Viscosity and transient solvent accessibility of Trp-63 in the native conformation of lysozyme

Evolution of the concept of conformational dynamics of enzyme functions over half of a century: A personal view

To most physicists, it was always evident that conformational fluctuation is an inherent property of all molecules. Its existence in proteins was mentioned first by Linderström-Lang and Schellman in 1959 based on their hydrogen-deuterium exchange experiments. The "induced fit" mechanism to explain ligand-induced conformational changes was suggested by Koshland in 1958. Straub combined these two concepts in his "fluctuation fit" theory in 1964. The era of protein X-ray crystallography imposed a static view of protein structures. With proteins becoming accessible to NMR analysis, conformational dynamics could be mapped, and a new wave of dynamic interpretation of enzymatic catalysis and molecular recognition appeared. Energy landscapes, energy funnels, conformational selection, conformational distribution shifts are now frequent terms in interpreting biomolecular recognition and enzymatic catalysis. All these interpretations are based on the concept that evolution uses the conformational fluctuations of enzymes to develop efficient and dynamic catalytic machines. In a resurrection of the original "fluctuation fit" concept, it is generally recognized now that spatial and temporal events of catalysis are equally important to describe its mechanism. This special issue, dedicated to the memory of Henryk Eisenberg, prompted us to look back at the last 50 years of development of a concept that-like other important concepts-appeared, evolved and became accepted during the period covered by the scientific lifespan of Henryk.

Viscosity Dependence of Some Protein and Enzyme Reaction Rates: Seventy-Five Years after Kramers

Kramers rate theory is a milestone in chemical reaction research, but concerns regarding the basic understanding of condensed phase reaction rates of large molecules in viscous milieu persist. Experimental studies of Kramers theory rely on scaling reaction rates with inverse solvent viscosity, which is often equated with the bulk friction coefficient based on simple hydrodynamic relations. Apart from the difficulty of abstraction of the prefactor details from experimental data, it is not clear why the linearity of rate versus inverse viscosity, k ∝ η(-1), deviates widely for many reactions studied. In most cases, the deviation simulates a power law k ∝ η(-n), where the exponent n assumes fractional values. In rate-viscosity studies presented here, results for two reactions, unfolding of cytochrome c and cysteine protease activity of human ribosomal protein S4, show an exceedingly overdamped rate over a wide viscosity range, registering n values up to 2.4. Although the origin of this extraordinary reaction friction is not known at present, the results indicate that the viscosity exponent need not be bound by the 0-1 limit as generally suggested. For the third reaction studied here, thermal dissociation of CO from nativelike cytochrome c, the rate-viscosity behavior can be explained using Grote-Hynes theory of time-dependent friction in conjunction with correlated motions intrinsic to the protein. Analysis of the glycerol viscosity-dependent rate for the CO dissociation reaction in the presence of urea as the second variable shows that the protein stabilizing effect of subdenaturing amounts of urea is not affected by the bulk viscosity. It appears that a myriad of factors as diverse as parameter uncertainty due to the difficulty of knowing the exact reaction friction and both mode and consequences of protein-solvent interaction work in a complex manner to convey as though Kramers rate equation is not absolute.

Internal friction in enzyme reactions

The empirical concept of internal friction was introduced 20 years ago. This review summarizes the results of experimental and theoretical studies that help to uncover the nature of internal friction. After the history of the concept, we describe the experimental challenges in measuring and interpreting internal friction based on the viscosity dependence of enzyme reactions. We also present speculations about the structural background of this viscosity dependence. Finally, some models about the relationship between the energy landscape and internal friction are outlined. Alternative concepts regarding the viscosity dependence of enzyme reactions are also discussed.

Temperature derivative spectroscopy to monitor the autoxidation decay of cytochromes P450

Temperature derivative spectroscopy (TDS), a type of relaxation spectroscopy, is a powerful tool to study protein dynamics (Berendzen, J.; Braunstein, D. Proc. Natl. Acad. Sci. U. S. A. 1990, 87, 1). We developed the version of temperature derivative spectroscopy to monitor kinetics of autoxidation of cytochromes P450 and applied it to study the properties of the oxy-ferrous complex of a human membrane bound P450, CYP19A1 (aromatase), and that of a bacterial soluble P450, CYP101 when bound with their most common substrates, androstenedione (AD) and camphor, respectively. TDS extends the panel of methods that can be used to monitor heme protein kinetics, providing a rapid measurement technique and enabling measurement of the autoxidation rate over a wide range of temperatures, yielding the activation energy as well as absolute reaction rate in a single experiment.

