Recently, Cohen et. al. have reported their findings on their ability to trap molecules in a novel Anti-Brownian Electrokinetic (ABEL) Trap (SPIE 2005, PNAS 2006). By actively manipulating electric fields, the ABEL trap is able to confine a molecule within a prescribed region. In addition to demonstrating the ability to trap micro-spheres and large proteins, the ABEL Trap has also been used to confine and directly observe the equilibrium conformational dynamics of λ-DNA, a macromolecule with a radius of gyration of roughly 0.7 microns.

As a complement to these experiments, we present numerical results obtained via Brownian Dynamic (BD) Simulations. BD simulations were implemented using both the bead-spring and bead-rod formalisms, not only to corroborate the experimental results but also to further our understanding regarding the dominant forces acting in the ABEL trap.

Simulations with fluctuating hydrodynamic interactions reveal that the center of mass displacements of a polymer can be used to examine diffusivity correlations. In accordance with previous results, we find that at short times the apparent diffusivity is about 1.7% greater than the long time diffusivity (Dubois-Violette & DeGennes 1967). This difference is a direct consequence of hydrodynamic interactions, which introduce a timescale over which molecular conformations decay. Since, diffusivity is, to some extent, dependent on the conformation of molecules, the correlations introduced by hydrodynamic interactions lead to non-zero correlations in short-time diffusivities as well (Sunthar et. al., Europhys. Letters 2006).

Secondly, conformational correlations in the ABEL Trap were examined using stretched exponential functions, which arise in processes characterized by a spectrum of relaxation times (Lindsey & Patterson, 1980). Excluded Volume interactions (EV), which we conjecture to be dominant in the ABEL trap, were included using narrow repulsive gaussian potentials. EV interactions are primarily governed by the excluded volume parameter, which corresponds to the strength of the EV interactions. Bead-rod simulations for short polymer chains were performed, keeping the excluded volume parameter constant, and the results were extrapolated to the length corresponding to λ-DNA. This procedure allows us to examine the effect of excluded volume on the nature of the decay of conformational correlations. Our simulations show that the inclusion of intramolecular EV allows the numerical results to be commensurate with experimental results. Furthermore, using the ABEL trap, one might be able to directly extract the value of excluded volume parameter for a given polymeric system, which can then be used to appropriately account for EV forces in numerical simulations.