Vincent Ferretti

PReMod: a database of genome-wide mammalian cis-regulatory module predictions

We describe PReMod, a new database of genome-wide cis-regulatory module (CRM) predictions for both the human and the mouse genomes. The prediction algorithm, described previously in Blanchette et al. (2006) Genome Res., 16, 656–668, exploits the fact that many known CRMs are made of clusters of phylogenetically conserved and repeated transcription factors (TF) binding sites. Contrary to other existing databases, PReMod is not restricted to modules located proximal to genes, but in fact mostly contains distal predicted CRMs (pCRMs). Through its web interface, PReMod allows users to (i) identify pCRMs around a gene of interest; (ii) identify pCRMs that have binding sites for a given TF (or a set of TFs) or (iii) download the entire dataset for local analyses. Queries can also be refined by filtering for specific chromosomal regions, for specific regions relative to genes or for the presence of CpG islands. The output includes information about the binding sites predicted within the selected pCRMs, and a graphical display of their distribution within the pCRMs. It also provides a visual depiction of the chromosomal context of the selected pCRMs in terms of neighboring pCRMs and genes, all of which are linked to the UCSC Genome Browser and the NCBI. PReMod: .

Conserved segment identification

The quantitative study of evolution based on comparative map data is dependent on the definition and identification of conserved segments remaining after interchromosomal exchanges such as reciprocal translocation. Because of experimental error and, more important, extensive local intrachromosomal rearrangement, it is difficult to reconstruct the configuration of conserved segments produced by interchromosomal exchanges. We present a formula to evaluate possible conserved segments and an algorithm which seeks the partition of the genome into segments optimal under this evaluation. Application is made to the human-mouse comparison.

Conserved segment identification.

The quantitative study of evolution based on comparative map data is dependent on the definition and identification of conserved segments remaining after interchromosomal exchanges such as reciprocal translocation. Because of experimental error and, more important, extensive local intrachromosomal rearrangement, it is difficult to reconstruct the configuration of conserved segments produced by interchromosomal exchanges. We present a formula to evaluate possible conserved segments and an algorithm which seeks the partition of the genome into segments optimal under this evaluation. Application is made to the human-mouse comparison.

On the Nadeau-Taylor Theory of Conserved Chromosome Segments

The quantification of comparative genomics dates from 1984 with the work of Nadeau and Taylor on estimating interchromosomal exchange rates based on the rearrangement of chromosomal segments in human versus mouse genomes. We reformulate their analysis in terms of a probabilistic model based on spatial homogeneity and independence of breakpoints and gene distribution. We study the marginal distribution of the number of genes per segment and the distribution of the number of non-empty segments as a function of the number of genes and segments. We propose a rapid algorithm for identifying a given number of conserved segments in noisy comparative map data. Finally, we propose a model which incorporates a degree of in-homogeneity in the distribution of genes and/or breakpoints. Comparative maps of human and mouse genomes serve as test data throughout.

THE EMPIRICAL DISCOVERY OF PHYLOGENETIC INVARIANTS

An invariant 4 of a tree T under a k-state Markov model, where the time parameter is identified with the edges of T, allows us to recognize whether data on N observed species can be associated with the N terminal vertices of T in the sense of having been generated on T rather than on any other tree with N terminals. The invariance is with respect to the (time) lengths associated with the edges of the tree. We propose a general method of finding invariants of a parametrized functional form. It involves calculatiing the probability f of all kN data possibilities for each of m edge-length configurations of T, then solving for the parameters using the m equations of form Q(f) = 0. We apply this to the case of quadratic invariants for unrooted binary trees with four terminals, for all k, using the Jukes-Cantor type of Markov matrix. We report partial results on finding the smallest algebraically independent set of invariants.

A remarkable nonlinear invariant for evolution with heterogeneous rates

A model for DNA or protein sequence evolution is proposed where each position belongs to one of two distinct classes. The two classes evolve at different rates. For a phylogeny on four species, we find a cubic function of 4-tuple occurrence frequencies that is nontrivially invariant no matter what the proportion of positions in each rate class. This result refutes the major criticism of nonlinear polynomial invariants.

A CONTINUOUS ANALOG FOR RNA FOLDING

A linear segment in which a number of pairs of intervals of equal length are identified as potential stems is the subject of a folding problem analogous to inference of RNA secondary structure. A quantity of free energy (or equivalently, energy per unit length) is associated with each stem, and the various types of loops are assigned energy costs as a function of their lengths. Inference of stable structures can then be carried out in the same way as in RNA folding. More important, perturbation of stem lengths and energy densities (modelling various mutational processes affecting nucleotide sequences) allows the delineation of domains of stability of various foldings, through the explicit calculation of their boundaries, in a low-dimensional parameter space.

Allele and locus classification in electrophoretic population studies

The electrophoretic separation of protein variants having slightly different mobilities is a basic tool of biochemical population genetics. In certain situations it is difficult to determine how to classify the variants as alleles of a number of genetic loci, that is, as variant subsets within each of which the Mendelian laws hold. In this article, we develop and analyze a series of algorithms for solving various versions and generalizations of this problem of optimal classification.