Shina Caroline Lynn Kamerlin

At the Dawn of the 21st Century: Is Dynamics the Missing Link for Understanding Enzyme Catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as “coupling between conformational and chemical motions,” “landscape searches” and “entropy funnels.” It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies. Proteins 2010.

Progress in ab initio QM/MM free-energy simulations of electrostatic energies in proteins: accelerated QM/MM studies of pKa, redox reactions and solvation free energies.

Hybrid quantum mechanical/molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting different types of QM/MM calculations of electrostatic energies (and related properties) here, our focus will be on pKa calculations. This reflects the fact that pKas of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pKa calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pKa calculations using QM/MM-FEP have led to discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor and a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that, by using this approach, we are able to reproduce the relevant side chain pKas with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.

Enzyme millisecond conformational dynamics do not catalyze the chemical step

The idea that enzymes catalyze reactions by dynamical coupling between the conformational motions and the chemical coordinates has recently attracted major experimental and theoretical interest. However, experimental studies have not directly established that the conformational motions transfer energy to the chemical coordinate, and simulating enzyme catalysis on the relevant timescales has been impractical. Here, we introduce a renormalization approach that transforms the energetics and dynamics of the enzyme to an equivalent low-dimensional system, and allows us to simulate the dynamical coupling on a ms timescale. The simulations establish, by means of several independent approaches, that the conformational dynamics is not remembered during the chemical step and does not contribute significantly to catalysis. Nevertheless, the precise nature of this coupling is a question of great importance.

Catalysis by dihydrofolate reductase and other enzymes arises from electrostatic preorganization, not conformational motions

The proposal that enzymatic catalysis is due to conformational fluctuations has been previously promoted by means of indirect considerations. However, recent works have focused on cases where the relevant motions have components toward distinct conformational regions, whose population could be manipulated by mutations. In particular, a recent work has claimed to provide direct experimental evidence for a dynamical contribution to catalysis in dihydrofolate reductase, where blocking a relevant conformational coordinate was related to the suppression of the motion toward the occluded conformation. The present work utilizes computer simulations to elucidate the true molecular basis for the experimentally observed effect. We start by reproducing the trend in the measured change in catalysis upon mutations (which was assumed to arise as a result of a “dynamical knockout” caused by the mutations). This analysis is performed by calculating the change in the corresponding activation barriers without the need to invoke dynamical effects. We then generate the catalytic landscape of the enzyme and demonstrate that motions in the conformational space do not help drive catalysis. We also discuss the role of flexibility and conformational dynamics in catalysis, once again demonstrating that their role is negligible and that the largest contribution to catalysis arises from electrostatic preorganization. Finally, we point out that the changes in the reaction potential surface modify the reorganization free energy (which includes entropic effects), and such changes in the surface also alter the corresponding motion. However, this motion is never the reason for catalysis, but rather simply a reflection of the shape of the reaction potential surface.

Coarse-Grained (Multiscale) Simulations in Studies of Biophysical and Chemical Systems

Recent years have witnessed an explosion in computational power, leading to attempts to model ever more complex systems. Nevertheless, there remain cases for which the use of brute-force computer simulations is clearly not the solution. In such cases, great benefit can be obtained from the use of physically sound simplifications. The introduction of such coarse graining can be traced back to the early usage of a simplified model in studies of proteins. Since then, the field has progressed tremendously. In this review, we cover both key developments in the field and potential future directions. Additionally, particular emphasis is given to two general approaches, namely the renormalization and reference potential approaches, which allow one to move back and forth between the coarse-grained (CG) and full models, as these approaches provide the foundation for CG modeling of complex systems.

The empirical valence bond model: theory and applications

Recent years have seen an explosion in computer power, allowing for the examination of ever more challenging problems. For instance, a recent simulation study, which was the first of its kind, was able to actually explore the dynamical nature of enzyme catalysis on a millisecond timescale (Pisliakov AV, Cao J, Kamerlin SCL, Warshel A. Proc Natl Acad Sci U S A 2009, 106:17359.), something that as recently as a year or two ago would have been considered impossible. However, the questions that need addressing are nevertheless very complex, and experimental approaches can unfortunately often be inconclusive (Åqvist J, Kolmodin K, Florián J, Warshel A, Chem Biol 1999, 6:R71.) in answering them. Therefore, it is essential to have an approach that is both reliable and able to capture complex systems in order to resolve long‐standing controversies [particularly with regards to questions such as the origin of enzyme catalysis, where the relevant energy contributions cannot be separated without some computational models (Warshel A, Sharma PK, Kato M, Xiang Y, Liu H, Olsson MHM, Chem Rev 2006, 106:3210.)]. Herein, we will present the empirical valence bond (EVB) approach, which, at present, is arguably the most powerful tool for examining chemical reactivity in the condensed phase. We will illustrate the effectiveness of the EVB method when evaluating, for instance, catalytic effects and demonstrate that it is currently the optimal tool for elucidating challenging problems such as understanding the catalytic power of enzymes. Finally, the increasing appreciation of this approach can maybe best illustrated not only by its proliferation but also by attempts to capture its basic chemistry under a different name, as will be discussed in this work.

