Brownian Dynamics Simulation of Dna in Complex Geometries

This dissertation is concerned with the dynamics of a long DNA molecule in complex geometries, driven by either electrostatic field or flow field. This is accomplished primarily through the use of Brownian dynamics simulation, which captures the essential physics at mesoscopic length scale, and allows us to simulate events happening on long time scale, such as DNA pore translocation and cyclic dynamics of a tethered DNA molecule in shear flow. Our work is novel in that, accurate and efficient algorithms have been designed and developed for both electric field-driven and flow-driven systems in complex geometries. We have focused on three distinct problems, which we describe below. In the electric field-driven case, we propose a novel class of electric field-actuated soft mechanical control element for microfluidics. This type of element employs the idea that under confinement a single polymer molecule is essentially a nanoscale porous media. The chain could block the passageway of relatively large analytes such as cells. At the same time, polyelectrolyte molecules, such as DNA, could deform and squeeze through narrow pores when a sufficiently strong electric field is applied. Brownian dynamics (BD)/Finite Element Method (FEM) simulation efficiently explore the design space, and results demonstrate that the On/Off switching could be iv achieved within a proper parameter space. To study the effects of a solid impenetrable wall on the dynamics of a nearby DNA molecule, we examine the cyclic dynamics of a single DNA molecule tethered to a hard wall in shear flow, using Brownian dynamics simulation. We focus on the dynamics of the free end (last bead) of the tethered chain and we examined the crosscorrelation function and power spectral density of the chain extensions in the flow and gradient directions as a function of chain length N and dimensionless shear rate Wi. Extensive simulation results suggest a classical fluctuation-dissipation stochastic process and question the existence of periodicity of the cyclic dynamics, as previously claimed. We support our numerical findings with a simple analytical calculation for a harmonic dimer in shear flow. In the case of flow-driven DNA molecule in micro/nano-fluidics, one big challenge is that an efficient algorithm is required to calculate fluctuating hydrodynamic interactions (HI) in complex geometries. We have developed an accelerated immersed boundary method that allows fast calculation of Brownian motion of polymer chains and other particles in complex geometries with HI. With this new method, the first detailed analysis of a recent set of interesting nanofluidic experiments involving DNA dynamics in a complex flow geometry is performed. This analysis explains the observed dynamics over a wide range of parameter values (flow rate, molecular wieght) and illustrates the important quantitative effect of the hydrodynamic interactions on the behavior of the system.