Quantitative Interpretation Of Partial Specific Volumes

We commence this section by summarizing the traditional interpretation of partial specific volume measurements in terms of protein solvation 9,11-20 . Since this subject is the topic of Chapter 11, however, the approach is only treated in sufficient detail to allow direct comparisons to be made with the interpretation based on the statistical-mechanical concept of excluded volume. We shall restrict our discussion to cases where the solvent and solution are incompressible, this being a very good...

References

Problems of Biological Physics. Moscow, Nauka (1977) (in Russian). 2. Chernavskaya, N. M., and Chernavskii, D. S. Tunnel Electron Transport in Photosynthesis. Moscow, Moscow Univ. Press (1977) (in Russian). 3. Volkenstein, M. V. Molecular Biophysics. Moscow, Nauka (1975) (in Russian). 4. Austin, R. M., Beeson, K. W., Eisenstein, L., Frauenfelder, H., and Cunsalus, I. E. Dynamics of ligand binding to myoglobin. Biochemistry 14 5355-5373 (1975). 5. Shaitan, K. V., and Rubin, A....

Hemoglobin as a Knot Free Matrix Protein

The mixed character of the first and third oxygenation states satisfies the requirements for molecular resonance the protein fluctuates between the two spin states of equal free energy. Takashima and Lumry 114 did indeed find resonance effects at 25 and 75 oxygenation in dielectric-relaxation studies, but their results have been challenged. Battistel et al. 115 found a large heat capacity spike consistent with two-state behavior near 25 oxygenation on varying oxygenation at constant...

Permeability of Proteins

That there are only three fi-factor groups, and thus three major substructures in the proteins we have examined, is not obvious from the B factors. Rather, it has been established by the finding in proton-exchange experiments that the site rate constants for exchange fall into three well-separated groups 5 . The B-factors and proton-exchange data give somewhat similar information but in different forms. The two are particularly powerful sources of information about conformational dynamics. B...

Direct Site Occupancy Measurements Cannot Define the Thermodynamic Interaction

This discussion permits us to approach now the relation between thermodynamic interaction and experimentally measured binding at sites. Protein-ligand contacts can be measured by a number of nonthermodynamic techniques that report the site occupancy by a specific ligand. This can be the perturbation of a spectral property of the protein or of the ligand, for example, UV absorption of fluorescence. It can also be the evolution or absorption of heat measured by microcalorimetry. Careful...

M

Where om, the partition coefficient pertaining to solute concentration C , may be determined experimentally by frontal gel chromatography 50 from the relationship 51,52 V denotes the median bisector of the elution profile from a frontal gel chromatography experiment with applied solute concentration C on a column with void volume Vo and total accessible volume Vt. The activity coefficients of the solute Eq. (10) in the mobile (a) and stationary (P) phases are given by where the additional term...

General Basis of the Phenomenon

Because of the mutual cancellation of thermal terms in free-energy changes, enthalpy and entropy changes tend to have the same sign and same proportionate changes. This cancellation is exact and a rigorous consequence of thermodynamics but since thermal terms are only parts of H or U and S, the totals of the latter do not demonstrate the tendency exactly. This important consequence of Benzinger's discovery is not experimentally obvious in gas-phase primary bond rearrangements because the...

Info

Figure 8 Schematic representation of mechanisms of cosolvent exclusion that are independent of the chemical nature of the protein surface. (A) Steric exclusion Re, the radius of the cosolvent, being much greater than that of water, a shell with volume Vs is created around the protein. This shell being enriched with water, the observation is preferential exclusion of the cosolvent. (B) Solvent component distribution at an interface due to the perturbation of the surface tension of water (a) by...

Identification And Coverage Of Sorption Sites And Some Critical Hydration Levels In The Sorption Isotherm

There has been some debate as to the sites of water sorption and the extent of coverage, particularly with regard to the participation of sites along the polypeptide backbone. Even the amount of bound water has been difficult to define unambiguously. The physical properties of water interacting with proteins have been studied with a variety of techniques, including dielectric relaxation methods (see Chapter 4), infrared and NMR spectroscopy, Rayleigh scattering of Mossbauer radiation (RSMR)...

