CPM Seminar

DNA dynamics in the bulk and in a quasi-one-dimensional confinement

Aniket Bhattacharya

Department of Physics
University of Central Florida

We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^3/4 with time due to bending motions, and the Rouse-like regime t^2ν/(1+2ν) where ν is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the pre-factors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l²_p (at a time proportional to l³_p). A second crossover (to diffusive motion) occurs when the MSD is of order R². Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D = 2 dimensions where ν=3/4.

We then discuss the effect of confinement where we find the monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model. Under extreme confinement we demonstrate how a direct estimate of the Odijk's deflection length can be obtained from the simulation data. In this regime we discuss the discrepancy of the lattice model often used for very long chain under quasi 1D confinement where a renormalization of the persistence length is required to reconcile the simulation data obtained from the off-lattice simulation using bead- spring model. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates and under confinement.

[1] Aiqun Huang, Ramesh Adhikari, Aniket Bhattacharya, and Kurt Binder, Universal monomer dynamics of a two dimensional semiflexible chain, Euro Phys. Lett. 105, 18002 (2014).
[2] Aiqun Huang, Aniket Bhattacharya, and Kurt Binder, Conformations, Transverse Fluctuations and Crossover Dynamics of a Semi-Flexible Chain in Two Dimensions, J. Chem. Phys. 140, 214902 (2014).
[3] Aiqun Huang, H.-P Hsu, Aniket Bhattacharya, and Kurt Binder, Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles, J. Chem. Phys. 143, 243102 (2015).
[4] Aiqun Huang and Aniket Bhattacharya, DNA confined in a two-dimensional strip geometry, Euro Phys. Lett. 106, 18004 (2014).