Volume-exclusion effects in tethered-particle experiments: bead size matters

Abstract

We give a theoretical analysis of bead motion in tethered-particle experiments, a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. Our analysis reveals that the proximity of the tethered bead to a nearby surface gives rise to a volume-exclusion effect, resulting in an entropic stretching-force on the molecule that changes its statistical properties. In addition, volume exclusion brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as bead size and contour length of the molecule. We present analytic and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally testable prediction for the probability distribution of the bead center measured from the polymer attachment point.

FIG. 1

Schematic showing the tethered particle method. (a) The tether is attached to a specific point on the bead; z is the height of this point. r denotes the position of the center of the bead. (b) The vector R from the attachment point to the bead center can rotate and is described by two angles. These rotations are more constrained for small values of z. Note that in the figure the width of DNA is not to scale, it is much smaller in real experiments.

FIG. 2

Scaling behavior of bead excursion, normalized by coil size parameter, versus the excursion number N_R. Curves: analytical theory in the Gaussian-chain approximation (Eq. 10). Circles: Monte Carlo calculation for a semiflexible chain with ξ = 50 nm, L = 1245 bp, and various values of R.

FIG. 3

Solid curves: Theoretical prediction of the probability distributions for the projected distance r⊥, taking bead radius R = 250 nm, persistence length ξ = 50 nm, and contour length L = 1000 bp (left curve) and 2000 (right curve). Dashed curve: Two dimensional Gaussian distribution with the same mean-square excursion as the left curve.