Kinetic Isotope Effects for Concerted Multiple Proton Transfer:  A Direct Dynamics Study of an Active-Site Model of Carbonic Anhydrase II

Abstract

The rate constant of the reaction catalyzed by the enzyme carbonic anhydrase II, which removes carbon dioxide from body fluids, is calculated for a model of the active site. The rate-determining step is proton transfer from a zinc-bound water molecule to a histidine residue via a bridge of two or more water molecules. The structure of the active site is known from X-ray studies except for the number and location of the water molecules. Model calculations are reported for a system of 58 atoms including a four-coordinated zinc ion connected to a methylimidazole molecule by a chain of two waters, constrained to reproduce the size of the active site. The structure and vibrational force field are calculated by an approximate density functional treatment of the proton-transfer step at the Self-Consistent-Charge Density Functional Tight Binding (SCC-DFTB) level. A single transition state is found indicating concerted triple proton transfer. Direct-dynamics calculations for proton and deuteron transfer and combinations thereof, based on the Approximate Instanton Method and on Variational Transition State Theory with Tunneling Corrections, are in fair agreement and yield rates that are considerably higher and kinetic isotope effects (KIEs) that are somewhat higher than experiment. Classical rate constants obtained from Transition State Theory are smaller than the quantum values but the corresponding KIEs are five times larger. For multiple proton transfer along water bridges classical KIEs are shown to be generally larger than quantum KIEs, which invalidates the standard method to distinguish tunneling and over-barrier transfer. In the present case, a three-way comparison of classical and quantum results with the observed data is necessary to conclude that proton transfer along the bridge proceeds by tunneling. The results suggest that the two-water bridge is present in low concentrations but makes a substantial contribution to proton transport because of its high efficiency. Bridging structures containing more water molecules may have lower energies but are expected to be less efficient. The observed exponential dependence of the KIEs on the deuterium concentration in H(2)O/D(2)O mixtures implies concerted transfer and thus rules out substantial contributions from structures that lead to stepwise transfer via solvated hydronium ions, which presumably dominate proton transfer in less efficient carbonic anhydrase isozymes.

Transition state theory can be used in studies of enzyme catalysis: lessons from simulations of tunnelling and dynamical effects in lipoxygenase and other systems

“…Perhaps for this reason, microscopic estimates ) of the parameters in equation (2.11) for the reaction catalysed by lipoxygenase were found to be very different than those obtained by fitting equation (2.11) to the observed isotope effects Lehnert & Solomon 2003;Smedarchina et al 2003). The treatment of NQM effects can be accomplished on a more quantitative level by including the adiabatic limit and modifying the centroid path integral approach (Gillan 1987;Voth et al 1989;Voth 1996).…”

Multidimensional Tunneling, Recrossing, and the Transmission Coefficient for Enzymatic Reactions

“…87,135 This method is more closely related to (but more approximate than) the methods discussed in the next section than to electron transfer theory.…”

Efficient estimators for quantum instanton evaluation of the kinetic isotope effects: Application to the intramolecular hydrogen transfer in pentadiene

“…These quantum effects have also been observed in several numerical simulations. [4][5][6][7] Most simulations include quantum effects by semiclassical ͑SC͒ approximations or by treating one or two degrees of freedom quantum mechanically and the rest classically.…”