Barrier Compression and Its Contribution to Both Classical and Quantum Mechanical Aspects of Enzyme Catalysis

Abstract

It is generally accepted that enzymes catalyze reactions by lowering the apparent activation energy by transition state stabilization or through destabilization of ground states. A more controversial proposal is that enzymes can also accelerate reactions through barrier compression-an idea that has emerged from studies of H-tunneling reactions in enzyme systems. The effects of barrier compression on classical (over-the-barrier) reactions, and the partitioning between tunneling and classical reaction paths, have largely been ignored. We performed theoretical and computational studies on the effects of barrier compression on the shape of potential energy surfaces/reaction barriers for model (malonaldehyde and methane/methyl radical anion) and enzymatic (aromatic amine dehydrogenase) proton transfer systems. In all cases, we find that barrier compression is associated with an approximately linear decrease in the activation energy. For partially nonadiabatic proton transfers, we show that barrier compression enhances, to similar extents, the rate of classical and proton tunneling reactions. Our analysis suggests that barrier compression-through fast promoting vibrations, or other means-could be a general mechanism for enhancing the rate of not only tunneling, but also classical, proton transfers in enzyme catalysis.

Enhancement of the droplet nucleation in a dense supersaturated Lennard-Jones vapor

“…Here we can repeat the clarification that Ref. 100 proposed the problematic idea of compression by dynamical vibrations (and also promoted this idea incorrectly as being consistent with experiments) while it is also presented as being identical to our findings. 102 Unfortunately, it is hard to accept the argument that both works meant the same.…”

“…100 Unfortunately, not only do calculations of the actual change in barrier upon increases in pressure appear to be negligible relative to the catalytic effect, but also, the only real evidence for the compressive effect is the change in tunneling (see Section VIII B), and the observed effect is such that under high pressure, the donor-acceptor distance increases rather than decreases. This issue is analyzed in further detail in Section VIII B and Ref.…”

Calculation of the Quantum-Mechanical Tunneling in Bound Potentials

“…This is shown in Figure 2 for a piecewise quadratic continuous potential. The double-well potential simply specifies which energies out of the continuum of the scattering energy states to include into the Boltzmann averaging in (9). For an asymmetric potential, the reactant well may have eigenstates below the asymptote 0 of the product well.…”

“…To understand the role of tunneling for a specific system a typical approach is to construct an electronic potential energy profile of a double-well character, along onedimensional reaction coordinate, and to compute tunneling probabilities using the quasiclassical Wentzel-KramersBrillouin (WKB) approximation. This was done, for example, in recent studies of the barrier shape effect on the classical and QM contributions to reactivity in enzyme catalysis [8][9][10] and in a study of the tunneling control of reactivity in carbenes [6]. Our goal here is to define and analyze QM reaction probabilities and thermal reaction rate constants in the bound potentials in a more rigorous way than the WKB theory.…”

“…The quantum tunneling is known to be very sensitive to the barrier shape and energy, as shown, for example, in the context of enzyme catalysis by Hay and coworkers [9]. Thus, to assess the importance of QM tunneling we propose an adaptation of definitions of the QM tunneling probability and reaction rate constant based on exact energy levels of the bound system and exact QM tunneling through the barrier of the corresponding scattering system.…”