Multiple-Time-Scale Dynamics in Enzyme Catalysis

Abstract

We study the influence of protein dynamics on enzymatic function using techniques from computational biophysics and statistical physics. Lactate dehydrogenase (LDH) was the model system used in our investigations. This enzyme the catalyzes the reversible reduction of pyruvate to lactate utilizing NADH as a cofactor.;Recent experimental studies suggest that LDH binds its substrate via the formation of a LDH/NADH-substrate encounter complex through a select-fit mechanism, whereby only a minority population of LDH/NADH is binding-competent. We performed molecular dynamics calculations to explore the variations in structure accessible to the binary complex with a focus on identifying structures that seem likely to be binding-competent and which are in accord with the known experimental characterization of forming binding-competent species. We found that LDH/NADH samples quite a range of protein conformations within our 2.148 ns calculation, some of which yield quite facile access of solvent to the active site. The results suggest that the mobile loop of LDH is perhaps just partially open in these conformations and that multiple open conformations, yielding multiple binding pathways, are likely. These open conformations do not require large-scale unfolding/melting of the binary complex. Rather, open versus closed conformations are due to subtle protein and water rearrangements. Nevertheless, the large heat capacity change observed between binding-competent and binding-incompetent can be explained by changes in solvation and an internal rearrangement of hydrogen bonds. We speculate that such a strategy for binding may be necessary to get a ligand efficiently to a binding pocket that is located fairly deep within the protein's interior.;The nitric oxide-inducible L-Lactate dehydrogenase-1 in Staphylococcus aureus (SaLDH1) provides an important survival strategy against the host immune response by allowing this pathogen to maintain redox homeostasis during nitrosative stress. Under this condition, lactate production becomes the sole mechanism for regenerating NAD+. Preliminary experimental results indicate that the catalytic efficiency of the enzyme in this direction of the reaction is higher by at least an order of magnitude compared to the formation of pyruvate. An outstanding difference between LDHs from S. aureus, dogfish and human muscle is the natural alanine substitution at position 85 in SaLDH1, which in the equivalent position in dogfish and human muscle is an arginine. This "hinge" arginine provides a stabilizing salt bridge interaction with the pyrophosphate moiety of the cofactor. Our molecular dynamics simulation results suggest that wildtype SaLDH1 indeed exhibits greater tendency to sample open active site loop conformations than an A85R mutant. The interaction between the arginine 85 and pyrophosphate in the cofactor most likely shifts the equilibrium towards closed-loop product complexes. The loop opening step was determined as the rate limiting step in pig heart LDH. Our results suggest that the loss of the stabilizing salt bridge interaction perhaps allows faster loop movement and turnover in SaLDH1.;Lastly, we describe the result of our research to elucidate the physical origin of catalysis in LDH. Previous results from our group had determined that subpicosecond motions are important for catalysis in LDH. Furthermore, transition path sampling with committor distribution analysis revealed that the residence time in the transition state is on the order of 10 fs. Yet the overall turnover rate of this enzyme is in the millisecond timescale. Our evidence suggests that this is likely due to the heterogeneity in enzyme structure and that not all structures are equally competent to promote the reaction, i.e. in terms of the donor-acceptor (D-A) distance. We hypothesize that only a tiny subset of the conformation space of the enzyme is catalytically competent. We will describe our multistep strategy to address the problem. We searched for catalytically competent enzyme conformations using Langevin Dynamics and simulated annealing. We then implemented a recently developed technique from statistical physics, the finite-temperature string method, to locate the minimum free energy pathway between catalytically active conformations. Calculating the relative free energy of the enzymatic conformation along the conformational transition pathway showed that the catalytically competent conformations are indeed high free energy, i.e. low probability, states. We further showed that along a transition pathway that brings the enzyme to a catalytically competent conformation, the free energy barrier to the chemical reaction is lower in the short D-A but low probability conformations. We, therefore, suggest that in human heart Lactate dehydrogenase catalysis can in part be explained as a probabilistic search for the rare species where the free energy barrier to chemistry is low and where the fast promoting motions of the protein matrix are efficiently utilized.