A methodology for determining amino-acid substitution matrices from set covers

We introduce a new methodology for the determination of amino-acid substitution matrices for use in the alignment of proteins. The new methodology is based on a pre-existing set cover on the set of residues and on the undirected graph that describes residue exchangeability given the set cover. For fixed functional forms indicating how to obtain edge weights from the set cover and, after that, substitution-matrix elements from weighted distances on the graph, the resulting substitution matrix can be checked for performance against some known set of reference alignments and for given gap costs. Finding the appropriate functional forms and gap costs can then be formulated as an optimization problem that seeks to maximize the performance of the substitution matrix on the reference alignment set. We give computational results on the BAliBASE suite using a genetic algorithm for optimization. Our results indicate that it is possible to obtain substitution matrices whose performance is either comparable to or surpasses that of several others, depending on the particular scenario under consideration

An Alternative Model of Amino Acid Replacement

The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same background distribution of amino acids, an assumption that is incompatible with the observed heterogeneity of protein amino acid profiles and with the success of profile multiple sequence alignment. We propose an alternative model of amino acid replacement during protein evolution based upon the assumption that the variation of the amino acid background distribution from one residue to the next is sufficient to explain the observed sequence correlations of homologs. The resulting dynamical model of independent replacements drawn from heterogeneous backgrounds is simple and consistent, and provides a unified homology match score for sequence-sequence, sequence-profile and profile-profile alignment.Comment: Minor improvements. Added figure and reference

Regulatory motif discovery using a population clustering evolutionary algorithm

This paper describes a novel evolutionary algorithm for regulatory motif discovery in DNA promoter sequences. The algorithm uses data clustering to logically distribute the evolving population across the search space. Mating then takes place within local regions of the population, promoting overall solution diversity and encouraging discovery of multiple solutions. Experiments using synthetic data sets have demonstrated the algorithm's capacity to find position frequency matrix models of known regulatory motifs in relatively long promoter sequences. These experiments have also shown the algorithm's ability to maintain diversity during search and discover multiple motifs within a single population. The utility of the algorithm for discovering motifs in real biological data is demonstrated by its ability to find meaningful motifs within muscle-specific regulatory sequences

From quantum groups to genetic mutations

In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation is assumed to depend on the "distance" between the codons. Preliminary general predictions of the model are compared with experimental data, with a satisfactory agreement.Comment: 11 pages, Talk at Int.Conf."Symmetries in Science XIII", Bregenz July 20-24 200

Back-translation for discovering distant protein homologies

Frameshift mutations in protein-coding DNA sequences produce a drastic change in the resulting protein sequence, which prevents classic protein alignment methods from revealing the proteins' common origin. Moreover, when a large number of substitutions are additionally involved in the divergence, the homology detection becomes difficult even at the DNA level. To cope with this situation, we propose a novel method to infer distant homology relations of two proteins, that accounts for frameshift and point mutations that may have affected the coding sequences. We design a dynamic programming alignment algorithm over memory-efficient graph representations of the complete set of putative DNA sequences of each protein, with the goal of determining the two putative DNA sequences which have the best scoring alignment under a powerful scoring system designed to reflect the most probable evolutionary process. This allows us to uncover evolutionary information that is not captured by traditional alignment methods, which is confirmed by biologically significant examples.Comment: The 9th International Workshop in Algorithms in Bioinformatics (WABI), Philadelphia : \'Etats-Unis d'Am\'erique (2009

Adaptive evolution of transcription factor binding sites

The regulation of a gene depends on the binding of transcription factors to specific sites located in the regulatory region of the gene. The generation of these binding sites and of cooperativity between them are essential building blocks in the evolution of complex regulatory networks. We study a theoretical model for the sequence evolution of binding sites by point mutations. The approach is based on biophysical models for the binding of transcription factors to DNA. Hence we derive empirically grounded fitness landscapes, which enter a population genetics model including mutations, genetic drift, and selection. We show that the selection for factor binding generically leads to specific correlations between nucleotide frequencies at different positions of a binding site. We demonstrate the possibility of rapid adaptive evolution generating a new binding site for a given transcription factor by point mutations. The evolutionary time required is estimated in terms of the neutral (background) mutation rate, the selection coefficient, and the effective population size. The efficiency of binding site formation is seen to depend on two joint conditions: the binding site motif must be short enough and the promoter region must be long enough. These constraints on promoter architecture are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive evolution of genetic switches and of signal integration through binding cooperativity between different sites. Experimental tests of this picture involving the statistics of polymorphisms and phylogenies of sites are discussed.Comment: published versio

Dynamics of transcription factor binding site evolution

Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ~10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of "pre-sites" or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genetics.Comment: 28 pages, 15 figure