Fractional brownian motion: Theory and application to DNA walk

Lim, S. C. and Muniandy, S. V. (2000) Fractional brownian motion: Theory and application to DNA walk. In: Proceedings of the First Workshop Biological Physics. World Scientific Publishing, pp. 214-233. ISBN 9789812811301

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Official URL: http://adsabs.harvard.edu/abs/2001biph.conf..214L

Abstract

This paper briefly reviews the theory of fractional Brownian motion (FBM) and its generalization to multifractional Brownian motion (MBM). FBM and MBM are applied to a biological system namely the DNA sequence. By considering a DNA sequence as a fractal random walk, it is possible to model the noncoding sequence of human retinoblastoma DNA as a discrete version of FBM. The average scaling exponent or Hurst exponent of the DNA walk is estimated to be H = 0.60 ± 0.05 using the monofractal R/S analysis. This implies that the mean square fluctuation of DNA walk belongs to anomalous superdiffusion type. We also show that the DNA landscape is not monofractal, instead one has multifractal DNA landscape. The empirical estimates of the Hurst exponent falls approximately within the range H ~ 0.62 - 0.72. We propose two multifractal models, namely the MBM and multiscale FBM to describe the existence of different Hurst exponents in DNA walk.

Item Type: Book Section
Additional Information: PROCEEDINGS OF THE WORKSHOP ON BIOLOGICAL PHYSICS; 214-233 Biological physics Workshop; 1st, Biological physics
Subjects: T Technology > T Technology (General)
Depositing User: Ms Suzilawati Abu Samah
Date Deposited: 03 Jan 2014 01:06
Last Modified: 03 Jan 2014 01:06
URI: http://shdl.mmu.edu.my/id/eprint/4714

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