Dynamic aspect of kinetics of reaction catalyzed by lactate dehydrogenase

The influence of solvent viscosity on the kinetic parameters of the pyruvate reduction reaction catalyzed by lactate dehydrogenase has been investigated. The viscosity was adjusted by sucrose and glycerol solutions at concentrations from 0 to 44% and from 0 to 63%, respectively. The reaction rate decreased abruptly with an increase in viscosity. The study of different reaction stages (enzyme-substrate complex formation, catalysis, inhibitory complex decomposition, competitive inhibition by chlorine ions) revealed that the catalysis (and the related conformational changes) is the only stage (of the above mentioned) that depends markedly on the solvent viscosity. The reaction is insensitive to the changes in the dielectric properties of the solution induced by the addition of alcohols and dioxane. The observed power dependence of the rate constant on viscosity is explained in terms of Kramer's theory which considers the proton transition through the activation barrier to be a diffusion in the field of random forces. The influence of solvent viscosity on enzymic kinetics indicates a direct relation between solvent dynamics and relevant protein conformational movements.     

Possible coupling of chemical to structural dynamics in subtilisin BPN' catalyzed hydrolysis

The viscosity dependence of enzymatic catalysis was examined in subtilisin BPN' catalyzed hydrolysis of N-succinyl-Ala-Ala-Pro-Phe-p-nitroanilide and N-succinyl-Ala-Ala-Pro-Phe-thiobenzyl ester. The viscosity of the reaction medium was varied by added glycerol, ethylene glycol, sucrose, glucose, fructose, poly(ethylene glycol) and Ficoll-400. Responses of the Michaelis-Menten parameters associated with hydrolysis were calculated from data obtained by spectrophotometric techniques. The reactions with these two substrates have catalytic rates well below the diffusion-controlled limit and thus enable us to study the viscosity effects on catalytic steps of non-transport nature. It was found that the Km values for both amide and ester reactions remained relatively independent of cosolvents. On the other hand, while the kcat values for amide were insensitive to cosolvents, those for ester were substantially attenuated except in the case of poly(ethylene glycol). The observed rate attenuations cannot be explained by changes in proton activity, water activity, dielectric constant of the reaction medium or shifts of any kinetically important pKa. Instead, the results can be adequately described by microviscosity effects on the unimolecular deacylation step with a coupling constant of 0.65 +/- 0.11. In addition, the different viscosity dependence in the acylation vs deacylation step can be rationalized in terms of fluctuation-dependent chemical dynamics of proton transfers in the context of the Bogris-Hynes model.     

Viscosity-dependent structural fluctuations in enzyme catalysis.

The effect of viscosity on the rate of catalysis of carboxypeptidase A has been tested. By use of the tripeptide carbobenzoxy-l-alanyl-l-alanyl-l-alanine [Z(L-Ala)3] as substrate, it was shown that most of the effect on the hydrolysis rate caused by the presence of 30 or 40% methanol or glycerol in aqueous solution can be ascribed to a contribution of viscosity to the catalytic rate constant, kcat. Arrhenius plots of kcat in 30 and 40% glycerol or methanol are linear and almost parallel. When the rate constants are "corrected" for the viscosity of various media, the difference between the various Arrhenius plots is considerably reduced; it vanishes, within experimental error, when the effect of the dielectric constant of the solutions is taken into account as well. It is proposed that the viscosity of the medium can influence the rate-limiting step of the enzymic reaction, which is the rate of transitions over the energy barrier preceding product formation. According to the suggested mechanism, the enzyme--substrate complex can overcome this energy barrier by viscosity-dependent structural fluctuations. The quantitative agreement between the theory and the experimental results suggests that (a) due to the temperature dependence of the viscosity of the solution, the potential energy barrier of the reaction is about 5 kcal/mol lower than the observed activation energy and (b) information about the structural flexibility of the complex can be obtained by kinetic measurements.     

Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium

The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)₅₀, (AlaGly)₂₅, and (AlaGly)₇₅ polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.     

Measuring solution viscosity and its effect on enzyme activity

In proteins, some processes require conformational changes involving structural domain diffusion. Among these processes are protein folding, unfolding and enzyme catalysis. During catalysis some enzymes undergo large conformational changes as they progress through the catalytic cycle. According to Kramers theory, solvent viscosity results in friction against proteins in solution, and this should result in decreased motion, inhibiting catalysis in motile enzymes. Solution viscosity was increased by adding increasing concentrations of glycerol, sucrose and trehalose, resulting in a decrease in the reaction rate of the H⁺-ATPase from the plasma membrane ofKluyveromyces lactis. A direct correlation was found between viscosity (η) and the inhibition of the maximum rate of catalysis (V _max). The protocol used to measure viscosity by means of a falling ball type viscometer is described, together with the determination of enzyme kinetics and the application of Kramers’ equation to evaluate the effect of viscosity on the rate of ATP hydrolysis by the H⁺-ATPase. Published: May 1, 2003     

