FIG. 1. A free-energy profile along a reaction coordinate for the enzymatic reaction in the regime of the low substrate concentration. The reaction involves the formation of the ES from the free enzyme (E) and substrate (S) in solution and the formation of the activated complex [(ES)]. The symbols Km and kcat, are, respectively, the activation, binding and apparent activation free energies, the equilibrium constant for the dissociation of the ES complex, and the second order rate constant for the enzyme-catalyzed reaction. The symbol A is the pre-exponential factor in the expression for the rate constant (5). The reason for using the lowercase “g” as a symbol for activation barriers is explained in ref. 5. The figure demonstrates that Δg is independent of the magnitude of the ground state destabilization (ΔΔGb).

The difficulty of finding logical explanations for the reduction of led to many proposals that can be eliminated in hindsight by considering the evolutionary pressure on enzymes that evolved to optimize kcat/Km. That is, as seen from Fig. 1, no ground state destabilization (ΔΔGb) will help to reduce Δg. Thus, it is not useful, at least from an evolutionary point of view, to use ground state destabilization mechanisms. This point can be verified easily by going backward in evolution and considering the effect of mutations on Δg, kcat, and Km (see below).

Before examining which mechanisms work and which do not work, it is important to realize that many of the outstanding questions in this field cannot be resolved uniquely by current experimental approaches. That is. enzyme transition states can-not be isolated experimentally and, although indirect experiments are very valuable, they cannot be interpreted without some model for structure-function correlation. In addition, it is important to realize that the issue of enzyme catalysis is an energy issue, and, as such, it cannot be resolved without the ability of dissecting the observed energy to the individual contributions. Finally, in analyzing the effect of enzymes on it is essential to focus on the proper reference state, thus avoiding considerations of irrelevant factors. One of the most effective ways of doing so involves comparison of the given assumed mechanism in the enzyme active site with the same mechanism in a solvent cage, where all of the reactants are at a contact distance (5) (Fig. 2). This definition allows one to avoid the rather trivial question associated with bringing the reactant to the same solvent cage (5) and to focus on the origin of the difference between kcat and kcage. In

FIG. 2. A comparison of the free-energy profiles for an enzymatic reaction and for a reaction proceeding via an identical mechanism in a reference solvent cage. The symbols E, S, and Saq designate the enzyme, the substrate, and the substrate in the bulk solvent, respectively. The activation free-energy corresponds to the same reaction mechanism assumed for the given enzymatic reaction (i.e., it does not necessarily correspond to the actual reaction in solution). This can be determined by using experimental information for the related elementary reaction(s) or by using ab initio calculations.

other words, such an analysis forces one to focus on the true reason for the fact that kcat is much larger than kcage. The rate constant kcage can be evaluated from experimental information about elementary reactions in solutions (5, 6) and/or ab initio calculations in solution (7, 8), but such studies are not practiced by most workers in the field, in part because of the difficulties in estimating the energetics of some reaction intermediates in aqueous solution and the frequent reluctance to ask quantitative questions about energetics. Thus, in many cases, the discussion of the catalytic power of enzymes overlooks the most important question: How large is the effect of the enzyme environment? Instructive works documented the large acceleration of the reaction rate in different enzymes (9, 10) by comparing kcat/Km to the second-order rate constant in water. However, such a comparison includes the effect of the binding energy (ΔGbind) and does not tell us about the effect of the enzyme environment on For example, our recent analysis of the catalytic reaction of ribonuclease (T.M.Glennon and A.W., unpublished work) indicated that this enzyme provides the transition state stabilization, as large as ≈24 kcal/mol. This fact (which is not mentioned in the vast literature about ribonucleases) presents a major theoretical challenge because it is hard to see how simple environmental effects can lead to such a large free-energy change. Trying to address such problems quantitatively forces one to quantify the effects of different catalytic factors and to offer a concrete explanation for the overall reduction of

  

Trying, for example, to explain the differential binding of the ground state and the transition state by van der Waals interactions can be accomplished only by invoking the repulsive part of these forces. Consequently, these forces can be involved only in ground state destabilization effects (which eventually were found to be inconsistent with the flexibility of proteins). As far as the van der Waals attraction between the enzyme and substrate is concerned, it is very similar for the ground and transition states. This insensitivity to the exact structure is caused by the nature of the London dispersion forces that are approximately proportional to the number of interacting atoms. Similarly, hydrophobic forces cannot provide large differential binding for the ground and transition state of the reacting fragments. Finally, even electrostatic effects, which do contribute to the transition state stabilization, accomplish this stabilization in a complex way (see below) that was not realized by early workers in the field.



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