Multivariate Hawkes process models of the occurrence of regulatory elements.

BACKGROUND: A central question in molecular biology is how transcriptional regulatory elements (TREs) act in combination. Recent high-throughput data provide us with the location of multiple regulatory regions for multiple regulators, and thus with the possibility of analyzing the multivariate distribution of the occurrences of these TREs along the genome. RESULTS: We present a model of TRE occurrences known as the Hawkes process. We illustrate the use of this model by analyzing two different publically available data sets. We are able to model, in detail, how the occurrence of one TRE is affected by the occurrences of others, and we can test a range of natural hypotheses about the dependencies among the TRE occurrences. In contrast to earlier efforts, pre-processing steps such as clustering or binning are not needed, and we thus retain information about the dependencies among the TREs that is otherwise lost. For each of the two data sets we provide two results: first, a qualitative description of the dependencies among the occurrences of the TREs, and second, quantitative results on the favored or avoided distances between the different TREs. CONCLUSIONS: The Hawkes process is a novel way of modeling the joint occurrences of multiple TREs along the genome that is capable of providing new insights into dependencies among elements involved in transcriptional regulation. The method is available as an R package from http://www.math.ku.dk/~richard/ppstat/.

Distribution of CRISPR spacer matches in viruses and plasmids of crenarchaeal acidothermophiles and implications for their inhibitory mechanism.

Transcripts from spacer sequences within chromosomal repeat clusters [CRISPRs (clusters of regularly interspaced palindromic repeats)] from archaea have been implicated in inhibiting or regulating the propagation of archaeal viruses and plasmids. For the crenarchaeal thermoacidophiles, the chromosomal spacers show a high level of matches ( approximately 30%) with viral or plasmid genomes. Moreover, their distribution along the virus/plasmid genomes, as well as their DNA strand specificity, appear to be random. This is consistent with the hypothesis that chromosomal spacers are taken up directly and randomly from virus and plasmid DNA and that the spacer transcripts target the genomic DNA of the extrachromosomal elements and not their transcripts.