Comparison studies of the human heart and Bacillus stearothermophilus lactate dehydrogreanse by transition path sampling

Protein Dynamics and Enzymatic Catalysis

This Perspective presents a review of our work and that of others in the highly controversial topic of the coupling of protein dynamics to reaction in enzymes. We have been involved in studying this topic for many years. Thus, this perspective will naturally present our own views, but it also is designed to present an overview of the variety of viewpoints of this topic, both experimental and theoretical. This is obviously a large and contentious topic.

Analogues of Oxamate, Pyruvate, and Lactate as Potential Inhibitors of Plasmodium knowlesi Lactate Dehydrogenase Identified Using Virtual Screening and Verified via Inhibition Assays

Malaria management remains a challenge, due to the resistance of malaria parasites to current antimalarial agents. This resistance consequently delays the global elimination of malaria throughout the world. Hence, the demand is increasing for new and effective antimalarial drugs. The identification of potential drugs that target Pk-LDH can be obtained through virtual screening analyses, as this has been previously applied to discover Pf-LDH inhibitors. In this study, the selected candidates from our virtual screening analyses were subsequently tested against purified Pk-LDH, and verified through an inhibition of Pk-LDH via enzymatic activity assays. Virtual screening analysis from this study showed that 3,3-Difluoropyrrolidine hydrochloride and 3-hydroxytetrahydrofuran exhibited binding affinity values of −3.25 kcal/mol and −3.74, respectively. These compounds were selected for evaluation towards inhibitory activity against Pk-LDH assays, including two compounds from a previous study which are oxalic acid and glycolamide. The earlier compounds were structurally similar to lactate and pyruvate, and the latter two compounds were structurally similar to a known LDH inhibitor, oxamate. Among all of the compounds tested, oxalic acid showed the highest inhibition activity at 54.12%; interestingly, this correlated well with the virtual screening analyses, which showed that this compound was the best among the oxamate analogues, with a binding affinity value of −2.59 kcal/mol. Hence, further exploration and development of this compound may result in a promising antimalarial drug for malaria treatment, especially for infection involving P. knowlesi.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

Role of Protein Motions in Catalysis by Formate Dehydrogenase

We have analyzed the reaction catalyzed by formate dehydrogenase using transition path sampling. This system has recently received experimental attention using infrared spectroscopy and heavy-enzyme studies. Some of the experimental results point to the possible importance of protein motions that are coupled to the chemical step. We found that the residue Val123 that lies behind the nicotinamide ring occasionally comes into van der Waals contact with the acceptor and that in all reactive trajectories, the barrier-crossing event is preceded by this contact, meaning that the motion of Val123 is part of the reaction coordinate. Experimental results have been interpreted with a two-dimensional formula for the chemical rate, which cannot capture effects such as the one we describe.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Roles of Closed- and Open-Loop Conformations in Large-Scale Structural Transitions of l-Lactate Dehydrogenase

The mechanism of l-lactate generation from pyruvate by l-lactate dehydrogenase (LDH) from the rabbit muscle was studied theoretically by the multistructural microiteration (MSM) method combined with the quantum mechanics/molecular mechanics (QM/MM)-ONIOM method, where the MSM method describes the MM environment as a weighted average of multiple different structures that are fully relaxed during geometry optimization or a reaction path calculation for the QM part. The results showed that the substrate binding and product states were stabilized only in the open-loop conformation of LDH and the reaction occurred in the closed-loop conformation. In other words, before and after the chemical reaction, a large-scale structural transition from the open-loop conformation to the closed-loop conformation and vice versa occurred. The closed-loop conformation stabilized the transition state of the reaction. In contrast, the open-loop conformation stabilized the substrate binding and final states. In other words, the closed- to open-loop transition at the substrate binding state urges capture of the substrate molecule, the subsequent open- to closed-loop transition promotes the product generation, and the final closed- to open-loop transition at the final state prevents the reverse reaction going back to the substrate binding state. It is thus suggested that the exchange of stability between the closed- and open-loop conformations at different states promotes the catalytic cycle.

Mechanistic Insights on Human Phosphoglucomutase Revealed by Transition Path Sampling and Molecular Dynamics Calculations

Human α-phosphoglucomutase 1 (α-PGM) catalyzes the isomerization of glucose-1-phosphate into glucose-6-phosphate (G6P) through two sequential phosphoryl transfer steps with a glucose-1,6-bisphosphate (G16P) intermediate. Given that the release of G6P in the gluconeogenesis raises the glucose output levels, α-PGM represents a tempting pharmacological target for type 2 diabetes. Here, we provide the first theoretical study of the catalytic mechanism of human α-PGM. We performed transition-path sampling simulations to unveil the atomic details of the two catalytic chemical steps, which could be key for developing transition state (TS) analogue molecules with inhibitory properties. Our calculations revealed that both steps proceed through a concerted S_N 2-like mechanism, with a loose metaphosphate-like TS. Even though experimental data suggests that the two steps are identical, we observed noticeable differences: 1) the transition state ensemble has a well-defined TS region and a late TS for the second step, and 2) larger coordinated protein motions are required to reach the TS of the second step. We have identified key residues (Arg23, Ser117, His118, Lys389), and the Mg²⁺ ion that contribute in different ways to the reaction coordinate. Accelerated molecular dynamics simulations suggest that the G16P intermediate may reorient without leaving the enzymatic binding pocket, through significant conformational rearrangements of the G16P and of specific loop regions of the human α-PGM.

