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     

Kinetics of the lactate dehydrogenase reaction in high-viscosity media

The effect of the medium viscosity on kinetics parameters of lactate dehydrogenase reaction was studied. The viscosity increase results in a sharp decline in the catalytic rate for both the pyruvate reduction and lactate oxidation reactions. It is shown that the catalytic step and its associated conformational motions is the only step which is considerably retarded when the viscosity increases. The reaction is not sensitive to changes in the dielectric properties of the medium. An inverse power function observed between the rate constant and viscosity cannot be explained by the theory of absolute reaction rates. However, it can easily be interpreted on the basis of the Kramers theory dealing with the transition over the activation barrier as a diffusional motion in the field of random forces. The influence of the medium's viscosity on the kinetic parameters indicates the existence of strong coupling between the dynamics of the solvent and the conformational motions of the protein molecule, which are correlated with the catalytic step.     

The kinetics of conformation change as determinant of Rubisco's specificity

The molecular basis of Rubisco's specificity is investigated in terms of the structure and kinetics of the enzyme. We propose that the rates of the conformational changes (closing/opening) of the binding niche exert a crucial influence on apparent binding rates and the enzyme's specificity. An extended reaction scheme for binding and conformational kinetics is presented and expressed in a mathematical model. The closed conformation, known from X-ray structures, is assumed to be necessary for binding of the gaseous substrates (carbon dioxide and oxygen) and for catalysis. Opening the niche interrupts catalysis and enables a fast exchange of those molecules between the internal cavity and the surrounding solvent. Our model predicts that specificity of Rubisco for CO₂ increases with the rate by which the niche opens. This is due to the fact that binding of the carbon dioxide is faster than oxygen binding, which is hampered by spin inversion. The apparent rate of carbon dioxide binding correlates with the repetition rate of the conformational change, and the rate of oxygen binding with the probability of the closed state. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pre-steady-state and stopped-flow fluorescence analysis of Escherichia coli ribonuclease III: insights into mechanism and conformational changes associated with binding and catalysis

To better understand substrate recognition and catalysis by RNase III, we examined steady-state and pre-steady-state reaction kinetics, and changes in intrinsic enzyme fluorescence. The multiple turnover cleavage of a model RNA substrate shows a pre-steady-state burst of product formation followed by a slower phase, indicating that the steady-state reaction rate is not limited by substrate cleavage. RNase III catalyzed hydrolysis is slower at low pH, permitting the use of pre-steady-state kinetics to measure the dissociation constant for formation of the enzyme-substrate complex (K(d)=5.4(+/-0.6) nM), and the rate constant for phosphodiester bond cleavage (k(c)=1.160(+/-0.001) min(-1), pH 5.4). Isotope incorporation analysis shows that a single solvent oxygen atom is incorporated into the 5' phosphate of the RNA product, which demonstrates that the cleavage step is irreversible. Analysis of the pH dependence of the single turnover rate constant, k(c), fits best to a model for two or more titratable groups with pK(a) of ca 5.6, suggesting a role for conserved acidic residues in catalysis. Additionally, we find that k(c) is dependent on the pK(a) value of the hydrated divalent metal ion included in the reaction, providing evidence for participation of a metal ion hydroxide in catalysis, potentially in developing the nucleophile for the hydrolysis reaction. In order to assess whether conformational changes also contribute to the enzyme mechanism, we monitored intrinsic tryptophan fluorescence. During a single round of binding and cleavage by the enzyme we detect a biphasic change in fluorescence. The rate of the initial increase in fluorescence was dependent on substrate concentration yielding a second-order rate constant of 1.0(+/-0.1)x10(8) M(-1) s(-1), while the rate constant of the second phase was concentration independent (6.4(+/-0.8) s(-1); pH 7.3). These data, together with the unique dependence of each phase on divalent metal ion identity and pH, support the hypothesis that the two fluorescence transitions, which we attribute to conformational changes, correlate with substrate binding and catalysis.     

