Hydrophobic interaction in the liquid phases of globular protein solutions: structure factor parameters

We develop a simple correspondence between hydrophobic surface topology of globular proteins and and an effective protein-protein adhesiveness parameter of the Baxter type. We discuss within this framework analytical interpretation of the structure factor governing static light scattering. Typeset using REVTEX 1 Hydrophobic amino-acid residues exposed at the surface of globular proteins are able to avoid the aqueous environment to an extent by burying themselves in globule-globule contacts. There exists in this sense an effective globule-globule adhesive potential, which, from a thermal perspective, mirrors the strong entropic character of hydrophobicity, driving a general tendency of proteins to cluster with increasing temperature. In principle, the effect is experimentally accessible via measurement of scattered light intensity at low wavenumber qd << 1, I ∼ cS0(c), where S0 denotes the q = 0 limit of the structure factor, c is the protein concentration, and d characterises the protein globule lengthscale. Our objective here is to supplement the usual DLVO interpretation of S0 adopted, for example, in recent scattering studies of lysozyme and β-lactoglobulin, with a semi-empirical incorporation of the hydrophobic adhesive mechanism. We do this in the following by first establishing an effective attractive well interaction between proteins, having an explicit temperature dependence derived from thermodynamic data, and then mapping the well interaction onto the adhesiveness parameter of Baxter, this latter being very amenable to liquid state analysis. The starting point is a formulation of ‘hydrophobic surface tension’ γ according to a typical transfer free energy ∆F ∼ 2 kcal/mol of a single nonpolar amino-acid residue between water and a hydrophobic environment, i.e., γ = g∆F/a (1) where g is some geometrical factor less than one, and a ∼ 1nm is a typical residue dimension. An empirical temperature dependence γ(T ) follows via this expression by extrapolating from room temperature thermodynamic data available for ∆F , ∆F (T ) = ∆H +∆Cp(T − T0)− T [∆S 0 +∆Cp ln(T/T0)],