Conclusions

With more than 500 protein structures determined to date, many refined at high resolution, the protein structure database 106 offers a rich resource for visualizing protein-solvent interactions. Internal solvent molecules, integral to the protein structure and stability, are clearly defined and highly conserved in related structures. The same also applies to some tightly bound solvent molecules, occupying surface pockets and crevices, and solvent molecules in active sites or binding pockets can...

Examples Of Partial Compensation

Figure 5 shows an example of partial compensation based on the binding of a series of cations by gramicidin A 8 , This linear polypeptide was dispersed in lipid lysophosphocholine, thereby causing the gramicidin chains to fold into structures that contain channels that specifically bind cations from aqueous solution. In the figure, the cations are arranged so that the strength of binding, as measured by AG , increases from left to right. AH and T AS always have the same sign but differ in...

Free Volume and Dielectric Constant

Protein conformations and their properties are, of course, determined by the electrostatic fields and their changes as much as by entropy. The adjustability of local dielectric constants is one of the major benefits of the discovery of proteins. All electrostatic interactions are increased by lowering the effective dielectric constant, and the lower the latter, the larger the change. The dielectric constant decreases because the mobility of the groups with permanent polarization is reduced. So...

The Anatomy of an Enzyme

The HIV-1 protease is a good model enzyme structure since in this elegant molecule the catalytic mechanism is virtually obvious from the construction of the protein. The HIV-1 protease consists of two functional domains, which in this enzyme are two identical proteins. The several structural features required for the catalytic mechanism and their organization are shown in Fig. 14. The two proteins are joined at the base by residues at the C-terminal ends, which produce the strong hinge by the...

Modular Construction of Knot Matrix Proteins

It is now apparent that proteins in this class are constructed by combining substructures. Evolution has a family of knots to use in new experiments and also a broader and more variable family of matrices. The elementary unit is the functional domain defined in a broad way by its knot and in a most specific way by its matrix and surface. Much of evolution consists of experiments in which matrix and surface modifications are tested for acceptance or rejection, but the experiments are roughly of...

Atom Number

Figure 4 Single-atom B factors for bovine pancreatic trypsin inhibitor B factor plot. All named residues are highly conserved. The six half-cystines form three disulfide bonds but nearby residues are not conserved and have variable B values depending on the crystal form. The three small clusters that combine into the single primary knot are each strongly stabilized by dispersion forces among aromatic residues and they combine by strong hydrogen bonds. The plot shows a distinct palindromic...

The Internal Barriers

The solvent effects on the internal transitions B A and B M are small compared with what is found for the entry-release mechanism (Fig. 4). Figure 7 illustrates this statement for structural relaxation rates bm- The figure also shows the solvent relaxation rates (75 glycerol-water) for comparison. The temperature dependence and, thus, the activation energies are entirely different. Furthermore, below 200 K the solvent dynamics is slower than the protein conformational change. The protein...

Cocrystallization Of Proteins With Inorganic And Organic Ionic Ligands

Crystallization of many proteins actually is often cocrystallization it requires an added ligand. A requirement for a cocrystallizing ligand usually is first seen in experimental screening attempts to get the first crystals and seeds. Ammonium sulfate normally is regarded as a salting-out agent, which includes its behavior as an electrolyte, as an exclusion agent akin to what neutral polymers do, and as a solvent component affecting the activity of water 41 . Part of its overall role may be...

Effective Thermodynamic Radii Of Globular Proteins

In most studies of thermodynamic nonideality in protein solutions, the stance has been taken that the Stokes radius of a globular protein provides a reasonable estimate of its effective hydrated radius for use in covolume calculations 21,22,47-49,53-58 , As noted elsewhere 59 , there would be no theoretical objection to this substitution of a hydrodynamic parameter for a thermodynamic quantity if the protein were in fact an impenetrable sphere. Since, however, the Stokes radius of a protein...

