The modular structure of informational sequences

On the origin of long-range correlations in texts

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical properties of our linguistic output has to be highly correlated in time. An example are the robust observations, still largely not understood, of correlations on arbitrary long scales in literary texts. In this paper we explain how long-range correlations flow from highly structured linguistic levels down to the building blocks of a text (words, letters, etc..). By combining calculations and data analysis we show that correlations take form of a bursty sequence of events once we approach the semantically relevant topics of the text. The mechanisms we identify are fairly general and can be equally applied to other hierarchical settings.

Peptide vocabulary analysis reveals ultra-conservation and homonymity in protein sequences

A new algorithm is presented for vocabulary analysis (word detection) in texts of human origin. It performs at 60%-70% overall accuracy and greater than 80% accuracy for longer words, and approximately 85% sensitivity on Alice in Wonderland, a considerable improvement on previous methods. When applied to protein sequences, it detects short sequences analogous to words in human texts, i.e. intolerant to changes in spelling (mutation), and relatively context-independent in their meaning (function). Some of these are homonyms of up to 7 amino acids, which can assume different structures in different proteins. Others are ultra-conserved stretches of up to 18 amino acids within proteins of less than 40% overall identity, reflecting extreme constraint or convergent evolution. Different species are found to have qualitatively different major peptide vocabularies, e.g. some are dominated by large gene families, while others are rich in simple repeats or dominated by internally repetitive proteins. This suggests the possibility of a peptide vocabulary signature, analogous to genome signatures in DNA. Homonyms may be useful in detecting convergent evolution and positive selection in protein evolution. Ultra-conserved words may be useful in identifying structures intolerant to substitution over long periods of evolutionary time.

Revisiting the relationship between compositional sequence complexity and periodicity

BACKGROUND

Given a big sequence fragment or a set of functionally related sequences we consider two problems of a sequence analysis associated with the given sequence(s). The first problem is to measure sequence complexity (repetitiveness, compactness) to estimate how informative the set as a whole is. Usually an obtained measure should be compared with an appropriate random background calculated using permutation of the given sequences. We propose a novel and effective approach for background information measurement instead of the usual sequence reshuffling. The second problem is to detect a periodic bias to determine if it is one of the set features. Sequence periodicity, when sometimes one has in mind hidden periodicity, is a very basic genomic property. The sequence period of 3, which is considered to characterize coding sequences, and period 10-11, which may be due to the alternation of hydrophobic and hydrophilic amino acids, DNA curvature, and bendability were discovered and described. Searching for periodical biases brought significant results in the study of sequence-dependent nucleosome positioning: nucleosomal sites carry hidden period of about 10.4 bases.

RESULTS

Calculated differences between genomic sequences and background showed high biological relevancy of the method that we proposed in this study. Our algorithm was applied to a few natural and artificial datasets. We constructed a simple "periodic" dataset by replacement of every tenth dinucleotide in each sequence of a trial set by the same dinucleotide "CC". We showed that the method reveals the introduced periodicity and that this periodical pattern carries higher information than in uninterrupted subsequences. An application of the method to the nucleosomal dataset revealed a weak pseudo-periodicity of 10.4 nucleotides confirming previous knowledge. An application of the method to Escherichia coli datasets revealed the well-known periodicity of 3bp as a genic attribute, a secondary genic period slightly larger than 11bp, and an intergenic period a bit smaller than 11bp.

CONCLUSIONS

We reported a novel compositional complexity-based method for sequence analysis. We found that the difference between the sequence complexity of a natural sequence and of background is especially high for a set consisting exclusively of coding sequences. Hidden periodicities were found with no need of any preliminary assumptions regarding a composition of periodic elements. We illustrated the power of the method by studying the sets with known weak periodic properties: a nucleosomal database and sets of different regions of E. coli. We showed that the method conveniently indicated all kinds of periodicity and related features in these sets of DNA sequences.

Condensed representation of DNA primary sequences

With rapid reporting of DNA sequences derived from automated DNA sequencing techniques, the problem of reviewing and ordering such information has become acute. We have introduced a condensed representation of primary sequences of DNA that offers an alternative method of registering DNA. The advantage of the condensed codes for DNA is that it not only offers fast, qualitative comparisons of DNA but also allows quantitative comparisons of DNA from different sources. The approach is outlined for a particular human beta globin sequence extract. Using the condensed representation of the primary DNA sequences, comparisons are made between primary sequences for Exon 1 of human beta globin and seven other beta globins.

Distributions of distances in information strings

Distances between identical symbols in information strings (biological, language, computer programs (*.exe files) are described with a different precision with four distributions: exponential, Weibull, log-normal and negative binomial. The correlations are sometimes highly significant.