Catalytic efficiency of enzymes: a theoretical analysis

Abstract

This brief review analyzes the underlying physical principles of enzyme catalysis, with an emphasis on the role of equilibrium enzyme motions and conformational sampling. The concepts are developed in the context of three representative systems, namely, dihydrofolate reductase, ketosteroid isomerase, and soybean lipoxygenase. All of these reactions involve hydrogen transfer, but many of the concepts discussed are more generally applicable. The factors that are analyzed in this review include hydrogen tunneling, proton donor-acceptor motion, hydrogen bonding, pKa shifting, electrostatics, preorganization, reorganization, and conformational motions. The rate constant for the chemical step is determined primarily by the free energy barrier, which is related to the probability of sampling configurations conducive to the chemical reaction. According to this perspective, stochastic thermal motions lead to equilibrium conformational changes in the enzyme and ligands that result in configurations favorable for the breaking and forming of chemical bonds. For proton, hydride, and proton-coupled electron transfer reactions, typically the donor and acceptor become closer to facilitate the transfer. The impact of mutations on the catalytic rate constants can be explained in terms of the factors enumerated above. In particular, distal mutations can alter the conformational motions of the enzyme and therefore the probability of sampling configurations conducive to the chemical reaction. Methods such as vibrational Stark spectroscopy, in which environmentally sensitive probes are introduced site-specifically into the enzyme, provide further insight into these aspects of enzyme catalysis through a combination of experiments and theoretical calculations.

Figure 1

Schematic depiction of an adiabatic hydrogen transfer reaction. The free energy is plotted along the collective reaction coordinate, with the free energy barrier denoted by ΔG^‡. The dashed red curve and red arrow indicate the decrease in the free energy barrier when the nuclear quantum effects of the transferring hydrogen are included. DA denotes the hydrogen donor-acceptor distance, which is typically larger at the reactant and product (i.e., minima) and smaller at the transition state (i.e., top of the barrier) because the donor and acceptor must get closer for the hydrogen to transfer.

Figure 2

Schematic depiction of a nonadiabatic PCET reaction. The free energies of the two diabatic states corresponding to the electron on its donor (D_e⁻A_e, blue) and acceptor (D_eA_e⁻, red) are plotted along the collective reaction coordinate, and the free energy barrier is denoted by ΔG^‡. In the upper figures surrounded by dotted lines, the proton potential energy curves for the two diabatic states at the crossing point are plotted as functions of the hydrogen coordinate using the same color scheme as used to distinguish the two diabatic states. The ground state reactant and product proton vibrational wavefunctions are depicted, and the overlap is shaded in purple. When the proton donor-acceptor distance, D_pA_p, is large, the overlap is small, and when this distance decreases, the overlap increases.

Figure 3

Chemical reactions catalyzed by each of the three representative enzymes. (A) DHFR catalyzes a process involving hydride transfer from NADPH to protonated DHF. (B) KSI catalyzes a process involving two sequential proton transfer steps: (1) proton transfer from a carbon of the steroid to Asp40, resulting in a dienolate intermediate, and (2) proton transfer from Asp40 to another carbon of the substrate, leading to an overall isomerization reaction. (C) SLO catalyzes the hydrogen abstraction from the linoleic acid substrate to the iron cofactor. This process is thought to occur by a PCET mechanism. Part (C) reproduced with permission from Ref. .

Figure 4

Schematic depiction of the role of conformational sampling in the chemical step of an enzyme reaction. The free energy is plotted along the collective reaction coordinate. The evolution from reactant (left minimum, blue) to transition state (top of barrier, red) is caused by stochastic thermal motions, which lead to equilibrium conformational changes (purple arrow) to produce configurations that are conducive to the chemical reaction. The bond rearrangement (i.e., the breaking and forming of chemical bonds) occurs near the top of the barrier (red arrow). For hydrogen transfer reactions, hydrogen tunneling also occurs near the top of the barrier. The reacting entities (i.e., donor and acceptor) are depicted by a triangle and a square, which are further apart in the reactant and product but closer at the transition state. The changes in orientation of the shapes represent changes in orientation of the reacting entities, as well as changes in hydrogen bonding interactions and electrostatics along the collective reaction coordinate. The effects of breaking and forming chemical bonds are not explicitly shown in these shapes.

Figure 5

Schematic representation of the standard free energy landscape for the catalytic network of an enzyme reaction. Conformational changes occur along both axes. The conformational changes occurring along the Reaction Coordinate axis correspond to the environmental reorganization that facilitates the chemical reaction. In contrast, the conformational changes occurring along the Ensemble Conformations axis represent the ensembles of configurations existing at all stages along the reaction coordinate, leading to a large number of parallel catalytic pathways. The reaction paths can slide along and between both coordinates. For real enzymes, the number of maxima and minima along the coordinates is expected to be greater than shown. The free energy landscape and dominant catalytic pathways will be altered by external conditions and protein mutations. Figure and portions of caption reproduced from Ref. .