A Generalized Topological Entropy for Analyzing the Complexity of DNA Sequences

Abstract

Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy. As an application the generalized topological entropy in introns, exons and promoter regions was computed, respectively. The results indicate that the entropy of introns is higher than that of exons, and the entropy of the exons is higher than that of the promoter regions for each chromosome, which suggest that DNA sequence of the promoter regions is more regular than the exons and introns.

Genome-Wide Prediction of DNA Methylation Using DNA Composition and Sequence Complexity in Human

“…In general, it studies combinatorial features of sequence by investigating factor complexity, and complexity function and topological entropy are two important research topics in this area [60,71,72,73,74,75]. More precisely, to study DNA sequence, here we restricted attentions on a four-letter alphabet $\mathrm{normal\Omega }=\{A,C,G,T\}$.…”

DNA entropy reveals a significant difference in complexity between housekeeping and tissue specific gene promoters

“…Five studies, applying definitions of topological entropy (Karamanos et al, 2006), Shannon entropy (Mantegna et al, 1995;Stanley et al, 1999), linguistic complexity (Troyanskaya et al, 2002) and lossless compression (Liu et al, 2008), conclude that non-coding DNA has a lower entropy than coding DNA. In contrast, 3 studies, one applying Shannon entropy (Mazaheri et al, 2010) and a 2 applying topological entropy (Koslicki 2011;Jin et al, 2014) conclude that non-coding DNA has higher entropy than coding DNA. The variation likely results from the differing and often very small DNA datasets used (Table 1), which for some analyses reflects the emphasis on the theoretical entropy calculation rather than its biological application.…”

“…The variation likely results from the differing and often very small DNA datasets used (Table 1), which for some analyses reflects the emphasis on the theoretical entropy calculation rather than its biological application. In addition some studies have defined noncoding DNA as intergenic DNA only (e.g., Mazaheri et al, 2010) or intronic DNA only (Koslicki 2011;Jin et al, 2014), whilst others have included both types of DNA as non-coding (Karamanos et al, 2006). If differences in entropies between different types of DNA are small, then it is not surprising that studies using different datasets and definitions have reached different conclusions.…”

“…Two recent studies both apply definitions of topological entropy to systematic random samples of genes from all chromosomes in the human genome, and conclude that introns have a higher entropy than exons (Koslicki 2011;Jin et al, 2014). This can be explained by the fact that entropy is a measure of the randomness of a DNA sequence, and introns are expected to be more random as they have fewer functional signals and are less conserved than exons (Koslicki 2011;Jin et al, 2014).…”

“…This can be explained by the fact that entropy is a measure of the randomness of a DNA sequence, and introns are expected to be more random as they have fewer functional signals and are less conserved than exons (Koslicki 2011;Jin et al, 2014). It has also been concluded that exons have a higher entropy than gene promoters (Jin et al, 2014), which could reflect the presence of multiple functional elements within the promoters which are under selection pressure. These include transcription factor binding sites (TFBSs) characterised by short sequence motifs that are highly degenerate.…”