Barrier Crossing in Dihydrofolate Reductasedoes not involve a rate-promoting vibration

Geometry of Charge Density as a Reporter on the Role of the Protein Scaffold in Enzymatic Catalysis: Electrostatic Preorganization and Beyond

Enzymes host active sites inside protein macromolecules, which have diverse, often incredibly complex, and atom-expensive structures. It is an outstanding question what the role of these expensive scaffolds might be in enzymatic catalysis. Answering this question is essential to both enzymology and the design of artificial enzymes with proficiencies that will match those of the best natural enzymes. Protein rigidifying the active site, contrasted with the dynamics and vibrational motion promoting the reaction, as well as long-range electrostatics (also known as electrostatic preorganization) were all proposed as central contributions of the scaffold to the catalysis. Here, we show that all these effects inevitably produce changes in the quantum mechanical electron density in the active site, which in turn defines the reactivity. The phenomena are therefore fundamentally inseparable. The geometry of the electron density-a scalar field characterized by a number of mathematical features such as critical points-is a rigorous and convenient descriptor of enzymatic catalysis and a reporter on the role of the protein. We show how this geometry can be analyzed, linked to the reaction barriers, and report in particular on intramolecular electric fields in enzymes. We illustrate these tools on the studies of electrostatic preorganization in several representative enzyme classes, both natural and artificial. We highlight the forward-looking aspects of the approach.

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.

Comparison of the Role of Protein Dynamics in Catalysis by Dihydrofolate Reductase from E. coli and H. sapiens

Dihydrofolate reductase (DHFR) is a well-studied, clinically relevant enzyme known for being highly dynamic over the course of its catalytic cycle. However, the role dynamic motions play in the explicit hydride transfer from the nicotinamide cofactor to the dihydrofolate substrate remains unclear because reaction initiation and direct spectroscopic examination on the appropriate time scale for such femtosecond to picosecond motions is challenging. Here, we employ pre-steady-state kinetics to observe the hydride transfer as directly as possible in two different species of DHFR: Escherichia coli and Homo sapiens. While the hydride transfer has been well-characterized in DHFR from E. coli, improvements in time resolution now allow for sub-millisecond dead times for stopped-flow spectroscopy, which reveals that the maximum rate is indeed faster than previously recorded. The rate in the human enzyme, previously only estimated, is also able to be directly observed using cutting-edge stopped-flow instrumentation. In addition to the pH dependence of the hydride transfer rates for both enzymes, we examine the primary H/D kinetic isotope effect to reveal a temperature dependence in the human enzyme that is absent from the E. coli counterpart. This dependence, which appears above a temperature of 15 °C is a shared feature among other hydride transfer enzymes and is also consistent with computational work suggesting the presence of a fast promoting-vibration that provides donor-acceptor compression on the time scale of catalysis to facilitate the chemistry step.

Temperature-Dependent Kinetic Isotope Effects in R67 Dihydrofolate Reductase from Path-Integral Simulations

Calculation of temperature-dependent kinetic isotope effects (KIE) in enzymes presents a significant theoretical challenge. Additionally, it is not trivial to identify enzymes with available experimental accurate intrinsic KIEs in a range of temperatures. In the current work, we present a theoretical study of KIEs in the primitive R67 dihydrofolate reductase (DHFR) enzyme and compare with experimental work. The advantage of R67 DHFR is its significantly lower kinetic complexity compared to more evolved DHFR isoforms. We employ mass-perturbation-based path-integral simulations in conjunction with umbrella sampling and a hybrid quantum mechanics-molecular mechanics Hamiltonian. We obtain temperature-dependent KIEs in good agreement with experiments and ascribe the temperature-dependent KIEs primarily to zero-point energy effects. The active site in the primitive enzyme is found to be poorly preorganized, which allows excessive water access to the active site and results in loosely bound reacting ligands.

Multiple Reaction Pathways in the Morphinone Reductase-Catalyzed Hydride Transfer Reaction

Morphinone reductase (MR) is an important model system for studying the contribution of protein motions to H-transfer reactions. In this research, we used quantum mechanical/molecular mechanics (QM/MM) simulation together with transition path sampling (TPS) simulation to study two important topics of current research on MR: the existence of multiple catalytic reaction pathways and the involvement of fast protein motions in the catalytic process. We have discovered two reaction pathways for the wild type and three reaction pathways for the N189A mutant. With the committor distribution analysis method, we found reaction coordinates for all five reaction pathways. Only one wild-type reaction pathway has a rate-promoting vibration from His186, while all of the other four pathways do not involve any protein motions in their catalytic process through the transition state. The rate-promoting vibration in the wild-type MR, which comes from a direction perpendicular to the donor-acceptor axis, functions to decrease the donor-acceptor distance by causing a subtle "out-of-plane" motion of a donor atom. By comparing reaction pathways between the two enzymes, we concluded that the major effect of the N189A point mutation is to increase the active site volume by altering the active site backbone and eliminating the Asn189 side chain. This effect causes a different NADH geometry at the reactant state, which very well explains the different reaction mechanisms between the two enzymes, as well as the disappearance of the His186 rate-promoting vibrations in the N189A mutant. The unfavorable geometry of the NADH pyridine ring induced by the N189A point mutation is the potential cause of multiple reaction pathways in N189A mutants.

