Article

# Diffusion-controlled 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: 2.31). 10/2005; 72(3 Pt 1):031804. DOI:10.1103/PhysRevE.72.031804 Source: PubMed

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**ABSTRACT:**Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.The Journal of Chemical Physics 06/2012; 136(23):234903. · 3.16 Impact Factor -
##### Article: Sequence and Temperature Dependence of the End-to-End Collision Dynamics of Single-Stranded DNA.

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**ABSTRACT:**Intramolecular collision dynamics play an essential role in biomolecular folding and function and, increasingly, in the performance of biomimetic technologies. To date, however, the quantitative studies of dynamics of single-stranded nucleic acids have been limited. Thus motivated, here we investigate the sequence composition, chain-length, viscosity, and temperature dependencies of the end-to-end collision dynamics of single-stranded DNAs. We find that both the absolute collision rate and the temperature dependencies of these dynamics are base-composition dependent, suggesting that base stacking interactions are a significant contributor. For example, whereas the end-to-end collision dynamics of poly-thymine exhibit simple, linear Arrhenius behavior, the behavior of longer poly-adenine constructs is more complicated. Specifically, 20- and 25-adenine constructs exhibit biphasic temperature dependencies, with their temperature dependences becoming effectively indistinguishable from that of poly-thymine above 335 K for 20-adenines and 328 K for 25-adenines. The differing Arrhenius behaviors of poly-thymine and poly-adenine and the chain-length dependence of the temperature at which poly-adenine crosses over to behave like poly-thymine can be explained by a barrier friction mechanism in which, at low temperatures, the energy barrier for the local rearrangement of poly-adenine becomes the dominant contributor to its end-to-end collision dynamics.Biophysical Journal 06/2013; 104(11):2485-92. · 3.67 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**A common theoretical approach to calculating reaction kinetics is to approximate a high-dimensional conformational search with a one-dimensional diffusion along an effective reaction coordinate. We employed Brownian dynamics simulations to test the validity of this approximation for loop formation kinetics in the worm-like chain polymer model. This model is often used to describe polymers that exhibit backbone stiffness beyond the monomer length scale. We find that one-dimensional diffusion models overestimate the looping time and do not predict the quantitatively correct dependence of looping time on chain length or capture radius. Our findings highlight the difficulty of describing high-dimensional polymers with simple kinetic theories.The Journal of Chemical Physics 05/2013; 138(17):174908. · 3.16 Impact Factor

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