title: Revisiting the relationship between compositional sequence complexity and periodicity.
abstract: 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.
authors.affiliation: Genome Diversity Center, University of Haifa, Haifa, Israel. bolshoy@research.haifa.ac.il
authors.forename: Alexander
authors.initials: A
authors.lastname: Bolshoy
mesh_terms: D000465:Algorithms; D001483:Base Sequence; D030561:Databases, Nucleic Acid; D029968:Escherichia coli Proteins / Q000737:chemistry*; D008969:Molecular Sequence Data; D010363:Pattern Recognition, Automated; D010507:Periodicity; D012984:Software
chemical_list: D029968:Escherichia coli Proteins