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Link Homologies and the Refined Topological Vertex  [PDF]
Sergei Gukov,Amer Iqbal,Can Kozcaz,Cumrun Vafa
Mathematics , 2007, DOI: 10.1007/s00220-010-1045-4
Abstract: We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the of Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorifying quantum group invariants associated with other representations (R_1, R_2). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.
Robinson-Foulds Supertrees
Mukul S Bansal, J Gordon Burleigh, Oliver Eulenstein, David Fernández-Baca
Algorithms for Molecular Biology , 2010, DOI: 10.1186/1748-7188-5-18
Abstract: We introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (na?ve) solutions by a factor of Θ(n) and Θ(n2) respectively (where n is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.Our heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.Supertree methods provide a formal approach for combining small phylogenetic trees with incomplete species overlap in order to build comprehensive species phylogenies, or supertrees, that contain all species found in the input trees. Supertree analyses have produced the first family-level phylogeny of flowering plants [1] and the first phylogeny of nearly all extant mammal species [2]. They have also enabled phylogenetic analyses using large-scale genomic data sets in bacteria, across eukaryotes, and within plants [3,4] and have helped elucidate the origin of eukaryotic genomes [5]. Furthermore, supertrees have been used to examine rates and patterns of species diversification [1,2], to test hy
Constructing majority-rule supertrees
Jianrong Dong, David Fernández-Baca, FR McMorris
Algorithms for Molecular Biology , 2010, DOI: 10.1186/1748-7188-5-2
Abstract: We study a variant of one of Cotton and Wilkinson's methods, called majority-rule (+) supertrees. After proving that a key underlying problem for constructing majority-rule (+) supertrees is NP-hard, we develop a polynomial-size exact integer linear programming formulation of the problem. We then present a data reduction heuristic that identifies smaller subproblems that can be solved independently. While this technique is not guaranteed to produce optimal solutions, it can achieve substantial problem-size reduction. Finally, we report on a computational study of our approach on various real data sets, including the 121-taxon, 7-tree Seabirds data set of Kennedy and Page.The results indicate that our exact method is computationally feasible for moderately large inputs. For larger inputs, our data reduction heuristic makes it feasible to tackle problems that are well beyond the range of the basic integer programming approach. Comparisons between the results obtained by our heuristic and exact solutions indicate that the heuristic produces good answers. Our results also suggest that the majority-rule (+) approach, in both its basic form and with data reduction, yields biologically meaningful phylogenies.A supertree method begins with a collection of phylogenetic trees with possibly different leaf (taxon) sets, and assembles them into a larger phylogenetic tree, a supertree, whose taxon set is the union of the taxon sets of the input trees. Interest in supertrees was sparked by Gordon's paper [1]. Since then, particularly during the past decade, there has been a flurry of activity with many supertree methods proposed and studied from the algorithmic, theoretical, and biological points of view. The appeal of supertree synthesis is that it can combine disparate data to provide a high-level perspective that is harder to attain from individual trees. A recent example of the use of this approach is the species-level phylogeny of nearly all extant Mammalia constructed by Bin
Ordering uniform supertrees by their spectral radii  [PDF]
Xiying Yuan
Mathematics , 2015,
Abstract: A connected and acyclic hypergraph is called a supertree. In this paper we mainly focus on the spectral radii of uniform supertrees. Li, Shao and Qi determined the first two $k$-uniform supertrees with large spectral radii among all the $k$-uniform supertrees on $n$ vertices [H. Li, J. Shao, L. Qi, The extremal spectral radii of $k$-uniform supertrees, arXiv:1405.7257v1, May 2014]. By applying the operation of moving edges on hypergraphs and using the weighted incidence matrix method we extend the above order to the fourth $k$-uniform supertree.
Maximum Likelihood Supertrees  [PDF]
Mike Steel,Allen Rodrigo
Quantitative Biology , 2007,
Abstract: We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description (as a median tree, minimising a weighted sum of distances to the input trees). We show that this approach to ML supertree reconstruction is statistically consistent (it converges on the true species supertree as more input trees are combined), in contrast to the widely-used MRP method, which we show can be statistically inconsistent under the exponential error model. We also show that this statistical consistency extends to an ML approach for constructing species supertrees from gene trees. In this setting, incomplete lineage sorting (due to coalescence rates of homologous genes being lower than speciation rates) has been shown to lead to gene trees that are frequently different from species trees, and this can confound efforts to reconstruct the species phylogeny correctly.
The trypanosomatid evolution workshop London School of Hygiene and Tropical Medicine
Stevens, Jamie;
Memórias do Instituto Oswaldo Cruz , 2000, DOI: 10.1590/S0074-02762000000400011
Abstract: the trypanosome evolution workshop, a joint meeting of the university of exeter and the london school of hygiene and tropical medicine, focused on topics relating to trypanosomatid and vector evolution. the meeting, sponsored by the wellcome trust, the special programme for research and training in tropical disease of world health organization and the british section of the society of protozoologists, brought together an international group of experts who presented papers on a wide range of topics including parasite and vector phylogenies, molecular methodology and relevant biogeographical data.
