Do dynamic effects play a significant role in enzymatic catalysis? A theoretical analysis of formate dehydrogenase

A method for quantifying how the activity of an enzyme is affected by the net charge of its nearest crowded neighbor

The electrostatic effects of protein crowding have not been systematically explored. Rather, protein crowding is generally studied with co‐solvents or crowders that are electrostatically neutral, with no methods to measure how the net charge (Z) of a crowder affects protein function. For example, can the activity of an enzyme be affected electrostatically by the net charge of its neighbor in crowded milieu? This paper reports a method for crowding proteins of different net charge to an enzyme via semi‐random chemical crosslinking. As a proof of concept, RNase A was crowded (at distances ≤ the Debye length) via crosslinking to different heme proteins with Z = +8.50 ± 0.04, Z = +6.39 ± 0.12, or Z = −10.30 ± 1.32. Crosslinking did not disrupt the structure of proteins, according to amide H/D exchange, and did not inhibit RNase A activity. For RNase A, we found that the electrostatic environment of each crowded neighbor had significant effects on rates of RNA hydrolysis. Crowding with cationic cytochrome c led to increases in activity, while crowding with anionic “supercharged” cytochrome c or myoglobin diminished activity. Surprisingly, electrostatic crowding effects were amplified at high ionic strength (I = 0.201 M) and attenuated at low ionic strength (I = 0.011 M). This salt dependence might be caused by a unique set of electric double layers at the dimer interspace (maximum distance of 8 Å, which cannot accommodate four layers). This new method of crowding via crosslinking can be used to search for electrostatic effects in protein crowding.

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.

Heavy Enzymes and the Rational Redesign of Protein Catalysts

An unsolved mystery in biology concerns the link between enzyme catalysis and protein motions. Comparison between isotopically labelled "heavy" dihydrofolate reductases and their natural-abundance counterparts has suggested that the coupling of protein motions to the chemistry of the catalysed reaction is minimised in the case of hydride transfer. In alcohol dehydrogenases, unnatural, bulky substrates that induce additional electrostatic rearrangements of the active site enhance coupled motions. This finding could provide a new route to engineering enzymes with altered substrate specificity, because amino acid residues responsible for dynamic coupling with a given substrate present as hotspots for mutagenesis. Detailed understanding of the biophysics of enzyme catalysis based on insights gained from analysis of "heavy" enzymes might eventually allow routine engineering of enzymes to catalyse reactions of choice.

Temperature dependence of dynamic, tunnelling and kinetic isotope effects in formate dehydrogenase

The origin of the catalytic power of enzymes has been a question of debate for a long time. In this regard, the possible contribution of protein dynamics in enzymatic catalysis has become one of the most controversial topics. In the present work, the hydride transfer step in the formate dehydrogenase (FDH EC 1.2.1.2) enzyme is studied by means of molecular dynamic (MD) simulations with quantum mechanics/molecular mechanics (QM/MM) potentials in order to explore any correlation between dynamics, tunnelling effects and the rate constant. The temperature dependence of the kinetic isotope effects (KIEs), which is one of the few tests that can be studied by experiments and simulations to shed light on this debate, has been computed and the results have been compared with previous experimental data. The classical mechanical free energy barrier and the number of recrossing trajectories seem to be temperature-independent while the quantum vibrational corrections and the tunnelling effects are slightly temperature-dependent over the interval of 5-45 °C. The computed primary KIEs are in very good agreement with previous experimental data, being almost temperature-independent within the standard deviations. The modest dependence on the temperature is due to just the quantum vibrational correction contribution. These results, together with the analysis of the evolution of the collective variables such as the electrostatic potential or the electric field created by the protein on the key atoms involved in the reaction, confirm that while the protein is well preorganised, some changes take place along the reaction that favour the hydride transfer and the product release. Coordinates defining these movements are, in fact, part of the real reaction coordinate.

Quantifying the limits of transition state theory in enzymatic catalysis

While being one of the most popular reaction rate theories, the applicability of transition state theory to the study of enzymatic reactions has been often challenged. The complex dynamic nature of the protein environment raised the question about the validity of the nonrecrossing hypothesis, a cornerstone in this theory. We present a computational strategy to quantify the error associated to transition state theory from the number of recrossings observed at the equicommittor, which is the best possible dividing surface. Application of a direct multidimensional transition state optimization to the hydride transfer step in human dihydrofolate reductase shows that both the participation of the protein degrees of freedom in the reaction coordinate and the error associated to the nonrecrossing hypothesis are small. Thus, the use of transition state theory, even with simplified reaction coordinates, provides a good theoretical framework for the study of enzymatic catalysis.