Evolution Conserves the Network of Coupled Residues in Dihydrofolate Reductase

Understanding protein motions and their role in enzymatic reactions is an important and timely topic in enzymology. Protein motions that are involved in the chemical step of catalysis are particularly intriguing but difficult to identify. A global network of coupled residues in Escherichia coli dihydrofolate reductase (E. coli DHFR), which assists in catalyzing the chemical step, has previously been demonstrated through quantum mechanical/molecular mechanical and molecular dynamics simulations as well as bioinformatic analyses. A few specific residues (M42, G121, F125, and I14) were shown to function synergistically with measurements of single-turnover rates and the temperature dependence of intrinsic kinetic isotope effects (KIEsint) of site-directed mutants. This study hypothesizes that the global network of residues involved in the chemical step is evolutionarily conserved and probes homologous residues of the potential global network in human DHFR through measurements of the temperature dependence of KIEsint and computer simulations based on the empirical valence bond method. We study mutants M53W and S145V. Both of these remote residues are homologous to network residues in E. coli DHFR. Non-additive isotope effects on activation energy are observed between M53 and S145, indicating their synergistic effect on the chemical step in human DHFR, which suggests that both of these residues are part of a network affecting the chemical step in enzyme catalysis. This finding supports the hypothesis that human and E. coli DHFR share similar networks, consistent with evolutionary preservation of such networks.

Promoting Vibrations and the Function of Enzymes. Emerging Theoretical and Experimental Convergence

A complete understanding of enzyme catalysis requires knowledge of both transition state features and the detailed motions of atoms that cause reactant molecules to form and traverse the transition state. The seeming intractability of the problem arises from the femtosecond lifetime of chemical transition states, preventing most experimental access. Computational chemistry is admirably suited to short time scale analysis but can be misled by inappropriate starting points or by biased assumptions. Kinetic isotope effects provide an experimental approach to transition state structure and a method for obtaining transition state analogues but, alone, do not inform how that transition state is reached. Enzyme structures with transition state analogues provide computational starting points near the transition state geometry. These well-conditioned starting points, combined with the unbiased computational method of transition path sampling, provide realistic atomistic motions involved in transition state formation and passage. In many, but not all, enzymatic systems, femtosecond local protein motions near the catalytic site are linked to transition state formation. These motions are not inherently revealed by most approaches of transition state theory, because transition state theory replaces dynamics with the statistics of the transition state. Experimental and theoretical convergence of the link between local catalytic site vibrational modes and catalysis comes from heavy atom ("Born-Oppenheimer") enzymes. Fully labeled and catalytic site local heavy atom labels perturb the probability of finding enzymatic transition states in ways that can be analyzed and predicted by transition path sampling. Recent applications of these experimental and computational approaches reveal how subpicosecond local catalytic site protein modes play important roles in creating the transition state.

Directed Evolution as a Probe of Rate Promoting Vibrations Introduced via Mutational Change

In this article, we study with transition path sampling and reaction coordinate analysis how directed evolution in the Kemp eliminase family of artificial enzymes makes differential use of rapid rate promoting vibrations as a component of their chemical mechanism. Even though this family was initially created by placing the expected active site in a fixed protein matrix, we find a shift from largely static to more dynamic active sites that make use of donor-acceptor compression as the evolutionary process proceeds. We see that this introduction of dynamics significantly shifts the order of processes in the reaction. We also suggest that the lack of "design for dynamics" may help explain the relatively low proficiency of such designed enzymes.

Contribution of buried distal amino acid residues in horse liver alcohol dehydrogenase to structure and catalysis

The dynamics of enzyme catalysis range from the slow time scale (∼ms) for substrate binding and conformational changes to the fast time (∼ps) scale for reorganization of substrates in the chemical step. The contribution of global dynamics to catalysis by alcohol dehydrogenase was tested by substituting five different, conserved amino acid residues that are distal from the active site and located in the hinge region for the conformational change or in hydrophobic clusters. X-ray crystallography shows that the structures for the G173A, V197I, I220 (V, L, or F), V222I, and F322L enzymes complexed with NAD⁺ and an analogue of benzyl alcohol are almost identical, except for small perturbations at the sites of substitution. The enzymes have very similar kinetic constants for the oxidation of benzyl alcohol and reduction of benzaldehyde as compared to the wild-type enzyme, and the rates of conformational changes are not altered. Less conservative substitutions of these amino acid residues, such as G173(V, E, K, or R), V197(G, S, or T), I220(G, S, T, or N), and V222(G, S, or T) produced unstable or poorly expressed proteins, indicating that the residues are critical for global stability. The enzyme scaffold accommodates conservative substitutions of distal residues, and there is no evidence that fast, global dynamics significantly affect the rate constants for hydride transfers. In contrast, other studies show that proximal residues significantly participate in catalysis.

