Millisecond dynamics in glutaredoxin during catalytic turnover is dependent on substrate binding and absent in the resting states

Conformational dynamics is important for enzyme function. Which motions of enzymes determine catalytic efficiency and whether the same motions are important for all enzymes, however, are not well understood. Here we address conformational dynamics in glutaredoxin during catalytic turnover with a combination of NMR magnetization transfer, R(2) relaxation dispersion, and ligand titration experiments. Glutaredoxins catalyze a glutathione exchange reaction, forming a stable glutathinoylated enzyme intermediate. The equilibrium between the reduced state and the glutathionylated state was biochemically tuned to exchange on the millisecond time scale. The conformational changes of the protein backbone during catalysis were followed by (15)N nuclear spin relaxation dispersion experiments. A conformational transition that is well described by a two-state process with an exchange rate corresponding to the glutathione exchange rate was observed for 23 residues. Binding of reduced glutathione resulted in competitive inhibition of the reduced enzyme having kinetics similar to that of the reaction. This observation couples the motions observed during catalysis directly to substrate binding. Backbone motions on the time scale of catalytic turnover were not observed for the enzyme in the resting states, implying that alternative conformers do not accumulate to significant concentrations. These results infer that the turnover rate in glutaredoxin is governed by formation of a productive enzyme-substrate encounter complex, and that catalysis proceeds by an induced fit mechanism rather than by conformer selection driven by intrinsic conformational dynamics.     

Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field

Chorismate mutase is a key model system in the development of theories of enzyme catalysis. To analyze the physical nature of catalytic interactions within the enzyme active site and to estimate the stabilization of the transition state (TS) relative to the substrate (differential transition state stabilization, DTSS), we have carried out nonempirical variation-perturbation analysis of the electrostatic, exchange, delocalization, and correlation interactions of the enzyme-bound substrate and transition-state structures derived from ab initio QM/MM modeling of Bacillus subtilis chorismate mutase. Significant TS stabilization by approximately -23 kcal/mol [MP2/6-31G(d)] relative to the bound substrate is in agreement with that of previous QM/MM modeling and contrasts with suggestions that catalysis by this enzyme arises purely from conformational selection effects. The most important contributions to DTSS come from the residues, Arg90, Arg7, Glu78, a crystallographic water molecule, Arg116, and Arg63, and are dominated by electrostatic effects. Analysis of the differential electrostatic potential of the TS and substrate allows calculation of the catalytic field, predicting the optimal location of charged groups to achieve maximal DTSS. Comparison with the active site of the enzyme from those of several species shows that the positions of charged active site residues correspond closely to the optimal catalytic field, showing that the enzyme has evolved specifically to stabilize the TS relative to the substrate.     

Conformer selection and intensified dynamics during catalytic turnover in chymotrypsin

Intensified searching: In enzymes, conformational dynamics are linked to the catalytic reaction coordinate. A novel analytical approach was used to monitor catalysis-linked dynamics in chymotrypsin, revealing that in some enzymes, catalysis is promoted by intensified, but undirected conformational sampling after substrate binding.     

Role of protein dynamics in reaction rate enhancement by enzymes

An integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active assemblies and internal motions are closely linked to function such as enzyme catalysis. Further, the motion of solvent bound to external regions of protein impacts internal motions and, therefore, protein function. Recently, we discovered a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization. Detailed studies suggest that this network, extending from surface regions to active site, is a conserved part of enzyme structure and has a role in promoting catalysis. In this report, theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network are presented. Using a new technique, kinetic energy was added to protein vibrational modes corresponding to conformational fluctuations in the network. The results reveal that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibrational modes is observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier recrossings. Simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network presented here indicates that protein dynamics plays a role in rate enhancement by enzymes. Therefore, coupled networks in enzymes have wide implications in understanding allostericity and cooperative effects, as well as protein engineering and drug design.     

