Virus Replication as a Phenotypic Version of Polynucleotide Evolution

In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. By taking into account beneficial effects we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium" and transient. Finally, based on these quantitative results we are able to draw some qualitative conclusions.Comment: 23 pages, 1 figure, 2 tables. arXiv admin note: substantial text overlap with arXiv:1110.336

Comparative analysis of the secretome and interactome of Trypanosoma cruzi and Trypanosoma rangeli reveals species specific immune response modulating proteins

Chagas disease, a zoonosis caused by the flagellate protozoan Trypanosoma cruzi, is a chronic and systemic parasitic infection that affects ~5–7 million people worldwide, mainly in Latin America. Chagas disease is an emerging public health problem due to the lack of vaccines and effective treatments. According to recent studies, several T. cruzi secreted proteins interact with the human host during cell invasion. Moreover, some comparative studies with T. rangeli, which is non-pathogenic in humans, have been performed to identify proteins directly involved in the pathogenesis of the disease. In this study, we present an integrated analysis of canonical putative secreted proteins (PSPs) from both species. Additionally, we propose an interactome with human host and gene family clusters, and a phylogenetic inference of a selected protein. In total, we identified 322 exclusively PSPs in T. cruzi and 202 in T. rangeli. Among the PSPs identified in T. cruzi, we found several trans-sialidases, mucins, MASPs, proteins with phospholipase 2 domains (PLA2-like), and proteins with Hsp70 domains (Hsp70-like) which have been previously characterized and demonstrated to be related to T. cruzi virulence. PSPs found in T. rangeli were related to protozoan metabolism, specifically carboxylases and phosphatases. Furthermore, we also identified PSPs that may interact with the human immune system, including heat shock and MASP proteins, but in a lower number compared to T. cruzi. Interestingly, we describe a hypothetical hybrid interactome of PSPs which reveals that T. cruzi secreted molecules may be down-regulating IL-17 whilst T. rangeli may enhance the production of IL-15. These results will pave the way for a better understanding of the pathophysiology of Chagas disease and may ultimately lead to the identification of molecular targets, such as key PSPs, that could be used to minimize the health outcomes of Chagas disease by modulating the immune response triggered by T. cruzi infection

A maximality result for orthogonal quantum groups

We prove that the quantum group inclusion $O_n \subset O_n^*$ is "maximal", where $O_n$ is the usual orthogonal group and $O_n^*$ is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum group $O_n\subset G\subset O_n^*$. In order to prove this result, we use: (1) the isomorphism of projective versions $PO_n^*\simeq PU_n$, (2) some maximality results for classical groups, obtained by using Lie algebras and some matrix tricks, and (3) a short five lemma for cosemisimple Hopf algebras.Comment: 10 page

Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation

Copyright © 2011 Springer. The final publication is available at www.springerlink.comWe consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells