Symbolic Complexity for Nucleotide Sequences: A Sign of the Genome Structure

TL;DR

This paper presents a new method to estimate the complexity of symbolic sequences, applied to genomes, revealing exponential and linear behaviors in complexity functions and similarities among related species.

Contribution

Introduces a novel complexity estimation technique for symbolic sequences and applies it to genomes, uncovering characteristic complexity patterns and phylogenetic similarities.

Findings

Genomes exhibit exponential complexity for small words and linear for larger words.

Phylogenetically related species have similar complexity functions.

The method accurately estimates complexity in known symbolic dynamical systems.

Abstract

We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly. We use this technique to estimate the complexity function for genomes of several organisms under the assumption that a genome is a sequence produced by a (unknown) dynamical system. We show that the genome of several organisms share the property that their complexity functions behaves exponentially for words of small length $\ell$ ($0\leq \ell \leq 10$) and linearly for word lengths in the range $11 \leq \ell \leq 50$. It is also found that the species which are phylogenetically close each other have similar complexity functions calculated from a sample of their corresponding coding regions.