Multifractal analysis of DNA walks and trails

TL;DR

This paper investigates the fractal properties of DNA sequences by applying a generalized detrended fluctuation analysis, revealing that DNA walks and trails are monofractal with quantifiable fractal dimensions.

Contribution

It introduces a generalized DFA method to analyze DNA sequences and demonstrates that DNA walks and trails are monofractal, providing a new approach to characterize DNA's long-range order.

Findings

DNA walks exhibit monofractal structure regardless of local trends.

DNA trails have a fractal dimension related to the Hurst exponent of DNA walks.

Comparison with box-counting method highlights effects of finite length and local trends.

Abstract

The characterization of the long-range order and fractal properties of DNA sequences has proved a difficult though highly rewarding task due mainly to the mosaic character of DNA consisting of many interwoven patches of various lengths with different nucleotide constitutions. We apply here a recently proposed generalization of the detrended fluctuation analysis method to show that the DNA walk construction, in which the DNA sequence is viewed as a time series, exhibits a monofractal structure regardless of the existence of local trends in the series. In addition, we point out that the monofractal structure of the DNA walks carries over to an apparently alternative graphical construction given by the projection of the DNA walk into the $d$ spatial coordinates, termed DNA trails. In particular, we calculate the fractal dimension $D_t$ of the DNA trails using a well-known result of fractal theory linking $D_t$ to the Hurst exponent $H$ of the corresponding DNA walk. Comparison with estimates obtained by the standard box-counting method allows the evaluation of both finite-length and local trends effects.