Catalysis by ribonuclease A is limited by the rate of substrate association

The value of k(cat)/K(M) for catalysis of RNA cleavage by ribonuclease (RNase) A can exceed 10(9) M(-1) s(-1) in a solution of low salt concentration. This value approaches that expected for the diffusional encounter of the enzyme and its substrate. To reveal the physicochemical constraints upon catalysis by RNase A, the effects of salt concentration, pH, solvent isotope, and solvent viscosity on catalysis were determined with synthetic substrates that bind to all of the enzymic subsites and thereby enable a meaningful analysis. The pK(a) values determined from pH-k(cat)/K(M) profiles at 0.010, 0.20, and 1.0 M NaCl are inconsistent with the known macroscopic pK(a) values of RNase A. This incongruity indicates that catalysis of RNA cleavage by RNase A is limited by the rate of substrate association, even at 1.0 M NaCl. The effect of solvent isotope and solvent viscosity on catalysis support this conclusion. The data are consistent with a mechanism in which RNase A associates with RNA in an intermediate complex, which is stabilized by Coulombic interactions, prior to the formation of a Michaelis complex. Thus, RNase A has evolved to become an enzyme limited by physics rather than chemistry, a requisite attribute of a perfect catalyst.     

Site directed mutagenesis at position 193 of human trypsin 4 alters the rate of conformational change during activation: role of local internal viscosity in protein dynamics

Upon activation of trypsinogen four peptide segments flanked by hinge glycine residues undergo conformational changes. To test whether the degree of conformational freedom of hinge regions affects the rate of activation, we introduced amino acid side chains of different characters at one of the hinges (position 193) and studied their effects on the rate constant of the conformational change. This structural rearrangement leading to activation was triggered by a pH-jump and monitored by intrinsic fluorescence change in the stopped-flow apparatus. We found that an increase in the size of the side chain at position 193 is associated with the decrease of the reaction rate constant. To analyze the thermodynamics of the reaction, temperature dependence of the reaction rate constants was examined in a wide temperature range (5-60 degrees C) using a novel temperature-jump/stopped-flow apparatus developed in our laboratory. Our data show that the mutations do not affect the activation energy (the exponential term) of the reaction, but they significantly alter the preexponential term of the Arrhenius equation. The effect of solvent viscosity on the rate constants of the conformational change during activation of the wild type enzyme and its R193G and R193A mutants was determined and evaluated on the basis of Kramers' theory. Based on this we propose that the reaction rate of this conformational transition is regulated by the internal molecular friction, which can be specifically modulated by mutagenesis in the hinge region.     

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.     

Kinetic studies on beta-site amyloid precursor protein-cleaving enzyme (BACE). Confirmation of an iso mechanism

The steady-state kinetic mechanism of beta-amyloid precursor protein-cleaving enzyme (BACE)-catalyzed proteolytic cleavage was evaluated using product and statine- (Stat(V)) or hydroxyethylene-containing (OM99-2) peptide inhibition data, solvent kinetic isotope effects, and proton NMR spectroscopy. The noncompetitive inhibition pattern observed for both cleavage products, together with the independence of Stat(V) inhibition on substrate concentration, suggests a uni-bi-iso kinetic mechanism. According to this mechanism, the enzyme undergoes multiple conformation changes during the catalytic cycle. If any of these steps are rate-limiting to turnover, an enzyme form preceding the rate-limiting conformational change should accumulate. An insignificant solvent kinetic isotope effect (SKIE) on k(cat)/K(m), a large inverse solvent kinetic isotope effect on k(cat), and the absence of any SKIE on the inhibition onset by Stat(V) during catalysis together indicate that the rate-limiting iso-step occurs after formation of a tetrahedral intermediate. A moderately short and strong hydrogen bond (at delta 13.0 ppm and phi of 0.6) has been observed by NMR spectroscopy in the enzyme-hydroxyethylene peptide (OM99-2) complex that presumably mimics the tetrahedral intermediate of catalysis. Collapse of this intermediate, involving multiple steps and interconversion of enzyme forms, has been suggested to impose a rate limitation, which is manifested in a significant SKIE on k(cat). Multiple enzyme forms and their distribution during catalysis were evaluated by measuring the SKIE on the noncompetitive (mixed) inhibition constants for the C-terminal reaction product. Large, normal SKIE values were observed for these inhibition constants, suggesting that both kinetic and thermodynamic components contribute to the K(ii) and K(is) expressions, as has been suggested for other iso-mechanism featuring enzymes. We propose that a conformational change related to the reprotonation of aspartates during or after the bond-breaking event is the rate-limiting segment in the catalytic reaction of beta-amyloid precursor protein-cleaving enzyme, and ligands binding to other than the ground-state forms of the enzyme might provide inhibitors of greater pharmacological relevance.     

