Abstract
In recent years, the analysis of genomes by means of strings of length k occurring in the genomes, called k-mers, has provided important insights into the basic mechanisms and design principles of genome structures. In the present study, we focus on the proper choice of the value of k for applying information theoretic concepts that express intrinsic aspects of genomes. The value k = lg2(n), where n is the genome length, is determined to be the best choice in the definition of some genomic informational indexes that are studied and computed for seventy genomes. These indexes, which are based on information entropies and on suitable comparisons with random genomes, suggest five informational laws, to which all of the considered genomes obey. Moreover, an informational genome complexity measure is proposed, which is a generalized logistic map that balances entropic and anti-entropic components of genomes and is related to their evolutionary dynamics. Finally, applications to computational synthetic biology are briefly outlined.
Highlights
The analysis of genomes by means of strings of length k occurring in the genomes, called k-mers, has provided important insights into the basic mechanisms and design principles of genome structures
Many studies have approached the investigation of DNA strings and genomes by means of algorithms, information theory and formal languages[11,12,13,14,15,16,17,18,19,20,21,22], and methods were developed for investigating whole genome structures
We prove that preferential lengths exist for computing entropies, and in correspondence with these lengths, some informational indexes can be defined that exhibit “informational laws” and characterize an informational structure of genomes
Summary
The analysis of genomes by means of strings of length k occurring in the genomes, called k-mers, has provided important insights into the basic mechanisms and design principles of genome structures. In genome analyses based on dictionaries, concepts from formal language theory, probability, and information theory are naturally combined by providing new perspectives in the investigation of genomes, which may disclose the internal logics of their structures. A point that is crucial in genome analyses based on k-mers is the value of k that is more adequate for specific investigations This issue becomes extremely evident when computing the entropy of a genome. We follow an information theoretic line of investigation based on k-mer dictionaries and entropies[16,26,27,31,32,33], which is aimed at defining and computing informational indexes for a representative set of www.nature.com/scientificreports/
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