Measurement of Enzyme Isotope Effects

Enzyme isotope effects, or the kinetic effects of "heavy" enzymes, refer to the effect of isotopically labeled protein residues on the enzyme's activity or physical properties. These effects are increasingly employed in the examination of the possible contributions of protein dynamics to enzyme catalysis. One hypothesis assumed that isotopic substitution of all ¹²C, ¹⁴N, and nonexchangeable ¹H by ¹³C, ¹⁵N, and ²H, would slow down protein picosecond to femtosecond dynamics without any effect on the system's electrostatics following the Born-Oppenheimer approximation. It was suggested that reduced reaction rates reported for several "heavy" enzymes accords with that hypothesis. However, numerous deviations from the predictions of that hypothesis were also reported. Current studies also attempt to test the role of individual residues by site-specific labeling or by labeling a pattern of residues on activity. It appears that in several systems the protein's fast dynamics are indeed reduced in "heavy" enzymes in a way that reduces the probability of barrier crossing of its chemical step. Other observations, however, indicated that slower protein dynamics are electrostatically altered in isotopically labeled enzymes. Interestingly, these effects appear to be system dependent, thus it might be premature to suggest a general role of "heavy" enzymes' effect on catalysis.

Catalytic-site design for inverse heavy-enzyme isotope effects in human purine nucleoside phosphorylase

Heavy-enzyme isotope effects (¹⁵N-, ¹³C-, and ²H-labeled protein) explore mass-dependent vibrational modes linked to catalysis. Transition path-sampling (TPS) calculations have predicted femtosecond dynamic coupling at the catalytic site of human purine nucleoside phosphorylase (PNP). Coupling is observed in heavy PNPs, where slowed barrier crossing caused a normal heavy-enzyme isotope effect (k_chemlight/k_chemheavy > 1.0). We used TPS to design mutant F159Y PNP, predicted to improve barrier crossing for heavy F159Y PNP, an attempt to generate a rare inverse heavy-enzyme isotope effect (k_chemlight/k_chemheavy < 1.0). Steady-state kinetic comparison of light and heavy native PNPs to light and heavy F159Y PNPs revealed similar kinetic properties. Pre-steady-state chemistry was slowed 32-fold in F159Y PNP. Pre-steady-state chemistry compared heavy and light native and F159Y PNPs and found a normal heavy-enzyme isotope effect of 1.31 for native PNP and an inverse effect of 0.75 for F159Y PNP. Increased isotopic mass in F159Y PNP causes more efficient transition state formation. Independent validation of the inverse isotope effect for heavy F159Y PNP came from commitment to catalysis experiments. Most heavy enzymes demonstrate normal heavy-enzyme isotope effects, and F159Y PNP is a rare example of an inverse effect. Crystal structures and TPS dynamics of native and F159Y PNPs explore the catalytic-site geometry associated with these catalytic changes. Experimental validation of TPS predictions for barrier crossing establishes the connection of rapid protein dynamics and vibrational coupling to enzymatic transition state passage.

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.

Protein motions and dynamic effects in enzyme catalysis

The role of protein motions in promoting the chemical step of enzyme catalysed reactions remains a subject of considerable debate. Here, a unified view of the role of protein dynamics in dihydrofolate reductase catalysis is described. Recently the role of such motions has been investigated by characterising the biophysical properties of isotopically substituted enzymes through a combination of experimental and computational analyses. Together with previous work, these results suggest that dynamic coupling to the chemical coordinate is detrimental to catalysis and may have been selected against during DHFR evolution. The full catalytic power of Nature's catalysts appears to depend on finely tuning protein motions in each step of the catalytic cycle.

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations

The coenzyme nicotinamide adenine dinucleotide (NAD⁺) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD⁺/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD⁺/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD⁺/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD⁺/NADH cofactor in simulations of biological systems.