Palindromic Patterns in the Polypeptide Chains of Some Enzymes

The palindromic pattern is found in the B factors for those enzymes formed as a result of an ancient gene doubling. When the functional domains are separate protein units, their B-factor palindrome is a natural consequence of the residue palindrome since the two proteins always seem to be connected at either their C-terminal or their N-terminal regions. When both functional domains are on the same single polypeptide chain, there is no corresponding palindromic pattern in the residues, rather...

Direct And Indirect Interactions

We now return to the folding reaction (Eq. (3)), with the understanding that U and F are represented by one configuration each (this is case (a) discussed in the preceding section.) In this case, we can fix the position and orientation of the molecule. The total change in the Gibbs energy is AG(U F) At (U -> F) + 8G(U -> F) (29) Since the molecules are devoid of translational and rotational degrees of freedom, the quantity A U on the rhs of Eq. (29) is simply the change in the potential...

The Surface Barrier

In aqueous solutions, nearly all dissociated ligands escape to the solvent at physiological temperatures, Ns 0.96 (Fig. 2a). the barrier at the surface is therefore small compared with the internal barriers. In partially hydrated films, however, Ns is much reduced (Fig. 2b). Figure 4 shows the CO binding kinetics of a myoglobin film initially hydrated to 0.25 g g that is exposed to a gentle vacuum. Both the amplitude, Ns, and the recombination rate of S + L A decrease in similar proportion with...

A

Figure 2 Appearance of solvent molecules in electron density maps, from the x-ray structure analysis of azurin at 1.8 A resolution 21 . Maps shown are (a) a difference map with coefficients F0 - Fc and (b) a 2F0 - Fc map. Peaks 1, 2, and 3 are present in both maps and are probable new, discrete solvents sites. Peaks 4 and 5 are present only in the F0 - F0 map (a) and are more doubtful. The peak labeled S proved to be a sulfate ion, bound to the side chain of His 83. Peaks 6 and 7 were already...

W

Where Cp is the experimental heat capacity of the protein-water system, Cp,i is the partial specific heat capacity of pure liquid water (component 1), h is the hydration of the protein in g water g protein, and wi h ( 1 + h) and W2 1 (1 + h) are the mass fractions of water and protein, respectively. Yang and Rupley 36 identified four regions that they assigned to the coverage of chemically different classes of sorption site. Region I (dilute solution to 0.38 h) corresponds to the addition of...

Brownian Dynamics

The Brownian theory is an ingenious way of describing the dynamic interaction between a particle and its surrounding medium. Viewing this medium as a viscous continuum enables one to introduce viscosity as a friction-related property of the system. The extension of the picture to the atomic scale elicits conceptual difficulties, which are probably associated with the deviations from the ideal behavior observed experimentally. This section is concerned with basic concepts of Brownian dynamics...

Quantum Thermodynamics

As can be seen in Table 1, the total entropies of formation and their motive parts are inversely related to the strength of the metal lattice. This is a consequence of the quantum nature of vibrational excitation, which requires use of the correct partition function rather than that for the classic limit. In applying Benzinger's discovery to a model system of harmonic oscillators, Rhodes discusses in detail this quantum feature of thermodynamics 90 . It can certainly be important for processes...

Ionbinding Thermochemistry

Inorganic salting out, inasmuch as it involves binding inorganic ions, particularly anions, to proteins, is a form of coprecipitation, and when crystals are obtained, of cocrystallization. The MCC technique partly parallels conventional inorganic salting out use of organic ions instead of inorganic ions for the same ultimate purpose coprecipitation and cocrystallization to isolate proteins. For both approaches, it would be helpful to have new and improved thermodynamic data. Heat conduction...

Salt Counterion Contraction Of Proteins From Acidexpanded Conformation

Acid unfolding and expansion of proteins is the leading example of how low-pH charging of proteins imposes physicochemical changes on the macromolecules. There are some uncoiling constraints, notably disulfide cross-links that prevent complete swelling to random coils. Major expansion occurs, however, with added hydration and penetration by water. Macromolecule expansion relieves excess electrostatic free energy, and repulsion between charged side chains. In low ionic strengths, 0.01-0.15,...

