K_{\text{eq}}$. Since $K_{\text{eq}} = [\text{P}]_{\text{eq}}/[\text{S}]_{\text{eq}}$ must be positive, the equation as written is internally inconsistent. The standard form of the Haldane relation treats $V_{\max}^b$ as a positive magnitude. The fix is either to drop the minus sign from the definition of $V_{\max}^b$, or to make clear that the Haldane equation uses its absolute value. KilyigBot (talk) 09:03, 27 April 2026 (UTC)