Examinations of the Chemical Step in Enzyme Catalysis

Advances in computational and experimental methods in enzymology have aided comprehension of enzyme-catalyzed chemical reactions. The main difficulty in comparing computational findings to rate measurements is that the first examines a single energy barrier, while the second frequently reflects a combination of many microscopic barriers. We present here intrinsic kinetic isotope effects and their temperature dependence as a useful experimental probe of a single chemical step in a complex kinetic cascade. Computational predictions are tested by this method for two model enzymes: dihydrofolate reductase and thymidylate synthase. The description highlights the significance of collaboration between experimentalists and theoreticians to develop a better understanding of enzyme-catalyzed chemical conversions.

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.

Enzymatic Kinetic Isotope Effects from First-Principles Path Sampling Calculations

In this study, we develop and test a method to determine the rate of particle transfer and kinetic isotope effects in enzymatic reactions, specifically yeast alcohol dehydrogenase (YADH), from first-principles. Transition path sampling (TPS) and normal mode centroid dynamics (CMD) are used to simulate these enzymatic reactions without knowledge of their reaction coordinates and with the inclusion of quantum effects, such as zero-point energy and tunneling, on the transferring particle. Though previous studies have used TPS to calculate reaction rate constants in various model and real systems, it has not been applied to a system as large as YADH. The calculated primary H/D kinetic isotope effect agrees with previously reported experimental results, within experimental error. The kinetic isotope effects calculated with this method correspond to the kinetic isotope effect of the transfer event itself. The results reported here show that the kinetic isotope effects calculated from first-principles, purely for barrier passage, can be used to predict experimental kinetic isotope effects in enzymatic systems.

The Effect of Protein Mass Modulation on Human Dihydrofolate Reductase

Dihydrofolate reductase (DHFR) from Escherichia coli has long served as a model enzyme with which to elucidate possible links between protein dynamics and the catalyzed reaction. Such physical properties of its human counterpart have not been rigorously studied so far, but recent computer-based simulations suggest that these two DHFRs differ significantly in how closely coupled the protein dynamics and the catalyzed C-H → C hydride transfer step are. To test this prediction, two contemporary probes for studying the effect of protein dynamics on catalysis were combined here: temperature dependence of intrinsic kinetic isotope effects (KIEs), which are sensitive to the physical nature of the chemical step, and protein mass modulation, which slows down fast dynamics (femto- to picosecond time scale) throughout the protein. The intrinsic H/T KIEs of human DHFR, like those of E. coli DHFR, are shown to be temperature-independent in the range from 5 to 45 °C, indicating fast sampling of donor and acceptor distances (DADs) at the reaction's transition state (or tunneling ready state, TRS). Mass modulation of these enzymes through isotopic labeling with (13)C, (15)N, and (2)H at nonexchangeable hydrogens yields an 11% heavier enzyme. The additional mass has no effect on the intrinsic KIEs of the human enzyme. This finding indicates that the mass modulation of the human DHFR affects neither DAD distribution nor the DAD's conformational sampling dynamics. Furthermore, reduction in the enzymatic turnover number and the dissociation rate constant for the product indicate that the isotopic substitution affects kinetic steps that are not the catalyzed C-H → C hydride transfer. The findings are discussed in terms of fast dynamics and their role in catalysis, the comparison of calculations and experiments, and the interpretation of isotopically modulated heavy enzymes in general.

Phase Space Bottlenecks in Enzymatic Reactions

The definition of a transition state on an individual reactive trajectory is made via a committor analysis. In the past, the bottleneck definition has often been applied in configuration space. This is an approximation, and in order to expand this definition, we are revisiting an enzyme in which we had identified a fast subpicosecond motion that makes the reaction possible. First we used a time-series analysis method to identify the exact time when this motion initiates donor-acceptor compression. Then we modified the standard committor analysis of transition path sampling to identify events in phase space and found that there is a dividing surface in phase space significantly earlier than the configurationally defined transition-state crossing.

Hydride Transfer in DHFR by Transition Path Sampling, Kinetic Isotope Effects, and Heavy Enzyme Studies

Escherichia coli dihydrofolate reductase (ecDHFR) is used to study fundamental principles of enzyme catalysis. It remains controversial whether fast protein motions are coupled to the hydride transfer catalyzed by ecDHFR. Previous studies with heavy ecDHFR proteins labeled with (13)C, (15)N, and nonexchangeable (2)H reported enzyme mass-dependent hydride transfer kinetics for ecDHFR. Here, we report refined experimental and computational studies to establish that hydride transfer is independent of protein mass. Instead, we found the rate constant for substrate dissociation to be faster for heavy DHFR. Previously reported kinetic differences between light and heavy DHFRs likely arise from kinetic steps other than the chemical step. This study confirms that fast (femtosecond to picosecond) protein motions in ecDHFR are not coupled to hydride transfer and provides an integrative computational and experimental approach to resolve fast dynamics coupled to chemical steps in enzyme catalysis.

