# Scaling of the average crossing number in equilateral random walks, knots and proteins

## Details

Serval ID

serval:BIB_69DF70FFD76D

Type

**Inproceedings**: an article in a conference proceedings.

Collection

Publications

Institution

Title

Scaling of the average crossing number in equilateral random walks, knots and proteins

Title of the conference

Physical and Numerical Models in Knot Theory

Organization

Conference on Knots Random Walks and Biomolecules. Les Diablerets, Switzerland, Jul 14-17, 2003

ISBN

981-256-187-0

Publication state

Published

Issued date

2005

Volume

36

Series

Series on Knots and Everything

Pages

219-231

Language

english

Notes

We compare here the scaling behaviour of the mean average crossing number (ACN) of equilateral random walks in linear and closed form with the corresponding scaling of natural protein structures. We have shown recently that the scaling of (ACN) of equilateral random walks of length n follows the relation (ACN) = 3/16 n ln n + bn and that a similar result holds for equilateral random polygons Furthermore, our earlier numerical studies indicated that when random polygons of length n, are divided into individual knot types, the (ACN(K)) for each knot type K can be described by a function of the form (ACN(K)) = alpha(n -n(0)) ln(n - n(0)) + b(n - n(0)) + c where a, b and c are constants depending on K and no is the minimal number of segments required to form K-14. Here we analyze in addition natural protein structures and observe that the relation (ACN) = 3/16 n ln n + bn also describes accurately the scaling Of (ACN) of protein backbones.

Create date

24/01/2008 11:25

Last modification date

20/08/2019 15:24