Biochemistry: The Chemical Reactions of Living Cells, Volume 2 - D. Metzler 1980

Enzymes: Protein Catalysts of Cells
Fundamentals of Enzyme Kinetics
Reversible Enzymatic Reactions

For many enzymatic reactions, the equilibrium position is strongly shifted in one direction, though some reactions proceed readily in both directions. Since a catalyst accelerates both the forward and reverse reactions, The Effect of the enzyme on the reverse reaction must also be taken into account. Let us denote the maximum velocity of the forward reaction as V_f, and that of the reverse reaction as V_r. Accordingly, let the Michaelis constant for the forward reaction be denoted by K_MS, and for the reverse reaction by K_MP.

As with any chemical reaction, the rate constants of the forward and reverse reactions and the Equilibrium Constant of a reversible enzymatic process are related by a specific equation. It is very easily derived by taking into account that at equilibrium the rates of the forward and reverse reactions are equal (v_f = v_r). For an enzymatic system consisting of a single substrate and a single product, the Haldane relation holds true¹)

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Since this relation imposes constraints on The values of the maximum velocities and Michaelis constants for the forward and reverse reactions, it can prove highly useful when discussing Metabolic Regulation. Let us consider the case where the maximum velocity of the forward reaction (V_f) is high, while the constant K_MS is quite low (strong substrate binding). If the reaction is readily reversible (K_eq ≈ 1) and the maximum velocities of the forward and reverse reactions are roughly equal, then relation (6-33) implies that product P is also bound quite tightly by the enzyme. If, however, V_r ≪ V_f, then the constant K_MP must be much smaller than K_MS. In this situation, product P will remain tightly bound to the enzyme and, owing to the low V_r, hinder its catalytic activity. Such product inhibition can occasionally lead to the blocking of an entire metabolic pathway, and a sequence of Enzymes will be able to function in the forward direction only if the product is rapidly removed by a subsequent reaction catalyzed by a second enzyme. Thus, the first enzyme acts as a sort of valve that halts the flow in the metabolic pathway whenever the concentration of the product generated by this enzyme increases.

¹⁾ This relation is named after the English enzymologist and kineticist J. B. S. Haldane, who introduced it in his book Enzymes [31].

it with molecule B. The number of different variants here is enormous [1–6].