Semiflexible Chains in Confined Spaces

Abstract

We develop an analytical method for studying the properties of a non-interacting Wormlike Chain (WLC) in confined geometries. The mean field-like theory replaces the rigid constraints of confinement with average constraints, thus allowing us to develop a tractable method for treating a WLC wrapped on the surface of a sphere, and fully encapsulated within it. The efficacy of the theory is established by reproducing the exact correlation functions for a WLC confined to the surface of a sphere. In addition, the coefficients in the free energy are exactly calculated. We also describe the behavior of a surface-confined chain under external tension that is relevant for single molecule experiments on histone-DNA complexes. The force-extension curves display spatial oscillations, and the extension of the chain, whose maximum value is bounded by the sphere diameter, scales as $f^{-1}$ at large forces, in contrast to the unconfined chain that approaches the contour length as $f^{-1/2}$. A WLC encapsulated in a sphere, that is relevant for the study of the viral encapsulation of DNA, can also be treated using the MF approach. The predictions of the theory for various correlation functions are in excellent agreement with Langevin simulations. We find that strongly confined chains are highly structured by examining the correlations using a local winding axis. The predicted pressure of the system is in excellent agreement with simulations but, as is known, is significantly lower than the pressures seen for DNA packaged in viral capsids.

29 pages, 8 figures

References in corpus (9)

• Forces During Bacteriophage DNA Packaging and Ejection
• DNA Spools under Tension
• Dynamics of DNA Ejection From Bacteriophage
• Kinetics of Interior Loop Formation in Semiflexible Chains
• Semiflexible Chains under Tension
• Semiflexible Polymer Confined in Closed Spaces
• Brownian Motion and Polymer Statistics on Certain Curved Manifolds
• Force steps during viral DNA packaging ?
• Unwrapping of DNA-protein complexes under external stretching

Cited by in corpus (6)

• Breakdown of the Kratky-Porod Wormlike Chain Model for Semiflexible Polymers in Two Dimensions
• Buckling of stiff polymer rings in weak spherical confinement
• Stochastic curvature of enclosed semiflexible polymers
• Entropic competition in polymeric systems under geometrical confinement
• From Octopus to Dendrite - Semiflexible Polyelectrolyte Brush Condensates in Trivalent Counterion Solution
• Compression-induced continuous phase transition in the buckling of a semiflexible filament for two and three dimensions