Incorporating Fast Protein Dynamics into Enzyme Design: A Proposed Mutant Aromatic Amine Dehydrogenase

In recent years, there has been encouraging progress in the engineering of enzymes that are designed to catalyze reactions not accelerated by natural enzymes. We tested the possibility of reengineering an existing enzyme by introducing a fast protein motion that couples to the reaction. Aromatic amine dehydrogenase is a system that has been shown to use a fast substrate motion as part of the reaction mechanism. We identified a mutation that preserves this fast motion but also introduces a favorable fast motion near the active site that did not exist in the native enzyme. Transition path sampling was used for the analysis of the atomic details of the mechanism.

Structurally Linked Dynamics in Lactate Dehydrogenases of Evolutionarily Distinct Species

We present new findings about how primary and secondary structure affects the role of fast protein motions in the reaction coordinates of enzymatic reactions. Using transition path sampling and committor distribution analysis, we examined the difference in the role of these fast protein motions in the reaction coordinate of lactate dehydrogenases (LDHs) of Apicomplexa organisms Plasmodium falciparum and Cryptosporidium parvum. Having evolved separately from a common malate dehydrogenase ancestor, the two enzymes exhibit several important structural differences, notably a five-amino acid insertion in the active site loop of P. falciparum LDH. We find that these active site differences between the two organisms' LDHs likely cause a decrease in the contribution of the previously determined LDH rate-promoting vibration to the reaction coordinate of P. falciparum LDH compared to that of C. parvum LDH, specifically in the coupling of the rate-promoting vibration and the hydride transfer. This effect, while subtle, directly shows how changes in structure near the active site of LDH alter catalytically important motions. Insights provided by studying these alterations would prove to be useful in identifying LDH inhibitors that specifically target the isozymes of these parasitic organisms.

Triple Isotope Effects Support Concerted Hydride and Proton Transfer and Promoting Vibrations in Human Heart Lactate Dehydrogenase

Transition path sampling simulations have proposed that human heart lactate dehydrogenase (LDH) employs protein promoting vibrations (PPVs) on the femtosecond (fs) to picosecond (ps) time scale to promote crossing of the chemical barrier. This chemical barrier involves both hydride and proton transfers to pyruvate to form l-lactate, using reduced nicotinamide adenine dinucleotide (NADH) as the cofactor. Here we report experimental evidence from three types of isotope effect experiments that support coupling of the promoting vibrations to barrier crossing and the coincidence of hydride and proton transfer. We prepared the native (light) LDH and a heavy LDH labeled with ¹³C, ¹⁵N, and nonexchangeable ²H (D) to perturb the predicted PPVs. Heavy LDH has slowed chemistry in single turnover experiments, supporting a contribution of PPVs to transition state formation. Both the [4-²H]NADH (NADD) kinetic isotope effect and the D₂O solvent isotope effect were increased in dual-label experiments combining both NADD and D₂O, a pattern maintained with both light and heavy LDHs. These isotope effects support concerted hydride and proton transfer for both light and heavy LDHs. Although the transition state barrier-crossing probability is reduced in heavy LDH, the concerted mechanism of the hydride-proton transfer reaction is not altered. This study takes advantage of triple isotope effects to resolve the chemical mechanism of LDH and establish the coupling of fs-ps protein dynamics to barrier crossing.

Targeting a Rate-Promoting Vibration with an Allosteric Mediator in Lactate Dehydrogenase

We present a new type of allosteric modulation in which a molecule bound outside the active site modifies the chemistry of an enzymatic reaction through rapid protein dynamics. As a test case for this type of allostery, we chose an enzyme with a well-characterized rate-promoting vibration, lactate dehydrogenase; identified a suitable small molecule for binding; and used transition path sampling to obtain ensembles of reactive trajectories. We found that the small molecule significantly affected the reaction by changing the position of the transition state and, through applying committor distribution analysis, showed that it removed the protein component from the reaction coordinate. The ability of a small-molecule to disrupt enzymatic reactions through alteration of subpicosecond protein motion opens the door for new experimental studies on protein motion coupled to enzymatic reactions and possibly the design of drugs to target these enzymes.

