Theory of the effect of pH and ionic strength on the nucleation of protein crystals

Abstract

Proteins can be crystallized from pH buffered aqueous solutions of inert strong electrolytes. The appearance of crystals is preceded by the formation of crystal nuclei which are oligomers of protein molecules bound by non-covalent forces. Being amphoteric, individual protein molecules in solution are macro-ions whose charge depends upon pH. As it is unlikely that these macro-ions agglomerate to form oligomers with complete retention of charge, we suggest, and confirm by experiment, that the formation of crystal nuclei is accompanied by H + exchange with the buffer. The rate of agglomeration of like-charged macro-ions to form nuclei will also be affected by Coulomb repulsion. The strength of the bare Coulomb force will be reduced and the rate of agglomeration accelerated, however, by the plasma screening produced by the ions of the strong electrolyte. Using a theory incorporating these effects, we show that nucleation rates generally increase as the size of the critical nucleus decreases toward its lower bound set by the size of a dimer. The nucleation rates at low pH and also near pH=pI, where the protein molecules are neutral, are very large and represent sets of conditions particularly favorable to crystal production.