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1.  Statistical methods for detecting periodic fragments in DNA sequence data 
Biology Direct  2011;6:21.
Period 10 dinucleotides are structurally and functionally validated factors that influence the ability of DNA to form nucleosomes, histone core octamers. Robust identification of periodic signals in DNA sequences is therefore required to understand nucleosome organisation in genomes. While various techniques for identifying periodic components in genomic sequences have been proposed or adopted, the requirements for such techniques have not been considered in detail and confirmatory testing for a priori specified periods has not been developed.
We compared the estimation accuracy and suitability for confirmatory testing of autocorrelation, discrete Fourier transform (DFT), integer period discrete Fourier transform (IPDFT) and a previously proposed Hybrid measure. A number of different statistical significance procedures were evaluated but a blockwise bootstrap proved superior. When applied to synthetic data whose period-10 signal had been eroded, or for which the signal was approximately period-10, the Hybrid technique exhibited superior properties during exploratory period estimation. In contrast, confirmatory testing using the blockwise bootstrap procedure identified IPDFT as having the greatest statistical power. These properties were validated on yeast sequences defined from a ChIP-chip study where the Hybrid metric confirmed the expected dominance of period-10 in nucleosome associated DNA but IPDFT identified more significant occurrences of period-10. Application to the whole genomes of yeast and mouse identified ~ 21% and ~ 19% respectively of these genomes as spanned by period-10 nucleosome positioning sequences (NPS).
For estimating the dominant period, we find the Hybrid period estimation method empirically to be the most effective for both eroded and approximate periodicity. The blockwise bootstrap was found to be effective as a significance measure, performing particularly well in the problem of period detection in the presence of eroded periodicity. The autocorrelation method was identified as poorly suited for use with the blockwise bootstrap. Application of our methods to the genomes of two model organisms revealed a striking proportion of the yeast and mouse genomes are spanned by NPS. Despite their markedly different sizes, roughly equivalent proportions (19-21%) of the genomes lie within period-10 spans of the NPS dinucleotides {AA, TT, TA}. The biological significance of these regions remains to be demonstrated. To facilitate this, the genomic coordinates are available as Additional files 1, 2, and 3 in a format suitable for visualisation as tracks on popular genome browsers.
This article was reviewed by Prof Tomas Radivoyevitch, Dr Vsevolod Makeev (nominated by Dr Mikhail Gelfand), and Dr Rob D Knight.
PMCID: PMC3111405  PMID: 21527008
2.  Pitfalls of the most commonly used models of context dependent substitution 
Biology Direct  2009;4:10.
Correction to Lindsay H, Yap VB, Ying H, Huttley GA: Pitfalls of the most commonly used models of context dependent substitution. Biology Direct 2008, 3:52
PMCID: PMC2662811
3.  Pitfalls of the most commonly used models of context dependent substitution 
Biology Direct  2008;3:52.
Neighboring nucleotides exert a striking influence on mutation, with the hypermutability of CpG dinucleotides in many genomes being an exemplar. Among the approaches employed to measure the relative importance of sequence neighbors on molecular evolution have been continuous-time Markov process models for substitutions that treat sequences as a series of independent tuples. The most widely used examples are the codon substitution models. We evaluated the suitability of derivatives of the nucleotide frequency weighted (hereafter NF) and tuple frequency weighted (hereafter TF) models for measuring sequence context dependent substitution. Critical properties we address are their relationships to an independent nucleotide process and the robustness of parameter estimation to changes in sequence composition. We then consider the impact on inference concerning dinucleotide substitution processes from application of these two forms to intron sequence alignments from primates.
We prove that the NF form always nests the independent nucleotide process and that this is not true for the TF form. As a consequence, using TF to study context effects can be misleading, which is shown by both theoretical calculations and simulations. We describe a simple example where a context parameter estimated under TF is confounded with composition terms unless all sequence states are equi-frequent. We illustrate this for the dinucleotide case by simulation under a nucleotide model, showing that the TF form identifies a CpG effect when none exists. Our analysis of primate introns revealed that the effect of nucleotide neighbors is over-estimated under TF compared with NF. Parameter estimates for a number of contexts are also strikingly discordant between the two model forms.
Our results establish that the NF form should be used for analysis of independent-tuple context dependent processes. Although neighboring effects in general are still important, prominent influences such as the elevated CpG transversion rate previously identified using the TF form are an artifact. Our results further suggest as few as 5 parameters may account for ~85% of neighboring nucleotide influence.
This article was reviewed by Dr Rob Knight, Dr Josh Cherry (nominated by Dr David Lipman) and Dr Stephen Altschul (nominated by Dr David Lipman).
PMCID: PMC2628887  PMID: 19087239

Results 1-3 (3)