Shuffling Active Site Substate Populations Affects Catalytic Activity: The Case of Glucose Oxidase

Glucose oxidase has wide applications in the pharmaceutical, chemical, and food industries. Many recent studies have enhanced key properties of this enzyme using directed evolution, yet without being able to reveal why these mutations are actually beneficial. This work presents a synergistic combination of experimental and computational methods, indicating how mutations, even when distant from the active site, positively affect glucose oxidase catalysis. We have determined the crystal structures of glucose oxidase mutants containing molecular oxygen in the active site. The catalytically important His516 residue has been previously shown to be flexible in the wild-type enzyme. The molecular dynamics simulations performed in this work allow us to quantify this floppiness, revealing that His516 exists in two states: catalytic and noncatalytic. The relative populations of these two substates are almost identical in the wild-type enzyme, with His516 readily shuffling between them. In the glucose oxidase mutants, on the other hand, the mutations enrich the catalytic His516 conformation and reduce the flexibility of this residue, leading to an enhancement in their catalytic efficiency. This study stresses the benefit of active site preorganization with respect to enzyme conversion rates by reducing molecular reorientation needs. We further suggest that the computational approach based on Hamiltonian replica exchange molecular dynamics, used in this study, may be a general approach to screening in silico for improved enzyme variants involving flexible catalytic residues.

Benchmarking Quantum Mechanics/Molecular Mechanics (QM/MM) Methods on the Thymidylate Synthase-Catalyzed Hydride Transfer

Given the ubiquity of hydride-transfer reactions in enzyme-catalyzed processes, identifying the appropriate computational method for evaluating such biological reactions is crucial to perform theoretical studies of these processes. In this paper, the hydride-transfer step catalyzed by thymidylate synthase (TSase) is studied by examining hybrid quantum mechanics/molecular mechanics (QM/MM) potentials via multiple semiempirical methods and the M06-2X hybrid density functional. Calculations of protium and tritium transfer in these reactions across a range of temperatures allowed calculation of the temperature dependence of kinetic isotope effects (KIE). Dynamics and quantum-tunneling effects are revealed to have little effect on the reaction rate, but are significant in determining the KIEs and their temperature dependence. A good agreement with experiments is found, especially when computed for RM1/MM simulations. The small temperature dependence of quantum tunneling corrections and the quasiclassical contribution term cancel each other, while the recrossing transmission coefficient seems to be temperature-independent over the interval of 5-40 °C.

Structural and Kinetic Studies of Formate Dehydrogenase from Candida boidinii

The structure of formate dehydrogenase from Candida boidinii (CbFDH) is of both academic and practical interests. First, this enzyme represents a unique model system for studies on the role of protein dynamics in catalysis, but so far these studies have been limited by the availability of structural information. Second, CbFDH and its mutants can be used in various industrial applications (e.g., CO2 fixation or nicotinamide recycling systems), and the lack of structural information has been a limiting factor in commercial development. Here, we report the crystallization and structural determination of both holo- and apo-CbFDH. The free-energy barrier for the catalyzed reaction was computed and indicates that this structure indeed represents a catalytically competent form of the enzyme. Complementing kinetic examinations demonstrate that the recombinant CbFDH has a well-organized reactive state. Finally, a fortuitous observation has been made: the apoenzyme crystal was obtained under cocrystallization conditions with a saturating concentration of both the cofactor (NAD(+)) and inhibitor (azide), which has a nanomolar dissociation constant. It was found that the fraction of the apoenzyme present in the solution is less than 1.7 × 10(-7) (i.e., the solution is 99.9999% holoenzyme). This is an extreme case where the crystal structure represents an insignificant fraction of the enzyme in solution, and a mechanism rationalizing this phenomenon is presented.

Transition state theory for enzyme kinetics

This article is an essay that discusses the concepts underlying the application of modern transition state theory to reactions in enzymes. Issues covered include the potential of mean force, the quantization of vibrations, the free energy of activation, and transmission coefficients to account for nonequilibrium effect, recrossing, and tunneling.