Dihydrofolate reductase as a model for studies of enzyme dynamics and catalysis

Dihydrofolate reductase from Escherichia coli (ecDHFR) serves as a model system for investigating the role of protein dynamics in enzyme catalysis. We discuss calculations predicting a network of dynamic motions that is coupled to the chemical step catalyzed by this enzyme. Kinetic studies testing these predictions are presented, and their potential use in better understanding the role of these dynamics in enzyme catalysis is considered. The cumulative results implicate motions across the entire protein in catalysis.

Network of remote and local protein dynamics in dihydrofolate reductase catalysis

Molecular dynamics calculations and bionformatic studies of dihydrofolate reductase (DHFR) have suggested a network of coupled motions across the whole protein that is correlated to the reaction coordinate. Experimental studies demonstrated that distal residues G121, M42 and F125 in E. coli DHFR participate in that network. The missing link in our understanding of DHFR catalysis is the lack of a mechanism by which such remote residues can affect the catalyzed chemistry at the active site. Here, we present a study of the temperature dependence of intrinsic kinetic isotope effects (KIEs) that indicates synergism between a remote residue in that dynamic network, G121, and the active site's residue I14. The intrinsic KIEs for the I14A-G121V double mutant showed steeper temperature dependence (ΔE_a(T-H)) than expected from comparison of the wild type and two single mutants. That effect was non-additive, i.e., ΔE_a(T-H)G121V +ΔE_{a(T-H) I14A} < ΔE_{a(T-H) double mutant}, which indicates a synergism between the two residues. This finding links the remote residues in the network under investigation to the enzyme's active site, providing a mechanism by which these residues can be coupled to the catalyzed chemistry. This experimental evidence validates calculations proposing that both remote and active site residues constitute a network of coupled promoting motions correlated to the bond activation step (C-H→C hydride transfer in this case). Additionally, the effect of I14A and G121V mutations on single turnover rates was additive rather than synergistic. Although single turnover rate measurements are more readily available and thus more popular than assessing intrinsic kinetic isotope effects, the current finding demonstrates that for these rates, which in DHFR reflect several microscopic rate constants, can fall short of revealing the nature of the C-H bond activation per se.

Transition States and transition state analogue interactions with enzymes

Enzymatic transition states have lifetimes of a few femtoseconds (fs). Computational analysis of enzyme motions leading to transition state formation suggests that local catalytic site motions on the fs time scale provide the mechanism to locate transition states. An experimental test of protein fs motion and its relation to transition state formation can be provided by isotopically heavy proteins. Heavy enzymes have predictable mass-altered bond vibration states without altered electrostatic properties, according to the Born-Oppenheimer approximation. On-enzyme chemistry is slowed in most heavy proteins, consistent with altered protein bond frequencies slowing the search for the transition state. In other heavy enzymes, structural changes involved in reactant binding and release are also influenced. Slow protein motions associated with substrate binding and catalytic site preorganization are essential to allow the subsequent fs motions to locate the transition state and to facilitate the efficient release of products. In the catalytically competent geometry, local groups move in stochastic atomic motion on the fs time scale, within transition state-accessible conformations created by slower protein motions. The fs time scale for the transition state motions does not permit thermodynamic equilibrium between the transition state and stable enzyme states. Isotopically heavy enzymes provide a diagnostic tool for fast coupled protein motions to transition state formation and mass-dependent conformational changes. The binding of transition state analogue inhibitors is the opposite in catalytic time scale to formation of the transition state but is related by similar geometries of the enzyme-transition state and enzyme-inhibitor interactions. While enzymatic transition states have lifetimes as short as 10(-15) s, transition state analogues can bind tightly to enzymes with release rates greater than 10(3) s. Tight-binding transition state analogues stabilize the rare but evolved enzymatic geometry to form the transition state. Evolution to efficient catalysis optimized this geometry and its stabilization by a transition state mimic results in tight binding. Release rates of transition state analogues are orders of magnitude slower than product release in normal catalytic function. During catalysis, product release is facilitated by altered chemistry. Compared to the weak associations found in Michaelis complexes, transition state analogues involve strong interactions related to those in the transition state. Optimum binding of transition state analogues occurs when the complex retains the system motions intrinsic to transition state formation. Conserved dynamic motion retains the entropic components of inhibitor complexes, improving the thermodynamics of analogue binding.

