A Hilly path through the thermodynamics and statistical mechanics of protein solutions

Abstract

The opus of Don Winzor in the fields of physical and analytical biochemistry is a major component of that certain antipodean approach to this broad area of research that blossomed in the second half of the twentieth century. The need to formulate problems in terms of thermodynamic nonideality posed the challenge of describing a clear route from molecular interactions to the parameters that biochemists routinely measure. Mapping out this route required delving into the statistical mechanics of solutions of macromolecules, and at every turn mathematically complex, rigorous, general results that had previously been derived previously, often by Terrell Hill, came to the fore. Central to this work were the definition of the "thermodynamic activity", the pivotal position of the polynomial expansion of the osmotic pressure in terms of molar concentration and the relationship of virial coefficients to details of the forces between limited-size groups of interacting molecules. All of this was richly exploited in the task of taking account of excluded volume and electrostatic interactions, especially in the use of sedimentation equilibrium to determine values of constants for molecular association reactions. Such an approach has proved relevant to the study of molecular interactions generally, even those between the main macromolecular solute and components of the solvent, by using techniques such as exclusion and affinity chromatography as well as light scattering.

Global multi-method analysis of interaction parameters for reversibly self-associating macromolecules at high concentrations

“…This naturally leads to different choices how virial coefficients are defined, a problem that has been laid out long ago by Hill and Chen 27 , 37 . For a nonideal monomer–dimer system, for example, the second virial coefficient B 2 may be defined after separately accounting for monomer and dimer populations in chemical equilibrium with equilibrium constant K , or it may be operationally defined to include all attractive interactions including those producing dimers, resulting in an apparent virial coefficient B 2 * = B 2 – K 27 , 37 . As pointed out by Hill and Chen, the decision of which viewpoint to take cannot be made on the basis of thermodynamics, and both are valid.…”

“…Previously, Hill and Chen have examined the impact of self-association on similarly operationally defined second virial coefficient, which may be measured directly, for example, by sedimentation equilibrium 27 , 37 . In this case, it was also found that the apparent virial coefficient decreases with stronger self-association, …”

Foreword to ‘Quantitative and analytical relations in biochemistry’—a special issue in honour of Donald J. Winzor’s 80th birthday

“…In that regard, the early demonstration that the displacement of protein equilibria, by small as well as macromolecular cosolutes, found rational explanation in terms of excluded volume (Winzor and Wills 1986) suggested that molecular crowding and protein solvation could be considered as the same phenomena. However trying to establish an equivalence of the quantitative expressions for the two phenomena required a return to earlier theoretical treatments (Wills 2016). The outcome of those revisionary deliberations was the realisation that, for highly concentrated systems, differing analytical results would be gained based on the choice of concentration scale (molar or molal) to define the system thermodynamics.…”

“…In this special issue, Don's colleagues, scientific collaborators and former students have contributed an array of articles concerned with biosensor analysis (Karlsson 2016), analytical ultracentrifugation (Harding et al 2016), dynamic light scattering (Stetefeld et al 2016), turbidimetric analysis (Zhao et al 2016), protein-ribonucleic acid interaction (Jones 2016), computer modelling of amyloid formation (Schor et al 2016), protein denaturation (Chebotareva et al 2016), statistical mechanics (Wills 2016), structural phage biology (Arisaka et al 2016), neutron scattering (Scott 2016), nuclear magnetic resonance analysis of mass transfer (Shishmarev and Kuchel 2016), electrophoresis (Laue et al 2016), thermodynamic nonideality (Rao et al 2016) and protein-DNA interactions (Munro et al 2016). Prefatory comments have also been added by two long-time research collaborators and fellow passengers through time, Professor Emeritus William H. Sawyer (Sawyer 2016) and Dr. Allen P. Minton (Minton 2016).…”

A review and summary of the contents of biophysical reviews volume 8, 2016

“…A Hilly path through the thermodynamics and statistical mechanics of protein solutions. Wills (2016).…”