On the interpretation of the observed linear free energy relationship in phosphate hydrolysis: a thorough computational study of phosphate diester hydrolysis in solution.

The hydrolysis of phosphate esters is crucially important to biological systems, being involved in, among other things, signaling, energy transduction, biosynthesis, and the regulation of protein function. Despite this, there are many questions that remain unanswered in this important field, particularly with regard to the preferred mechanism of hydrolysis of phosphate esters, which can proceed through any of multiple pathways that are either associative or dissociative in nature. Previous comparisons of calculated and observed linear free energy relationships (LFERs) for phosphate monoester dianions with different leaving groups showed that the TS character gradually changes from associative to dissociative with the increasing acidity of the leaving group, while reproducing the experimental LFER. Here, we have generated ab initio potential energy surfaces for the hydrolysis of phosphate diesters in solution, with a variety of leaving groups. Once again, the reaction changes from a compact concerted pathway to one that is more expansive in character when the acidity of the leaving group increases. When such systems are examined in solution, it is essential to take into consideration the contribution of solute to the overall activation entropy, which remains a major computational challenge. The popular method of calculating the entropy using a quasi-harmonic approximation appears to markedly overestimate the configurational entropy for systems with multiple occupied energy wells. We introduce an improved restraint release approach for evaluating configurational entropies and apply this approach to our systems. We demonstrate that when this factor is taken into account, it is possible to reproduce the experimental LFER for this system with reasonable accuracy.

ParaDynamics: An Effective and Reliable Model for Ab Initio QM/MM Free Energy Calculations and Related Tasks

Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

Examining the case for the effect of barrier compression on tunneling, vibrationally enhanced catalysis, catalytic entropy and related issues.

The idea that tunneling is enhanced by the compression of the donor–acceptor distance has attracted significant interest. In particular, recent studies argued that this proposal is consistent with pressure effects on enzymatic reactions, and that the observed pressure effects support the idea of vibrationally enhanced catalysis. However, a careful analysis of the current works reveals serious inconsistencies in the evidence presented to support these hypotheses. Apparently, tunneling decreases upon compression, and external pressure does not lead to the applicable compression of the free energy surface. Additionally, pressure experiments do not provide actual evidence for vibrationally enhanced catalysis. Finally, the temperature dependence of the entropy change in hydride transfer reactions is shown to reflect simple electrostatic effects.

Associative Versus Dissociative Mechanisms of Phosphate Monoester Hydrolysis: On the Interpretation of Activation Entropies

Phosphate monoester and anhydride hydrolysis is ubiquitous in biology, being involved in, amongst other things, signal transduction, energy production, and the regulation of protein function. Therefore, this reaction has understandably been the focus of intensive research. Nevertheless, the precise mechanism by which phosphate monoester hydrolysis proceeds remains controversial. Traditionally, it has been assumed and frequently implied that a near-zero activation entropy is indicative of a dissociative pathway. Herein, we examine free-energy surfaces for the hydrolysis of the methyl phosphate dianion and the methyl pyrophosphate trianion in aqueous solution. In both cases, the reaction can proceed through either compact or expansive concerted (A(N)D(N)) transition states, with fairly similar barriers. We have evaluated the activation entropies for each transition state and demonstrate that both associative and dissociative transition states have near-zero entropies of activation that are in good agreement with experimental values. Therefore, we believe that the activation entropy alone is not a useful diagnostic tool, as it depends not only on bond orders at the transition state, but also on other issues that include (but are not limited to) steric factors determining the configurational volumes available to reactants during the reaction, solvation and desolvation effects that may be associated with charge redistribution upon approaching the transition state and entropy changes associated with intramolecular degrees of freedom as the transition state is approached.