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.
Similar content being viewed by others
References
Adams ET Jr, Fujita H (1963) Sedimentation equilibrium in reacting systems. In: Williams JW (ed) Ultracentrifugal analysis in theory and experiment. Academic, New York
Bird RB, Spotz EL, Hirschfelder JO (1950) The third virial coefficient for non-polar gases. J Chem Phys 18:1395–1402
Brinkman HC, Hermans JJ (1949) The effect of non-homogeneity of molecular weight on the scattering of light by high polymer solutions. J Chem Phys 17:574–576
Casassa EF, Eisenberg H (1964) Thermodynamic analysis of multicomponent solutions. Adv Prot Chem 19:287–395
Hill TL (1954) Virial expansions of the osmotic pressure in the Donnan membrane equilibrium. J Chem Phys 22:1251–1252
Hill TL (1955a) Theory of protein solutions. I. J Chem Phys 23:623–636
Hill TL (1955b) Theory of protein solutions. II. J Chem Phys 23:2270–2274
Hill TL (1956a) Osmotic pressure, protein solutions and active transport I. J Am Chem Soc 78:4281–4284
Hill TL (1956b) On the theory of the Donnan membrane equilibrium. Discuss Faraday Soc 21:31–45
Hill TL (1957) Theory of solutions. I. J Am Chem Soc 79:4885–4890
Hill TL (1958) Osmotic pressure, protein solutions and active transport II. J Am Chem Soc 80:2923–2926
Hill TL (1959) Theory of solutions. II. Osmotic pressure virial expansion and light scattering in two component solutions. J Chem Phys 30:93–97
Hill TL (1968) Thermodynamics for chemists and biologists. Addison Wesley, Reading
Hill TL, Chen YD (1973) Theory of aggregation in solution. I. General equations and application to the stacking of bases, nucleosides, etc. Biopolymers 12:1285–1312
Jacobsen MP, Wills PR, Winzor DJ (1996) Thermodynamic analysis of the effects of small inert cosolutes in the ultracentrifugation of noninteracting proteins. Biochemistry 35:13173–13179
Kirkwood JG, Buff FP (1951) The statistical mechanical theory of solutions. I. J Chem Phys 19:774–777
McMillan WG, Mayer JE (1945) The statistical thermodynamics of multicomponent systems. J Chem Phys 13:276–305
Nichol LW, Ogston AG, Wills PR (1981) Effect of inert polymers on protein self-association. FEBS Lett 126:18–20
Nichol LW, Wills PR, Winzor DJ (1979) An examination of the forms of scatchard plots of binding results outside domains of sigmoidality. J Theor Biol 80:39–50
Ogston AG, Winzor DJ (1975) Treatment of thermodynamic nonideality in equilibrium studies on associating solutes. J Phys Chem 79:2496–2500
Patel TR, Nikodemus D, Besong TMD et al (2015) Biophysical analysis of a lethal laminin alpha-1 mutation reveals altered self-interaction. Matrix Biol 49:93–105
Portman KL, Long J, Carr S et al (2014) Enthalpy/entropy compensation effects from cavity desolvation underpin broad ligand binding selectivity for rat odorant binding protein 3. Biochemistry 53:2371–2379
Scatchard (1946) Physical chemistry of protein solutions. I. Derivation of the equations for the osmotic pressure. J Am Chem Soc 68:2315–2319
Scott DJ, Wills PR, Winzor DJ (2010) Allowance for the effect of protein charge in the characterization of nonideal solute self-association by sedimentation equilibrium. Biophys Chem 149:83–91
Stockmayer WH (1950) Light scattering in multi-component systems. J Chem Phys 18:58–61
Williams SJ, Sohn KH, Wan L et al (2014) Structural basis for assembly and function of a heterodimeric plant immune receptor. Science 344:299–303
Wills PR (1986) Scrapie, ribosomal proteins and biological information (1986). J Theor Biol 122:157–178
Wills PR, Comper WD, Winzor DJ (1993) Thermodynamic non-ideality in macromolecular solutions: interpretation of virial co-efficients. Arch Biochem Biophys 300:206–212
Wills PR, Georgalis Y (1981) Concentration dependence of the diffusion coefficient of a dimerizing protein: bovine pancreatic trypsin inhibitor. J Phys Chem 85:3978–3984
