Orientational Fluctuations and Bimodality in Semiflexible Nunchucks.

Panayotis Benetatos,Mohammadhosein Razbin

doi:10.3390/polym13122031

Panayotis Benetatos, Mohammadhosein Razbin

Open Access

https://doi.org/10.3390/polym13122031

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Abstract

Semiflexible nunchucks are block copolymers consisting of two long blocks with high bending rigidity jointed by a short block of lower bending stiffness. Recently, the DNA nanotube nunchuck was introduced as a simple nanoinstrument that mechanically magnifies the bending angle of short double-stranded (ds) DNA and allows its measurement in a straightforward way [Fygenson et al., Nano Lett. 2020, 20, 2, 1388–1395]. It comprises two long DNA nanotubes linked by a dsDNA segment, which acts as a hinge. The semiflexible nunchuck geometry also appears in dsDNA with a hinge defect (e.g., a quenched denaturation bubble or a nick), and in end-linked stiff filaments. In this article, we theoretically investigate various aspects of the conformations and the tensile elasticity of semiflexible nunchucks. We analytically calculate the distribution of bending fluctuations of a wormlike chain (WLC) consisting of three blocks with different bending stiffness. For a system of two weakly bending WLCs end-jointed by a rigid kink, with one end grafted, we calculate the distribution of positional fluctuations of the free end. For a system of two weakly bending WLCs end-jointed by a hinge modeled as harmonic bending spring, with one end grafted, we calculate the positional fluctuations of the free end. We show that, under certain conditions, there is a pronounced bimodality in the transverse fluctuations of the free end. For a semiflexible nunchuck under tension, under certain conditions, there is bimodality in the extension as a function of the hinge position. We also show how steric repulsion affects the bending fluctuations of a rigid-rod nunchuck.

Highlights

Semiflexible polymers are macromolecules with a finite bending stiffness
Under certain conditions, there is a pronounced bimodality in the distribution of transverse positional fluctuations
We theoretically investigated several aspects of the conformational and elastic behavior of the semiflexible nunchucks

Summary

Introduction

Semiflexible polymers are macromolecules with a finite bending stiffness. Some of the most important biomolecules, such as DNA or the structural elements of the cytoskeleton (F-actin, microtubules, intermediate filaments), are natural semiflexible polymers [1]. The twopoint orientational probability distribution of the WLC, unlike the quantum rotator density operator or propagator, is not invariant under full rotations of the tangent vector at a point along the chain contour. Such a rotation corresponds to a different conformation of the polymer. Fygenson et al [7] attached both ends of short double-stranded DNA (dsDNA) chains to fluorescently labeled DNA nanotubes confined to fluctuate in two dimensions They extracted the distribution of the bending angle of the dsDNA through direct imaging of the nanotubes. We point out that even though Equations (13) and (14) rely on the validity of the weakly bending approximation, Equation (15) is exact

Conformational Probabilities of Kinked and Hinged Stiff Chains

Rigid-Rod Nunchuck with Excluded Volume Interaction

Bimodality in the Tensile Elasticity of a Semiflexible Nunchuck

Conclusions