DNA viewed as an out-of-equilibrium structure

Abstract

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a low order Markov chain of order up to r = 6. Although detailed balance seems to hold at the level of purine-pyrimidine notation it fails when all four basepairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain we study the exit distances from a specific symbol, the distribution of recurrence distances and the Hurst exponent, all of which show power law tails and long range characteristics. These results suggest that human DNA can be viewed as a non-equilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method we construct a model DNA sequence. This method allows to keep all long range and short range statistical characteristics of the original sequence. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture point-to-point details. *

Complexity measures for the evolutionary categorization of organisms

“…In particular, regarding strand asymmetry we develop a different view than the one usually adopted in the literature. Specifically, as argued in a recent work by the present authors (Provata et al, 2014), spatial asymmetry is probed in single DNA strands and is found to give different information content when read from left-to-right than from right-to-left, indicating that DNA chromosomes can be regarded as out-of-equilibrium structures. It must be noted that the difference in the A and T content (or the C and G one) is not identical with the asymmetry produced in the reading sense.…”

“…In parallel, interesting correlations related to the presence of the CpG islands were discovered (Arneodo et al, 2011;Polak and Arndt, 2009;Li and Miramontes, 2006;Zhang and Chen, 2005;Freudenberg et al, 2009;Li and Holste, 2005;Clement and Arndt, 2011;Carpena et al, 2011) and their occurrence was connected with the central role of the CG complex as a structural element of the promoter sequences (Katsaloulis et al, 2006(Katsaloulis et al, , 2009. Long range correlations were further demonstrated in the word frequency (Ebeling and Nicolis, 1991), in the information content (Roman-Roldann et al, 1996;Provata et al, 2014), in the size distribution of noncoding sequences (Almirantis and Provata, 1999), in the distribution of repeats (Massip and Arndt, 2013) and in the persistence and antipersistence of symbols (Almirantis and Provata, 1999;Melnyk et al, 2005;Zhou et al, 2004;Marx et al, 2006). Strand asymmetry has also been studied extensively in DNA literature, in the sense of a departure from intrastrand equifrequency between the A and T nucleotides and the C and G ones (Elson and Chargaff, 1952;Rudner et al, 1968;Lobry, 1996;Francino and Ochman, 1997).…”

“…One particular factor which accentuates asymmetry is clustering of homologous nucleotides. Indeed, in Provata et al (2014) long range correlations were recorded in the clustering properties (exit distance and recurrence distributions), a characteristic frequently observed in out-of-equilibrium structures. In the same work the natural human DNA strands were compared against different stochastic processes using entropy and information measures, demonstrating marked deviation from stochasticity.…”

“…We examine long DNA sequences and whole chromosomes from five organisms belonging to distinctly different evolutionary classes, the primates (one organism, Homo sapiens), the transition single-to multi-cell eukaryotes (one organism, Polysphondylium pallidum), the single cell eukaryotes (one organism, Saccharomyces cerevisiae) and bacteria (two organisms, Escherichia coli and Bacillus subtilis). For their comparison we use the evolutionary measures previously applied to the human chromosome 10 (Provata et al, 2014). These measures are borrowed from the theory of nonlinear dynamics, statistical mechanics and information theory and they are investigated here as potential indicators of evolution, permitting to discriminate between organisms belonging to different evolutionary classes.…”

Kinetics and thermodynamics of exonuclease-deficient DNA polymerases

“…This quantity, which is often called information Shannon entropy, is studied to characterize the complexity of DNA symbolic sequences in various biological organisms [56][57][58]. The overall disorder per nucleotide is observed to vary from the value D(α) ≃ 1.339 assuming the sequence α is a first-order Markov chain, down to D(α) ≃ 1.273 if α is a 8 th -order Markov chain, which suggests the existence of long-range correlations besides the fact that the four nucleotides occur with unequal probabilities in typical DNA sequences [57,58]. In the present paper, the template is supposed to be a Bernoulli chain with equal probabilities ν 1 (n) = It should be pointed out that the sequence carries information to the extent that it is replicated, transcripted, or translated into proteins in living organisms.…”