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.     

Speed of Conformational Change: Comparing Explicit and Implicit Solvent Molecular Dynamics Simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.     

Viscosity dependence of ethidium-DNA intercalation kinetics

The kinetics of ethidium intercalation into double-stranded poly[d(G-C)] were investigated by use of repetitive pressure-jump chemical relaxation at 20 degrees C in low ionic strength (0.1 M NaCl) aqueous buffers containing either glycerol or methanol. The viscosity of the various solvents differed by more than an order of magnitude while other physical properties (e.g., dielectric constant) remained approximately constant. The single-reciprocal kinetic relaxation time (tau -1) increases linearly with DNA concentration. The observed association rate constant is lower in all organic-aqueous mixtures than in water and is inversely proportional to the viscosity. These results provide evidence for an additional step in the intercalation mechanism which is identified as an obligatory DNA conformational change preceding ethidium intercalation. From the data presented, the equilibrium constant of this local conformational change is approximately 10(-3), i.e., greatly favoring the structure incapable of intercalation. The corresponding kinetics were not directly determined; however, in order to be consistent with all of the data the forward and/or reverse rate constants of the conformational change must be larger than the rate of the intercalation reaction. Thus, it is proposed that the rate of the conformational change back to the nonintercalating B-DNA structure is greater than approximately 500 s-1, implying a rate of opening greater than approximately 0.5 s-1, in agreement with other hydrogen exchange and NMR data. The observed overall rate constant for the dissociation of ethidium is inversely proportional to the solvent density, possibly reflecting a dependence on the solvent free volume. The overall volume change of intercalation is less negative in the organic-aqueous solvent mixtures than in water.     

Effect of solution viscosity on intramolecular electron transfer in sulfite oxidase

Our previous studies have shown that the rate constant for intramolecular electron transfer (IET) between the heme and molybdenum centers of chicken liver sulfite oxidase varies from approximately 20 to 1400 s(-1) depending upon reaction conditions [Pacheco, A., Hazzard, J. T., Tollin, G., and Enemark, J. H. (1999) J. Biol. Inorg. Chem. 4, 390-401]. These two centers are linked by a flexible polypeptide loop, suggesting that conformational changes, which alter the Mo-Fe distance, may play an important role in the observed IET rates. In this study, we have investigated IET in sulfite oxidase using laser flash photolysis as a function of solution viscosity. The solution viscosity was varied over the range of 1.0-2.0 cP by addition of either polyethylene glycol 400 or sucrose. In the presence of either viscosogen, an appreciable decrease in the IET rate constant value is observed with an increase in the solvent viscosity. The IET rate constant exhibits a linear dependence on the negative 0.7th power of the viscosity. Steady-state kinetics and EPR experiments are consistent with the interpretation that viscosity, and not other properties of the added viscosogens, is responsible for the dependence of IET rates on the solvent composition. The results are consistent with the role of conformational changes on IET in sulfite oxidase, which helps to clarify the inconsistency between the large rate constant for IET between the Mo and Fe centers and the long distance (approximately 32 A) between these two metal centers observed in the crystal structure [Kisker, C., Schindelin, H., Pacheco, A., Wehbi, W., Garnett, R. M., Rajagopalan, K. V., Enemark, J. H., and Rees, D. C. (1997) Cell 91, 973-983].     

Conformational dynamics and solvent viscosity effects in carboxypeptidase-A-catalyzed benzoylglycylphenyllactate hydrolysis

We have used a new approach to the dynamics of hydrolytic metalloenzyme catalysis based on investigations of both external solvent viscosity effects and kinetic 2H isotope effects. The former reflects solvent and protein dynamics, and the nuclear reorganization distribution among damped protein motion and intramolecular friction-free nuclear motion. The isotope effect represents proton tunnelling and reorganization in the hydrogen bond network around the active site. We illustrate the approach by new spectrophotometric and pH-titration data for carboxypeptidase-A-catalyzed benzoylglycyl-L-phenyllactate hydrolysis. This substrate exhibits both a significant inverse fractional power law viscosity dependence over wide ranges controlled by glycerol and sucrose, and a kinetic 2H isotope effect of 1.65. The analogous benzoylglycylphenylalanine hydrolysis has a smaller isotope effect (1.3) and no viscosity dependence. Viscosity variation has no effect on the CD spectra in the 180-240-nm range. In terms of stochastic chemical rate theory, the data correspond to an enzyme-peptide substrate complex with a 'tight' structure protected from the solvent. In comparison, the enzyme-ester substrate complex is 'softer', strongly coupled to the solvent, and the rate-determining step is accompanied by proton transfer or by substantial reorganization in the hydrogen bonds near the active site.     

