An immersed boundary method for Brownian dynamics simulation of polymers in complex geometries: application to DNA flowing through a nanoslit with embedded nanopits.

This work presents an immersed boundary method that allows fast Brownian dynamics simulation of solutions of polymer chains and other Brownian objects in complex geometries with fluctuating hydrodynamics. The approach is based on the general geometry Ewald-like method, which solves the Stokes equation with distributed regularized point forces in O(N) or O(NlogN) operations, where N is the number of point forces in the system. Time-integration is performed using a midpoint algorithm and Chebyshev polynomial approximation proposed by Fixman. This approach is applied to the dynamics of a genomic DNA molecule driven by flow through a nanofluidic slit with an array of nanopits on one wall of the slit. The dynamics of the DNA molecule was studied as a function of the Péclet number and chain length (the base case being λ-DNA). The transport characteristics of the hopping dynamics in this device differ at low and high Péclet number, and for long DNA, relative to the pit size, the dynamics is governed by the segments residing in the pit. By comparing with results that neglect them, hydrodynamic interactions are shown to play an important quantitative role in the hopping dynamics.