Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems, and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterize and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.Comment: This paper was submitted at the Journal of Mathematical Biology, Springer on 07th July 2015, in its current form (barring image references on the last page and cosmetic changes owning to rebuild for arXiv). The complete body of work presented here was included and defended as a part of my PhD thesis in Nov 2015 at the University of Ber

Assessing the Applicability of the GTR Nucleotide Substitution Model Through Simulations

The General Time Reversible (GTR) model of nucleotide substitution is at the core of many distance-based and character-based phylogeny inference methods. The procedure described by Waddell and Steel (1997), for estimating distances and instantaneous substitution rate matrices, R, under the GTR model, is known to be inapplicable under some conditions, ie, it leads to the inapplicability of the GTR model. Here, we simulate the evolution of DNA sequences along 12 trees characterized by different combinations of tree length, (non-)homogeneity of the substitution rate matrix R, and sequence length. We then evaluate both the frequency of the GTR model inapplicability for estimating distances and the accuracy of inferred alignments. Our results indicate that, inapplicability of the Waddel and Steel’s procedure can be considered a real practical issue, and illustrate that the probability of this inapplicability is a function of substitution rates and sequence length

Reptilian-transcriptome v1.0, a glimpse in the brain transcriptome of five divergent Sauropsida lineages and the phylogenetic position of turtles

<p>Abstract</p> <p>Background</p> <p>Reptiles are largely under-represented in comparative genomics despite the fact that they are substantially more diverse in many respects than mammals. Given the high divergence of reptiles from classical model species, next-generation sequencing of their transcriptomes is an approach of choice for gene identification and annotation.</p> <p>Results</p> <p>Here, we use 454 technology to sequence the brain transcriptome of four divergent reptilian and one reference avian species: the Nile crocodile, the corn snake, the bearded dragon, the red-eared turtle, and the chicken. Using an in-house pipeline for recursive similarity searches of >3,000,000 reads against multiple databases from 7 reference vertebrates, we compile a reptilian comparative transcriptomics dataset, with homology assignment for 20,000 to 31,000 transcripts per species and a cumulated non-redundant sequence length of 248.6 Mbases. Our approach identifies the majority (87%) of chicken brain transcripts and about 50% of <it>de novo </it>assembled reptilian transcripts. In addition to 57,502 microsatellite loci, we identify thousands of SNP and indel polymorphisms for population genetic and linkage analyses. We also build very large multiple alignments for Sauropsida and mammals (two million residues per species) and perform extensive phylogenetic analyses suggesting that turtles are not basal living reptiles but are rather associated with Archosaurians, hence, potentially answering a long-standing question in the phylogeny of Amniotes.</p> <p>Conclusions</p> <p>The reptilian transcriptome (freely available at <url>http://www.reptilian-transcriptomes.org</url>) should prove a useful new resource as reptiles are becoming important new models for comparative genomics, ecology, and evolutionary developmental genetics.</p

Numerical approximation of a mechanochemical interface model for skin appendage

We introduce a model for the mass transfer of molecular activators and inhibitors in two media separated by an interface, and study its interaction with the deformations exhibited by the two-layer skin tissue where they occur. The mathematical model results in a system of nonlinear advection-diffusion-reaction equations including cross-diffusion, and coupled with an interface elasticity problem. We propose a Galerkin method for the discretisation of the set of governing equations, involving also a suitable Newton linearisation, partitioned techniques, non-overlapping Schwarz alternating schemes, and high-order adaptive time stepping algorithms. The experimental accuracy and robustness of the proposed partitioned numerical methods is assessed, and some illustrating tests in 2D and 3D are provided to exemplify the coupling effects between the mechanical properties and the advection-diffusion-reaction interactions involving the two separate layers

2× genomes - depth does matter

The use of low coverage genomes in comparative evolutionary analyses skews estimates of gene gains and losses

Somitic positional information guides self-organized patterning of snake scales

Two influential concepts in tissue patterning are Wolpert’s positional information and Turing’s self-organized reaction–diffusion (RD). The latter establishes the patterning of hair and feathers. Here, our morphological, genetic, and functional—by CRISPR-Cas9–mediated gene disruption—characterization of wild-type versus “scaleless” snakes reveals that the near-perfect hexagonal pattern of snake scales is established through interactions between RD in the skin and somitic positional information. First, we show that ventral scale development is guided by hypaxial somites and, second, that ventral scales and epaxial somites guide the sequential RD patterning of the dorsolateral scales. The RD intrinsic length scale evolved to match somite periodicity, ensuring the alignment of ribs and scales, both of which play a critical role in snake locomotion