Structural reorganization and preorganization in enzyme active sites: comparisons of experimental and theoretically ideal active site geometries in the multistep serine esterase reaction cycle

Many enzymes catalyze reactions with multiple chemical steps, requiring the stabilization of multiple transition states during catalysis. Such enzymes must strike a balance between the conformational reorganization required to stabilize multiple transition states of a reaction and the confines of a preorganized active site in the polypeptide tertiary structure. Here we investigate the compromise between structural reorganization during the catalytic process and preorganization of the active site for a multistep enzyme-catalyzed reaction, the hydrolysis of esters by the Ser-His-Asp/Glu catalytic triad. Quantum mechanical transition states were used to generate ensembles of geometries that can catalyze each individual step in the mechanism. These geometries are compared to each other by superpositions of catalytic atoms to find "consensus" geometries that can catalyze all steps with minimal rearrangement. These consensus geometries are found to be excellent matches for the natural active site. Preorganization is therefore found to be the major defining characteristic of the active site, and reorganizational motions often proposed to promote catalysis have been minimized. The variability of enzyme active sites observed by X-ray crystallography was also investigated empirically. A catalog of geometrical parameters relating active site residues to each other and to bound inhibitors was collected from a set of crystal structures. The crystal-structure-derived values were then compared to the ranges found in quantum mechanically optimized structures along the entire reaction coordinate. The empirical ranges are found to encompass the theoretical ranges when thermal fluctuations are taken into account. Therefore, the active sites are preorganized to a geometry that can be objectively and quantitatively defined as minimizing conformational reorganization while maintaining optimal transition state stabilization for every step during catalysis. The results provide a useful guiding principle for de novo design of enzymes with multistep mechanisms.     

Perspective: pre-chemistry conformational changes in DNA polymerase mechanisms

In recent papers, there has been a lively exchange concerning theories for enzyme catalysis, especially the role of protein dynamics/pre-chemistry conformational changes in the catalytic cycle of enzymes. Of particular interest is the notion that substrate-induced conformational changes that assemble the polymerase active site prior to chemistry are required for DNA synthesis and impact fidelity (i.e., substrate specificity). High-resolution crystal structures of DNA polymerase β representing intermediates of substrate complexes prior to the chemical step are available. These structures indicate that conformational adjustments in both the protein and substrates must occur to achieve the requisite geometry of the reactive participants for catalysis. We discuss computational and kinetic methods to examine possible conformational change pathways that lead from the observed crystal structure intermediates to the final structures poised for chemistry. The results, as well as kinetic data from site-directed mutagenesis studies, are consistent with models requiring pre-chemistry conformational adjustments in order to achieve high fidelity DNA synthesis. Thus, substrate-induced conformational changes that assemble the polymerase active site prior to chemistry contribute to DNA synthesis even when they do not represent actual rate-determining steps for chemistry.     

Catalytic itinerary in 1,3-1,4-β-glucanase unraveled by QM/MM metadynamics. Charge is not yet fully developed at the oxocarbenium ion-like transition state

Retaining glycoside hydrolases (GHs), key enzymes in the metabolism of polysaccharides and glycoconjugates and common biocatalysts used in chemoenzymatic oligosaccharide synthesis, operate via a double-displacement mechanism with the formation of a glycosyl-enzyme intermediate. However, the degree of oxocarbenium ion character of the reaction transition state and the precise conformational itinerary of the substrate during the reaction, pivotal in the design of efficient inhibitors, remain elusive for many GHs. By means of QM/MM metadynamics, we unravel the catalytic itinerary of 1,3-1,4-β-glucanase, one of the most active GHs, belonging to family 16. We show that, in the Michaelis complex, the enzyme environment restricts the conformational motion of the substrate to stabilize a (1,4)B/(1)S(3) conformation of the saccharide ring at the -1 subsite, confirming that this distortion preactivates the substrate for catalysis. The metadynamics simulation of the enzymatic reaction captures the complete conformational itinerary of the substrate during the glycosylation reaction ((1,4)B/(1)S(3) -(4)E/(4)H(3) - (4)C(1)) and shows that the transition state is not the point of maximum charge development at the anomeric carbon. The overall catalytic mechanism is of dissociative type, and proton transfer to the glycosidic oxygen is a late event, clarifying previous kinetic studies of this enzyme.     