Wills PR, Georgalis Y, Dijk J, Winzor DJ (1995) Measurement of thermodynamic nonideality arising from volume-exclusion between proteins and polymers. Biophys Chem 57:37–46
Wills PR, Hall DR, Winzor DJ (2000a) Interpretation of thermodynamic nonideality in sedimentation equilibrium experiments on proteins. Biophys Chem 84:217–225
Wills PR, Jacobsen MP, Winzor DJ (1996) Direct analysis of solute self-association by sedimentation equilibrium. Biopolymers 38:119–130
Wills PR, Jacobsen MP, Winzor DJ (2000b) Analysis of sedimentation equilibrium distributions reflecting nonideal macromolecular associations. Biophys J 79:2178–2187
Wills PR, Nichol LW, Siezen RJ (1980) The Indefinite association of lysozyme; consideration of composition-dependent activity coefficients. Biophys Chem 11:71–82
Wills PR, Scott DJ, Winzor DJ (2012) Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization. Anal Biochem 422:28–32
Wills PR, Winzor DJ (1993) Thermodynamic analysis of ‘preferental solvation’ in protein solutions. Biopolymers 33:1627–1629
Wills PR, Winzor DJ (2001) Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions. Biophys Chem 91:253–262
Wills PR, Winzor DJ (2002) Exact theory of sedimentation equilibrium made useful. Prog Colloid Polym Sci 119:113–120
Wills PR, Winzor DJ (2005) Van der Waals phase transition in protein solutions. Acta Crystallogr D61:832–836
Wills PR, Winzor DJ (2009) Direct allowance for the effects of thermodynamic nonideality in the quantitative characterization of protein self-association by osmometry. Biophys Chem 145:64–71
Wills PR, Winzor DJ (2011) Allowance for thermodynamic nonideality in the characterization of protein interactions by spectral techniques. Biophys Chem 158:21–25
Winzor DJ, Deszczynski M, Harding SE, Wills PR (2007) Nonequivalence of second virial coefficients from sedimentation equilibrium and light scattering studies of protein solutions. Biophys Chem 128:46–55
Winzor DJ, Wills PR (1986) Effect of thermodynamic non-ideality on protein interactions: equivalence of interpretations based on excluded volume and preferential solvation. Biophys Chem 25:243–251
Winzor DJ, Wills PR (1995) Thermodynamic nonideality of enzyme solutions supplemented with inert solutes: yeast hexokinase revisited. Biophys Chem 57:103–110
Winzor DJ, Wills PR (2003) Allowance for thermodynamic non-ideality in the characterization of protein self-association by frontal exclusion chromatography:hemoglobin revisited. Biophys Chem 104:345–359
Winzor DJ, Wills PR (2006) Molecular crowding effects of linear polymers in protein solutions. Biophys Chem 119:186–195
Winzor DJ, Wills PR (2007) Characterization of weak protein dimerization by direct analysis of sedimentation equilibrium distributions: the INVEQ approach. Anal Biochem 368:168–177
Winzor DJ, Scott DJ, Wills PR (2007) A simpler analysis for the measurement of second virial coefficients by self-interaction chromatography. Anal Biochem 371:21–25
Woolley P, Wills PR (1985) Excluded-volume effect of inert macromolecules on the melting of nucleic acids. Biophys Chem 22:89–94
Acknowledgments
I express my heartfelt gratitude to Don for 37 prime years of rich scientific comradeship.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Pete R. Wills declares that he has no conflicts of interest.
Ethical approval
This article does not contain any studies with human participants (except in their role as colleagues) or animals performed by any of the authors.
Rights and permissions
About this article
Cite this article
Wills, P.R. A Hilly path through the thermodynamics and statistical mechanics of protein solutions. Biophys Rev 8, 291–298 (2016). https://doi.org/10.1007/s12551-016-0226-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12551-016-0226-6