Dispelling the effects of a sorceress in enzyme catalysis

Enzymes are superb and fascinating catalysts. Understanding the origins of their catalytic power remains one of the “grand challenges” of biology and biochemistry. What has been optimized by evolution to make enzymes so efficient? Harnessing these abilities in designed catalysts would transform our ability to design protein and biomimetic catalysts for practical applications. Using computer simulation, Kazemi et al. (1) have now analyzed a classic example in enzymology, and show that a long-cherished and influential theory of enzyme catalysis is wrong.

What is the “magic” that gives enzymes their catalytic power (2)? “Since any discussion of this kind is likely to be considered incomplete in these busy times without the introduction of a new name or acronym” (some things don’t change!), Bill Jencks invoked a mythical sorceress, Circe, to name his hypothesis on enzyme action (3). This “Circe effect’” has been one of the most influential ideas in enzymology. According to legend, Circe lured Odysseus’s men into her mansion, drugged them, and transformed them into pigs. Jencks’s hypothesis is that enzymes function by luring molecules into their active site, and work their transformative magic by holding them bound. The reactive molecules are bound tightly, so are destabilized and react more easily. One particular facet of this hypothesis is that the bound reacting molecules—substrates—are less mobile, and less able to change conformation when bound tightly in the active site. The substrates are brought into the right orientation for reaction and, critically, are restrained, so changing shape less than they would in solution. Their entropy is reduced, and this reduction in entropy was proposed to be at the heart of enzyme catalysis.

Central to Jencks’s case was cytidine deaminase, an enzyme involved in pyrimidine salvage: it catalyses the hydrolytic deamination of cytidine and deoxycytidine to form uridine and deoxyuridine, respectively. Experiments show that binding of the substrate, cytidine, to the Escherichia coli enzyme is disfavored by entropy: the contribution to the binding free energy at room temperature is large and unfavorable (TΔS = −7.6 kcal/mol) (4). Cytidine also reacts spontaneously—although very slowly—in aqueous solution, so it is possible to compare the enzyme-catalyzed reaction with its uncatalyzed counterpart. The reaction in solution has a high energy barrier, Δ^‡G = 30.4 kcal/mol, at 25 °C (the rate constant is related to Δ^‡G by transition state theory). The contribution to the barrier from entropy (TΔ^‡S = 8.3 kcal/mol) is almost exactly the same as the change in entropy for binding (TΔS = −7.6 kcal/mol). The same reaction in E. coli cytidine deaminase is of course very much faster, with a free-energy barrier of only Δ^‡G = 14 kcal/mol at 25 °C. Entropy makes almost no contribution to the reaction in the enzyme (TΔ^‡S = 0.9 kcal/mol). Thus, a reaction with a significant entropy penalty in solution proceeds with apparently no entropy barrier in the enzyme. Strikingly, the difference in activation entropy seems to be the same as the reduction in entropy when the substrate binds. Apparently, cytidine is lured into the active site, where it is pinned down in a conformation suitable for reaction; it can’t wriggle or rotate, so its entropy is reduced. The binding energy “pays the price” for lowering the entropy of the substrate. The figures suggest that this reduction in entropy is central to barrier lowering by the enzyme, vital to catalysis. Or is it?

Indirect conclusions, interpretation of macroscopic data, inspired hypotheses, and extrapolation from physical organic chemistry were almost all that was possible in analyzing enzyme-catalyzed reactions when Jencks wrote. Direct analysis of enzyme-catalyzed reactions by experiment alone remains extremely difficult even now. It has often proved difficult even to establish the chemical mechanisms of enzymes, and many “textbook” mechanisms have been found to be incorrect. In addition, understanding catalysis (i.e., why the reaction is faster in the enzyme) requires comparing the enzyme-catalyzed reaction to an equivalent nonbiological reaction (e.g., the same reaction in solution, either uncatalyzed or with a simple chemical catalyst). So it has been difficult to test Jencks’s proposals, which have nevertheless, and not without controversy, become part of the conceptual bedrock used to explain (and teach) enzyme catalysis.

At around the same time that Jencks published his Circe proposal, the first steps were being made in developing computational molecular simulation methods for modeling chemical reactions in enzymes (5, 6). Simulations have become a vital tool for analyzing enzyme-catalyzed reactions, as recognized by the 2013 Nobel Prize in chemistry. Reactions can be simulated in atomic detail, today with high levels of accuracy. Molecular calculations on reactions can be used to determine likely mechanisms, dissect interactions, and analyze individual contributions to reactivity and catalysis. The contribution of entropy to catalysis, for example, can be calculated from simulations (7).