How Transfer Free Energy Modulates Protein Reactions

As shown by Eq. (1), the effect of cosolvent on a reaction in a solvent of a given composition is defined by the change in preferential binding of the cosolvent to the protein during the course of the reaction. Its effect relative to water is given by the difference between the transfer free energies in the two end states of the reaction. Examination of a large number of cosolvents by dialysis equilibrium has shown that all of the stabilizing and salting out agents are preferentially excluded...

The Conformation Coordinate for Catalysis

Figure 16 led first to the recognition of a single conformational process underlying the catalytic function of chymotrypsin and trypsin, but the description of this process as an expansion-contraction of conformation has become well established only recently using B-factor data to compare free enzymes with their substrate and inhibitor complexes. Several kinds of intermediate states are possible in these complexes and it is not always easy to tell the pertinent class of an example. Those...

Es e2es e1Q

Can be taken as a measure of the polarizability of the protein-water system, and this is plotted as a function of the number of bound water molecules N in Fig. 4 for the cases of lysozyme and cytochrome c. The straight lines shown in Fig. 4 represent the gradient expected if the protein-bound water exhibits its full dipole moment (as normal bulk water) with m 1.84 D. For hydrations up to 32 water molecules per lysozyme molecule, the factor (e) is relatively insensitive to the degree of...

Phosphorescence Fluorescence and Circular Dichroism

Some proteins demonstrate high phosphorescence yields, usually indole phosphorescence, when fully hydrated and at ordinary temperatures. This is unusual behavior in an ostensibly nonrigid physical system since internal conversion of triplet states is very sensitive to motion and to paramagnetic quenchers such as oxygen. In the absence of such quenchers, a variety of shorter-lived triplet states are demonstrated by new phosphorescence emission. As a probe of both local dynamics and the diffusion...

Acknowledgments

Many of the ideas developed in this chapter evolved through innumerable discussions with Dr. Rufus Lumry. He has been a constant source of inspiration and encouragement, and I am indebted to him. Special thanks are also due to Dr. Stephen Provencher for his advice over the years in the application and development of CONTIN, which has been so important to the analysis and interpretation of our hydrogen exchange and positron lifetime data. Thanks are also due to Dr. Frederick Walz for many...

Relation Between Preferential Interactions And Transfer Free Energy

Thermodynamic Definition of Binding As discussed above, the effect of a cosolvent on a chemical reaction can be expressed through the change either in preferential interactions or in the transfer free energy during the course of the reaction. The first has as reference state the solution of the given composition, the second pure water. Therefore, the change in preferential binding tells the direction in which a cosolvent will displace an equilibrium at the given cosolvent concentration at...

The Discovery of Knots and Matrices

As already mentioned, in 1981 Gregory was able to extract the probability-density functions for the proton exchange rate constants by using Provencher's numerical method for Laplace transforms. With the isotopic exchange data for HEW lysozyme in free solution, he found the probability-density function (pdf) to have the three peaks 5 shown in Fig. 2. This characteristic of the pdf has been confirmed by proton-exchange data for some other proteins, but its generalization now depends primarily on...

Genetic Conservation of Knots

Perhaps the strongest support for the knot concept comes from comparisons of the sequences of proteins from the same family. So long as the proteins have a common ancestry, their knots are the same or very nearly so since the few such residue differences we have so far found are like-for-like exchanges, such as tyrosine for phenyalanine. Insertions and deletions produce large changes in matrices and surfaces, but in enzymes demonstrating palindromy, the spacing of the knot residues along the...

Variability Among Group I Clusters

Thus far three qualitatively different classes of group I clusters have appeared. The first is typified by the clusters of the trypsin proteases in which a large fraction of group I atoms are on residues located sequentially along the peptide. The helix Figure 5 Atoms with group i Bfactors in bovine pancreatic trypsin inhibitor (pictorial presentation). Atoms with group I B factors are shown as van der Waals spheres. In addition to the conserved residues, which also are in group I for...

Reliability of Deductions from B Factors

The Debye-Waller factors, henceforth to be called B factors, determined in x-ray-diffraction studies of protein crystals, provides a wealth of information about the construction of proteins as well as invaluable information about conformational dynamics. They are calculated for each nonhydrogen atom from the dispersion of the x-ray scattering and can be simply converted to the mean-square displacement of an atom (the positional variance) from an ideal lattice point in the crystal lattice, jjl2....

