Evolution of enzyme catalytic power. Characteristics of optimal catalysis evaluated for the simplest plausible kinetic model

1. Evolutionary changes in the structure of an enzyme that provide an increase in its K_m value are considered. Provided that K_m increases as a result of increases in the forward rate constants of the catalysis relative to the reverse rate constants, the enzyme catalyses the conversion of a fixed concentration of its substrate more rapidly when its structure provides that K_m>S] than when K_m<S]. 2. Catalytic efficiency of enzymes is discussed in terms of the simplest plausible model, the Haldane (1930) Enzymes, Longmans, London] reversible three-step model: Formula: see text] The rate equation for the forward reaction of this model (formation of P) may be written in the simple form: Formula: see text] K_eq. is the equilibrium constant (=P]_eq./S]_eq.), and k_cat.=V/E]_T, where E]_T is the total enzyme concentration. 3. To assess the effectiveness of an enzyme, it is necessary only to determine the extent to which the constraints of a particular kinetic mechanism permit v₂ (v when K_m»S]) to approach v_d (the diffusion-limited rate). 4. The value of the optimal rate of catalysis (v_opt., the maximal value of v₂) is dictated by the equilibrium constant for the reaction, K_eq.; v₂=v_d/a, where Formula: see text] when k₊₁ is assumed equal to k₋₃, and v_opt.=v_d/a_min.. When K_eq.≥1, it is necessary that k₊₂»k₋₁ for a to take its minimum value, a_min.; when K_eq.«1, it is necessary only that k₊₂»K_eq.·k₋₁, i.e. a can equal a_min. even if k₊₂<k₋₁. When K_eq.»1, v_opt.=v_d; when K_eq.=1, v_opt.=v_d/2, and when K_eq.«1, v_opt.=K_eq.·v_d. 5. The analysis, together with predicted effects of evolutionary pressure, suggests that in practice the rates of the fastest enzyme-catalysed freely reversible reactions might be expected to be lower than the value of k₊₁E]_TS] by about an order of magnitude, particularly if K_eq.<1. 6. The existing literature suggests that, in general, appropriate values of K_m have evolved for the provision of high rates of catalysis but that many values of k_cat. are not large enough to provide optimal rates of catalysis unless the value of k₊₁ in vivo is lower than its value in free solution.