Peter R. Wills

Effect of inert polymers on protein self-association

In [l] polyethylene glycol (PEG) was reported to stimulate the self-association of the pyruvate dehydrogenase complex isolated from Azotobacter vinelandii. They state that the exact reasons for this phenomenon are not clear at present. It is our purpose to point out that this effect has a thermodynamic explanation in terms of the excluded volume interaction between the protein and the polymer. While we restrict our discussion to the consideration of protein self-association reactions, we refer to the detailed work in [2] on the effect of inert polymers on enzyme activity. The observation [2] that dextran promotes the inhibition of trypsin by serum albumin was interpreted in a manner consistent with the argument presented here. The biological significance of various aspects of polymer interactions has been reviewed in [3].

Direct analysis of solute self-association by sedimentation equilibrium

An improved procedure is described for the characterization of solute self-association by sedimentation equilibrium, Whereas previous statistical-mechanical approaches to allowance for the effects of thermodynamic nonideality have entailed tedious iteration because of their specification of activity coefficients in terms of the equilibrium concentrations of all species, such reliance upon knowledge of the solution composition is avoided by the adaptation of an alternative statistical-mechanical formulation [T. L. Hill and Y. D. Chen (1973) Biopolymers, Vol. 12, pp. 1285-1312 ] in which thermodynamic nonideality is expressed in terms of total solute concentration. The development of an analysis in terms of a relationship with total solute concentration as the experimental variable allows this attribute of the Adams-Fujita approach to be retained without sacrifice of statistical-mechanical rigor. Its use is illustrated by application to Rayleigh interferometric records of sedimentation equilibrium distributions reflecting α-chymotrypsin dimerization and lysozyme self-association.

Effects of thermodynamic nonideality on protein interactions. Equivalence of interpretations based on excluded volume and preferential solvation

Published results on the stabilization of proteins by sucrose (J.C. Lee and S.N. Timasheff, J. Biol. Chem. 256 (1981) 7193) have been reexamined and interpreted in terms of thermodynamic nonideality. The composition dependence of activity coefficients may be accounted for on a statistical-mechanical basis using the concept of excluded volume. An expression is derived in which the effect of sucrose on determination of the partial specific volume of a protein, previously interpreted in terms of preferential protein solvation, is also seen to be attributable to excluded volume. Gel chromatographic studies of the reversible unfolding of alpha-chymotrypsin are presented which demonstrate temperature- and sucrose-mediated changes in the effective volume of the enzyme. These measurements support the quantitative interpretation of the stabilization in terms of thermodynamic nonideality arising from the difference between covolumes for sucrose and the two isomeric states of alpha-chymotrypsin. By establishing the equivalence of the two approaches that have been used to account for the effects of inert solutes on protein transitions, the present investigation eliminates the need for any distinction between such solutes on the basis of molecular size; and also enhances greatly the potential sensitivity of thermodynamic nonideality as a means of probing protein isomerizations, since greater displacement of the equilibrium position may be effected by small rather than by macromolecular solutes present at the same weight concentrations.

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins.

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.

MEASUREMENT OF THERMODYNAMIC NONIDEALITY ARISING FROM VOLUME-EXCLUSION INTERACTIONS BETWEEN PROTEINS AND POLYMERS

The effective thermodynamic radii of 23 ribosomal proteins from the 50 S subunit have been determined by gel chromatography on Sephadex G-50, thereby supporting the contention that most of the proteins of the 50 S ribosomal unit exhibit reasonably globular structures. To investigate further the usefulness of modelling proteins as spheres, the second virial coefficient describing excluded volume interactions of some ribosomal proteins with two inert polymers, polyethylene glycol (PEG) and dextran, has been determined by gel chromatography and/or sedimentation equilibrium techniques. Protein-polymer excluded volumes obtained with PEG 20000 and Dextran T70 as the space-filling solute are shown to conform reasonably well with a quantitative expression describing interaction between an impenetrable sphere and an ideal Brownian path (K.M. Jansons and C.G. Phillips, J. Colloid Interface Sci., 137 (1990) 75).

Thermodynamic nonideality of enzyme solutions supplemented with inert solutes: yeast hexokinase revisited

Published experimental results on the activating effect of polyethylene glycol on the interaction of yeast hexokinase with glucose (R.P. Rand, N.L. Fuller, P. Butko, G. Francis and P. Nicholls, Biochemistry, 32 (1993) 5925) are reinterpreted in statistical-mechanical terms of excluded volume. Of particular interest is the ability of this standard treatment of thermodynamic nonideality to accommodate the observed non-exponential dependence of the activation upon osmotic pressure of the polyethylene glycol solution--a dependence which is not predicted by analyses based on the concept of osmotic stress that was invoked originally to account for the results.

Analysis of Sedimentation Equilibrium Distributions Reflecting Nonideal Macromolecular Associations

A rigorous statistical-mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226-2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.

Autocatalysis, Information and Coding

Autocatalytic self-construction in macromolecular systems requires the existence of a reflexive relationship between structural components and the functional operations they perform to synthesise themselves. The possibility of reflexivity depends on formal, semiotic features of the catalytic structure-function relationship, that is, the embedding of catalytic functions in the space of polymeric structures. Reflexivity is a semiotic property of some genetic sequences. Such sequences may serve as the basis for the evolution of coding as a result of autocatalytic self-organisation in a population of assignment catalysts. Autocatalytic selection is a mechanism whereby matter becomes differentiated in primitive biochemical systems. In the case of coding self-organisation, it corresponds to the creation of symbolic information. Prions are present-day entities whose replication through autocatalysis reflects aspects of biological semiotics less obvious than genetic coding.

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of alpha-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+10) under conditions of low ionic strength (0.05 M).

Excluded-volume effect of inert macromolecules on the melting of nucleic acids.

It is shown on the basis of the excluded-volume effect that inert macromolecules may be expected to suppress the dissociation of double-helical nucleic acids into single helices and thus to raise the melting point of the double helix. The rise in melting temperature of the ribonucleic acid [poly(I).poly(C)] caused by dextran polymers and by poly(ethylene oxide) is described and compared with the theoretical prediction. Good agreement was found in respect of the extent of the rise in melting point and in respect of its dependence upon polymer length. An additional dependence upon the identify of the polymer was attributed to detailed effects of shape in solution.