Folding funnels and conformational transitions via hinge-bending motions

In this article we focus on presenting a broad range of examples illustrating low-energy transitions via hinge-bending motions. The examples are divided according to the type of hinge-bending involved; namely, motions involving fragments of the protein chains, hinge-bending motions involving protein domains, and hinge-bending motions between the covalently unconnected subunits. We further make a distinction between allosterically and nonallosterically regulated proteins. These transitions are discussed within the general framework of folding and binding funnels. We propose that the conformers manifesting such swiveling motions are not the outcome of “induced fit” binding mechanism; instead, molecules exist in an ensemble of conformations that are in equilibrium in solution. These ensembles, which populate the bottoms of the funnels,a priori contain both the “open” and the “closed” conformational isomers. Furthermore, we argue that there are no fundamental differences among the physical principles behind the folding and binding funnels. Hence, there is no basic difference between funnels depicting ensembles of conformers of single molecules with fragment, or domain motions, as compared to subunits in multimeric quaternary structures, also showing such conformational transitions. The difference relates only to the size and complexity of the system. The larger the system, the more complex its corresponding fused funnel(s). In particular, funnels associated with allosterically regulated proteins are expected to be more complicated, because allostery is frequently involved with movements between subunits, and consequently is often observed in multichain and multimolecular complexes. This review centers on the critical role played by flexibility and conformational fluctuations in enzyme activity. Internal motions that extend over different time scales and with different amplitudes are known to be essential for the catalytic cycle. The conformational change observed in enzyme-substrate complexes as compared to the unbound enzyme state, and in particular the hinge-bending motions observed in enzymes with two domains, have a substantial effect on the enzymatic catalytic activity. The examples we review span the lipolytic enzymes that are particularly interesting, owing to their activation at the water-oil interface; an allosterically controlled dehydrogenase (lactate dehydrogenase); a DNA methyltransferase, with a covalently-bound intermediate; large-scale flexible loop motions in a glycolytic enzyme (TIM); domain motion in PGK, an enzyme which is essential in most cells, both for ATP generation in aerobes and for fermentation in anaerobes; adenylate kinase, showing large conformational changes, owing to their need to shield their catalytic centers from water; a calcium-binding protein (calmodulin), involved in a wide range of cellular calcium-dependent signaling; diphtheria toxin, whose large domain motion has been shown to yield “domain swapping” the hexameric glutamate dehydrogenase, which has been studied both in a thermophile and in a mesophile; an allosteric enzyme, showing subunit motion between the R and the T states (aspartate transcarbamoylase), and the historically well-studied lac represoor. Nonallosteric subunit transitions are also addressed with some examples (aspartate receptor andBamHI endonuclease). Hence, using this enzyme-catalysis-centered discussion, we address energy funnel landscapes of large-scale conformational transitions, rather than the faster, quasi-harmonic, thermal fluctuations.     

Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium

The mechanics of the conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium have been considered. The variational principles for the energy-dissipation rate during conformational motions in a viscous medium and the rate of the potential energy decrease of a macromolecule during conformational relaxation have been analyzed. The seeming contradiction between this principle and the principle of the minimum energy-dissipation rate is resolved. It is shown that the energy-dissipation rate must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill the deterministic nature of classical trajectories. The generalization and analysis of the influence of thermal fluctuations and external forces on the variational principles for the conformational relaxation of macromolecules is carried out. A visual graphical geometric depiction has been developed using hyperspheres in the space of the velocities of chain nodes to describe conformational movements along many degrees of freedom in a viscous medium. The equipartition of the energy-dissipation rates (and the rates of potential energy decrease) among the conformational degrees of freedom is discussed.     

Conformational selection and induced changes along the catalytic cycle of Escherichia coli dihydrofolate reductase

Protein function often involves changes between different conformations. Central questions are how these conformational changes are coupled to the binding or catalytic processes during which they occur, and how they affect the catalytic rates of enzymes. An important model system is the enzyme dihydrofolate reductase (DHFR) from Escherichia coli, which exhibits characteristic conformational changes of the active‐site loop during the catalytic step and during unbinding of the product. In this article, we present a general kinetic framework that can be used (1) to identify the ordering of events in the coupling of conformational changes, binding, and catalysis and (2) to determine the rates of the substeps of coupled processes from a combined analysis of nuclear magnetic resonance R₂ relaxation dispersion experiments and traditional enzyme kinetics measurements. We apply this framework to E. coli DHFR and find that the conformational change during product unbinding follows a conformational‐selection mechanism, that is, the conformational change occurs predominantly prior to unbinding. The conformational change during the catalytic step, in contrast, is an induced change, that is, the change occurs after the chemical reaction. We propose that the reason for these conformational changes, which are absent in human and other vertebrate DHFRs, is robustness of the catalytic rate against large pH variations and changes to substrate/product concentrations in E. coli. Proteins 2012;. © 2012 Wiley Periodicals, Inc.     

