Condensed Matter Theory

Abstract:

We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson-Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an "average base" description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.

Abstract:

Synchronization of actively oscillating organelles such as cilia and flagella facilitates self-propulsion of cells and pumping fluid in low Reynolds number environments. To understand the key mechanism behind synchronization induced by hydrodynamic interaction, we study a model of rigid-body rotors making fixed trajectories of arbitrary shape under driving forces that are arbitrary functions of the phase. For a wide class of geometries, we obtain the necessary and sufficient conditions for synchronization of a pair of rotors. We also find a novel synchronized pattern with an oscillating phase shift. Our results shed light on the role of hydrodynamic interactions in biological systems, and could help in developing efficient mixing and transport strategies in microfluidic devices.

Abstract:

Using particle-tracking techniques, the translational and rotational diffusion of paralyzed E. coli with and without flagella are studied experimentally. The position and orientation of the bacteria are tracked in the lab frame and their corresponding mean-square displacements are analyzed in the lab frame and in the body frame to extract the intrinsic anisotropic translational diffusion coefficients as well as the rotational diffusion coefficient for both strains. The deflagellated strain is found to show an anisotropic translational diffusion, with diffusion coefficients that are compatible with theoretical estimates based on its measured geometrical features. The corresponding translational diffusion coefficients of the flagellated strain have been found to be reduced as compared to those of the deflagellated counterpart. Similar results have also been found for the rotational diffusion coefficients of the two strains. Our results suggest that the presence of flagella --even as a passive component-- has a significant role in the dynamics of E. coli, and should be taken into account in theoretical studies of its motion.

Abstract:

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ϵ = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α > d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2).