Thermodynamics of nucleotide binding to actomyosin V and VI: a positive heat capacity change accompanies strong ADP binding

We have measured the energetics of ATP and ADP binding to single-headed actomyosin V and VI from the temperature dependence of the rate and equilibrium binding constants. Nucleotide binding to actomyosin V and VI can be modeled as two-step binding mechanisms involving the formation of collision complexes followed by isomerization to states with high nucleotide affinity. Formation of the actomyosin VI-ATP collision complex is much weaker and slower than for actomyosin V. A three-step binding mechanism where actomyosin VI isomerizes between two conformations, one competent to bind ATP and one not, followed by rapid ATP binding best accounts for the data. ADP binds to actomyosin V more tightly than actomyosin VI. At 25 degrees C, the strong ADP-binding equilibria are comparable for actomyosin V and VI, and the different overall ADP affinities arise from differences in the ADP collision complex affinity. The actomyosin-ADP isomerization leading to strong ADP binding is entropy driven at >15 degrees C and occurs with a large, positive change in heat capacity (DeltaC(P) degrees ) for both actomyosin V and VI. Sucrose slows ADP binding and dissociation from actomyosin V and VI but not the overall equilibrium constants for strong ADP binding, indicating that solvent viscosity dampens ADP-dependent kinetic transitions, presumably a tail swing that occurs with ADP binding and release. We favor a mechanism where strong ADP binding increases the dynamics and flexibility of the actomyosin complex. The heat capacity (DeltaC(P) degrees ) and entropy (DeltaS degrees ) changes are greater for actomyosin VI than actomyosin V, suggesting different extents of ADP-induced structural rearrangement.

Kinetics of diffusion-assisted reactions in microheterogeneous systems

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.

Microscopic viscosity and rotational diffusion of proteins in a macromolecular environment

The Stokes-Einstein-Debye equation is currently used to obtain information on protein size or on local viscosity from the measurement of the rotational correlation time. However, the implicit assumptions of a continuous and homogeneous solvent do not hold either in vivo, because of the high density of macromolecules, or in vitro, where viscosity is adjusted by adding viscous cosolvents of various size. To quantify the consequence of nonhomogeneity, we have measured the rotational Brownian motion of three globular proteins with molecular mass from 66 to 4000 kD in presence of 1.5 to 2000 kD dextrans as viscous cosolvents. Our results indicate that the linear viscosity dependence of the Stokes-Einstein relation must be replaced by a power law to describe the rotational Brownian motion of proteins in a macromolecular environment. The exponent of the power law expresses the fact that the protein experiences only a fraction of the hydrodynamic interactions of macromolecular cosolvents. An explicit expression of the exponent in terms of protein size and cosolvent's mass is obtained, permitting definition of a microscopic viscosity. Experimental data suggest that a similar effective microviscosity should be introduced in Kramers' equation describing protein reaction rates.

Viscosity dependence of the electron transfer rate from bound cytochrome c to P840 in the photosynthetic reaction center of the green sulfur bacterium Chlorobium tepidum

Anomalous high viscosity dependence was found in the rate of reaction between the bound cytochrome c and the primary donor bacteriochlorophyll dimer (P840) of the reaction center complex purified from the green sulfur bacterium Chlorobium tepidum. The cytochrome has a primary structure with the N-terminal three membrane-spanning helices connected to the extended C-terminal heme-containing hydrophilic moiety. The rate constant of the reaction decreased from 5.0 x 10(3) s-1 to 1.0 x 10 s-1 as the glycerol concentration increased from 0 to 60% (v/v) at 295 K, showing a linear dependence on the -2.4th power of the specific viscosity. The glycerol effect was fully reversible. The extraordinary high viscosity dependence cannot be explained by the simple diffusive Brownian fluctuation model and suggests that the electron transfer mechanism is dependent on the unique conformational fluctuations of the heme-containing moiety of cytochrome c.