Kazemi et al. (1) have applied simulation methods to this classic problem. Previously, Kazemi and Åqvist (8) established the mechanism of the uncatalyzed cytidine (and dihydrocytidine) deamination reaction in water by calculation of Arrhenius plots for various possible mechanisms, and testing which mechanism gave results in best agreement with experiment. This process requires many simulations across a range of temperatures to calculate the activation free energy Δ^‡G at each temperature. Computational Arrhenius plots of Δ^‡G/T against 1/T give the activation entropy and enthalpy from Δ^‡G/T = Δ^‡H/T − Δ^‡S. These simulations showed that the transition state involves attack by a neutral water molecule, with three water molecules participating closely. The authors calculated activation free energy, Δ^‡G, and also the activation enthalpy Δ^‡H and entropy Δ^‡S, agree very well with those found from experiment. This in itself is an impressive demonstration of the mechanistic insight that can now be achieved by “brute force” molecular simulations (8).

Molecular dynamics (MD) simulations on this scale require a potential energy function that is fast, but modeling reactions is beyond the simple functional forms and single-structure representation of the empirical molecular mechanics (MM) ball-and-spring forcefields used for most protein MD simulations. In principle, a quantum mechanical (QM) electronic structure method (such as calculations based on density functional theory, DFT) could be used to simulate reactions: these do not require parameterization and are a good way to model transition states and identify chemical mechanisms, for example, in calculations on small models of enzyme active sites (9). Even though such methods can now be applied to quite large systems, they are too computationally demanding for long MD simulations of enzymes. Hybrid (QM/MM) methods combining QM and MM can give highly accurate results for the energy barriers of enzyme-catalyzed reactions (10), but are still relatively computationally intensive. Extensive simulations of reactions in enzymes are possible with empirical valence bond (EVB) methods, which are simple, MM-type techniques, but include valence bond representations of different chemical structures, with energy functions able to model bond making and breaking (11). An EVB model first has to be developed by fitting its various parameters, which can be done by reference either to experimental data (e.g., for a reaction in solution) or QM results (e.g., for a small model). Kazemi and Åqvist (8) obtained similar results for the reaction in water regardless of which of these two calibration procedures they used. These simulations identified the mechanism, and also provide a rationale for the observed entropy penalty for the solution reaction: forming the transition state is entropically unfavorable, but this is almost entirely a result of the entropy of the solvent, not the reacting cytidine itself: ordering water molecules at the transition state reduces their entropy, making the barrier to reaction high.

What about the reaction in the enzyme? Why is the activation entropy so much lower in the enzyme? Well of course, as with the reaction in water, the essential first step is again to establish the mechanism. E. coli cytidine deaminase contains a zinc ion that is bound tightly at the active site. Kazemi et al. (1) first identified the likely mechanism of reaction in the enzyme, using DFT calculations on a small model containing the zinc ion, a few important amino acid sidechains, and the cytidine substrate. The DFT calculations show that a water molecule is deprotonated by Glu104 in cytidine deaminase and the resulting hydroxide ion (bound to zinc) is the nucleophile that attacks the

Using computer simulation, Kazemi et al. have now analyzed a classic example in enzymology, and show that a long-cherished and influential theory of enzyme catalysis is wrong.

substrate. The mechanism is clearly different from solution, where a neutral water molecule attacks cytidine.

The DFT calculations were used to parameterize an EVB model of the reaction in the enzyme. MD simulations, repeated multiple times, with this EVB model, gave the free-energy profile for the whole reaction (which involves several steps). By calculating the barrier for each step at different temperatures, van’t Hoff and Arrhenius plots can be constructed to show the temperature dependence of the reaction. The calculated thermodynamic activation parameters (Δ^‡G, Δ^‡H, and Δ^‡S) for the reaction in the enzyme agree very well with experiment; the mechanism is also consistent with experimental kinetic isotope effects. Kazemi et al. (1) also show that the hydroxide mechanism would have a much higher barrier in solution. None of the reaction steps in the enzyme has a large activation entropy: this is because the active site is well organized to catalyze the reaction. The structure of the enzyme is preorganized in a configuration suitable for reaction, and this is at the heart of its catalytic activity. This preorganization of enzymes seems to be generally important in their catalytic ability (12).

The similarity of the entropy change for binding to the difference in activation entropy between the enzyme and water seems to be purely coincidental. The reaction mechanisms are very different: the zinc ion at the active site makes formation of a nucleophilic hydroxide favorable, and the active site structure allows the various steps of the reaction to take place with little energy cost for reorganization (in contrast to reaction in solution, for which ordering water molecules in the transition state is significantly entropically unfavorable). The reacting groups and catalytic metal ion are well oriented for the reaction to take place. “Freezing out” of substrate motions, although a concept perhaps as seductively attractive as Circe herself, is not actually important in catalysis.

Ever since enzymes were first discovered, the sources of their catalytic powers have been a source of debate and controversy. Many hypotheses have been advanced, often based on solid experimental data and thorough, well-developed arguments. As the example of cytidine deaminase shows, however, interpretations of hard data can be wrong. Even the most reliable experimental data can be misleading, drawing enzymologists into beguiling but false conclusions, from which it may be hard to escape. Simulations have an essential role in determining enzyme mechanisms, analyzing contributions to catalysis, and in interpreting experiments [e.g., to reveal and quantify dynamical effects (13)]. As the work of Kazemi et al. (1) shows, simulations are revealing the pragmatic molecular sorcery of biological catalysis (14).