Single-polymer Brownian motor: A simulation study

Numerical simulation is used to study a single polymer chain in a flashing ratchet potential to determine how the mechanism of this Brownian motor system is affected by the presence of internal degrees of freedom. The polymer is modeled by a freely jointed chain with $N$ monomers in which the monomers interact via a repulsive Lennard-Jones potential and neighboring monomers on the chain are connected by finite extensible nonlinear elastic bonds. Each monomer is acted upon by a 1D asymmetric, piecewise linear potential of spatial period $L$ comparable to the radius of gyration of the polymer. This potential is also characterized by a localization time, ${t}_{\text{on}}$, and by a free diffusion time, ${t}_{\text{off}}$. We characterize the average motor velocity as a function of $L$, ${t}_{\text{off}}$, and $N$ to determine optimal parameter ranges, and we evaluate motor performance in terms of finite dispersion, Peclet number, rectification efficiency, stall force, and transportation of a load against a viscous drag. We find that the polymer motor performs qualitatively better than a single particle in a flashing ratchet: with increasing $N$, the polymer loses velocity much more slowly than expected in the absence of internal degrees of freedom, and the motor stall force increases linearly with $N$. To understand these cooperative aspects of motor operation, we analyze relevant Rouse modes. The experimental feasibility is analyzed and the parameters of the model are scaled to those of $\ensuremath{\lambda}$-DNA. Finally, in the context of experimental realization, we present initial modeling results for a 2D flashing ratchet constructed using an electrode array, and find good agreement with the results of 1D simulations although the polymer in the 2D potential sometimes briefly ``detaches'' from the electrode surface.