Protein−Macromolecule Interactions

Although the interactions between proteins and various types of macromolecules are of considerable technological interest,1 little theoretical work has been done that makes use of the fact that proteins are often comparatively small particles. Thus, our interest is in a regime opposite to that focused on in the usual depletion theories.2 Here, a protein will be viewed, perhaps naively, as a small hard sphere whose dielectric permittivity is negligible compared to that of water. Its interaction otherwise with some macromolecular segment will be inert. Some time ago, de Gennes already presented several, not so widely known, preliminary calculations of a spherical particle interacting with a semidilute solution of polymers.3 One supposition he made concerning the irrelevance of a certain scale, will be proved here. My aim is to present a scaling analysis of the interaction between a small sphere and a macromolecule, particularly in dilute solution. Though obviously of restricted validity, the expressions derived may prove helpful in qualitatively understanding phase separation phenomena occurring in nondilute suspensions. We first consider a protein sphere of radius a immersed in an aqueous solution containing a semidilute polymer which is well soluble. Its Kuhn length is AK, and the excluded volume between two segments is â ) AK. In a self-consistent field approximation, the polymer segment density ψ2(r b) at position r b is given by2