Analysis of steric partition behavior of molecules in membranes using statistical physics. Application to gel chromatography and electrophoresis

Abstract

The principles of statistical physics are used to formulate general expressions for the steric partition behavior of molecules in both random and ordered membrane structures that may be applied to any shape of the solute and/or the volume-excluding element of the membrane. These expressions fully define partitioning in terms of the volume excluded to point molecules and to finite-sized molecules. The mean effective exclusion volume for a molecule is calculated as a function of a global interaction energy, which varies with position, conformation, and orientation of the molecule. It allows consideration of electrostatic and other nonsteric factors. To test the model, specific partition functions are derived for several simple geometries describing the membrane and solute. Frequently, the derived expressions agree with past analyses; however, a new expression describing partitioning within an random network of fibers is derived. It agrees with past results only in the limit of low exclusion volumes. With greater volume exclusions, past results greatly overestimate the partition function. It is applied to gel electrophoresis and chromatography and survives testing with available experimental data. Unlike past analyses, it predicts nonlinear Ferguson plots for agarose gel electrophoresis. In addition, an analytical expression predicting the minimum radius of a sphere excluded from a random fiber matrix is derived, tested, and found to agree with experimental data.