Electrostatic Effects on Partitioning of Proteins in Aqueous Two-Phase Systems: I. pH and Charge Equilibria

Abstract

The charge on a protein molecule is obviously an average, and here the role of charge distribution is accounted for by using Hill's small system thermodynamics. The conventional equation of protein charging is obtained in a very simple manner, and with a more accurate description of the electrostatic effects some insight into anomalous effects is also obtained. The importance of straightening out the charge effects becomes obvious in treating the more complicated system of partitioning proteins in an aqueous two-polymer two-phase system. Correct dependence of the partition coefficient on the charge is obtained. This takes the form that the logarithm of the partition coefficient is proportional to the square of the charge at low charges and only to the charge at large values, in keeping with the experimental data. However, it is only easy to get some form of upper limit and difficult to quantify individual cases because of the large number of variables involved and because detailed data are unavailable. An explanation has been given as to why the logarithm of the partition coefficient versus charge (z p or z 2 p) plots have varying slopes and intercepts. This explanation lies in the asymmetry of the polymer distribution and thus provides an explanation as to why the protein partitions unequally, in that the asymmetrically distributed polymers affect the charge and ion equilibria in proteins differently and thus partition proteins differently into the two phases. Obviously, the polymer molecular weight distribution is a key feature in determining this asymmetry and, with one polymer bimodally distributed, it is possible to show that if some amount of the same polymer of a larger molecular weight is added it steepens the partitioning, but a lower molecular weight fraction has no effect.