Protein dynamics and enzymatic chemical barrier passage

Abstract

After many decades of investigation, the manner in which enzymes increase the rate of chemical reactions, at times by a factor of 10(17) compared to the rate of the corresponding solution phase reaction, is still opaque. A topic of significant discussion in the literature of the past 5-10 years has been the importance of protein dynamics in this process. This Feature Article will discuss the authors' work on this still controversial topic with focus on both methodology and application to real systems. The end conclusion of this work has been that for specific enzymes under study protein dynamics on both rapid time scales of barrier crossing (termed promoting vibrations by the authors) and of conformational fluctuations are central to the function of biological catalysts. In another enzyme we will discuss, the results are far less clear. The manner of the coupling of chemistry to protein dynamics has deep implications for protein architecture, both natural and created, and recent results reinforce the complexity of the protein form that has evolved to support these functions.

Figure 1

A ribbon diagram of a monomer of human heart lactate dehydrogenase. The donor and acceptor: the nicotinamide ring, and lactate are colored red. The promoting vibration residues, Val31, Gly32, Met33, Leu65, Gln66 (yellow) are compressed towards the active site bringing the NC4 of the nicotinamide ring and substrate carbon closer together while Arg106 (yellow) relaxes away locking the substrate in product formation. These residues span the entire length of the monomer to the edge of the protein.

Figure 2

Preliminary results of a computational heating experiment. The nicotinamide ring is heated as described and the temperature of the solvent, protein and residues along the promoting vibration are monitored. The promoting vibration is clearly hotter than the rest of the protein indicating a preferred direction of thermal energy transfer.

Figure 3

Commitment probability values were calculated for both PNP (top panel) and LDH (lower panel) along sample trajectories from the reactive path ensembles for the respective enzymes. It is clear that the transition region for LDH is far shorter in time duration than for PNP, but even for PNP, the residence time is on the order of 10–20 fsecs.

Figure 4

A diagram showing the residues that move and the direction of movement as a reaction crosses the separatrix in the DHFR reaction. Donor and acceptor are shown as a blue and green ball respectively. There is clearly no well-defined promoting vibration, and as yet we are able to show no rapid motions as parts of the reaction coordinate. It is also clear from the protein that the limited protein scaffold prevents the formation of the type of compressive promoting vibration seen in LDH.

Figure 5a

Converged average potential energies between stable, low-distance donor acceptor conformations. The energies are computed using finite temperature string methods. Numerical labels are arbitrary names given to clusters of conformations that structural analysis showed to be identical. The x-axis, which denotes conformational variation, is the string image number.

Figure 5b

The converged free energy corresponding to one of the potential energy curves above (red curve labeled 7–90.) Note that the minima in average potential energy are on the edges of a rising free energy. The minima on Figure 5a given in string images correspond to −.50 and + .69 angstroms in Δ-RMSD units along the string coordinate on 5b.

Figure 6

Overlay of the active site residues of 4 representative potential energy stable conformations (three of which are part of Figure 5a.) Residues belonging to the same conformation are shown with the same color. At the top of the picture, the active site loop is shown (residues 96–106, its residues 100 and 106 are shown explicitly) The 4 residues at the bottom of the figure are related to each other by a simple translation. However, the important residues His193, Arg106, Gln100 and Asp194 are being pushed by the active site loop (which has a different closed position in each of the 4 conformations), and their geometric arrangement is different in a non-trivial way among the 4 conformations. Transitions between these conformations were seen to always involve partial loop opening.

Figure 7

The chemical barrier to reaction along the free energy path of the conformational transformation in Figure 6b. The reaction proceeds from right (Lactate) to left (Pyruvate). The lowest chemical barrier is obtained at the end point high free energy (rare) conformations. The highest barrier to reaction occurs at the lowest free energy conformation – the minimum in Figure 5b.

Figure 8

Shown above are snapshots of two members of the separatrix found from the largest Monte Carlo step TPS simulation we have accomplished on LDH. Green and yellow, and red and blue show the 2 structures of the promoting vibration and the NADH/lactate respectively. These 2 members are the most separated in trajectory space, and it is clear that at the separatrix, they almost perfectly overlay. It is shown that common motions guide each path over the transition surface are evident in the complete overlap of the configurations at the transition state.

Figure 9

2 DHFR configurations are presented as the chemistry passes the separatrix, as in Figure 8 above for LDH. These configurations show a bit more variability than those of LDH in Figure 8, as expected given the far more flexible protein structure, but even in this case; there is very strong overlap of the 2 configurations.