Background. Transcriptional regulation in eukaryotes is often multifactorial, involving multiple transcription factors binding to the same transcription control region (e.g., upstream activating sequences and enhancers), and to understand the regulatory content of eukaryotic genomes it is necessary to consider the co-occurrence and spatial relationships of individual binding sites. The identification of sequences conserved among related species (often known as phylogenetic footprinting) has been successfully used to identify individual transcription factor binding sites. Here, we extend this concept of functional conservation to higher-order features of transcription control regions involved in the multifactorial control of gene expression.Results. We used the genome sequences of four yeast species of the genus Saccharomyces to identify sequences potentially involved in multifactorial control of gene expression. We found 1,117 potential regulatory "templates": pairs of hexameric sequences that are jointly conserved in transcription regulatory regions and also exhibit non-random relative spacing. Many of the individual sequences in these templates correspond to known transcription factor binding sites, and the sets of genes containing a particular template in their transcription control regions tend to be differentially expressed in conditions where the corresponding transcription factors are known to be active.Conclusions. The incorporation of both joint conservation and spacing constraints of sequence pairs predicts groups of target genes that were specific for common patterns of gene expression. Our work suggests that positional information, especially the relative spacing between transcription factor binding sites, may represent a common organizing principle of transcription control regions.

In [13] we reported the genome sequences of S. paradoxus, S. mikatae and S. bayanus and compared these three yeast species to their close relative, S. cerevisiae. Genome-wide comparative analysis allowed the identification of functionally important sequences, both coding and non-coding. In this companion paper we describe the mathematical and algorithmic results underpinning the analysis of these genomes.We developed statistical methods for the systematic de-novo identification of regulatory motifs. Without making use of co-regulated gene sets, we discovered virtually all previously known DNA regulatory motifs as well as several noteworthy novel motifs. With the additional use of gene ontology information, expression clusters and transcription factor binding profiles, we assigned candidate functions to the novel motifs discovered.Our results demonstrate that entirely automatic genome-wide annotation, gene validation, and discovery of regulatory motifs is possible. Our findings are validated by the extensive experimental knowledge in yeast, confirming their applicability to other genomes.

We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in IR 3 .The al- gorithm is the first for this problem with provable guarantees.Given a "good sample" from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases.The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples.The output mesh interpolates, rather than approximates, the input points.Our algorithm is based on the three-dimensional Voronoi diagram.Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.