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

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.

Keywords

• rotational diffusion
• gel diffusion
• electric birefringence
• DNA dynamics