Effect of Hydrodynamic Interactions on DNA Dynamics in Extensional Flow: Simulation and Single Molecule Experiment Charles M. Schroeder, † Eric S. G. Shaqfeh,* ,‡ and Steven Chu § Department of Chemical Engineering, Stanford University, Stanford, California 94305; Departments of Chemical and Mechanical Engineering, Stanford University, Stanford, California 94305; and Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305 Received March 18, 2004; Revised Manuscript Received August 26, 2004 ABSTRACT: Intramolecular hydrodynamic interactions (HI) in flexible polymer chains influence both the equilibrium and nonequilibrium physical properties of macromoecules. In this work, we utilize a combination of single molecule experimental techniques and Brownian dynamics (BD) simulation to investigate the role of HI and excluded-volume (EV) interactions for DNA molecules ranging in contour length from 150 to 1300 µm. Epifluorescence microscopy is used to directly observe the dynamics of DNA molecules in planar extensional flow, and a semiimplicit bead-spring BD algorithm with fluctuating HI and EV interactions is presented. Quantitatitative agreement between ensemble average transient molecular extension in experiment and BD simulation is shown for DNA with 150 µm contour length. Simulations show polymer conformation hysteresis for larger DNA chains (1300 µm in length) when HI and EV parameters are chosen such that simulation results match the experimental polymer relaxation time and polymer stretch at flow strengths below the coil-stretch transition. Furthermore, conformation- dependent resistivities are extracted from BD simulation for DNA chains 1300 µm in length, and this drag functionality is utilized in a coarse-grained Brownian dumbbell model with variable resistivity. Finally, steady-state molecular extension results from the coarse-grained model are compared to simple polymer kinetic theory for a dumbbell with variable resistivity. 1. Introduction The nonequilibrium behavior of flexible polymer molecules in flows of dilute solutions is complex, and an accurate description of the dynamics of long-chain macromolecules can be a daunting task. Traditionally, bulk rheological experiments including flow bire- fringence 1-3 and light scattering measurements 4,5 were used to infer information regarding polymer conforma- tion, orientation, and chain stretch in strong flows. More recently, the advent of single molecule visualizations using fluorescence microscopy has allowed for the direct observation of individual DNA molecules in flows of dilute solutions in shear, 6 planar extensional, 7,8 and general two-dimensional mixed flows. 9 Experimental results from these studies have elucidated complex polymer behavior in a number of ways. First, studies of DNA allow for observation of well-characterized, mono- disperse polymer chains of known contour length, 10 with equilibrium properties such as chain diffusivity 11 and polymer relaxation times known within small degrees of experimental uncertainty. Furthermore, observation of transient molecular stretch reveals rich individual- istic molecular behavior with regard to chain configu- ration. 7 Dilute solution studies involving DNA are performed at extremely low concentrations (≈10 -5 c*, where c* is the polymer overlap concentration) such that interpolymer interactions are absent and cause no flow- induced changes to a well-defined, spatially homoge- neous flow field. Results including transient and steady chain stretch in flow have allowed for significant progress to be made in areas of model development and simulation algorithm testing. Model parameters may be chosen such that the simulation accurately captures known properties of DNA molecules, and the nonequi- librium microstructual information between experiment and simulation may be directly compared. A careful coupling of single molecule visualization and Brownian dynamics simulation of polymer chains provides a powerful combination of tools to study the dynamics of polymer chains in flow. Many previous Brownian dynamics simulations of bead-spring and bead-rod models for lambda DNA chains have included the assumption that polymer chains are free-draining, 12-14 albeit the authors calcu- late bead drag coefficients to match the longest polymer relaxtion time measured from experiment. As discussed below, such models for lambda DNA show quantitative agreement with dynamical polymer behavior deter- mined from single molecule experiments. In a free- draining bead-spring polymer model, all of the beads move through the solvent without inducing perturba- tions to the solvent velocity. 15 However, in a realistic polymer chain, portions of the polymer disturb the solvent flow field, and nearby regions of the molecule are affected by these hydrodynamic interactions (HI). In the coiled state, interior monomer units are shielded from the full solvent velocity by outer portions of the molecule. However, in the fully extended conformation, monomer units are more exposed to the flow, and the effects of HI are diminished. In this state, the fluid exerts a more effective frictional grip on the polymer molecule. Hydrodynamic interactions have well-known effects on the linear viscoelastic (LVE) properties of poly- mers. 16,17 The longest polymer relaxtion time τ scales as molecular weight M like τ ∼ M 1.5 for HI-dominant † Department of Chemical Engineering. ‡ Departments of Chemical and Mechanical Engineering. § Departments of Physics and Applied Physics. * To whom correspondence should be addressed. E-mail: eric@ chemeng.stanford.edu. 9242 Macromolecules 2004, 37, 9242-9256 10.1021/ma049461l CCC: $27.50 © 2004 American Chemical Society Published on Web 11/02/2004