Evaluation from Protein Small Solute Covolume

The use of partial specific volume measurements to characterize thermodynamic nonideality reflecting the interaction of protein with small solute has already been described in Sec. III. We therefore restrict methodological discussion here to other methods that may also be used to evaluate the second virial coefficient Bam- 1. Determination by Equilibrium Dialysis or Gel Chromatography Provided that the dialysis membrane or gel chromatographic matrix is chosen to confine the protein to one...

Protein Isomerization

We have established the formal equivalence of the interpretations of thermodynamic nonideality based on preferential solvation and excluded volume concepts, and we have also indicated ways of evaluating parameters required for application of the latter. It therefore remains to substantiate the inference that statistical-mechanical interpretation is the more rewarding, for example, in predicting and employing to advantage the effects of thermodynamic nonideality as a probe for detecting and...

Virial Coefficients From Density Measurements

There have been many studies in which partial specific volume measurements have been used in conjunction with equilibrium dialysis to establish generality of the concept that the protein domain is preferentially occupied by solvent at the ex- pense of small inert solutes 9,11-20 . We now reassess that literature by reverting to a more fundamental thermodynamic parameter, viz., the second virial coefficient Bam, as a means of describing the nonideality of protein solutions effected by the...

Viscosity Effect

Solvent viscosity can be modified, under isothermal conditions, by adding viscous cosolvents. In that way, kinetic coefficients could be studied, as a function of the solvent viscosity, for a variety of biochemical and other reaction systems. The relation between viscosity and free volume in densed liquids, discussed in Sec. II, suggests ultrasonic absorption that probes volume-dependent structural dynamics could be a valuable tool in studying the solvent viscosity effects. These topics are...

Effect Of Hydration On Protein Dynamics

A variety of techniques have been employed to examine the effect of hydration on the dynamic properties of the protein and of water at the protein surface. The results of studies employing dielectric relaxation and Rayleigh scattering of Moss-bauer radiation (RSMR) are described in other chapters of this book. Rupley and Careri 3 have recently provided an extensive review of the literature in this field. In many cases, the critical hydration levels found with time-averaged properties are also...

Matrix Coprecipitate

Figure 3 Molecular basis of MCC, matrix coprecipitation-cocrystallization. Organic ion ligands force a tightened conformation on proteins in solution to which they bind. Ligands able to stack using their hydrophobic tails form a matrix and pull the reactions from the right by coprecipitating out product. If the system is well ordered, the product may be cocrystalline 52 , from 25,000 to 40,000 M l cm-1. Their coprecipitates with proteins are easy to analyze for ligand contents, giving vcoppt....

[ 3mt m1 dmA mi i dy 187127pn mj dm2Jr m3

Binding Is Replacement of Water by Ligand at a Site The result that, at dialysis equilibrium, the interaction of the protein with the mixed solvent, expressed as interaction with component 3, can be favorable or unfavorable follows because the amount of water and ligand found in the immediate domain of the protein is defined by the relative affinities of water and ligand for the protein. By definition, in an aqueous medium, the binding of one molecule of ligand to a site on a protein...

Glass Transitions In Proteins

Expansivity Glass

The idea that water acts as a plasticizer of the protein conformation is not new it was suggested many years ago by Bone and Pethig 102 on the basis of dielectric relaxation studies (see Chapter 4). In recent years, several studies of fully hydrated proteins and protein crystals also have indicated the existence of a glasslike dynamical transition at about 200 K in proteins. It is well known that glass transition temperatures for synthetic polymers decrease with increases in plasticizer...

Introduction

It has long been recognized that protein-water interactions play an important role in the determination and maintenance of the three-dimensional structure of proteins. Quite apart from its fundamental importance and interest, knowledge of processes occurring on hydration or dehydration of proteins is also important in biotechnological applications of proteins, such as their use as catalysts in anhydrous organic solvents, the stabilization of protein preparations for pharmaceutical use, and in...