Probing single-molecule enzyme active-site conformational state intermittent coherence

The relationship between protein conformational dynamics and enzymatic reactions has been a fundamental focus in modern enzymology. Using single-molecule fluorescence resonance energy transfer (FRET) with a combined statistical data analysis approach, we have identified the intermittently appearing coherence of the enzymatic conformational state from the recorded single-molecule intensity-time trajectories of enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in catalytic reaction. The coherent conformational state dynamics suggests that the enzymatic catalysis involves a multistep conformational motion along the coordinates of substrate-enzyme complex formation and product releasing, presenting as an extreme dynamic behavior intrinsically related to the time bunching effect that we have reported previously. The coherence frequency, identified by statistical results of the correlation function analysis from single-molecule FRET trajectories, increases with the increasing substrate concentrations. The intermittent coherence in conformational state changes at the enzymatic reaction active site is likely to be common and exist in other conformation regulated enzymatic reactions. Our results of HPPK interaction with substrate support a multiple-conformational state model, being consistent with a complementary conformation selection and induced-fit enzymatic loop-gated conformational change mechanism in substrate-enzyme active complex formation.     

Characterization of the transition state of functional enzyme dynamics

Through characterization of the solvent isotope effect on protein dynamics, we have examined determinants of the rate limitation to enzyme catalysis. A global conformational change in Ribonuclease A limits the overall rate of catalytic turnover. Here we show that this motion is sensitive to solvent deuterium content; the isotope effect is 2.2, a value equivalent to the isotope effect on the catalytic rate constant. We further demonstrate that the protein motion possesses a linear proton inventory plot, indicating that a single proton is transferred in the transition state. These results provide compelling evidence for close coupling between enzyme dynamics and function and demonstrate that characterization of the transition state for protein motion in atomic detail is experimentally accessible.     

Role of Mg2+ in hammerhead ribozyme catalysis from molecular simulation

Molecular dynamics simulations have been performed to investigate the role of Mg2+ in the full-length hammerhead ribozyme cleavage reaction. In particular, the aim of this work is to characterize the binding mode and conformational events that give rise to catalytically active conformations and stabilization of the transition state. Toward this end, a series of eight 12 ns molecular dynamics simulations have been performed with different divalent metal binding occupations for the reactant, early and late transition state using recently developed force field parameters for metal ions and reactive intermediates in RNA catalysis. In addition, hybrid QM/MM calculations of the early and late transition state were performed to study the proton-transfer step in general acid catalysis that is facilitated by the catalytic Mg2+ ion. The simulations suggest that Mg2+ is profoundly involved in the hammerhead ribozyme mechanism both at structural and catalytic levels. Binding of Mg2+ in the active site plays a key structural role in the stabilization of stem I and II and to facilitate formation of near attack conformations and interactions between the nucleophile and G12, the implicated general base catalyst. In the transition state, Mg2+ binds in a bridging position where it stabilizes the accumulated charge of the leaving group while interacting with the 2'OH of G8, the implicated general acid catalyst. The QM/MM simulations provide support that, in the late transition state, the 2'OH of G8 can transfer a proton to the leaving group while directly coordinating the bridging Mg2+ ion. The present study provides evidence for the role of Mg2+ in hammerhead ribozyme catalysis. The proposed simulation model reconciles the interpretation of available experimental structural and biochemical data, and provides a starting point for more detailed investigation of the chemical reaction path with combined QM/MM methods.     

