Elasticity of connected semiflexible quadrilaterals

Razbin, Mohammadhosein; Mashaghi, Alireza

doi:10.1039/d0sm01719a

Cited by 4 publications

(5 citation statements)

References 95 publications

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“…In future work, we extend our model to multiple (bio)polymer chains that are tangled together and to include intrachain bonds (known as hard contacts) as well as soft contacts. Analogous to how mechanical and folding kinetic properties of folded polymers were shown to be correlated with the number and arrangement of hard contacts [18][19][20]34 , we expect that the same will be true for soft contacts, though this has yet to be verified experimentally. Our tile-based model provides rigorous definitions for how to count the number and measure the complexity of the arrangement of soft contacts, and thus makes it possible to design experiments to test the mechanical properties of complexes made from self-entangled building blocks.…”

Section: Discussionmentioning

confidence: 86%

A tile model of circuit topology for self-entangled biopolymers

Flapan

Mashaghi

Wong

2023

Sci Rep

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Building on the theory of circuit topology for intra-chain contacts in entangled proteins, we introduce tiles as a way to rigorously model local entanglements which are held in place by molecular forces. We develop operations that combine tiles so that entangled chains can be represented by algebraic expressions. Then we use our model to show that the only knot types that such entangled chains can have are $$3_1$$ 3 1 , $$4_1$$ 4 1 , $$5_1$$ 5 1 , $$5_2$$ 5 2 , $$6_1$$ 6 1 , $$6_2$$ 6 2 , $$6_3$$ 6 3 , $$7_7$$ 7 7 , $$8_{12}$$ 8 12 and connected sums of these knots. This includes all proteins knots that have thus far been identified.

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Section: Discussionmentioning

confidence: 86%

A tile model of circuit topology for self-entangled biopolymers

Flapan

Mashaghi

Wong

2023

Sci Rep

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“…The conditional probability density to find the end point of the chain at position (x, y) with orientation θ, given that it is grafted at position (x 0 , y 0 ) with orientation ω, is denoted by G L,l p (x, y, θ|x 0 , y 0 , ω) and is called the positional-orientational propagator because it obeys the Chapman-Kolmogorov equation. In the weakly bending regime, the propagator is calculated in closed analytic form [3,5,[15][16][17][18][19]:…”

Section: The Positional-orientational Propagator Of a Wlc At The Stif...mentioning

confidence: 99%

Grafted Semiflexible Nunchucks with a Magnetic Bead Attached to the Free End

Razbin

Benetatos

2022

Polymers

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Semiflexible nunchucks are block copolymers, which consist of two long blocks of high bending stiffness jointed together by a short block of low bending stiffness. Semiflexible nunchucks that consist of two DNA nanorods jointed by a short segment of double-stranded (ds) DNA and confined in two dimensions have been used in recent experiments by Fygenson and coworkers as a tool to magnify the bending fluctuations of the linking dsDNA, which in turn are used to deduce the persistence length of dsDNA. In a recent theoretical analysis, we showed that in a semiflexible nunchuck with one end grafted, the fluctuations of the position of the free end that is transverse to the grafting direction exhibit a pronounced bimodality, provided that the bending stiffness of the hinge is not very large. In this article, we theoretically analyse a grafted semiflexible nunchuck with a magnetic bead attached to its free end. We show that a transverse magnetic field induces an asymmetry in the bimodal distribution of the transverse fluctuations of the free end. This asymmetry is very sensitive to interactions with a magnetic field and, in principle, could be used in magnetometry (the measurement of a magnetic field or the magnetic moment of the bead). We also investigate how the response of the bimodal distribution of the transverse fluctuations of the free end to a magnetic field depends on the bending stiffness of the nunchuck hinge. In addition, we analyse the closely related systems of a single filament and two filaments jointed at a kink point with one end grafted and the other end attached to a magnetic bead.

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“…In order to calculate it, we use the method introduced in Refs. [ 47 , 48 , 52 ]. We view this force as entropic, originating in the reduction of the number of configurations of the system due to the presence of the confining wall.…”

Section: Force Exerted On a Stiff Planar Wall By The Tip Of The Kinke...mentioning

confidence: 99%

“…All of the calculations are based on the Gaussian approximation of the WLC model, which is valid in the weakly bending regime (the stiff chain limit). The Gaussian two-point positional-orientational probability (propagator or Green’s function) has been used in the theoretical analysis of various systems of rod-like elements, such as semiflexible nunchucks [ 41 , 46 ], branched actin filaments [ 47 ], and semiflexible quadrilaterals [ 48 ].…”

Section: Introductionmentioning

confidence: 99%

Elasticity of Semiflexible ZigZag Nanosprings with a Point Magnetic Moment

Razbin

Benetatos

2022

Polymers

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Kinks can appear along the contour of semiflexible polymers (biopolymers or synthetic ones), and they affect their elasticity and function. A regular sequence of alternating kink defects can form a semiflexible nanospring. In this article, we theoretically analyze the elastic behavior of such a nanospring with a point magnetic dipole attached to one end while the other end is assumed to be grafted to a rigid substrate. The rod-like segments of the nanospring are treated as weakly bending wormlike chains, and the propagator (Green’s function) method is used in order to calculate the conformational and elastic properties of this system. We analytically calculate the distribution of orientational and positional fluctuations of the free end, the force-extension relation, as well as the compressional force that such a spring can exert on a planar wall. Our results show how the magnetic interaction affects the elasticity of the semiflexible nanospring. This sensitivity, which is based on the interplay of positional and orientational degrees of freedom, may prove useful in magnetometry or other applications.

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Elasticity of connected semiflexible quadrilaterals

Abstract: The analytic expressions for the probability densities associated with the thermal fluctuations and the elasticity of the structure are obtained.

Cited by 4 publications

References 95 publications

A tile model of circuit topology for self-entangled biopolymers

A tile model of circuit topology for self-entangled biopolymers

Grafted Semiflexible Nunchucks with a Magnetic Bead Attached to the Free End

Elasticity of Semiflexible ZigZag Nanosprings with a Point Magnetic Moment

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