Article
Diffusioncontrolled first contact of the ends of a polymer: crossover between two scaling regimes.
Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Physical Review E (Impact Factor: 2.33). 10/2005; 72(3 Pt 1):031804. DOI: 10.1103/PhysRevE.72.031804 Source: PubMed

Article: Polymer concepts in biophysics
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ABSTRACT: The recent advent of experimental techniques that study biological systems on the level of a single molecule have led to a number of exciting new results. These experiments have a variety of applications in understanding both the kinetics and equilibrium properties of biomolecules. By applying the concepts of polymer physics to these single molecule experiments, we are able to more fully understand the physical picture underlying a number of experimental observations. In this thesis, we use a variety of polymer models to develop a better understanding of many single molecule experiments. We show that the kinetics of loop formation in biopolymers can be generally understood as a combination of an equilibrium and dynamic part for a number of different polymer models. We study the extension of a homopolymer as a function of applied tension, and develop a simple theoretical framework for determining the effect of interactions on the stretching of the chain. We show that the measured hopping rates in a laser optical tweezer experiment are necessarily altered by the experimental setup, and suggest a method to accurately infer the correct hopping rates using accurately measured free energy profiles. We show that the effect of the experimental setup can be understood using a novel polymer model. Finally, we propose a Hamiltonianbased method to study the properties of spherically confined wormlike chains, which accurately determines the equilibrium properties of the system for strongly confined chains. In these studies, we are able to better understand the behavior of many disparate systems using relatively simple arguments from polymer theory.01/2008;  [Show abstract] [Hide abstract]
ABSTRACT: Is it possible to extract the size and structure of chromosomal territories (confined domain) from the encounter frequencies of chromosomal loci? To answer this question, we estimate the mean time for two monomers located on the same polymer to encounter, which we call the mean first encounter time in a confined microdomain (MFETC). We approximate the confined domain geometry by a harmonic potential well and obtain an asymptotic expression that agrees with Brownian simulations for the MFETC as a function of the polymer length, the radius of the confined domain, and the activation distance radius ε at which the two searching monomers meet. We illustrate the present approach using chromosome capture data for the encounter rate distribution of two loci depending on their distances along the DNA. We estimate the domain size that restricts the motion of one of these loci for chromosome II in yeast.Physical Review Letters 06/2013; 110(24). · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Using a novel theoretical approach, we study the mean firstencounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however, to incompatible results. We construct here for the first time a general theory that allows us to compute the MFET. The method is based on estimating the mean time for a Brownian particle to reach a narrow domain in the polymer configuration space. In dimension two and three, we find that the MFET depends mainly on the first eigenvalue of the associated FokkerPlanck operator and provide precise estimates that are confirmed by Brownian simulations. Interestingly, although many time scales are involved in the encounter process, its distribution can be well approximated by a single exponential, which has several consequences for modeling chromosome dynamics in the nucleus. Another application of our result is computing the mean time for a DNA molecule to form a closed loop (when its two ends meet for the first time).Physical Review Letters 09/2012; 109(10). · 7.73 Impact Factor
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