Site-specific mutagenesis of the alpha subunit of tryptophan synthase from Salmonella typhimurium. Changing arginine 179 to leucine alters the reciprocal transmission of substrate-induced conformational changes between the alpha and beta 2 subunits

Arginine 179 of the alpha subunit of tryptophan synthase of Salmonella typhimurium was changed to leucine by site-directed mutagenesis. The mutant alpha subunit was expressed in S. typhimurium, purified and crystallized as the alpha 2 beta 2 complex, and characterized by kinetic studies under steady-state reaction conditions. The rate of cleavage of indole 3-glycerol phosphate (alpha reaction) is reduced by 60% in the mutant alpha 2 beta 2 complex, whereas the rate of L-tryptophan synthesis from indole and L-serine (beta reaction) is unchanged. Thus, arginine 179 is not obligatory for catalysis, for binding of indole 3-glycerol phosphate, or for interaction of the alpha and beta 2 subunits. However, changing arginine 179 to leucine does have striking effects on ligand-dependent properties of this multienzyme complex. Ligands of the alpha subunit (DL-alpha-glycerophosphate and indole 3-propanol phosphate) which strongly inhibit the beta reaction of the native alpha 2 beta 2 complex have a slight stimulatory effect on the beta reaction of the mutant alpha 2 beta 2 complex. Likewise, L-serine, a ligand of the beta subunit which produces a 5-fold reduction in the Km for the alpha ligand indole 3-glycerol phosphate in the native alpha 2 beta 2 complex, has no effect on the mutant alpha 2 beta 2 complex. These results suggest that arginine 179 of the alpha subunit plays a role in the reciprocal transmission of substrate-induced conformational changes which occur between native alpha and beta 2 subunits in the alpha 2 beta 2 complex.     

Crystallographic binding studies with triosephosphate isomerases: conformational changes induced by substrate and substrate-analogues.

TIM catalyses the interconversion of a triosephosphate aldehyde into a triosephosphate ketone. This is a simple chemical reaction in which only protons are transferred. The crystallographic studies of TIM from chicken, yeast and trypanosome complexed with substrate and substrate analogues are discussed. The substrate binds in a deep pocket. On substrate binding, large conformational changes are induced in three loops. As a result of these conformational changes in the liganded structure, the active site pocket is sealed off from bulk solvent and the sidechain of the catalytic glutamate becomes optimally positioned for catalysis.     

Diffusion-limited rates for monoclonal antibody binding to cytochrome c.

The kinetic and spectroscopic changes accompanying the binding of two monoclonal antibodies to the oxidized form of horse heart cytochrome c have been investigated. The two epitopes recognized by the antibodies are distinct and noninteracting: antibody 2B5 binds to native cytochrome c near a type II turn (residue 44) while antibody 5F8 binds on the opposite face of the protein near the amino terminus of an alpha-helical segment (residue 60). Antibody-cytochrome c binding obeys a simple bimolecular reaction mechanism with second-order rate constants approaching those expected for diffusion-limited protein-protein interactions. The association rate constants have small activation enthalpies and are inversely dependent on solvent viscosity, as expected for diffusion-controlled reactions. There is a moderate ionic strength dependence of the rate of association between the 2B5 antibody and cytochrome c, with the rate constant increasing about 4-fold as the ionic strength is varied between 0.14 and 0 M. Comparison of the rates for antibody-cytochrome c complex formation for binding to the reduced-native, oxidized-native, and alkaline conformations shows that for MAb 2B5 the forward rate constant depends slightly on cytochrome c conformation. Investigation of the pH-induced transition between the native and alkaline conformational states for free cytochrome c and for antibody-cytochrome c complexes shows that antibody binding stabilizes the native form of the protein.(ABSTRACT TRUNCATED AT 250 WORDS)     

