Reaction coordinate of an enzymatic reaction revealed by transition path sampling

Abstract

The transition path sampling method previously applied in our group to the reaction catalyzed by lactate dehydrogenase was used to generate a transition path ensemble for this reaction. Based on analysis of the reactive trajectories generated, important residues behind the active site were implicated in a compressional motion that brought the donor-acceptor atoms of the hydride closer together. In addition, residues behind the active site were implicated in a relaxational motion, locking the substrate in product formation. Although this suggested that the compression-relaxation motions of these residues were important to catalysis, it remained unproven. In this work, we used committor distribution analysis to show that these motions are integral components of the reaction coordinate.

Fig. 1.

A monomer of LDH with atoms in the active site highlighted, specifically, the nicotinamide ring, substrate, active site histidine (red), and donor/acceptor axis residues (green and blue). Val-31, Gly-32, Met-33, Leu-65, and Gln-66 (in green) compressed toward the active site bringing the NC4 of the nicotinamide ring and substrate carbon closer together, whereas Arg-106 (blue) relaxes away, locking the substrate in product formation. These residues span the entire length of the monomer to the edge of the protein.

Fig. 2.

One possible visualization of reactive trajectory space. Regions P and L represent stable regions of phase space for pyruvate and lactate. The solid black line represents the transition surface. All of the relevant degrees of freedom that describe the reaction coordinate are orthogonal to this surface. If we appropriately identify the reaction coordinate, any configuration located on this surface should equally commit to the pyruvate and lactate regions.

Fig. 3.

Diagram of the binding site of LDH with bound NADH and pyruvate showing hydrogen bonds between the substrate and catalytically important residues of the protein. The catalytic event involves the hydride transfer of the C4 hydrogen of NADH from the pro-R side of the reduced nicotinamide ring to the C2 carbon of pyruvate and proton transfer from the imidozole group of His-193 to pyruvate's keto oxygen substrate

Fig. 4.

Shown above are snapshots of the active site of LDH from eight transition paths at 10 fs, the transition state, and 500 fs. Although each path represents a unique approach to crossing the separatrix from reactants to products, the common motions that guide each path over the transition surface are evident in the strong overlap of the configurations at the transition state.

Fig. 5.

Committor distributions from three putative reaction coordinates (from left to right): the first reaction coordinate describes the motions of only the hydride and proton from their respective donors and acceptors; the next reaction coordinate includes a dihedral of the NADH including NC5-NC4-NH4-NC3 atoms and a dihedral of the substrate; and the final reaction coordinate includes motions of the residues (Val-31, Gly-32, Met-33, Leu-65, and Gln-66) behind the cofactor and residue Arg-106 behind the substrate, along the donor/acceptor axis beyond the active site. These distributions are based on results tested on three individual trajectories where transition states were identified, and constrained trajectories were constructed from them. As the reaction coordinate is improved, the peak of the committor distribution approaches 0.5.

Fig. 6.

Committor distribution of five constrained trajectories where the reaction coordinate included the dynamic motions of the outside residues along the donor/acceptor axis (Val-31, Gly-32, Met-33, Leu-65, Gln-66, and Arg-106). Note that sampling a larger group of constrained ensembles significantly improves the distribution.

Fig. 7.

Commitment probability values were calculated for both lactate and pyruvate along a sample trajectory from the reactive path ensemble. The solid line represents probability values for lactate, and the dotted line represents probability values for pyruvate. The transition state was found at the 374-fs time slice.