Theory of Protein Solutions. I

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Abstract
A summary of a few results of the McMillan‐Mayer solution theory is given in Sec. II, in order to have available necessary equations in a form required in later sections. It is pointed out in Sec. III that binding equilibria in a solution can in principle be discussed equally rigorously either implicitly or explicitly. The definition of ``binding'' in an explicit formulation is, strictly speaking, somewhat arbitrary but the arbitrariness disappears for practical purposes if the binding forces are very strong. However, the purely thermodynamic results are rigorously independent of the exact definition used. With the aid of Secs. II and III, it is possible to formulate in Sec. IV a general theory of protein solutions, including the effect of binding of ions or molecules on protein molecules. The discussion here is restricted to a single protein species and a single type of molecule capable of being bound, but the generalization to any number of protein or bound species is easy and will be published later. The topics discussed are osmotic pressure virial expansion, number of bound molecules per protein molecule expanded in powers of the protein concentration, distribution functions for sets of protein molecules (including the radial distribution function), potentials of average force on sets of protein molecules, superposition approximation in relation to the osmotic pressure and the Born‐Green‐Yvon integrodifferential equation for the distribution functions, and, finally, the relation to the recent Kirkwood—Shumaker theory. The theory applies equally well to polyelectrolyte, colloidal, and other solutions, but the ``protein'' language is used throughout for definiteness.