Reaction Coordinate, Free Energy, and Rate of Intramolecular Proton Transfer in Human Carbonic Anhydrase II

Abstract

The role of structure and dynamics of an enzyme has been investigated at three different stages of its function including the chemical event it catalyzes. A one-pot computational method has been designed for each of these stages on the basis of classical and/or quantum mechanical-molecular mechanical molecular dynamics and transition path sampling simulations. For a pair of initial and final states A and B separated by a high free-energy barrier, using a two-stage selection process, several collective variables (CVs) are identified that can delineate A and B. However, these CVs are found to exhibit strong cross-coupling over the transition paths. A set of mutually orthogonal order parameters is then derived from these CVs and an optimal reaction coordinate, r, determined applying half-trajectory likelihood maximization along with a Bayesian information criterion. The transition paths are also used to project the multidimensional free energy surface and barrier crossing dynamics along r. The proposed scheme has been applied to the rate-determining intramolecular proton transfer reaction of the well-known enzyme human carbonic anhydrase II. The potential of mean force, F( r), in the absence of the chemical step is found to reproduce earlier results on the equilibrium population of two side-chain orientations of key residue His-64. Estimation of rate constants, k, from mean first passage times for the three different stages of catalysis shows that the rate-determining step of intramolecular proton transfer occurs with k ≃ 1.0 × 10 s, in close agreement with known experimental results.

Coordination Dynamics of Zinc Triggers the Rate Determining Proton Transfer in Human Carbonic Anhydrase II

“…The following optimum reaction coordinates have been derived for the reactions 1 and 2 using half trajectory likelihood maximization with a Bayesian information criterion …”

“…Based on a large number of experimental and computer simulation studies over the past couple of decades, a molecular level understanding of the intramolecular proton transfer between Zn‐wat and His‐64 has started emerging. An excess proton, generated by the deprotonation of Zn‐wat ( ), is translocated to the sidechain of His‐64, located about 10 Å away across the active site cavity with its sidechain pointing inward at Zn‐wat . Upon protonation, His‐64 rotates away from the active site through a narrow channel bordered by Asn‐62 and Trp‐5 and releases the proton to the bulk water/exogenous buffer .…”

“…The proton transfer path between Zn‐wat and inward His‐64 sidechain is mediated by a network of 2–4 active site water molecules that remain hydrogen bonded to each other up to 5–6 ps . A free energy barrier of about is encountered along this path due to reorganization of active site water molecules when the excess proton being translocated undergoes a transition between Eigen‐like to Zundel‐like structures . Such transitions have been shown to be coupled to the fluctuations of active site amino acid residues such as Tyr‐7, Asn‐62, Asn‐67, Gln‐92, Glu‐106, Thr‐199 and Thr‐200 .…”

“…Therefore, any reactive transition between these two states not only involves bond making/breaking, but also turns out to be rare in the timescale typical of molecular fluctuations. We have recently shown that such reactive events may be modeled by generating an ensemble of reactive transition paths using quantum mechanical‐molecular mechanical molecular dynamics (QM‐MM MD) simulation studies interfaced with transition path sampling (TPS) . This simulation method has been used in this article to model the proton transfer reactions starting from the states T and P .…”

“…Moreover, the reduced dynamics along r is expected to have the same rate as the multi‐dimensional barrier crossing. For each reaction studied in the present work, an optimum reaction coordinate has been determined using a recently developed one‐pot computational procedure . In this method, the ensemble of transition paths between the corresponding reactant and product states has been subjected to an extensive search to identify all collective variables (CVs) which exhibit different values in the reactant and product states.…”