Alternative determinism principle for topological analysis of chaos

The topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits has proved a powerful method, however knot theory can only be applied to three-dimensional systems. Still, the core principles upon which this approach is built, determinism and continuity, apply in any dimension. We propose an alternative framework in which these principles are enforced on triangulated surfaces rather than curves and show that in dimension three our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.Comment: Accepted for publication as Rapid Communication in Physical Review

Recovering probabilities for nucleotide trimming processes for T cell receptor TRA and TRG V-J junctions analyzed with IMGT tools

<p>Abstract</p> <p>Background</p> <p>Nucleotides are trimmed from the ends of variable (V), diversity (D) and joining (J) genes during immunoglobulin (IG) and T cell receptor (TR) rearrangements in B cells and T cells of the immune system. This trimming is followed by addition of nucleotides at random, forming the N regions (N for nucleotides) of the V-J and V-D-J junctions. These processes are crucial for creating diversity in the immune response since the number of trimmed nucleotides and the number of added nucleotides vary in each B or T cell. IMGT^®sequence analysis tools, IMGT/V-QUEST and IMGT/JunctionAnalysis, are able to provide detailed and accurate analysis of the final observed junction nucleotide sequences (tool "output"). However, as trimmed nucleotides can potentially be replaced by identical N region nucleotides during the process, the observed "output" represents a <it>biased </it>estimate of the "true trimming process."</p> <p>Results</p> <p>A probabilistic approach based on an analysis of the standardized tool "output" is proposed to infer the probability distribution of the "true trimmming process" and to provide plausible biological hypotheses explaining this process. We collated a benchmark dataset of TR alpha (TRA) and TR gamma (TRG) V-J rearranged sequences and junctions analysed with IMGT/V-QUEST and IMGT/JunctionAnalysis, the nucleotide sequence analysis tools from IMGT^®, the international ImMunoGeneTics information system^®, <url>http://imgt.cines.fr</url>. The standardized description of the tool output is based on the IMGT-ONTOLOGY axioms and concepts. We propose a simple first-order model that attempts to transform the observed "output" probability distribution into an estimate closer to the "true trimming process" probability distribution. We use this estimate to test the hypothesis that Poisson processes are involved in trimming. This hypothesis was not rejected at standard confidence levels for three of the four trimming processes: TRAV, TRAJ and TRGV.</p> <p>Conclusion</p> <p>By using trimming of rearranged TR genes as a benchmark, we show that a probabilistic approach, applied to IMGT^®standardized tool "outputs" opens the way to plausible hypotheses on the events involved in the "true trimming process" and eventually to an exact quantification of trimming itself. With increasing high-throughput of standardized immunogenetics data, similar probabilistic approaches will improve understanding of processes so far only characterized by the "output" of standardized tools.</p

Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models

We characterize the systematic changes in the topological structure of chaotic attractors that occur as spike-adding and homoclinic bifurcations are encountered in the slow-fast dynamics of neuron models. This phenomenon is detailed in the simple Hindmarsh-Rose neuron model, where we show that the unstable periodic orbits appearing after each spike-adding bifurcation are associated with specific symbolic sequences in the canonical symbolic encoding of the dynamics of the system. This allows us to understand how these bifurcations modify the internal structure of the chaotic attractors

Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator

Bifurcations and Averages in the Homoclinic Chaos of a Laser with a Saturable Absorber

The dynamical bifurcations of a laser with a saturable absorber were calculated, with the 3-2 level model, as function of the gain parameter. The average power of the laser is shown to have specific behavior at bifurcations. The succession of periodic-chaotic windows, known to occur in the homoclinic chaos, was studied numerically. A critical exponent of 1/2 is found on the tangent bifurcations from chaotic into periodic pulsations.Comment: 6 or 7 pages, 3 figures, publishe

Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator

Logarithmic periodicities in the bifurcations of type-I intermittent chaos

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.Comment: 4 pages, 6 figures, accepted for publication in PRL (2004

Evolution of the T-cell receptor (TR) Loci in the adaptive immune response: The tale of the TRG locus in mammals

T lymphocytes are the principal actors of vertebrates’ cell-mediated immunity. Like B cells, they can recognize an unlimited number of foreign molecules through their antigen-specific heterodimer receptors (TRs), which consist of αβ or γδ chains. The diversity of the TRs is mainly due to the unique organization of the genes encoding the α, β, γ, and δ chains. For each chain, multi-gene families are arranged in a TR locus, and their expression is guaranteed by the somatic recombination process. A great plasticity of the gene organization within the TR loci exists among species. Marked structural differences affect the TR γ (TRG) locus. The recent sequencing of multiple whole genome provides an opportunity to examine the TR gene repertoire in a systematic and consistent fashion. In this review, we report the most recent findings on the genomic organization of TRG loci in mammalian species in order to show differences and similarities. The comparison revealed remarkable diversification of both the genomic organization and gene repertoire across species, but also unexpected evolutionary conservation, which highlights the important role of the T cells in the immune response

The t cell receptor (Trb) locus in tursiops truncatus: From sequence to structure of the alpha/beta heterodimer in the human/dolphin comparison

The bottlenose dolphin (Tursiops truncatus) belongs to the Cetartiodactyla and, similarly to other cetaceans, represents the most successful mammalian colonization of the aquatic envi-ronment. Here we report a genomic, evolutionary, and expression study of T. truncatus T cell receptor beta (TRB) genes. Although the organization of the dolphin TRB locus is similar to that of the other artiodactyl species, with three in tandem D-J-C clusters located at its 3’ end, its unique-ness is given by the reduction of the total length due essentially to the absence of duplications and to the deletions that have drastically reduced the number of the germline TRBV genes. We have analyzed the relevant mature transcripts from two subjects. The simultaneous availability of rear-ranged T cell receptor α (TRA) and TRB cDNA from the peripheral blood of one of the two speci-mens, and the human/dolphin amino acids multi-sequence alignments, allowed us to calculate the most likely interactions at the protein interface between the alpha/beta heterodimer in complex with major histocompatibility class I (MH1) protein. Interacting amino acids located in the com-plementarity-determining region according to IMGT numbering (CDR-IMGT) of the dolphin variable V-alpha and beta domains were identified. According to comparative modelization, the atom pair contact sites analysis between the human MH1 grove (G) domains and the T cell receptor (TR) V domains confirms conservation of the structure of the dolphin TR/pMH