# MATH

@article{Fulk1992MATH, title={MATH}, author={Barbara J. Mushinski Fulk}, journal={Intervention in School and Clinic}, year={1992}, volume={27}, pages={236 - 240} }

Abstract: About a decade ago, biophysicists observed an approximately linear relationship between the combinatorial complexity of knotted DNA and the distance traveled in gel electrophoresis experiments [I}. Modeling the DNA as tightly knotted rope of uniform thickness, it was suggested that lengths of such tight knots (rescaled to have unit thickness) would grow linearly with crossing numbers, a simple measure of knot complexity. It turned out that this relationship is more subtle: some…

## 29,739 Citations

DNA elasticity: topology of self-avoidance

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We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self-avoiding ribbons and provide an underlying justification for…

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It follows that all circular micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids.

Protein-mediated DNA loops: effects of protein bridge size and kinks.

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This paper investigates the dependence of this probability upon the size of a protein bridge and/or the presence of a kink at half DNA length and finds that the looping free energy of a 100-base-pairs DNA decreases from 24 kBT to 13 kBT when the loop is closed by a protein of r=10 length.

From one cell to the whole froth: A dynamical map.

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It is proved that any froth can be reduced into a system of concentric shells, and the topological characteristics of all experimentally known tetrahedrally close-packed structures are retrieved.

Equation of state of looped DNA.

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- 2007

The functional form of the force-extension curve resembles that of straight DNA, yet with a strongly renormalized apparent persistence length, which means that the experimentally extracted single-molecule elasticity can also contain additional contributions that depend on the overall chain conformation and length.

Exponents governing the rarity of disjoint polymers in Brownian last passage percolation

- MathematicsProceedings of the London Mathematical Society
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In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two‐thirds…

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We introduce the Writhe Application Software Package (WASP) which can be used to characterise the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid…

An Exposition of the Madsen-Weiss Theorem

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The theorem of Madsen and Weiss [MW] identifies the homology of mapping class groups of surfaces, in a stable dimension range, with the homology of a certain infinite loopspace. This result is not…

Twist-bend coupling and the statistical mechanics of DNA: perturbation theory and beyond

- PhysicsbioRxiv
- 2018

A perturbative calculation of the effective torsional stiffness Ceff for small twist-bend coupling finds that the “bare” G is “screened” by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with G = 0, but with long-wavelength bending and twisting rigidities that are shifted by G-dependent amounts.