K. Yu. Gorbunov

An efficient algorithm for gene/species trees parsimonious reconciliation with losses, duplications and transfers

Tree reconciliation methods aim at estimating the evolutionary events that cause discrepancy between gene trees and species trees. We provide a discrete computational model that considers duplications, transfers and losses of genes. The model yields a fast and exact algorithm to infer time consistent and most parsimonious reconciliations. Then we study the conditions under which parsimony is able to accurately infer such events. Overall, it performs well even under realistic rates, transfers being in general less accurately recovered than duplications. An implementation is freely available at http://www.atgc-montpellier.fr/MPR.

Reconstructing the Evolution of Genes along the Species Tree

A model and algorithm are proposed to infer the evolution of a gene family described by the corresponding gene tree, with respect to the species evolution described by the corresponding species tree. The model describes the evolution using the new concept of a nested tree. The algorithm performance is illustrated by the example of several orthologous protein groups. The considered evolutionary events are speciation, gene duplication and loss, and horizontal gene transfer retaining the original gene copy. The transfer event with the loss of the original gene copy is considered as a combination of gene transfer and loss. The model maps each evolutionary event onto the species phylogeny.

The tree nearest on average to a given set of trees

We formulate the problem of constructing a tree which is the nearest on average to a given set of trees. The notion of “nearest” is formulated based on a conception of events such that counting their number makes it possible to distinguish each of the given trees from the desired one. These events are called divergence, duplication, loss, and transfer; other lists of events can also be considered. We propose an algorithm that solves this problem in cubic time with respect to the input data size. We prove correctness of the algorithm and a cubic estimate for its complexity.

Reconstruction of ancestral regulatory signals along a transcription factor tree

A model and an algorithm were developed to reconstruct the ancestral regulatory signals, first and foremost, for DNA-protein interactions, at inner nodes of a transcription factor phylogenetic tree on the basis of the modern signal distribution. The algorithm simultaneously infers the evolutionary scenario as a set of tree edges along which the signal diverged to the greatest extent. The model and algorithm were tested with simulation data and biological findings on the NrdR, MntR, and LacI signals.

Identification of Ancestral Genes That Introduce Incongruence between Protein- and Species Trees

Two new approaches to detecting potential incongruence between a protein family tree and a species tree are considered. The first approach is based on the substitution of a known mapping of the gene tree G into the species tree S with a somewhat analogous multivalued G-into-S mapping. The second approach is based on the elementary concepts of the fuzzy set theory. Two algorithms corresponding to these approaches are described in detail, and their implementation is shown using a simulation example and three protein families from the database of clusters of orthologous protein groups (COGs).

Modeling evolution of the bacterial regulatory signals involving secondary structure

An algorithm for modeling the evolution of the regulatory signals involving the interaction with RNA secondary structure is proposed. The algorithm implies that the species phylogenetic tree is known and is based on the assumption that the considered signals have a conserved secondary structure. The input data are the extant primary structure of a signal for all leaves of the phylogenetic tree; the algorithm computes the signal primary and secondary structures at all the nodes. Concurrently, the algorithm constructs a multiple alignment of the extant (in leaves) sites of a regulatory signal taking into account its secondary structure. The results of successful testing of the algorithm for three main types of attenuation regulation in bacteria—classic attenuation (threonine and leucine biosyntheses in Gammaproteobacteria), T-box (in Actinobacteria), and RFN-mediated (in Eubacteria) regulations—are described.

Search for Conserved Secondary Structures of RNA

We suggest a new algorithm to search a given set of the RNA sequences for conserved secondary structures. The algorithm is based on alignment of the sequences for potential helical strands. This procedure can be used to search for new structured RNAs and new regulatory elements. It is efficient for the genome-scale analysis. The results of various tests run with this algorithm are shown.

Geometric relationship between parallel hyperplanes, quadrics, and vertices of a hypercube

In a space of dimension 30 we find a pair of parallel hyperplanes, uniquely determined by vertices of a unit cube lying on them, such that strictly between the hyperplanes there are no vertices of the cube, though there are integer points. A similar two-sided example is constructed in dimension 37. We consider possible locations of empty quadrics with respect to vertices of the cube, which is a particular case of a discrete optimization problem for a quadratic polynomial on the set of vertices of the cube. We demonstrate existence of a large number of pairs of parallel hyperplanes such that each pair contains a large number of points of a prescribed set.

Linear algorithm for minimal rearrangement of structures

We propose a linear time and linear space algorithm which constructs a minimal sequence of operations rearranging one structure (directed graph of cycles and paths) into another. Structures in such a sequence may have a varying number of edges; a list of operations is fixed and includes deletion and insertion of a fragment of a structure. We give a complete proof that the algorithm is correct, i.e., finds the corresponding minimum.

Algorithm of Regulatory Signal Recognition in DNA Sequences

An algorithm is proposed for extracting regulatory signals from DNA sequences. The algorithm complexity is nearly quadratic. The results of testing the algorithm on artificial and natural sequences are presented.