Dangerous women of Hong Kong? Media construction of stigma in female sex workers

This study used a cultural model analysis to examine the Hong Kong print media’s social construction of stigma in respect to female sex workers. An analysis was conducted on captions and main headlines of two newspaper (Chinese and English) median in Hong Kong, 2003-2006. A total of 591 articles on sex workers were recruited in the analysis with 422 located from the Ming Pao and 169 articles the SCMP. A total of Sixty seven articles on health issues were identified. In Hong Kong, as in elsewhere, sex workers were commonly labeled as the sources of sexually transmitted diseases and as women who endangered the public safety through socially unacceptable occupations. They were also portrayed as “ugly”, “weak” and “powerless” in the articles identified. We conclude the Hong Kong print media plays a significant role in contributing to the stigmatization of sex workers, heightening health risk and vulnerability. Such social construction of public stigma then in turn, can be argued to contribute to a lessened propensity for female sex workers both seek and engage with formal health services.published_or_final_versio

Giant Galápagos tortoises; molecular genetic analyses identify a trans-island hybrid in a repatriation program of an endangered taxon

BACKGROUND: Giant Galápagos tortoises on the island of Española have been the focus of an intensive captive breeding-repatriation programme for over 35 years that saved the taxon from extinction. However, analysis of 118 samples from released individuals indicated that the bias sex ratio and large variance in reproductive success among the 15 breeders has severely reduced the effective population size (N(e)). RESULTS: We report here that an analysis of an additional 473 captive-bred tortoises released back to the island reveals an individual (E1465) that exhibits nuclear microsatellite alleles not found in any of the 15 breeders. Statistical analyses incorporating genotypes of 304 field-sampled individuals from all populations on the major islands indicate that E1465 is most probably a hybrid between an Española female tortoise and a male from the island of Pinzón, likely present on Española due to human transport. CONCLUSION: Removal of E1465 as well as its father and possible (half-)siblings is warranted to prevent further contamination within this taxon of particular conservation significance. Despite this detected single contamination, it is highly noteworthy to emphasize the success of this repatriation program conducted over nearly 40 years and involving release of over 2000 captive-bred tortoises that now reproduce in situ. The incorporation of molecular genetic analysis of the program is providing guidance that will aid in monitoring the genetic integrity of this ambitious effort to restore a unique linage of a spectacular animal

Changes in Hox genes' structure and function during the evolution of the squamate body plan

Hox genes are central to the specification of structures along the anterior-posterior body axis, and modifications in their expression have paralleled the emergence of diversity in vertebrate body plans. Here we describe the genomic organization of Hox clusters in different reptiles and show that squamates have accumulated unusually large numbers of transposable elements at these loci, reflecting extensive genomic rearrangements of coding and non-coding regulatory regions. Comparative expression analyses between two species showing different axial skeletons, the corn snake and the whiptail lizard, revealed major alterations in Hox13 and Hox10 expression features during snake somitogenesis, in line with the expansion of both caudal and thoracic regions. Variations in both protein sequences and regulatory modalities of posterior Hox genes suggest how this genetic system has dealt with its intrinsic collinear constraint to accompany the substantial morphological radiation observed in this group

Historical Constraints on Vertebrate Genome Evolution

Recent analyses indicated that genes with larger effect of knockout or mutation and with larger probability to revert to single copy after whole genome duplication are expressed earlier in development. Here, we further investigate whether tissue specificity of gene expression is constrained by the age of origin of the corresponding genes. We use 38 metazoan genomes and a comparative genomic application system to integrate inference of gene duplication with expression data from 17,503 human genes into a strictly phylogenetic framework. We show that the number of anatomical systems in which genes are expressed decreases steadily with decreased age of the genes’ first appearance in the phylogeny: the oldest genes are expressed, on average, in twice as many anatomical systems than the genes gained recently in evolution. These results are robust to different sources of expression data, to different levels of the anatomical system hierarchy, and to the use of gene families rather than duplication events. Finally, we show that the rate of increase in gene tissue specificity correlates with the relative rate of increase in the maximum number of cell types in the corresponding taxa. Although subfunctionalization and increase in cell type number throughout evolution could constitute, respectively, the proximal and ultimate causes of this correlation, the two phenomena are intermingled. Our analyses identify a striking historical constraint in gene expression: the number of cell types in existence at the time of a gene appearance (through duplication or de novo origination) tends to determine its level of tissue specificity for tens or hundreds of millions of years