Active-Loop Dynamics within the Michaelis Complex of Lactate Dehydrogenase from Bacillus stearothermophilus

Laser-induced temperature-jump relaxation spectroscopy was used to study the active site mobile-loop dynamics found in the binding of the NADH nucleotide cofactor and oxamate substrate mimic to lactate dehydrogenase in Bacillus stearothermophilus thermophilic bacteria (bsLDH). The kinetic data can be best described by a model in which NADH can bind only to the open-loop apoenzyme, oxamate can bind only to the bsLDH·NADH binary complex in the open-loop conformation, and oxamate binding is followed by closing of the active site loop preventing oxamate unbinding. The open and closed states of the loop are in dynamic equilibrium and interconvert on the submillisecond time scale. This interconversion strongly accelerates with an increase in temperature because of significant enthalpy barriers. Binding of NADH to bsLDH results in minor changes of the loop dynamics and does not shift the open-closed equilibrium, but binding of the oxamate substrate mimic shifts this equilibrium to the closed state. At high excess oxamate concentrations where all active sites are nearly saturated with the substrate mimic, all active site mobile loops are mainly closed. The observed active-loop dynamics for bsLDH is very similar to that previously observed for pig heart LDH.

Modulating Enzyme Catalysis through Mutations Designed to Alter Rapid Protein Dynamics

The relevance of sub-picosecond protein motions to the catalytic event remains a topic of debate. Heavy enzymes (isotopically substituted) provide an experimental tool for bond-vibrational links to enzyme catalysis. A recent transition path sampling study with heavy purine nucleoside phosphorylase (PNP) characterized the experimentally observed mass-dependent slowing of barrier crossing (Antoniou, D.; Ge, X.; Schramm, V. L.; Schwartz, S. D. J. Phys. Chem. Lett. 2012, 3, 3538). Here we computationally identify second-sphere amino acid residues predicted to influence the freedom of the catalytic site vibrational modes linked to heavy enzyme effects in PNP. We mutated heavy and light PNPs to increase the catalytic site vibrational freedom. Enzymatic barrier-crossing rates were converted from mass-dependent to mass-independent as a result of the mutations. The mutagenic uncoupling of femtosecond motions between catalytic site groups and reactants decreased transition state barrier crossing by 2 orders of magnitude, an indication of the femtosecond dynamic contributions to catalysis.

Enzyme homologues have distinct reaction paths through their transition states

Recent studies of the bacterial enzymes EcMTAN and VcMTAN showed that they have different binding affinities for the same transition state analogue. This was surprising given the similarity of their active sites. We performed transition path sampling simulations of both enzymes to reveal the atomic details of the catalytic chemical step, which may be the key for explaining the inhibitor affinity differences. Even though all experimental data would suggest the two enzymes are almost identical, subtle dynamic differences manifest in differences of reaction coordinate, transition state structure, and eventually significant differences in inhibitor binding. Unlike EcMTAN, VcMTAN has multiple distinct transition states, which is an indication that multiple sets of coordinated protein motions can reach a transition state. Reaction coordinate information is only accessible from transition path sampling approaches, since all experimental approaches report averages. Detailed knowledge could have a significant impact on pharmaceutical design.

The enzymatic reaction catalyzed by lactate dehydrogenase exhibits one dominant reaction path

Enzymes are the most efficient chemical catalysts known, but the exact nature of chemical barrier crossing in enzymes is not fully understood. Application of transition state theory to enzymatic reactions indicates that the rates of all possible reaction paths, weighted by their relative probabilities, must be considered in order to achieve an accurate calculation of the overall rate. Previous studies in our group have shown a single mechanism for enzymatic barrier passage in human heart lactate dehydrogenase (LDH). To ensure that this result was not due to our methodology insufficiently sampling reactive phase space, we implement high-perturbation transition path sampling in both microcanonical and canonical regimes for the reaction catalyzed by human heart LDH. We find that, although multiple, distinct paths through reactive phase space are possible for this enzymatic reaction, one specific reaction path is dominant. Since the frequency of these paths in a canonical ensemble is inversely proportional to the free energy barriers separating them from other regions of phase space, we conclude that the rarer reaction paths are likely to have a negligible contribution. Furthermore, the non-dominate reaction paths correspond to altered reactive conformations and only occur after multiple steps of high perturbation, suggesting that these paths may be the result of non-biologically significant changes to the structure of the enzymatic active site.

