Level structures on the Weierstrass family of cubics

Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For each N >= 2, we construct surfaces parametrizing the three standard kinds of level N structures on the smooth fibers of W. We then complete these surfaces to finite covers of A^2. Since W -> A^2 is the versal deformation space of a cusp singularity, these surfaces convey information about the level structure on any family of curves of genus g degenerating to a cuspidal curve. Our goal in this note is to determine for which values of N these surfaces are smooth over (0,0). From a topological perspective, the results determine the homeomorphism type of certain branched covers of S^3 with monodromy in SL_2(Z/N).Comment: LaTeX, 12 pages; added section giving a topological interpretation of the result

Distinguishing regional from within-codon rate heterogeneity in DNA sequence alignments

We present an improved phylogenetic factorial hidden Markov model (FHMM) for detecting two types of mosaic structures in DNA sequence alignments, related to (1) recombination and (2) rate heterogeneity. The focus of the present work is on improving the modelling of the latter aspect. Earlier papers have modelled different degrees of rate heterogeneity with separate hidden states of the FHMM. This approach fails to appreciate the intrinsic difference between two types of rate heterogeneity: long-range regional effects, which are potentially related to differences in the selective pressure, and the short-term periodic patterns within the codons, which merely capture the signature of the genetic code. We propose an improved model that explicitly distinguishes between these two effects, and we assess its performance on a set of simulated DNA sequence alignments

Idiopathic scoliosis and pineal lesions in Australian children

PURPOSE: To determine whether treatment of pineal lesions in children is associated with development of idiopathic scoliosis. METHODS: 38 boys and 10 girls with pineal lesions were identified. Their mean age at presentation was 10 years. The pineal pathology varied from cysts and epidermoid to teratoma, germinoma, pineocytoma, and glioblastoma. Treatment ranged from biopsy/extirpation to radiotherapy. RESULTS: 12 patients died. No scoliosis was found in any females or any of the deceased. Two boys had scoliosis: one had a 12-degree right upper thoracic curve with 32-degree kyphosis and the other had a 60-degree right thoracolumbar idiopathic curve, requiring a 2-stage arthrodesis. CONCLUSION: Pineal ablation is not related to the development of idiopathic scoliosis in humans

Multidimensional Scaling Reveals the Main Evolutionary Pathways of Class A G-Protein-Coupled Receptors

Class A G-protein-coupled receptors (GPCRs) constitute the largest family of transmembrane receptors in the human genome. Understanding the mechanisms which drove the evolution of such a large family would help understand the specificity of each GPCR sub-family with applications to drug design. To gain evolutionary information on class A GPCRs, we explored their sequence space by metric multidimensional scaling analysis (MDS). Three-dimensional mapping of human sequences shows a non-uniform distribution of GPCRs, organized in clusters that lay along four privileged directions. To interpret these directions, we projected supplementary sequences from different species onto the human space used as a reference. With this technique, we can easily monitor the evolutionary drift of several GPCR sub-families from cnidarians to humans. Results support a model of radiative evolution of class A GPCRs from a central node formed by peptide receptors. The privileged directions obtained from the MDS analysis are interpretable in terms of three main evolutionary pathways related to specific sequence determinants. The first pathway was initiated by a deletion in transmembrane helix 2 (TM2) and led to three sub-families by divergent evolution. The second pathway corresponds to the differentiation of the amine receptors. The third pathway corresponds to parallel evolution of several sub-families in relation with a covarion process involving proline residues in TM2 and TM5. As exemplified with GPCRs, the MDS projection technique is an important tool to compare orthologous sequence sets and to help decipher the mutational events that drove the evolution of protein families

Site-specific time heterogeneity of the substitution process and its impact on phylogenetic inference

<p>Abstract</p> <p>Background</p> <p>Model violations constitute the major limitation in inferring accurate phylogenies. Characterizing properties of the data that are not being correctly handled by current models is therefore of prime importance. One of the properties of protein evolution is the variation of the relative rate of substitutions across sites and over time, the latter is the phenomenon called heterotachy. Its effect on phylogenetic inference has recently obtained considerable attention, which led to the development of new models of sequence evolution. However, thus far focus has been on the quantitative heterogeneity of the evolutionary process, thereby overlooking more qualitative variations.</p> <p>Results</p> <p>We studied the importance of variation of the site-specific amino-acid substitution process over time and its possible impact on phylogenetic inference. We used the CAT model to define an infinite mixture of substitution processes characterized by equilibrium frequencies over the twenty amino acids, a useful proxy for qualitatively estimating the evolutionary process. Using two large datasets, we show that qualitative changes in site-specific substitution properties over time occurred significantly. To test whether this unaccounted qualitative variation can lead to an erroneous phylogenetic tree, we analyzed a concatenation of mitochondrial proteins in which Cnidaria and Porifera were erroneously grouped. The progressive removal of the sites with the most heterogeneous CAT profiles across clades led to the recovery of the monophyly of Eumetazoa (Cnidaria+Bilateria), suggesting that this heterogeneity can negatively influence phylogenetic inference.</p> <p>Conclusion</p> <p>The time-heterogeneity of the amino-acid replacement process is therefore an important evolutionary aspect that should be incorporated in future models of sequence change.</p

Pervasive Cryptic Epistasis in Molecular Evolution

The functional effects of most amino acid replacements accumulated during molecular evolution are unknown, because most are not observed naturally and the possible combinations are too numerous. We created 168 single mutations in wild-type Escherichia coli isopropymalate dehydrogenase (IMDH) that match the differences found in wild-type Pseudomonas aeruginosa IMDH. 104 mutant enzymes performed similarly to E. coli wild-type IMDH, one was functionally enhanced, and 63 were functionally compromised. The transition from E. coli IMDH, or an ancestral form, to the functional wild-type P. aeruginosa IMDH requires extensive epistasis to ameliorate the combined effects of the deleterious mutations. This result stands in marked contrast with a basic assumption of molecular phylogenetics, that sites in sequences evolve independently of each other. Residues that affect function are scattered haphazardly throughout the IMDH structure. We screened for compensatory mutations at three sites, all of which lie near the active site and all of which are among the least active mutants. No compensatory mutations were found at two sites indicating that a single site may engage in compound epistatic interactions. One complete and three partial compensatory mutations of the third site are remote and lie in a different domain. This demonstrates that epistatic interactions can occur between distant (>20Å) sites. Phylogenetic analysis shows that incompatible mutations were fixed in different lineages