Understanding noncovalent interactions: ligand binding energy and catalytic efficiency from ligand-induced reductions in motion within receptors and enzymes

Noncovalent interactions are sometimes treated as additive and this enables useful average binding energies for common interactions in aqueous solution to be derived. However, the additive approach is often not applicable, since noncovalent interactions are often either mutually reinforcing (positively cooperative) or mutually weakening (negatively cooperative). Ligand binding energy is derived (positively cooperative binding) when a ligand reduces motion within a receptor. Similarly, transition-state binding energy is derived in enzyme-catalyzed reactions when the substrate transition state reduces the motions within an enzyme. Ligands and substrates can in this way improve their affinities for these proteins. The further organization occurs with a benefit in bonding (enthalpy) and a limitation in dynamics (cost in entropy), but does not demand the making of new noncovalent interactions, simply the strengthening of existing ones. Negative cooperativity induces converse effects: less efficient packing, a cost in enthalpy, and a benefit in entropy.     

Release of enzyme strain during catalysis reduces the activation energy barrier

Several mechanisms have been considered as principal factors in enhancing the catalytic reaction velocity of enzymes: approximation, covalent catalysis, general acid-based catalysis, and strain. Among them, the strain on the substrate and/or the enzyme is often found to be brought about on association of the substrate and the enzyme. If this strain is released in the transition state, it contributes to enhancing the k(cat) value, although it does not change the k(cat)/K(m) value. In aspartate aminotransferase, however, we found by analysis of the Schiff base pK(a) values that the unliganded enzyme carries a strain in the protonated Schiff base formed between the coenzyme pyridoxal phosphate and a lysine residue. This bond is cleaved in most of the reaction intermediates, including the transition state. As a result, the activation energy between the free enzyme plus substrate and the transition state is decreased by 16 kJ/mol, equal to the value of the strain energy. The net effect of this strain is enhancement (10(3)-fold) of the catalytic efficiency in terms of k(cat)/K(m), the more important indicator of the catalytic efficiency at low concentration of the substrate.     

Crucial role of protein flexibility in formation of a stable reaction transition state in an α-amylase catalysis

Conformational flexibility of proteins provides enzymes with high catalytic activity. Although the conformational flexibility is known to be pivotal for the ligand binding and release, its role in the chemical reaction process of the reactive substrate remains unclear. We determined a transition state of an enzymatic reaction in a psychrophilic α-amylase by a hybrid molecular simulation that allows one to identify the optimal chemical state in an extensive conformational ensemble of protein. The molecular simulation uncovered that formation of the reaction transition state accompanies a large and slow movement of a loop adjacent to the catalytic site. Free energy calculations revealed that, although catalytic electrostatic potentials on the reactive moiety are formed by local and fast reorganization around the catalytic site, reorganization of the large and slow movement of the loop significantly contributes to reduction of the free energy barrier by stabilizing the local reorganization.     

Understanding enzyme catalysis by means of supramolecular artificial enzymes

Enzymes are biomacromolecules responsible for the abundant chemical biotransformations that sustain life. Recently, biochemists have discovered that multiple conformations and numerous parallel paths are involved during the processes catalyzed by enzymes. It is plausible that the entire macromolecular scaffold is involved in catalysis via cooperative motions that result in incredible catalytic efficiency. Moreover, some enzymes can very strongly bind the transition state with an association constant of up to 1024 M-1, suggesting that covalent bond formation is a possible process during the conversion of the transition state in enzyme catalysis, in addition to the concatenation of noncovalent interactions. Supramolecular chemistry provides fundamental knowledge about the relationships between the dynamic structures and functions of organized molecules. By tak-ing advantage of supramolecular concepts, numerous supramolecular enzyme mimics with complex and hierarchical structures have been designed and investigated. Through the study of supramolecular enzyme models, a great deal of information to aid our understanding of the mechanism of catalysis by natural enzymes has been acquired. With the development of supramolec-ular artificial enzymes, it is possible to replicate the features of natural enzymes with regards to their constitutional complexity and cooperative motions, and eventually decipher the conformation-based catalytic mystery of natural enzymes.     