Keep on moving: discovering and perturbing the conformational dynamics of enzymes

CONSPECTUS: Because living organisms are in constant motion, the word "dynamics" can hold many meanings to biologists. Here we focus specifically on the conformational changes that occur in proteins and how studying these protein dynamics may provide insights into enzymatic catalysis. Advances in integrating techniques such as X-ray crystallography, nuclear magnetic resonance, and electron cryomicroscopy (cryo EM) allow us to model the dominant structures and exchange rates for many proteins and protein complexes. For proteins amenable to atomic resolution techniques, the major questions shift from simply describing the motions to discovering their role in function. Concurrently, there is an increasing need for using perturbations to test predictive models of dynamics-function relationships. Examples are the catalytic cycles of dihydrofolate reductase (DHFR) and cyclophilin A (CypA). In DHFR, mutations that alter the ability of the active site to sample productive higher energy states on the millisecond time scale reduce the rate of hydride transfer significantly. Recently identified rescue mutations restore function, but the mechanism by which they do so remains unclear. The exact role of any changes in the dynamics remains an open question. For CypA, a network of side chains that exchange between two conformations is critical for catalysis. Mutations that lock the network in one state also reduce catalytic activity. A further understanding of enzyme dynamics of well-studied enzymes such as dihydrofolate reductase and cyclophilin A will lead to improvement in ability to modulate the functions of computationally designed enzymes and large macromolecular machines. In designed enzymes, directed evolution experiments increase catalytic rates. Detailed X-ray studies suggest that these mutations likely limit the conformational space explored by residues in the active site. For proteins where atomic resolution information is currently inaccessible, other techniques such as cryo-EM and high-resolution single molecule microscopy continue to advance. Understanding the conformational dynamics of larger systems such as protein machines will likely become more accessible and provide new opportunities to rationally modulate protein function.

Linking protein motion to enzyme catalysis

Enzyme motions on a broad range of time scales can play an important role in various intra- and intermolecular events, including substrate binding, catalysis of the chemical conversion, and product release. The relationship between protein motions and catalytic activity is of contemporary interest in enzymology. To understand the factors influencing the rates of enzyme-catalyzed reactions, the dynamics of the protein-solvent-ligand complex must be considered. The current review presents two case studies of enzymes—dihydrofolate reductase (DHFR) and thymidylate synthase (TSase)—and discusses the role of protein motions in their catalyzed reactions. Specifically, we will discuss the utility of kinetic isotope effects (KIEs) and their temperature dependence as tools in probing such phenomena.

Free energy simulations of active-site mutants of dihydrofolate reductase

This study employs hybrid quantum mechanics-molecular mechanics (QM/MM) simulations to investigate the effect of mutations of the active-site residue I14 of E. coli dihydrofolate reductase (DHFR) on the hydride transfer. Recent kinetic measurements of the I14X mutants (X = V, A, and G) indicated slower hydride transfer rates and increasingly temperature-dependent kinetic isotope effects (KIEs) with systematic reduction of the I14 side chain. The QM/MM simulations show that when the original isoleucine residue is substituted in silico by valine, alanine, or glycine (I14V, I14A, and I14G DHFR, respectively), the free energy barrier height of the hydride transfer reaction increases relative to the wild-type enzyme. These trends are in line with the single-turnover rate measurements reported for these systems. In addition, extended dynamics simulations of the reactive Michaelis complex reveal enhanced flexibility in the mutants, and in particular for the I14G mutant, including considerable fluctuations of the donor-acceptor distance (DAD) and the active-site hydrogen bonding network compared with those detected in the native enzyme. These observations suggest that the perturbations induced by the mutations partly impair the active-site environment in the reactant state. On the other hand, the average DADs at the transition state of all DHFR variants are similar. Crystal structures of I14 mutants (V, A, and G) confirmed the trend of increased flexibility of the M20 and other loops.

Evolution alters the enzymatic reaction coordinate of dihydrofolate reductase

How evolution has affected enzyme function is a topic of great interest in the field of biophysical chemistry. Evolutionary changes from Escherichia coli dihydrofolate reductase (ecDHFR) to human dihydrofolate reductase (hsDHFR) have resulted in increased catalytic efficiency and an altered dynamic landscape in the human enzyme. Here, we show that a subpicosecond protein motion is dynamically coupled to hydride transfer catalyzed by hsDHFR but not ecDHFR. This motion propagates through residues that correspond to mutational events along the evolutionary path from ecDHFR to hsDHFR. We observe an increase in the variability of the transition states, reactive conformations, and times of barrier crossing in the human system. In the hsDHFR active site, we detect structural changes that have enabled the coupling of fast protein dynamics to the reaction coordinate. These results indicate a shift in the DHFR family to a form of catalysis that incorporates rapid protein dynamics and a concomitant shift to a more flexible path through reactive phase space.

