Properties of liquids in small pores: Rates of diffusion of some solutes in cross-linked crystals of β-lactoglobulin

Abstract

The time-course of the diffusion of a series of bromine-containing solutes into a single, cross-linked, crystal of β-lactoglobulin has been followed by X-ray fluorescence measurements. From the measured relative diffusion coefficients in the crystal and the estimated free diffusion coefficients and particle radii for potassium bromide and lithium bromouridylate, the effective pore radius in the crystal has been estimated to be 8 to 13 Å, depending on the restriction equations used. There is no evidence for specific binding of either of these solutes to the protein. The radius estimates correspond well to the range of pore dimensions derived from the size of penetrating solutes and unit cell shrinkage on drying. With the reduction in diffusion rate adequately explained by physical pore restriction, no special properties need be attributed to the major part of the crystal liquid and it may be considered identical to water in bulk. Sodium o-bromobenzoate and 3-bromopropanol bind to the protein. After correction for the effect of these interactions, the diffusion coefficients of the unbound solute species are still too small to match those estimated from the pore sizes given above. The explanation for the difference in behavior of the two classes of solutes is not clear. The effect of high concentrations of sucrose on the diffusion of potassium bromide in the crystal is much larger than in free solution. The effect is at least qualitatively explained by a decrease in effective pore radius caused by the large hydrated sucrose molecules. Such interaction of two solutes may be expected to become more and more marked as the pore radius approaches the radius of the largest solute.