Spatial distribution of a depletion potential between a big solute of arbitrary geometry and a big sphere immersed in small spheres

Abstract

The hypernetted-chain integral equations are solved on a three-dimensional cubic grid to calculate the spatial distribution of the depletion potential between a big solute of arbitrary geometry and a big sphere immersed in small spheres forming the solvent. By analyzing the potential along a specific trajectory of the big sphere, effects due to the geometric feature of the big solute (step edges, trenches, corners, changing curvature, etc.) can be examined in detail. As an illustration, effects of the step edge on the lateral depletion potential along a wall surface are analyzed. Along the trajectory considered, the big sphere moves at constant height, starting on the center of the wall surface and moving horizontally past the edge. The big sphere is repelled from the edge into the wall surface, and to escape to the bulk it must overcome a significantly high free-energy barrier. As another illustration, simple model calculations are performed for the lock and key steric interaction between macromolecules. The potential at contact (i.e., the stabilization free energy) for the key that exactly fits the lock is far larger than for smaller and larger keys and considerably in excess of the value predicted by the Asakura–Oosawa theory.