Molecular dynamics explorations of active site structure in designed and evolved enzymes

This Account describes the use of molecular dynamics (MD) simulations to reveal how mutations alter the structure and organization of enzyme active sites. As proposed by Pauling about 70 years ago and elaborated by many others since then, biocatalysis is efficient when functional groups in the active site of an enzyme are in optimal positions for transition state stabilization. Changes in mechanism and covalent interactions are often critical parts of enzyme catalysis. We describe our explorations of the dynamical preorganization of active sites using MD, studying the fluctuations between active and inactive conformations normally concealed to static crystallography. MD shows how the various arrangements of active site residues influence the free energy of the transition state and relates the populations of the catalytic conformational ensemble to the enzyme activity. This Account is organized around three case studies from our laboratory. We first describe the importance of dynamics in evaluating a series of computationally designed and experimentally evolved enzymes for the Kemp elimination, a popular subject in the enzyme design field. We find that the dynamics of the active site is influenced not only by the original sequence design and subsequent mutations but also by the nature of the ligand present in the active site. In the second example, we show how microsecond MD has been used to uncover the role of remote mutations in the active site dynamics and catalysis of a transesterase, LovD. This enzyme was evolved by Tang at UCLA and Codexis, Inc., and is a useful commercial catalyst for the production of the drug simvastatin. X-ray analysis of inactive and active mutants did not reveal differences in the active sites, but relatively long time scale MD in solution showed that the active site of the wild-type enzyme preorganizes only upon binding of the acyl carrier protein (ACP) that delivers the natural acyl group to the active site. In the absence of bound ACP, a noncatalytic arrangement of the catalytic triad is dominant. Unnatural truncated substrates are inactive because of the lack of protein-protein interactions provided by the ACP. Directed evolution is able to gradually restore the catalytic organization of the active site by motion of the protein backbone that alters the active site geometry. In the third case, we demonstrate the key role of MD in combination with crystallography to identify the origins of substrate-dependent stereoselectivities in a number of Codexis-engineered ketoreductases, one of which is used commercially for the production of the antibiotic sulopenem. Here, mutations alter the shape of the active site as well as the accessibility of water to different regions of it. Each of these examples reveals something different about how mutations can influence enzyme activity and shows that directed evolution, like natural evolution, can increase catalytic activity in a variety of remarkable and often subtle ways.

The activating oxydianion binding domain for enzyme-catalyzed proton transfer, hydride transfer, and decarboxylation: specificity and enzyme architecture

The kinetic parameters for activation of yeast triosephosphate isomerase (ScTIM), yeast orotidine monophosphate decarboxylase (ScOMPDC), and human liver glycerol 3-phosphate dehydrogenase (hlGPDH) for catalysis of reactions of their respective phosphodianion truncated substrates are reported for the following oxydianions: HPO3(2-), FPO3(2-), S2O3(2-), SO4(2-) and HOPO3(2-). Oxydianions bind weakly to these unliganded enzymes and tightly to the transition state complex (E·S(‡)), with intrinsic oxydianion Gibbs binding free energies that range from -8.4 kcal/mol for activation of hlGPDH-catalyzed reduction of glycolaldehyde by FPO3(2-) to -3.0 kcal/mol for activation of ScOMPDC-catalyzed decarboxylation of 1-β-d-erythrofuranosyl)orotic acid by HOPO3(2-). Small differences in the specificity of the different oxydianion binding domains are observed. We propose that the large -8.4 kcal/mol and small -3.8 kcal/mol intrinsic oxydianion binding energy for activation of hlGPDH by FPO3(2-) and S2O3(2-), respectively, compared with activation of ScTIM and ScOMPDC reflect stabilizing and destabilizing interactions between the oxydianion -F and -S with the cationic side chain of R269 for hlGPDH. These results are consistent with a cryptic function for the similarly structured oxydianion binding domains of ScTIM, ScOMPDC and hlGPDH. Each enzyme utilizes the interactions with tetrahedral inorganic oxydianions to drive a conformational change that locks the substrate in a caged Michaelis complex that provides optimal stabilization of the different enzymatic transition states. The observation of dianion activation by stabilization of active caged Michaelis complexes may be generalized to the many other enzymes that utilize substrate binding energy to drive changes in enzyme conformation, which induce tight substrate fits.