Enzymatic effects on reactant and transition states. The case of chalcone isomerase

Chalcone isomerase catalyzes the transformation of chalcone to naringerin as a part of flavonoid biosynthetic pathways. The global reaction takes place through a conformational change of the substrate followed by chemical reaction, being thus an excellent example to analyze current theories about enzyme catalysis. We here present a detailed theoretical study of the enzymatic action on the conformational pre-equilibria and on the chemical steps for two different substrates of this enzyme. Free-energy profiles are obtained in terms of potentials of mean force using hybrid quantum mechanics/molecular mechanics potentials. The role of the enzyme becomes clear when compared to the counterpart equilibria and reactions in aqueous solution. The enzyme does not only favor the chemical reaction lowering the corresponding activation free energy but also displaces the conformational equilibria of the substrates toward the reactive form. These results, which can be rationalized in terms of the electrostatic interactions established in the active site between the substrate and the environment, agree with a more general picture of enzyme catalysis. According to this, an active site designed to accommodate the transition state of the reaction would also have consequences on the reactant state, stabilizing those forms which are geometrically and/or electronically closer to the transition structure.     

A Process Theory of Enzyme Catalytic Power – the Interplay of Science and Metaphysics

Enzymes are protein catalysts of extraordinary efficiency, capable of bringing about rate enhancements of their biochemical reactions that can approach factors of 10²⁰. Theories of enzyme catalysis, which seek to explain the means by which enzymes effect catalytic transformation of the substrate molecules on which they work, have evolved over the past century from the “lock-and-key” model proposed by Emil Fischer in 1894 to models that explicitly rely on transition state theory to the most recent theories that strive to provide accounts that stress the essential role of protein dynamics. In this paper, I attempt to construct a metaphysical framework within which these new models of enzyme catalysis can be developed. This framework is constructed from key doctrines of process thought, which gives ontologic priority to becoming over being, as well as tenets of a process philosophy of chemistry, which stresses environmentally responsive molecular transformation. Enzyme catalysis can now be seen not as enzyme acting on its substrate, but rather as enzyme and substrate entering into a relation which allows them to traverse the reaction coordinate as an ontologic unity.     

Quantum charge transport and conformational dynamics of macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a quantum charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder. We argue that collapsing conducting polymers may represent a physical realization of quantum small-world networks with dynamical rewiring probability.     

Analysis of the residual entropy of amorphous polyethylene at 0 K*

The residual entropy of amorphous polyethylene (PE) at 0 K is discussed within the framework of the heat capacity (C_p). The measured C_p of the liquid was extended from the glass transition to low temperature by separately finding its three parts—the vibrational, conformational, and external contributions—and extrapolating each to low temperature. The vibrational C_p was calculated from the frequency distributions of the group vibrations on the basis of force constants obtained from experimental infrared and Raman spectra as well as the skeletal vibrations in the amorphous solid (glass) obtained from fitting of the appropriate experimental C_p to Debye functions in the form suggested by Tarasov. The conformational part of C_p was evaluated from a fit of the heat capacity of the liquid, decreased by the contributions of the vibrational and external parts, to a one‐dimensional Ising model that can be extrapolated to 0 K and requires two discrete states described by stiffness, cooperativity, and a degeneracy parameter. The external part was computed from the experimental data for expansivity and compressibility, fitted to an empirical equation of state, and modified at low temperatures in accordance with the Nernst–Lindemann approximation. The computed C_p of the liquid PE agreed with the experiment from 600 K to the beginning of the glass transition at about 260 K. Extending the heat capacity to 0 K, bypassing the freezing of the large‐amplitude conformational motion in the glass transition, led to a positive residual entropy and enthalpy and avoided the so‐called Kauzmann paradox. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1245–1253, 2002