Protein mass-modulated effects in the catalytic mechanism of dihydrofolate reductase: beyond promoting vibrations

The role of fast protein dynamics in enzyme catalysis has been of great interest in the past decade. Recent “heavy enzyme” studies demonstrate that protein mass-modulated vibrations are linked to the energy barrier for the chemical step of catalyzed reactions. However, the role of fast dynamics in the overall catalytic mechanism of an enzyme has not been addressed. Protein mass-modulated effects in the catalytic mechanism of Escherichia coli dihydrofolate reductase (ecDHFR) are explored by isotopic substitution (¹³C, ¹⁵N, and non-exchangeable ²H) of the wild-type ecDHFR (l-DHFR) to generate a vibrationally perturbed “heavy ecDHFR” (h-DHFR). Steady-state, pre-steady-state, and ligand binding kinetics, intrinsic kinetic isotope effects (KIE_int) on the chemical step, and thermal unfolding experiments of both l- and h-DHFR show that the altered protein mass affects the conformational ensembles and protein–ligand interactions, but does not affect the hydride transfer at physiological temperatures (25–45 °C). Below 25 °C, h-DHFR shows altered transition state (TS) structure and increased barrier-crossing probability of the chemical step compared with l-DHFR, indicating temperature-dependent protein vibrational coupling to the chemical step. Protein mass-modulated vibrations in ecDHFR are involved in TS interactions at cold temperatures and are linked to dynamic motions involved in ligand binding at physiological temperatures. Thus, mass effects can affect enzymatic catalysis beyond alterations in promoting vibrations linked to chemistry.

How Accurate Are Transition States from Simulations of Enzymatic Reactions?

The rate expression of traditional transition state theory (TST) assumes no recrossing of the transition state (TS) and thermal quasi-equilibrium between the ground state and the TS. Currently, it is not well understood to what extent these assumptions influence the nature of the activated complex obtained in traditional TST-based simulations of processes in the condensed phase in general and in enzymes in particular. Here we scrutinize these assumptions by characterizing the TSs for hydride transfer catalyzed by the enzyme Escherichia coli dihydrofolate reductase obtained using various simulation approaches. Specifically, we compare the TSs obtained with common TST-based methods and a dynamics-based method. Using a recently developed accurate hybrid quantum mechanics/molecular mechanics potential, we find that the TST-based and dynamics-based methods give considerably different TS ensembles. This discrepancy, which could be due equilibrium solvation effects and the nature of the reaction coordinate employed and its motion, raises major questions about how to interpret the TSs determined by common simulation methods. We conclude that further investigation is needed to characterize the impact of various TST assumptions on the TS phase-space ensemble and on the reaction kinetics.

Simulations of remote mutants of dihydrofolate reductase reveal the nature of a network of residues coupled to hydride transfer

Recent experimental and theoretical studies have proposed that enzymes involve networks of coupled residues throughout the protein that participate in motions accompanying chemical barrier crossing. Here, we have examined portions of a proposed network in dihydrofolate reductase (DHFR) using quantum mechanics/molecular mechanics simulations. The simulations use a hybrid quantum mechanics-molecular mechanics approach with a recently developed semiempirical AM1-SRP Hamiltonian that provides accurate results for this reaction. The simulations reproduce experimentally determined catalytic rates for the wild type and distant mutants of E. coli DHFR, underscoring the accuracy of the simulation protocol. Additionally, the simulations provide detailed insight into how residues remote from the active site affect the catalyzed chemistry, through changes in the thermally averaged properties along the reaction coordinate. The mutations do not greatly affect the structure of the transition state near the bond activation, but we observe differences somewhat removed from the point of C-H cleavage that affect the rate. The mutations have global effects on the thermally averaged structure that propagate throughout the enzyme and the current simulations highlight several interactions that appear to be particularly important.

Preservation of protein dynamics in dihydrofolate reductase evolution

The hydride transfer reaction catalyzed by dihydrofolate reductase (DHFR) is a model for examining how protein dynamics contribute to enzymatic function. The relationship between functional motions and enzyme evolution has attracted significant attention. Recent studies on N23PP Escherichia coli DHFR (ecDHFR) mutant, designed to resemble parts of the human enzyme, indicated a reduced single turnover rate. NMR relaxation dispersion experiments with that enzyme showed rigidification of millisecond Met-20 loop motions (Bhabha, G., Lee, J., Ekiert, D. C., Gam, J., Wilson, I. A., Dyson, H. J., Benkovic, S. J., and Wright, P. E. (2011) Science 332, 234-238). A more recent study of this mutant, however, indicated that fast motions along the reaction coordinate are actually more dispersed than for wild-type ecDHFR (WT). Furthermore, a double mutant (N23PP/G51PEKN) that better mimics the human enzyme seems to restore both the single turnover rates and narrow distribution of fast dynamics (Liu, C. T., Hanoian, P., French, T. H., Hammes-Schiffer, S., and Benkovic, S. J. (2013) Proc. Natl. Acad. Sci. U.S.A. 110, 10159-11064). Here, we measured intrinsic kinetic isotope effects for both N23PP and N23PP/G51PEKN double mutant DHFRs over a temperature range. The findings indicate that although the C-H→C transfer and dynamics along the reaction coordinate are impaired in the altered N23PP mutant, both seem to be restored in the N23PP/G51PEKN double mutant. This indicates that the evolution of G51PEKN, although remote from the Met-20 loop, alleviated the loop rigidification that would have been caused by N23PP, enabling WT-like H-tunneling. The correlation between the calculated dynamics, the nature of C-H→C transfer, and a phylogenetic analysis of DHFR sequences are consistent with evolutionary preservation of the protein dynamics to enable H-tunneling from well reorganized active sites.