Different dynamical effects in mesophilic and hyperthermophilic dihydrofolate reductases

The role of protein dynamics in the reaction catalyzed by dihydrofolate reductase from the hyperthermophile Thermotoga maritima (TmDHFR) has been examined by enzyme isotope substitution ((15)N, (13)C, (2)H). In contrast to all other enzyme reactions investigated previously, including DHFR from Escherichia coli (EcDHFR), for which isotopic substitution led to decreased reactivity, the rate constant for the hydride transfer step is not affected by isotopic substitution of TmDHFR. TmDHFR therefore appears to lack the coupling of protein motions to the reaction coordinate that have been identified for EcDHFR catalysis. Clearly, dynamical coupling is not a universal phenomenon that affects the efficiency of enzyme catalysis.

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.

Unraveling the role of protein dynamics in dihydrofolate reductase catalysis

Protein dynamics have controversially been proposed to be at the heart of enzyme catalysis, but identification and analysis of dynamical effects in enzyme-catalyzed reactions have proved very challenging. Here, we tackle this question by comparing an enzyme with its heavy ((15)N, (13)C, (2)H substituted) counterpart, providing a subtle probe of dynamics. The crucial hydride transfer step of the reaction (the chemical step) occurs more slowly in the heavy enzyme. A combination of experimental results, quantum mechanics/molecular mechanics simulations, and theoretical analyses identify the origins of the observed differences in reactivity. The generally slightly slower reaction in the heavy enzyme reflects differences in environmental coupling to the hydride transfer step. Importantly, the barrier and contribution of quantum tunneling are not affected, indicating no significant role for "promoting motions" in driving tunneling or modulating the barrier. The chemical step is slower in the heavy enzyme because protein motions coupled to the reaction coordinate are slower. The fact that the heavy enzyme is only slightly less active than its light counterpart shows that protein dynamics have a small, but measurable, effect on the chemical reaction rate.

Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology

Computational enzymology is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/molecular mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mechanical method (i.e., a method that calculates the electronic structure of the active site) and including the enzyme environment with simpler molecular mechanical methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymology. A range of QM/MM methods is available, from cheaper and more approximate methods, which can be used for molecular dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymology, e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.

Good vibrations in enzyme-catalysed reactions

Fast motions (femtosecond to picosecond) and their potential involvement during enzyme-catalysed reactions have ignited considerable interest in recent years. Their influence on reaction chemistry has been inferred indirectly from studies of the anomalous temperature dependence of kinetic isotope effects and computational simulations. But can such motion reduce the width and height of energy barriers along the reaction coordinate, and contribute to quantum mechanical and/or classical nuclear-transfer chemistry? Here we discuss contemporary ideas for enzymatic reactions invoking a role for fast 'promoting' (or 'compressive') motions that, in principle, can aid hydrogen-transfer reactions. Of key importance is the direct demonstration of a role for compressive motions and the ability to understand in atomic detail the structural origin of these fast motions, but so far this has not been achieved. Here we discuss both indirect experimental evidence that supports a role for compressive motion and the additional insight gained from computational simulations.

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ∼91% by tunneling in the case of protium and ∼80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.

Application of Grote-Hynes theory to the reaction catalyzed by thymidylate synthase

A theoretical study of dynamic effects on the rate-limiting step of the thymidylate synthase catalyzed reaction has been carried out by means of Grote-Hynes theory, successfully predicting the values of the recrossing effects for a chemical reaction that involves the transfer of a classical light particle. The transmission coefficients, obtained at 278, 293, 303, and 313 K, are almost invariant and in all cases far from unity, revealing a significant coupling of the environment motions and the reaction coordinate. Nevertheless, their energetic contribution to the activation free energy represents less than 0.50 kcal/mol for each of the four tested temperatures. Calculation of the transmission coefficient for the isotopically labeled hydride transfer has rendered almost the same values, in agreement with the experimentally observed temperature-independent KIEs. Fourier transform of the time-dependent friction kernel at these four temperatures has allowed obtaining the transition-state friction spectra, which present very small dependence with temperature. Their analysis has led to the identification of some key vibrational modes governing the coupling between the reaction coordinate and the protein environment, thus identifying the relevant motions in the active site and obtaining a full picture of the role of each amino acid.