Depletion theory of protein transport in semi-dilute polymer solutions.

We consider the effect of polymer depletion on the transport (diffusion and electrophoresis) of small proteins through semi-dilute solutions of a flexible polymer. A self-consistent field theory may be set up in the important case of quasi-ideal interactions when the protein is small enough. Dynamic depletion, the reorganization of the depletion layer as the protein diffuses, is computed within a free-draining approximation. The transport of the dressed particle (protein + depletion layer) is tackled by extending Ogston's analysis of probe diffusion through fibrous networks to the case of a probe diffusing through a semi-dilute polymer inhomogeneous on the scale of the polymer correlation length. The resulting exponential retardation agrees almost quantitatively with that found in recent electrophoresis experiments of small proteins in polymer solutions that have been ascertained to be semi-dilute (S. P. Radko and A. Chrambach, Electrophoresis, 17:1094-1102, 1996; Biopolymers, 4:183-189, 1997).