Kinetics of Interior Loop Formation in Semiflexible Chains

Abstract

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean-field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison to the case are in excellent agreement with explicit Brownian dynamics simulations of worm-like chain (WLC) model. The interior looping times (${\tau }_{IC}$) can be greatly altered in cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then ${\tau }_{IC}$ increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (${\tau }_c$) and interior looping (${\tau }_{IC}$) times greatly increase at low ionic concentration. Because both ${\tau }_c$ and ${\tau }_{IC}$ are determined essentially by the effective persistence length ($l_p^{(R)}$) we computed $l_p^{(R)}$ by varying the range of the repulsive interaction between the monomers. For short range interactions $l_p^{(R)}$ nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.

38 pages, 8 Figures, J. Chem. Phys. (in press)

References in corpus (5)

• Radial distribution function of semiflexible polymers
• Persistence Length Changes Dramatically as RNA Folds
• Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients
• Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing
• Stretching DNA: Role of electrostatic interaction

Cited by in corpus (14)

• Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models
• Size, shape, and flexibility of RNA structures
• Semiflexible Chains in Confined Spaces
• Theory and Simulations of condensin mediated loop extrusion in DNA
• Conformational Heterogeneity in Human Interphase Chromosome Organization Reconciles the FISH and Hi-C Paradox
• Design principles governing the motility of myosin V
• Computation of the Mean First-Encounter Time Between the Ends of a Polymer Chain
• Modulation of DNA loop lifetimes by the free energy of loop formation
• Dynamics of end to end loop formation for an isolated chain in viscoelastic fluid
• Looping and reconfiguration dynamics of a flexible chain with internal friction
• Folding and unfolding kinetics of a single semiflexible polymer
• Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics
• Thermal Fracture Kinetics of Heterogeneous Semiflexible Polymers
• Effects of static and temporally fluctuating tensions on semiflexible polymer looping