Catalysis-Enhancement via Rotary Fluctuation of F1-ATPase

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F₁-ATPase (F₁) by attaching probes with different viscous drag coefficients at the rotary shaft of F₁. Individual rotation pauses of F₁ between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F₁ rate enhancement.     

Catalysis-Enhancement via Rotary Fluctuation of F1-ATPase

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F₁-ATPase (F₁) by attaching probes with different viscous drag coefficients at the rotary shaft of F₁. Individual rotation pauses of F₁ between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F₁ rate enhancement.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

The effect of solvent viscosity on the rate-determining step of fatty acid synthetase

The overall activity of an animal fatty acid synthetase at the saturation level of substrate concentration decreased when the solvent viscosity, eta, of the reaction mixture was increased with viscogens such as glycerol, sucrose, and polyethylene glycol. The activity of the enzyme changed roughly proportional to eta-P, where p = 1.0 for glycerol, p = 0.66 for sucrose, and p less than 0.6 for polyethylene glycol with different molecular sizes. The thioesterase activity, which catalyzes the final partial reaction in the multifunctional enzyme, was not affected by 5-fold increase of solvent viscosity with sucrose. These results suggested that the rate-determining step of the enzyme other than the thioesterase reaction involves a microscopic transport step, the rate of which is influenced by the solvent viscosity. The microscopic transport step may be related to the transfer of the reaction intermediate from one active site to another or to the motion of a larger part of the enzyme requisite for the catalytic reaction. In the solution containing glycerol, the rate-determining motion was primarily diffusion limited since the inverse of the initial rate was proportional to eta, i.e., p = 1. Since the substrate concentration was at a saturation level in this experiment, the viscosity-dependent step cannot be the encounter between the enzyme and substrates, but must be intramolecular in origin, most probably the reaction catalyzed by beta-ketoacyl synthetase. In solutions containing other viscogens, however, p was less than 1.0, indicating a significant involvement of chemical steps in the rate-determining step as well. Bovine serum albumin, when used as a proteinic viscogen, also decreased the initial rate.(ABSTRACT TRUNCATED AT 250 WORDS)     

A diffusion Michaelis-Menten mechanism: continuous conformational change in enzymatic kinetics

We present a simple model which extends the Michaelis-Menten mechanism by incorporating a continuous protein conformational change in enzymatic catalysis. This model can represent a quantitative version for "rack" or "induced fit" mechanisms. In the steady-state it leads to an equation of the Michaelis-Menten form, but with the catalytic step at the active site showing strong dependence on solvent viscosity. We suggest that a careful examination of solvent viscosity effects on enzymatic activity may serve as a test for the conformational change hypothesis.     

Role of the switch II region in the conformational transition of activation of Ha-ras-p21

The role of the switch II region in the conformational transition of activation of Ha-ras-p21 has been investigated by mutating residues predicted to act as hinges for the conformational transition of this loop (Ala59, Gly60, and Gly75) (Díaz JF, Wroblowski B, Schlitter J, Engelborghs Y, 1997, Proteins 28:434-451), as well as mutating the catalytic residue Gln61. The proposed mutations of the hinge residues decrease the rate of the conformational transition of activation as measured by the binding of BeF3- to the GDP-p21 complex. Also, the thermodynamic parameters of the binding reaction are altered by a factor between three and five, depending on the temperature. (Due to changes in activation and reaction enthalpies, partially compensated by entropy changes.) The control mutation Q61H in which only the catalytic residue is changed has only a limited effect on the kinetic rate constants of the conformational transition and on the thermodynamic parameters of the reaction. The fact that mutations of the hinge residues of the switch II region affect both the binding of the phosphate analog and the conformational transition of activation indicates that the switch II is implicated both in the early and the late states of the transition.     

