Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences

TL;DR

This study demonstrates that diffusively coupled Chebyshev maps can effectively model the multifractal spectrum of human genomic sequences, highlighting the role of rare configurations in genomic function.

Contribution

It introduces a novel application of coupled map lattices to replicate the multifractal properties of genomic sequences, emphasizing the importance of rare configurations.

Findings

CMLs closely reproduce the multifractal spectrum for q>0

Deviations occur for q<0 due to rare configurations

Modifying rare event statistics aligns the model with genomic data

Abstract

Symbolic sequences generated by coupled map lattices (CMLs) can be used to model the chaotic-like structure of genomic sequences. In this study it is shown that diffusively coupled Chebyshev maps of order 4 (corresponding to a shift of 4 symbols) very closely reproduce the multifractal spectrum $D_q$ of human genomic sequences for coupling constant $\alpha =0.35\pm 0.01$ if $q>0$. The presence of rare configurations causes deviations for $q<0$, which disappear if the rare event statistics of the CML is modified. Such rare configurations are known to play specific functional roles in genomic sequences serving as promoters or regulatory elements.