Complexity measures for the evolutionary categorization of organisms

Bioinformatics tools for the sequence complexity estimates

We review current methods and bioinformatics tools for the text complexity estimates (information and entropy measures). The search DNA regions with extreme statistical characteristics such as low complexity regions are important for biophysical models of chromosome function and gene transcription regulation in genome scale. We discuss the complexity profiling for segmentation and delineation of genome sequences, search for genome repeats and transposable elements, and applications to next-generation sequencing reads. We review the complexity methods and new applications fields: analysis of mutation hotspots loci, analysis of short sequencing reads with quality control, and alignment-free genome comparisons. The algorithms implementing various numerical measures of text complexity estimates including combinatorial and linguistic measures have been developed before genome sequencing era. The series of tools to estimate sequence complexity use compression approaches, mainly by modification of Lempel-Ziv compression. Most of the tools are available online providing large-scale service for whole genome analysis. Novel machine learning applications for classification of complete genome sequences also include sequence compression and complexity algorithms. We present comparison of the complexity methods on the different sequence sets, the applications for gene transcription regulatory regions analysis. Furthermore, we discuss approaches and application of sequence complexity for proteins. The complexity measures for amino acid sequences could be calculated by the same entropy and compression-based algorithms. But the functional and evolutionary roles of low complexity regions in protein have specific features differing from DNA. The tools for protein sequence complexity aimed for protein structural constraints. It was shown that low complexity regions in protein sequences are conservative in evolution and have important biological and structural functions. Finally, we summarize recent findings in large scale genome complexity comparison and applications for coronavirus genome analysis.

Spatial constrains and information content of sub-genomic regions of the human genome

Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities of DNA sequences (exonic, intronic, intergenic, repeat, unique) with the purpose to ask questions regarding the segmental organization of the human genome within the size distribution of these sequences. For this we developed an integrated methodology that is based upon the reconstructed phase space theorem, the non-extensive statistical theory of Tsallis, ML techniques, and a technical index, integrating the generated information, which we introduce and named complexity factor (COFA). Our analysis revealed that the size distribution of the genomic regions within chromosomes are not random but follow patterns with characteristic features that have been seen through its complexity character, and it is part of the dynamics of the whole genome. Finally, this picture of dynamics in DNA is recognized using ML tools for clustering, classification, and prediction with high accuracy.

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The lengths of DNA subgenomic entities satisfied the Tsallis non-extensive statistics

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The size distribution of the subgenomic entities within chromosomes follow specific patterns

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A technical index COFA was introduced to characterize the degree of complexity

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The degree of complexity behavior in DNA is identifiable using ML approaches

Uncovering patterns of the evolution of genomic sequence entropy and complexity

The lack of consensus concerning the biological meaning of entropy and complexity of genomes and the different ways to assess these data hamper conclusions concerning what are the causes of genomic entropy variation among species. This study aims to evaluate the entropy and complexity of genomic sequences of several species without using homologies to assess relationships among these variables and non-molecular data (e.g., the number of individuals) to seek a trigger of interspecific genomic entropy variation. The results indicate a relationship among genomic entropy, genome size, genomic complexity, and the number of individuals: species with a small number of individuals harbors large genome, and hence, low entropy but a higher complexity. We defined that the complexity of a genome relies on the entropy of each DNA segment within genome. Then, the entropy and complexity of a genome reflects its organization solely. Exons of vertebrates harbor smaller entropies than non-exon regions (likely by the repeats that accumulated from duplications), whereas other taxonomic groups do not present this pattern. Our findings suggest that small initial population might have defined current genomic entropy and complexity: actual genomes are less complex than ancestral ones. Besides, our data disagree with the relationship between phenotype and genomic entropies previously established. Finally, by establishing the relationship between genomic entropy/complexity with the number of individuals and genome size, under an evolutive perspective, ideas concerning the genomic variability may emerge.

Iterated function systems for DNA replication

The kinetic equations of DNA replication are shown to be exactly solved in terms of iterated function systems, running along the template sequence and giving the statistical properties of the copy sequences, as well as the kinetic and thermodynamic properties of the replication process. With this method, different effects due to sequence heterogeneity can be studied, in particular, a transition between linear and sublinear growths in time of the copies, and a transition between continuous and fractal distributions of the local velocities of the DNA polymerase along the template. The method is applied to the human mitochondrial DNA polymerase γ without and with exonuclease proofreading.

Kinetics and thermodynamics of living copolymerization processes

Theoretical advances are reported on the kinetics and thermodynamics of free and template-directed living copolymerizations. Until recently, the kinetic theory of these processes had only been established in the fully irreversible regime, in which the attachment rates are only considered. However, the entropy production is infinite in this regime and the approach to thermodynamic equilibrium cannot be investigated. For this purpose, the detachment rates should also be included. Inspite of this complication, the kinetics can be exactly solved in the regimes of steady growth and depolymerization. In this way, analytical expressions are obtained for the mean growth velocity, the statistical properties of the copolymer sequences, as well as the thermodynamic entropy production. The results apply to DNA replication, transcription and translation, allowing us to understand important aspects of molecular evolution.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Kinetics and thermodynamics of exonuclease-deficient DNA polymerases

A kinetic theory is developed for exonuclease-deficient DNA polymerases, based on the experimental observation that the rates depend not only on the newly incorporated nucleotide, but also on the previous one, leading to the growth of Markovian DNA sequences from a Bernoullian template. The dependencies on nucleotide concentrations and template sequence are explicitly taken into account. In this framework, the kinetic and thermodynamic properties of DNA replication, in particular, the mean growth velocity, the error probability, and the entropy production are calculated analytically in terms of the rate constants and the concentrations. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.