Conformational regulation of the EGFR kinase core by the juxtamembrane and C-terminal tail: a molecular dynamics study

The catalytic domain of epidermal growth factor receptor (EGFR) is activated by dimerization, which requires allosteric coupling between distal dimerization and catalytic sites. Although crystal structures of EGFR kinases, solved in various conformational states, have provided important insights into EGFR activation by dimerization, the atomic details of how dimerization signals are dynamically coupled to catalytic regions of the kinase core are not fully understood. In this study, we have performed unrestrained and targeted molecular dynamics simulations on the active and inactive states of EGFR, followed by principal component analysis on the simulated trajectories, to identify correlated motions in the EGFR kinase domain upon dimerization. Our analysis reveals that the conformational changes associated with the catalytic functions of the kinase core are highly correlated with motions in the juxtamembrane (JM) and C-terminal tail, two flexible structural elements that play an active role in EGFR kinase activation and dimerization. In particular, the opening and closing of the ATP binding lobe relative to the substrate binding lobe is highly correlated with motions in the JM and C-terminal tail, suggesting that ATP and substrate binding can be coordinated with dimerization through conformational changes in the JM and C-terminal tail. Our study pinpoints key residues involved in this conformational coupling, and provides new insights into the role of the JM and C-terminal tail segments in EGFR kinase functions.     

Alteration of hydrogen bonding in the vicinity of histidine 48 disrupts millisecond motions in RNase A

The motion of amino acid residues on the millisecond (ms) time scale is involved in the tight regulation of catalytic function in numerous enzyme systems. Using a combination of mutational, enzymological, and relaxation-compensated (15)N Carr-Purcell-Meiboom-Gill (CPMG) methods, we have previously established the conformational significance of the distant His48 residue and the neighboring loop 1 in RNase A function. These studies suggested that RNase A relies on an intricate network of hydrogen bonding interactions involved in propagating functionally relevant, long-range ms motions to the catalytic site of the enzyme. To further investigate the dynamic importance of this H-bonding network, this study focuses on the individual replacement of Thr17 and Thr82 with alanine, effectively altering the key H-bonding interactions that connect loop 1 and His48 to the rest of the protein. (15)N CPMG dispersion studies, nuclear magnetic resonance (NMR) chemical shift analysis, and NMR line shape analysis of point mutants T17A and T82A demonstrate that the evolutionarily conserved single H-bond linking His48 to Thr82 is essential for propagating ms motions from His48 to the active site of RNase A on the time scale of catalytic turnover, whereas the T17A mutation increases the off rate and conformational exchange motions in loop 1. Accumulating evidence from our mutational studies indicates that residues experiencing conformational exchange in RNase A can be grouped into two separate clusters displaying distinct dynamical features, which appear to be independently affected by mutation. Overall, this study illuminates how tightly controlled and finely tuned ms motions are in RNase A, suggesting that designed modulation of protein motions may be possible.     

Role of induced fit in enzyme specificity: a molecular forward/reverse switch

Enzyme structures solved with and without bound substrate often show that substrate-induced conformational changes bring catalytic residues into alignment, alter the local environment, and position the substrate for catalysis. Although the structural data are compelling, the role of conformational changes in enzyme specificity has been controversial in that specificity is a kinetic property that is not easy to predict based upon structure alone. Recent studies on DNA polymerization have illuminated the role of substrate-induced conformational changes in enzyme specificity by showing that the rate at which the enzyme opens to release the bound substrate is a key kinetic parameter. The slow release of a correct substrate commits it to the forward reaction so that specificity is determined solely by the rate of substrate binding, including the isomerization step, and not by the slower rate of the chemical reaction. In contrast, fast dissociation of an incorrect substrate favors release rather than reaction. Thus, the conformational change acts as a molecular switch to select the right substrate and to recognize and disfavor the reaction of an incorrect substrate. A conformational switch may also favor release rather than reverse reaction of the product.     

Mechanical modulation of catalytic power on F1-ATPase

The conformational fluctuation of enzymes has a crucial role in reaction acceleration. However, the contribution to catalysis enhancement of individual substates with conformations far from the average conformation remains unclear. We studied the catalytic power of the rotary molecular motor F(1)-ATPase from thermophilic Bacillus PS3 as it was stalled in transient conformations far from a stable pausing angle. The rate constants of ATP binding and hydrolysis were determined as functions of the rotary angle. Both rates exponentially increase with rotation, revealing the molecular basis of positive cooperativity among three catalytic sites: elementary reaction steps are accelerated via the mechanical rotation driven by other reactions on neighboring catalytic sites. The rate enhancement induced by ATP binding upon rotation was greater than that brought about by hydrolysis, suggesting that the ATP binding step contributes more to torque generation than does the hydrolysis step. Additionally, 9% of the ATP-driven rotary step was supported by thermal diffusion, suggesting that acceleration of the ATP docking process occurs via thermally agitated conformational fluctuations.     

A model of the mechanism of enzyme action in terms of protein conformational relaxation

A theoretical model of enzymatic reaction is formulated in which the modulation of the reaction coordinates by low-frequency conformational motions of the enzyme molecule causes the lowering of the activation energy barriers until they completely disappear. If the rates of electron transitions in the enzyme-substrate complex exceed the characteristic frequencies of conformational motions then the rate of the elementary enzymatic reaction shows hysteresis dependence on temperature and substrate concentration.