Increased dynamic effects in a catalytically compromised variant of Escherichia coli dihydrofolate reductase

Isotopic substitution ((15)N, (13)C, (2)H) of a catalytically compromised variant of Escherichia coli dihydrofolate reductase, EcDHFR-N23PP/S148A, has been used to investigate the effect of these mutations on catalysis. The reduction of the rate constant of the chemical step in the EcDHFR-N23PP/S148A catalyzed reaction is essentially a consequence of an increase of the quasi-classical free energy barrier and to a minor extent of an increased number of recrossing trajectories on the transition state dividing surface. Since the variant enzyme is less well set up to catalyze the reaction, a higher degree of active site reorganization is needed to reach the TS. Although millisecond active site motions are lost in the variant, there is greater flexibility on the femtosecond time scale. The "dynamic knockout" EcDHFR-N23PP/S148A is therefore a "dynamic knock-in" at the level of the chemical step, and the increased dynamic coupling to the chemical coordinate is in fact detrimental to catalysis. This finding is most likely applicable not just to hydrogen transfer in EcDHFR but also to other enzymatic systems.

Isotope effects as probes for enzyme catalyzed hydrogen-transfer reactions

Kinetic Isotope effects (KIEs) have long served as a probe for the mechanisms of both enzymatic and solution reactions. Here, we discuss various models for the physical sources of KIEs, how experimentalists can use those models to interpret their data, and how the focus of traditional models has grown to a model that includes motion of the enzyme and quantum mechanical nuclear tunneling. We then present two case studies of enzymes, thymidylate synthase and alcohol dehydrogenase, and discuss how KIEs have shed light on the C-H bond cleavages those enzymes catalyze. We will show how the combination of both experimental and computational studies has changed our notion of how these enzymes exert their catalytic powers.

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.

Connecting protein conformational dynamics with catalytic function as illustrated in dihydrofolate reductase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor-acceptor distances are essentially the same in the Michaelis complex state (~3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A.

Hydrogen tunneling links protein dynamics to enzyme catalysis

The relationship between protein dynamics and function is a subject of considerable contemporary interest. Although protein motions are frequently observed during ligand binding and release steps, the contribution of protein motions to the catalysis of bond making/breaking processes is more difficult to probe and verify. Here, we show how the quantum mechanical hydrogen tunneling associated with enzymatic C-H bond cleavage provides a unique window into the necessity of protein dynamics for achieving optimal catalysis. Experimental findings support a hierarchy of thermodynamically equilibrated motions that control the H-donor and -acceptor distance and active-site electrostatics, creating an ensemble of conformations suitable for H-tunneling. A possible extension of this view to methyl transfer and other catalyzed reactions is also presented. The impact of understanding these dynamics on the conceptual framework for enzyme activity, inhibitor/drug design, and biomimetic catalyst design is likely to be substantial.

Protein dynamics and the enzymatic reaction coordinate

This chapter discusses progress over the past 15 years in understanding the role of protein dynamics in enzymatically catalyzed chemical reactions. Research has shown that protein motion on all timescales from femtoseconds to milliseconds can contribute to function, and in particular in some enzymes there are sub-picosecond motions, on the same timescale as barrier passage, the couple directly to chemical transformation, and are thus part of the reaction coordinate. Approaches such as transition path sampling and committor analysis have greatly enhanced our understanding of these processes.

Quantum variational transition state theory for hydrogen tunneling in enzyme catalysis

Experiments in recent years have shown that there is a large kinetic isotope effect in the rate of transfer of hydrogen or deuterium in enzymatic reactions of soybean lipoxygenase-1. The kinetic isotope effect (KIE) is only weakly temperature dependent but varies significantly in the presence of mutants whose functional groups are located rather far from the reaction center. In this paper we suggest that variational transition state theory as applied to dissipative systems, above the crossover temperature between deep tunneling and thermal activation, may be used as a paradigm for understanding the dynamics of these reactions. We find that the theory fits the experimental data rather well. The effects of different mutants are readily interpreted in terms of the friction they exert on the reaction center. Increasing the distal functional group increases the friction and thus lowers the kinetic isotope effect.