Changes in protein architecture and subpicosecond protein dynamics impact the reaction catalyzed by lactate dehydrogenase

We have previously established the importance of a promoting vibration, a subpicosecond protein motion that propagates through a specific axis of residues, in the reaction coordinate of lactate dehydrogenase (LDH). To test the effect that perturbation of this motion would have on the enzymatic reaction, we employ transition path sampling to obtain transition path ensembles for four independent LDH enzymatic systems: the wild type enzyme, a version of the enzyme expressing heavy isotopic substitution, and two enzymes with mutations in the promoting vibration axis. We show that even slight changes in the promoting vibration of LDH result in dramatic changes in enzymatic chemistry. In the "heavy" version of the enzyme, we find that the dampening of the subpicosecond dynamics from heavy isotopic substitution leads to a drastic increase in the time of barrier crossing. Furthermore, we see that mutation of the promoting vibration axis causes a decrease in the variability of transition paths available to the enzymatic reaction. The combined results reveal the importance of the protein architecture of LDH in enzymatic catalysis by establishing how the promoting vibration is finely tuned to facilitate chemistry.

Heavy-enzyme kinetic isotope effects on proton transfer in alanine racemase

The catalytic effects of perdeuterating the pyridoxal phosphate-dependent enzyme alanine racemase from Geobacillus stearothermophilus are reported. The mass of the heavy perdeuterated form is ~5.5% greater than that of the protiated form, causing kinetic isotope effects (KIEs) of ~1.3 on k(cat) and k(cat)/K(M) for both L- and D-alanine. These values increase when Cα-deuterated alanine is used as the substrate. The heavy-enzyme KIEs of ~3 on k(cat)/K(M) with deuterated substrates are greater than the product of the individual heavy-enzyme and primary substrate KIEs. This breakdown of the rule of the geometric mean is likely due to coupled motion between the protein and the proton-transfer reaction coordinate in the rate-limiting step. These data implicate a direct role for protein vibrational motions in barrier crossing for proton-transfer steps in alanine racemase.

A hybrid elastic band string algorithm for studies of enzymatic reactions

A common challenge in theoretical biophysics is the identification of a minimum energy path (MEP) for the rearrangement of a group of atoms from one stable configuration to another. The structure with maximum energy along the MEP approximates the transition state for the process and the energy profile itself permits estimation of the transition rates. In this work we describe a computationally efficient algorithm for the identification of minimum energy paths in complicated biosystems. The algorithm is a hybrid of the nudged elastic band (NEB) and string methods. It has been implemented in the pDynamo simulation program and tested by examining elementary steps in the reaction mechanisms of three enzymes: citrate synthase, RasGAP, and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated using the new algorithm and previous versions of the NEB and string techniques, and also those obtained by the common method of adiabatic exploration of the potential energy surface as a function of predefined reaction coordinates. Precisely refined structures of the saddle points along the paths may be subsequently obtained with the climbing image variant of the NEB algorithm. Directions in which the utility of the methods that we have implemented can be further improved are discussed.

Enzymatic transition states, transition-state analogs, dynamics, thermodynamics, and lifetimes

Experimental analysis of enzymatic transition-state structures uses kinetic isotope effects (KIEs) to report on bonding and geometry differences between reactants and the transition state. Computational correlation of experimental values with chemical models permits three-dimensional geometric and electrostatic assignment of transition states formed at enzymatic catalytic sites. The combination of experimental and computational access to transition-state information permits (a) the design of transition-state analogs as powerful enzymatic inhibitors, (b) exploration of protein features linked to transition-state structure, (c) analysis of ensemble atomic motions involved in achieving the transition state, (d) transition-state lifetimes, and (e) separation of ground-state (Michaelis complexes) from transition-state effects. Transition-state analogs with picomolar dissociation constants have been achieved for several enzymatic targets. Transition states of closely related isozymes indicate that the protein's dynamic architecture is linked to transition-state structure. Fast dynamic motions in catalytic sites are linked to transition-state generation. Enzymatic transition states have lifetimes of femtoseconds, the lifetime of bond vibrations. Binding isotope effects (BIEs) reveal relative reactant and transition-state analog binding distortion for comparison with actual transition states.

On the Origin of the Chemical Barrier and Tunneling in Enzymes

This paper presents both a review of some recent results from our group and experimental groups, and some new theoretical results all of which are helping to form a more physically rigorous picture of the process of enzymatic catalysis. A common classical picture of enzymatic catalysis is the transition state tight binding model. Schwartz and Schramm1 have recently argued from both theoretical and experimental results that this picture is incorrect. We now investigate what the nature of barriers might be in enzymatic reactions, and what this viewpoint might imply for tunneling in a hydrogen transfer enzyme. For lactate dehydrogenase we conclude that the enzymes role in catalysis is at least partially to hunt through configuration space for those configurations that minimize chemical free energy barriers. Those configurations do not seem to be stable basins on the free energy surface, and in fact the overall free energy barrier to reaction may well largely be due to this stochastic hunt - both probabilistically and energetically. We suggest further computations to test this hypothesis.