title: Local Renyi entropic profiles of DNA sequences.
abstract: BACKGROUND
  In a recent report the authors presented a new measure of continuous entropy for DNA sequences, which allows the estimation of their randomness level. The definition therein explored was based on the Rényi entropy of probability density estimation (pdf) using the Parzen's window method and applied to Chaos Game Representation/Universal Sequence Maps (CGR/USM). Subsequent work proposed a fractal pdf kernel as a more exact solution for the iterated map representation. This report extends the concepts of continuous entropy by defining DNA sequence entropic profiles using the new pdf estimations to refine the density estimation of motifs.
  
  
  RESULTS
  The new methodology enables two results. On the one hand it shows that the entropic profiles are directly related with the statistical significance of motifs, allowing the study of under and over-representation of segments. On the other hand, by spanning the parameters of the kernel function it is possible to extract important information about the scale of each conserved DNA region. The computational applications, developed in Matlab m-code, the corresponding binary executables and additional material and examples are made publicly available at http://kdbio.inesc-id.pt/~svinga/ep/.
  
  
  CONCLUSIONS
  The ability to detect local conservation from a scale-independent representation of symbolic sequences is particularly relevant for biological applications where conserved motifs occur in multiple, overlapping scales, with significant future applications in the recognition of foreign genomic material and inference of motif structures.
authors.affiliation: Instituto de Engenharia de Sistemas e Computadores: Investigação e Desenvolvimento (INESC-ID), R, Alves Redol 9, 1000-029 Lisboa, Portugal. svinga@kdbio.inesc-id.pt
authors.forename: Susana
authors.initials: S
authors.lastname: Vinga
authors.forename: Jonas S
authors.initials: JS
authors.lastname: Almeida
mesh_terms: D001483:Base Sequence; D017124:Conserved Sequence / Q000235:genetics; D003627:Data Interpretation, Statistical; D019277:Entropy; D004926:Escherichia coli / Q000235:genetics; D005716:Game Theory; D016680:Genome, Bacterial; D006193:Haemophilus influenzae / Q000235:genetics; D008390:Markov Chains; D010363:Pattern Recognition, Automated / Q000379:methods; D011237:Predictive Value of Tests; D017422:Sequence Analysis, DNA / Q000379:methods*; D012984:Software; D035501:Uncertainty