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 ͑nucleation͒. It has been demonstrated that ͑a͒ the solute diffusion coefficient is necessarily concentration dependent; ͑b͒ 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 ͑BPTI͒ solutions that ͑a͒ the total surface energy of lysozyme and BPTI molecules in the metastable state is concentration dependent. ͑b͒ 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.

Multicomponent Diffusion in Crowded Solutions. 1. Mutual Diffusion in the Ternary System Poly(ethylene glycol) 400−NaCl−Water

“…The diffusion matrix is very sensitive to the thermodynamic stability of the system. In fact the conditions for thermodynamic stability imply that the trace of the diffusion matrix must be positive and the determinant be positive. , This determinant is zero only along the spinodal curve, so the experimental value of determinant || D ij || is a measure of the system thermodynamic stability. The || D ij || values at the compositions investigated are reported in Table and drawn in Figure .…”

Effect of Additives on the Crystallization of Lysozyme and Chymotrypsinogen A

“…Nucleation from solution is strongly dependent on supersaturation. There exists a critical supersaturation range S c that separates the region where no measurable nucleation occurs from that where abundant new phase forms instantaneously (referred to as “explosive nucleation” in this paper), and this critical supersaturation S c is generally affected by many parameters such as buffer, pH, precipitant/additive, stirring, seed, cooling/heating rate, crystallizer, external fields, etc. − In this study, explosive nucleation was approached through decreasing/increasing the temperature of saturated protein solution at a desired precipitant/additive concentration at a rate of 6 °C/h. The chosen cooling/heating rate ensured that protein solution could not undergo liquid−liquid phase separation or gelation. , A laser generator (Interlink TS-N) generating a laser beam of 660 nm was applied to detect turbidity.…”

Multicomponent Diffusion in Crowded Solutions. 2. Mutual Diffusion in the Ternary System Tetra(ethylene glycol)−NaCl−Water

“…The analysis of diffusion properties in aqueous solutions containing proteins and their precipitants has received increasing attention in recent years. − These studies have been motivated by international programs to use microgravity conditions to grow crystals of proteins suitable for structure determination, which might not otherwise be grown under earth's gravity. In microgravity diffusion is the dominant transport mechanism in the liquid phase .…”

“…[1][2][3][4][5] These studies have been motivated by international programs to use microgravity conditions to grow crystals of proteins suitable for structure determination, which might not otherwise be grown under earth's gravity. In microgravity diffusion is the dominant transport mechanism in the liquid phase.…”