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Enzyme catalysis evolved in an aqueous environment. The influence of solvent dynamics on catalysis is, however, currently poorly understood and usually neglected. The study of water dynamics in enzymes and the associated thermodynamical consequences is highly complex and has involved computer simulations, nuclear magnetic resonance (NMR) experiments, and calorimetry. Water tunnels that connect the active site with the surrounding solvent are key to solvent displacement and dynamics. The protocol herein allows for the engineering of these motifs for water transport, which affects specificity, activity and thermodynamics. By providing a biophysical framework founded on theory and experiments, the method presented herein can be used by researchers without previous expertise in computer modeling or biophysical chemistry. The method will advance our understanding of enzyme catalysis on the molecular level by measuring the enthalpic and entropic changes associated with catalysis by enzyme variants with obstructed water tunnels. The protocol can be used for the study of membrane-bound enzymes and other complex systems. This will enhance our understanding of the importance of solvent reorganization in catalysis as well as provide new catalytic strategies in protein design and engineering.     

Evidence for preorganization of the glmS ribozyme ligand binding pocket

We have examined the tertiary structure of the ligand-activated glmS ribozyme by a combination of methods with the aim of evaluating the magnitude of RNA conformational change induced by binding of the cofactor, glucosamine 6-phosphate (GlcN6P). Hydroxyl radical footprinting of a trans-acting ribozyme complex identifies several sites of solvent protection upon incubation of the RNA in Mg(2+)-containing solutions, providing initial evidence of the tertiary fold of the ribozyme. Under these folding conditions and at GlcN6P concentrations that saturate the ligand-induced cleavage reaction, we do not observe changes to this pattern. Cross-linking with short-wave UV light of the complex yielded similar overall results. In addition, ribozyme-substrate complexes cross-linked in the absence of GlcN6P could be gel purified and then activated in the presence of ligand. One of these active cross-linked species links the base immediately 3' of the cleavage site to a highly conserved region of the ribozyme core and could be catalytically activated by ligand. Combined with recent studies that argue that GlcN6P acts as a coenzyme in the reaction, our data point to a riboswitch mechanism in which ligand binds to a prefolded active site pocket and assists in catalysis via a direct participation in the reaction chemistry, the local influence on the geometry of the active site constituents, or a combination of both mechanisms. This mode of action is different from that observed for other riboswitches characterized to date, which act by inducing secondary and tertiary structure changes.     

Solvent Friction Changes the Folding Pathway of the Tryptophan Zipper TZ2

Because the rate of a diffusional process such as protein folding is controlled by friction encountered along the reaction pathway, the speed of folding is readily tunable through adjustment of solvent viscosity. The precise relationship between solvent viscosity and the rate of diffusion is complex and even conformation-dependent, however, because both solvent friction and protein internal friction contribute to the total reaction friction. The heterogeneity of the reaction friction along the folding pathway may have subtle consequences. For proteins that fold on a multidimensional free-energy surface, an increase in solvent friction may drive a qualitative change in folding trajectory. Our time-resolved experiments on the rapidly and heterogeneously folding β-hairpin TZ2 show a shift in the folding pathway as viscosity increases, even though the energetics of folding is unaltered. We also observe a nonlinear or saturating behavior of the folding relaxation time with rising solvent viscosity, potentially an experimental signature of the shifting pathway for unfolding. Our results show that manipulations of solvent viscosity in folding experiments and simulations may have subtle and unexpected consequences on the folding dynamics being studied.     

Correlated conformational fluctuations during enzymatic catalysis: Implications for catalytic rate enhancement

Correlated enzymatic conformational fluctuations are shown to contribute to the rate of enhancement achieved during catalysis. Cytidine deaminase serves as a model system. Crystallographic temperature factor data for this enzyme complexed with substrate analog, transition-state analog, and product are available, thereby establishing a measure of atomic scale conformational fluctuations along the (approximate) reaction coordinate. First, a neural network-based algorithm is used to visualize the decreased conformational fluctuations at the transition state. Second, a dynamic diffusion equation along the reaction coordinate is solved and shows that the flux velocity through the associated enzymatic conformation space is greatest at the transition state. These results suggest (1) that there are both dynamic and energetic restrictions to conformational fluctuations at the transition state, (2) that enzymatic catalysis occurs on a fluctuating potential energy surface, and (3) a form for the potential energy. The Michaelis-Menten equations are modified to describe catalysis on this fluctuating potential energy profile, leading to enhanced catalytic rates when fluctuations along the reaction coordinate are appropriately correlated. This represents a dynamic tuning of the enzyme for maximally effective transformation of the ES complex into EP.