Diffusion in supersaturated solutions: Application to the case of supersaturated protein solutions

Abstract

The derivation of solute diffusion coefficient from the quasiequilibrium probability density function of the underlying stochastic quantity-characteristic size of subcritical solute clusters, was carried out within the classical formalism of metastable state relaxation (nucleation). It has been demonstrated that (a) the solute diffusion coefficient is necessarily concentration dependent; (b) the concentration dependent solute diffusivity is the function of only two parameters, solute diffusivity at saturation and total surface energy of a solute molecule. This energy, in principle, can be also a function of solute concentration for supersaturated solutions such as protein supersaturated solutions. In addition to that it has been demonstrated for supersaturated solutions of the proteins such as lysozyme and Bovine Pancreatic Trypsin Inhibitor (BPTI) solutions that (a) the total surface energy of lysozyme and BPTI molecules in the metastable state is concentration dependent. (b) The solute diffusivity as a function of solute concentration, observed in supersaturated protein solutions such as lysozyme and BPTI, can be accurately reproduced (with error less than 1.2%) on the base of classical theory of the metastable state relaxation, given that the surface energy of the protein molecules is concentration dependent.