Rotational Diffusion of Macromolecules and Nanoparticles Modeled as Non-Overlapping Bead Arrays in an Effective Medium

Hengfu Wu,Stuart A Allison,Bahareh Kashani,Young Lee,Umar Twahir,Noni Whitley,Alishia Davis,Ebenezer Duodo,Cindy Pena

doi:10.3390/polym3020846

Abstract

In this work, the retarding influence of a gel on the rotational motion of a macromolecule is investigated within the framework of the Effective Medium (EM) model. This is an extension of an earlier study that considered the effect of a gel on the translational motion of a macromolecule [Allison, S. et al. J. Phys. Chem. B 2008, 112, 5858-5866]. The macromolecule is modeled as an array of non-overlapping spherical beads with no restriction placed on their size or configuration. Specific applications include the rotational motion of right circular cylinders and wormlike chains modeled as strings of identical touching beads. The procedure is then used to examine the electric birefringence decay of a 622 base pair DNA fragment in an agarose gel. At low gel concentration (M ≤ 0.010 gm/mL), good agreement between theory and experiment is achieved if the persistence length of DNA is taken to be 65 nm and the gel fiber radius of agarose is taken to be 2.5 nm. At higher gel concentrations, the EM model substantially underestimates the rotational relaxation time of DNA and this can be attributed to the onset of direct interactions that become significant when the effective particle size becomes comparable to the mean gel fiber spacing.

Highlights

The subject of biomolecular transport in congested media is of vital interest in such diverse subjects as drug delivery across membranes and the sieving action of a gel in electrophoresis
(units of 1/length) is the gel screening parameter. This parameter can be related to the gel concentration, M, and gel fiber radius, rf, by the relation [16,25]
Other external forces on the fluid may be present as well. This is true in modeling the transport of macroions in external electric fields [28]

Summary

Introduction

The subject of biomolecular transport in congested media is of vital interest in such diverse subjects as drug delivery across membranes and the sieving action of a gel in electrophoresis. The diffusion of a host particle through a rigid gel matrix is reduced, relative to diffusion in “free solution”, by long range hydrodynamic interaction and short range steric effects. For translational diffusion, these two effects can be considered separately [3,15,16,17]. A simple way of dealing with the contribution of long range hydrodynamic interaction makes use of the Effective Medium (EM) model originally developed by Brinkman [18], and Debye and Bueche [19]. The EM model has been applied to translational diffusion [3,4,16,21], rotational diffusion [20], electrophoresis [15,22], and the electrophoretic stretch of duplex DNA in gels [23,24]

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