CorGen—measuring and generating long-range correlations for DNA sequence analysis

CorGen is a web server that measures long-range correlations in the base composition of DNA and generates random sequences with the same correlation parameters. Long-range correlations are characterized by a power-law decay of the auto correlation function of the GC-content. The widespread presence of such correlations in eukaryotic genomes calls for their incorporation into accurate null models of eukaryotic DNA in computational biology. For example, the score statistics of sequence alignment and the performance of motif finding algorithms are significantly affected by the presence of genomic long-range correlations. We use an expansion-randomization dynamics to efficiently generate the correlated random sequences. The server is available a

Strong approximations of level exceedences related to multiple hypothesis testing

Particularly in genomics, but also in other fields, it has become commonplace to undertake highly multiple Student's $t$-tests based on relatively small sample sizes. The literature on this topic is continually expanding, but the main approaches used to control the family-wise error rate and false discovery rate are still based on the assumption that the tests are independent. The independence condition is known to be false at the level of the joint distributions of the test statistics, but that does not necessarily mean, for the small significance levels involved in highly multiple hypothesis testing, that the assumption leads to major errors. In this paper, we give conditions under which the assumption of independence is valid. Specifically, we derive a strong approximation that closely links the level exceedences of a dependent ``studentized process'' to those of a process of independent random variables. Via this connection, it can be seen that in high-dimensional, low sample-size cases, provided the sample size diverges faster than the logarithm of the number of tests, the assumption of independent $t$-tests is often justified.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ220 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Genomic DNA from animals shows contrasting strand bias in large and small subsequences

Abstract Background For eukaryotes, there is almost no strand bias with regard to base composition, with exceptions for origins of replication and transcription start sites and transcribed regions. This paper revisits the question for subsequences of DNA taken at random from the genome. Results For a typical mammal, for example mouse or human, there is a small strand bias throughout the genomic DNA: there is a correlation between (G - C) and (A - T) on the same strand, (that is between the difference in the number of guanine and cytosine bases and the difference in the number of adenine and thymine bases). For small subsequences – up to 1 kb – this correlation is weak but positive; but for large windows – around 50 kb to 2 Mb – the correlation is strong and negative. This effect is largely independent of GC%. Transcribed and untranscribed regions give similar correlations both for small and large subsequences, but there is a difference in these regions for intermediate sized subsequences. An analysis of the human genome showed that position within the isochore structure did not affect these correlations. An analysis of available genomes of different species shows that this contrast between large and small windows is a general feature of mammals and birds. Further down the evolutionary tree, other organisms show a similar but smaller effect. Except for the nematode, all the animals analysed showed at least a small effect. Conclusion The correlations on the large scale may be explained by DNA replication. Transcription may be a modifier of these effects but is not the fundamental cause. These results cast light on how DNA mutations affect the genome over evolutionary time. At least for vertebrates, there is a broad relationship between body temperature and the size of the correlation. The genome of mammals and birds has a structure marked by strand bias segments.</p

Strand bias structure in mouse DNA gives a glimpse of how chromatin structure affects gene expression

<p>Abstract</p> <p>Background</p> <p>On a single strand of genomic DNA the number of As is usually about equal to the number of Ts (and similarly for Gs and Cs), but deviations have been noted for transcribed regions and origins of replication.</p> <p>Results</p> <p>The mouse genome is shown to have a segmented structure defined by strand bias. Transcription is known to cause a strand bias and numerous analyses are presented to show that the strand bias in question is not caused by transcription. However, these strand bias segments influence the position of genes and their unspliced length. The position of genes within the strand bias structure affects the probability that a gene is switched on and its expression level. Transcription has a highly directional flow within this structure and the peak volume of transcription is around 20 kb from the A-rich/T-rich segment boundary on the T-rich side, directed away from the boundary. The A-rich/T-rich boundaries are SATB1 binding regions, whereas the T-rich/A-rich boundary regions are not.</p> <p>Conclusion</p> <p>The direct cause of the strand bias structure may be DNA replication. The strand bias segments represent a further biological feature, the chromatin structure, which in turn influences the ease of transcription.</p

Innovated higher criticism for detecting sparse signals in correlated noise

Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables are correlated. In this paper we show that, by exploiting the nature of the correlation, performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer. Indeed, it turns out that the case of independent noise is the most difficult of all, from a statistical viewpoint, and that more accurate signal detection (for a given level of signal sparsity and strength) can be obtained when correlation is present. We characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary. The boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is Toeplitz.Comment: Published in at http://dx.doi.org/10.1214/09-AOS764 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org