The role of dynamics in catalysis

For some enzymes, dynamics on the millisecond timescale play a critical role in catalysis. I don't think this is a particularly controversial or unclear statement, but then, I know what I mean by it. In the process of communication, however, the intended meaning sometimes gets lost or transformed. A statement that addresses an entire catalytic cycle, for instance, might be interpreted as addressing only the chemical step. This seems to have happened in a pair of papers that concern the transfer of energy from conformational rearrangements to a chemical reaction.

Consider a reaction scheme in which an enzyme loosely associates with substrates (E.S), then "closes" to form a tight, catalytically-competent complex that then undergoes a reaction with the rate k_chem:

Pisliakov et al. (1) ask whether the closing process can accelerate k_chem. They ask this question primarily because a group from Harvard University proposed that this was possible in a paper printed last year in J. Phys. Chem. B (2). In that paper, Min et al. performed some simulations suggesting that such an acceleration was at least possible, and consistent with some enzymatic data. Pisliakov et al. approach the question with simulations of the reaction of the phosphotransfer enzyme Adk with 2 ADP molecules to form ATP and AMP. As part of the catalytic cycle, the enzyme goes from an open state (PDB: 4AKE) where the ATP and AMP binding sites are exposed to solvent, to a closed state (PDB: 1ANK) where the substrates are shielded from the surrounding solution by ATP and AMP "lids" that close down over the active site.


One can, perhaps, imagine that when the enzyme closes around the substrates, some motion will occur that promotes the transfer of a phosphate group from one molecule to another. Pisliakov et al. use a three-tiered system of simulations to address the question, as a way of trying to get around the difficulty of dealing with the long timescales required. Their simulations allow them to adjust the energy barrier to match the experimental rates or accelerate the reaction so that the whole pathway can be simulated. In general, they find that conformational fluctuations do not enhance the chemical reaction rate in this system.

I have two main concerns about the science that was performed here. The first is that the energy barriers in the long-timescale experiment appear to be improperly paramaterized. In estimating these barriers for the phosphotransfer reaction in Adk, Pisliakov et al. used 260 /s as k_chem. However, although the actual reaction carried out by Adk follows an extremely complex scheme, the analysis performed by Wolf-Watz et al. utilized a simplified scheme that combined all post-association steps into a single k_cat. This is why the concordance between k_cat and k_open justifies the conclusion that lid-opening is rate-limiting. In principle, the experiments used for that paper are incapable of separating the opening and closing steps from the chemical step. Therefore we have no experimental knowledge of the phosphotransfer rate, except that it is greater than 260 /s. This perplexing error appears to have originated with Min et al., but I am surprised Warshel's group did not catch it.

This is not a major problem because the bulk of the conclusions of the experiment were drawn from a different simulation in which the energy barriers were lower, but this leads to my second concern. If the structural transition involves a very smooth and coherent rearrangement of the protein, then simply manipulating energy barriers should not result in a serious error of analysis. In reality, however, ensemble motions of protein elements are not going to be so directed or uniform. Structural rearrangements are not highly singular steps, but involve a large number of intermediates and transition states. Motions in the late stages of the structural transition that promote catalysis may well be missed by simplified models, or accelerated beyond productivity by lowering the energy barrier.

That said, I'm not particularly surprised that Pisliakov et al. find that energy from the conformational coordinate does not transfer to the chemical coordinate, nor do I disagree with the finding. Despite what Pisliakov et al. appear to believe, the papers that have come out of Dorothee's group don't argue that the millisecond motions contribute directly to the chemistry. Doro doesn't believe that for a second. Neither do I. The importance of dynamics has little to do with shoving the reaction along the chemistry coordinate, but everything to do with getting substrates bound and into a state where chemistry is possible.

Dynamics allow an enzyme to reconcile incompatible functional requirements. To efficiently function as a phosphotransfer enzyme (as opposed to a hydrolytic phosphatase), Adk must expel water from the active site during catalysis. If the active site is inaccessible to solution, however, there is no way for the substrates to diffuse into it. It is difficult to create a single, rigid fold that can accommodate both these demands, but by fluctuating between two states the problem is resolved quite easily. So yes, the dynamics are essential to catalysis, but that does not imply that the conformational and chemical energy coordinates are coupled.

More perplexing is the discussion of the hierarchy of motion, which Pisliakov et al. take to mean that nanosecond motions somehow contribute to the chemical coordinate. As I discussed when that paper was initially published, the question being addressed was whether and how motions on the fast timescale (ps-ns) in Adk were related to the slower (ms) motions of the lids. In a hierarchy of motion, fast timescale fluctuations enable or promote slow timescale dynamics. In the case of Adk, this means that nanosecond flexibility at structural hinges allow the millisecond motions of the ATP and AMP lids. It was not implied, then or since, that the nanosecond motions in question make a direct contribution to movement along the chemical coordinate. This is not to say that there are no researchers who believe that ns motions contribute to catalysis — I've previously mentioned some work on hydrogen tunneling that makes precisely this argument. In the specific case of Adk, however, the contribution of ns motions to catalysis consists entirely in their enabling of the slower ensemble motions of the nucleotide binding domains, and nobody but the Warshel group has suggested otherwise.

There is an ongoing disconnect in the literature concerning the role of dynamics in catalysis. While it is true that in many cases rates of structural transitions correlate with rates of catalysis, this does not imply that the conformational transition coordinate is linked to the chemical reaction coordinate by direct transfer of energy. It is more likely that the dynamics of the enzyme contribute to catalysis by generating reaction-competent states from reaction-incompetent states. This is not to say that dynamics cannot possibly make a contribution to phenomena such as hydrogen tunneling, but it strikes me as unlikely that motions on the millisecond timescale will contribute to a chemical coordinate. Experiments, rather than simulations, will be the ultimate test of the idea. However, in principle, this hypothesis can only be tested experimentally on enzymes where the conformational changes do not limit the chemical reaction rate. Because the rate of the chemical step is unknown in Adk, it may not be an appropriate model system for addressing this question.

1. Pisliakov, A., Cao, J., Kamerlin, S., & Warshel, A. (2009). Enzyme millisecond conformational dynamics do not catalyze the chemical step Proceedings of the National Academy of Sciences, 106 (41), 17359-17364 DOI: 10.1073/pnas.0909150106

2. Min, W., Xie, X., & Bagchi, B. (2008). Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis The Journal of Physical Chemistry B, 112 (2), 454-466 DOI: 10.1021/jp076533c

3. Wolf-Watz, M., Thai, V., Henzler-Wildman, K., Hadjipavlou, G., Eisenmesser, E., & Kern, D. (2004). Linkage between dynamics and catalysis in a thermophilic-mesophilic enzyme pair Nature Structural & Molecular Biology, 11 (10), 945-949 DOI: 10.1038/nsmb821