Kinetics and thermodynamics of phalloidin binding to actin filaments from three divergent species

We compared the kinetics and thermodynamics of rhodamine phalloidin binding to actin purified from rabbit skeletal muscle, Acanthamoeba castellanii, and Saccharomyces cerevisiae in 50 mM KCl, 1 mM MgCl2, and pH 7.0 buffer at 22 degrees C. Filaments of S. cerevisiae actin bind rhodamine phalloidin more weakly than Acanthamoeba and rabbit skeletal muscle actin filaments due to a more rapid dissociation rate in spite of a significantly faster association rate constant. The higher dissociation rate constant and lower binding affinity of rhodamine phalloidin for S. cerevisiae actin filaments provide a quantitative explanation for the inefficient staining of yeast actin filaments, compared with that of rabbit skeletal muscle actin filaments [Kron et al. (1992) Proc. Natl. Acad. Sci. U.S.A. 89, 4466-4470]. The temperature dependence of the rate constants was interpreted according to transition state theory. There is a small enthalpic difference (delta H++) between the ground states and the transition state. Consequently, the free energy of activation (delta G++) for association and dissociation of rhodamine phalloidin is dominated by entropic changes (delta S++). At equilibrium, rhodamine phalloidin binding generates a positive entropy change (delta S0). The rates of rhodamine phalloidin binding are independent of the pH, ionic strength, and filament length. Rhodamine covalently bound decreases the association rate and affinity of phalloidin for actin. The association rate constant is low for both phalloidin and rhodamine phalloidin because the filaments must undergo conformational changes (i.e. "breathe") to expose the phalloidin binding site [De La Cruz, E. M., & Pollard, T. D. (1994) Biochemistry 33, 14387-14392]. Raising the solvent microviscosity, but not the macroviscosity, dampens these conformational fluctuations, and phalloidin binding kinetics are inhibited. Yeast actin filaments bind rhodamine phalloidin more rapidly, suggesting that perhaps they are more flexible and can breathe more easily than rabbit or Acanthamoeba actin filaments.

Viscosity dependence of O2 escape from respiratory proteins as a function of cosolvent molecular weight

Laser photodissociation of respiratory proteins is followed by fast geminate recombination competing with escape of the oxygen molecule into the solvent. The escape rate from myoglobin or hemerythrin has been shown previously to exhibit a reciprocal power-law dependence on viscosity. We have reinvestigated oxygen escape from hemerythrin using a number of viscous cosolvents of varying molecular weight, from glycerol to dextrans up to 500 kDa. In isoviscous solutions, the strong viscosity dependence observed with small cosolvents is progressively reduced upon increasing the cosolvent's molecular weight and disappears at molecular weights greater than about 100 kDa. Thus, viscosity is not a suitable independent parameter to describe the data. The power of the viscosity dependence of the rate coefficient is shown here to be a function of the cosolvent's molecular weight, suggesting that local protein-solvent interactions rather than bulky viscosity are affecting protein dynamics.

Glycerol effects on protein flexibility: a tryptophan phosphorescence study

In exploring the dynamic properties of protein structure, numerous studies have focussed on the dependence of structural fluctuations on solvent viscosity, but the emerging picture is still not well defined. Exploiting the sensitivity of the phosphorescence lifetime of tryptophan to the viscosity of its environment we have used the delayed emission as an intrinsic probe of protein flexibility and investigated the effects of glycerol as a viscogenic cosolvent. The phosphorescence lifetime of alcohol dehydrogenase, alkaline phosphatase, apoazurin and RNase T1, as a function of glycerol concentration was studied at various temperatures. Flexibility data, which refer to rather rigid sites of the globular structures, point out that, for some concentration ranges glycerol, effects on the rate of structural fluctuations of alcohol dehydrogenase and RNase T1 do not obey Kramers' a power law on solvent viscosity and emphasize that cosolvent-induced structural changes can be important, even for inner cores of the macromolecule. When the data is analyzed in terms of Kramers' model, for the temperature range 0-30 degrees C one derives frictional coefficients that are relatively large (0.6-0.7) for RNase T1, where the probe is in a flexible region near the surface of the macromolecule and much smaller, less than 0.2, for the rigid sites of the other proteins. For the latter sites the frictional coefficient rises sharply between 40 and 60 degrees C, and its value correlates weakly with molecular parameters such as the depth of burial or the rigidity of a particular site. For RNase T1, coupling to solvent viscosity increases at subzero temperatures, with the coefficient becoming as large as 1 at -20 degrees C. Temperature effects were interpreted by proposing that solvent damping of internal protein motions is particularly effective for low frequency, large amplitude, structural fluctuations yielding highly flexible conformers of the macromolecule.

