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, 97 (22), 11899-904

How Important Are Entropic Contributions to Enzyme Catalysis?

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How Important Are Entropic Contributions to Enzyme Catalysis?

J Villa et al. Proc Natl Acad Sci U S A.

Abstract

The idea that enzymes accelerate their reactions by entropic effects has played a major role in many prominent proposals about the origin of enzyme catalysis. This idea implies that the binding to an enzyme active site freezes the motion of the reacting fragments and eliminates their entropic contributions, (delta S(cat)(double dagger))', to the activation energy. It is also implied that the binding entropy is equal to the activation entropy, (delta S(w)(double dagger))', of the corresponding solution reaction. It is, however, difficult to examine this idea by experimental approaches. The present paper defines the entropic proposal in a rigorous way and develops a computer simulation approach that determines (delta S(double dagger))'. This approach allows us to evaluate the differences between (delta S(double dagger))' of an enzymatic reaction and of the corresponding reference reaction in solution. Our approach is used in a study of the entropic contribution to the catalytic reaction of subtilisin. It is found that this contribution is much smaller than previously thought. This result is due to the following: (i) Many of the motions that are free in the reactants state of the reference solution reaction are also free at the transition state. (ii) The binding to the enzyme does not completely freeze the motion of the reacting fragments so that (delta S(double dagger))' in the enzymes is not zero. (iii) The binding entropy is not necessarily equal to (delta S(w)(double dagger))'.

Figures

Figure 1
Figure 1
Comparison of the free energy profiles Δg for a given reaction in a protein (Δgp) and in water (Δgw). The figure represents these free energy profiles in the absence (Δg) and presence (Δg′) of constraints for the movement of the reacting fragments. Note that Δgp corresponds approximately to kcat/Km (it is given by ΔGbind + Δgcat). The figure uses the notation of L for ligand rather than S for substrate to prevent confusion with the symbol S used for entropy.
Figure 2
Figure 2
Schematic representation of the translational and rotational degrees of freedom in the nucleophilic attack of a CH3O group on an amide. The figure depicts only the transition state, but the corresponding RS picture can be obtained by stretching the C ⋯ O distance. For simplicity we place the rotation axes on the attacking oxygen. As illustrated, R2 remains a free rotation in the TS, R1 becomes a low-frequency torsional oscillator, while T1, T2, and T3 become bending motions.
Figure 3
Figure 3
Thermodynamic cycle used for the evaluation of the entropy contribution to the activation free energy of the reaction. The fragments are fixed in (I′) and (II′) and allowed to move (as indicated by the shaded area) in (I) and (II). The same circle is also used for the reaction in water (see figure 1 of ref. 14).
Figure 4
Figure 4
ΔG′ values at different initial conditions: in water (Left), and in the protein site (Right). Black and gray bars correspond to ΔG′ in the reactant state and in the transition state, respectively. The figure represents the results of Table 1 for the simulations with region II radius of 14 Å, and the calculated values have been plotted in decreasing order of |ΔG′|.
Figure 5
Figure 5
Superposition of snapshots of the trajectories propagated at the last point of the FEP protocol where K changes from 0.003 to 0.0003 kcal/mol for the RS and the TS of the water surface (solid curve) and the protein surface (dashed curve). The free energy profiles are given in a schematic way. The 20 snapshots for each system were taken at equal time space during 50-ps runs. L designates ligand as in Fig. 1.

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