Condensed Matter Theory

Abstract:

We apply a recently-developed coarse-grained model of DNA, designed to capture the basic physics of nanotechnological DNA systems, to the study of a 'burnt-bridges' DNA motor consisting of a single-stranded cargo that steps processively along a track of single-stranded stators. We demonstrate that the model is able to simulate such a system, and investigate the sensitivity of the stepping process to the spatial separation of stators, finding that an increased distance can suppress successful steps due to the build up of unfavourable tension. The mechanism of suppression suggests that varying the distance between stators could be used as a method for improving signal-to-noise ratios for motors that are required to make a decision at a junction of stators.

Abstract:

We consider single particle and polymer translocation where the frictional properties experienced from the environment are changing in time. This work is motivated by the interesting frequency responsive behaviour observed when a polymer is passing through a pore with an oscillating width. In order to explain this better we construct general diffusive and non-diffusive frequency response of the gain in translocation time for a single particle in changing environments and look at some specific variations. For two state confinement, where the particle either has constant drift velocity or is stationary, we find exact expressions for both the diffusive and non-diffusive gain. We then apply this approach to polymer translocation under constant forcing through a pore with a sinusoidally varying width. We find good agreement for small polymers at low frequency oscillation with deviations occurring at longer lengths and higher frequencies. Unlike periodic forcing of a single particle at constant mobility, constant forcing with time dependent mobility is amenable to exact solution through manipulation of the Fokker-Planck equation.

Abstract:

Recent experiments on the green alga Chlamydomonas that swims using synchronized beating of a pair of flagella have revealed that it exhibits a run-and-tumble behavior similar to that of bacteria such as E. Coli. Using a simple purely hydrodynamic model that incorporates a stroke cycle and an intrinsic Gaussian white noise, we show that a stochastic run-and-tumble behavior could emerge, due to the nonlinearity of the combined synchronization-rotation-translation dynamics. This suggests the intriguing possibility that the alga might exploit nonlinear mechanics---as opposed to sophisticated biochemical circuitry as used by bacteria---to control its behavior.