Viscous cosolvent effect on the ultrasonic absorption of bovine serum albumin

Protein-ligand binding and enzyme activity have been shown to be regulated by solvent viscosity, induced by the addition of viscous cosolvents. This was indirectly interpreted as an effect on protein dynamics. However, viscous cosolvents might affect dynamic, e.g., viscosity, as well as thermodynamic properties of the solution, e.g., activity of solution components. This work was undertaken to examine the effect of viscous cosolvent on the structural dynamics of proteins and its correlation with dynamic and thermodynamic solution properties. For this purpose we studied the effect of viscous cosolvent on the specific ultrasonic absorption, delta mu, of bovine serum albumin, at pH = 7.0 and at 21 degrees C, and frequency range of 3-4 MHz. Ultrasonic absorption (UA) directly probes protein dynamics related to energy dissipation processes. It was found that the addition of sucrose, glycerol, or ethylene glycol increased the BSA delta mu. This increase correlates well with the solvent viscosity, but not with the cosolvent mass concentration, activity of the solvent components, dielectric constant, or the hydration of charged groups. On the grounds of these results and previously reported findings, as well as theoretical considerations, we propose the following mechanism for the solvent viscosity effect on the protein structural fluctuations, reflected in the UA: increased solvent viscosity alters the frequency spectrum of the polypeptide chain movements; attenuating the fast (small amplitude) movements, and enhancing the slow (large amplitude) ones. This modulates the interaction strength between the polypeptide and water species that "lubricates" the chain's movements, leading to larger protein-volume fluctuation and higher ultrasonic absorption. This study demonstrates that solvent viscosity is a regulator of protein structural fluctuations.

The effect of viscosity on the accessibility of the single tryptophan in human serum albumin

When reactions take place with one of the reactants tied to protein matrix, movements along the reaction coordinate towards the transition state can become coupled to structural fluctuations of the protein matrix. This investigation aims to test the assumptions underlying the arguments supporting such a coupling. A coupling is allowed only if the activation barrier is high and broad enough as shown to be the case for the proton catalyzed isotope exchange at Trp-63 of lysozyme. In the present investigation the activation barrier for the same reaction has been lowered radically in an effort to show that the coupling, as measured by the dependence of rate on solution viscosity, will diminish and ideally vanish, despite the unchanged effects of cosolvents on the chemical activities of all the reactants. The isotope exchange rate at the indole nitrogen of the single tryptophan residue of human serum albumin was measured with UV. This residue is rigidly held to the protein surface and the solvent access, although restricted, corresponds to a partially exposed residue. As a consequence, the isotope exchange rates and the bimolecular quenching rate of fluorescence by acrylamide, also measured, are high. The experiments were carried out at pH 5.2 where the molecule is in the N-form and the exchange is catalyzed by OH- ions. The activation energy of the hydroxyl catalyzed reaction is 22 kJ lower than for the proton catalyzed process. Under these conditions the exchange rate is viscosity independent both in the case of glycerol and in ethylene glycol.(ABSTRACT TRUNCATED AT 250 WORDS)

The coupling of catalytically relevant conformational fluctuations in subtilisin BPN' to solution viscosity revealed by hydrogen isotope exchange and inhibitor binding

We have measured the tritium outexchange of subtilisin BPN'. A consistent and rather small group of hydrogens was isolated by their sensitivity to inhibitor binding. The viscosity dependence of exchange from these inhibitor protected hydrogens was then examined in 0.05 M MES buffer, pH 6.5 and 10 degrees C. The viscosity of the reaction medium was varied by added glycerol and ethylene glycol. The exchange rates were corrected to be compared at identical hydroxyl ion and water activity. The salient observation is the strikingly similar viscosity coupling behavior when compared to the deacylation step of ester hydrolysis catalyzed by the same enzyme (Ng and Rosenberg, Biophysical Chemistry, 39 (1991) 57). We have obtained a viscosity coupling constant of 0.68 -/+ 0.18 for hydrogen exchange in glycerol (cf. 0.65 -/+ 0.11 for deacylation in glycerol, sucrose, glucose and fructose); 1.67 -/+ 0.07 for outexchange (cf. 1.92 -/+ 0.09 for deacylation), in the presence of ethylene glycol. The two reactions are very chemically dissimilar, yet they show very similar viscosity coupling behavior. This together with the well established role of structural fluctuations in hydrogen exchange implies a similar role of structural fluctuations in the deacylation step of subtilisin BPN' catalyzed ester hydrolysis.

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.

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.