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

Abstract

1. Evolutionary changes in the structure of an enzyme that provide an increase in its Km value are considered. Provided that Km 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 Km>[S] than when Km<[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] Keq. is the equilibrium constant (=[P]eq./[S]eq.), and kcat.=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 Km»[S]) to approach vd (the diffusion-limited rate). 4. The value of the optimal rate of catalysis (vopt., the maximal value of v2) is dictated by the equilibrium constant for the reaction, Keq.; v2=vd/a, where [Formula: see text] when k+1 is assumed equal to k−3, and vopt.=vd/amin.. When Keq.≥1, it is necessary that k+2»k−1 for a to take its minimum value, amin.; when Keq.«1, it is necessary only that k+2»Keq.·k−1, i.e. a can equal amin. even if k+2<k−1. When Keq.»1, vopt.=vd; when Keq.=1, vopt.=vd/2, and when Keq.«1, vopt.=Keq.·vd. 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+1[E]T[S] by about an order of magnitude, particularly if Keq.<1. 6. The existing literature suggests that, in general, appropriate values of Km have evolved for the provision of high rates of catalysis but that many values of kcat. are not large enough to provide optimal rates of catalysis unless the value of k+1in vivo is lower than its value in free solution.