Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

Abstract

We present a fully parametrized bead-spring chain model for stained -phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions ͑HI͒. Parameters are determined from equilibrium experimental data for 21 m stained -phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 m. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate (␥ ) that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as ␥ Ϫ6/11 and ␥ Ϫ14/11 , respectively. At higher shear rates, these become ␥ Ϫ2/3 and ␥ Ϫ4/3 . These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.

Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

“…After numerical computation, the results of molecule extension and probability distribution are compared to that obtained in experiment by Smith et al (1999). The plot of fractional extension for different Weissenberg numbers is also superimposed by that of different models, e.g., the bead-spring model with wormlike spring by Jendrejack et al (2002) and classical FENE dumbbell model by Hur & Shaqfeh (2000). We show that the FENE dumbbell model with IV can yield good agreement in simulation of λ-phage DNA molecules.…”

“…The dumbbell model without IV (Hur & Shaqfeh , 2000) and the wormlike model with hydrodynamic interactions (Jendrejack et al , 2002) are also superimposed in the plot. The classical FENE dumbbell model can not predict the extension result when Weissenburg number is high.…”

“…Simulation results will be compared with the experimental data by Smith et al (1999) and the simulation results of FENE model (Hur & Shaqfeh , 2000), as well as with the wormlike spring model with hydrodynamic interactions (Jendrejack et al , 2002).…”

Confined dynamics of a single DNA molecule

“…Jendrejack et al [8] proposed a bead and spring Brownian model in which hydrodynamics is accounted for via the Oseen tensor. However, this approach is difficult to apply in confined geometries because the hydrodynamics interaction tensor cannot be calculated analytically and a numerical procedure is required (see also [9,10]).…”

“…[11][12][13]). In the latter, the bead-and-spring model proposed by Jendrejack et al [8] is coupled with the multi-particle collision dynamics (MPCD) approach for the solvent developed by Malevanets & Kapral [14]; see also Gompper et al [15] for a thorough account of the applications. This method (sometimes called stochastic rotation dynamics) has been used for the last few years to analyse single polymer molecules in a solvent.…”