The trypanosomatid evolution workshop London School of Hygiene and Tropical Medicine  [cached]
Stevens Jamie
Memórias do Instituto Oswaldo Cruz , 2000,
Abstract: The trypanosome evolution workshop, a joint meeting of the University of Exeter and the London School of Hygiene and Tropical Medicine, focused on topics relating to trypanosomatid and vector evolution. The meeting, sponsored by The Wellcome Trust, The Special Programme for Research and Training in Tropical Disease of World Health Organization and the British Section of the Society of Protozoologists, brought together an international group of experts who presented papers on a wide range of topics including parasite and vector phylogenies, molecular methodology and relevant biogeographical data.
Origins of amino acid transporter loci in trypanosomatid parasites
Andrew P Jackson
BMC Evolutionary Biology , 2007, DOI: 10.1186/1471-2148-7-26
Abstract: Each locus was individually specified by its surrounding gene order and associated with homologs showing the same position ('homoeologs') in other species, where available. Bayesian and maximum likelihood phylogenies were in general agreement on systematic relationships and confirmed several 'orthology sets' of genes retained since divergence from the common ancestor. Reconciliation analysis quantified the scale of duplication and gene loss, as well as identifying further apparent orthology sets, which lacked conservation of genomic position. These instances suggested substantial genomic restructuring or transposition. Other analyses identified clear instances of evolutionary rate changes post-duplication, the effects of concerted evolution within tandem gene arrays and gene conversion events between syntenic loci.Despite their importance to cell function and parasite development, the repertoires of AAT loci in trypanosomatid parasites are relatively fluid in both complement and gene dosage. Some loci are ubiquitous and, after an ancient origin through transposition, originated through descent from the ancestral trypanosomatid. However, reconciliation analysis demonstrated that unilateral expansions of gene number through tandem gene duplication, transposition of gene duplicates to otherwise well conserved genomic positions, and differential patterns of gene loss have produced largely customised and idiosyncratic AAT repertoires in all three species. Not least in T. brucei, which seems to have retained fewer ancestral loci and has acquired novel loci through a complex mix of tandem and transpositive duplication.Amino acid transporter (AAT) proteins are crucial to the metabolism and physiology of trypanosomatid parasites [1]. Among these unicellular eukaryotes are Trypanosoma brucei, Trypanosoma cruzi and Leishmania major, which are causes of substantial human morbidity worldwide. These organisms have a digenetic life cycle, being transmitted into a vertebrate host f
The Limits on Trypanosomatid Morphological Diversity  [PDF]
Richard John Wheeler, Eva Gluenz, Keith Gull
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0079581
Abstract: Cell shape is one, often overlooked, way in which protozoan parasites have adapted to a variety of host and vector environments and directional transmissions between these environments. Consequently, different parasite life cycle stages have characteristic morphologies. Trypanosomatid parasites are an excellent example of this in which large morphological variations between species and life cycle stage occur, despite sharing well-conserved cytoskeletal and membranous structures. Here, using previously published reports in the literature of the morphology of 248 isolates of trypanosomatid species from different hosts, we perform a meta-analysis of the occurrence and limits on morphological diversity of different classes of trypanosomatid morphology (trypomastigote, promastigote, etc.) in the vertebrate bloodstream and invertebrate gut environments. We identified several limits on cell body length, cell body width and flagellum length diversity which can be interpreted as biomechanical limits on the capacity of the cell to attain particular dimensions. These limits differed for morphologies with and without a laterally attached flagellum which we suggest represent two morphological superclasses, the ‘juxtaform’ and ‘liberform’ superclasses. Further limits were identified consistent with a selective pressure from the mechanical properties of the vertebrate bloodstream environment; trypanosomatid size showed limits relative to host erythrocyte dimensions. This is the first comprehensive analysis of the limits of morphological diversity in any protozoan parasite, revealing the morphogenetic constraints and extrinsic selection pressures associated with the full diversity of trypanosomatid morphology.
Gene Expression in Trypanosomatid Parasites
Santiago Martínez-Calvillo,Juan C. Vizuet-de-Rueda,Luis E. Florencio-Martínez,Rebeca G. Manning-Cela,Elisa E. Figueroa-Angulo
Journal of Biomedicine and Biotechnology , 2010, DOI: 10.1155/2010/525241
Abstract: The parasites Leishmania spp., Trypanosoma brucei, and Trypanosoma cruzi are the trypanosomatid protozoa that cause the deadly human diseases leishmaniasis, African sleeping sickness, and Chagas disease, respectively. These organisms possess unique mechanisms for gene expression such as constitutive polycistronic transcription of protein-coding genes and trans-splicing. Little is known about either the DNA sequences or the proteins that are involved in the initiation and termination of transcription in trypanosomatids. In silico analyses of the genome databases of these parasites led to the identification of a small number of proteins involved in gene expression. However, functional studies have revealed that trypanosomatids have more general transcription factors than originally estimated. Many posttranslational histone modifications, histone variants, and chromatin modifying enzymes have been identified in trypanosomatids, and recent genome-wide studies showed that epigenetic regulation might play a very important role in gene expression in this group of parasites. Here, we review and comment on the most recent findings related to transcription initiation and termination in trypanosomatid protozoa.
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