Miguel Abreu

Effect of long-term laboratory propagation on Chlamydia trachomatis genome dynamics

It is assumed that bacterial strains maintained in the laboratory for long time shape their genome in a different fashion from the nature-circulating strains. Here, we analyzed the impact of long-term in vitro propagation on the genome of the obligate intracellular pathogen Chlamydia trachomatis. We fully-sequenced the genome of a historical prototype strain (L2/434/Bu) and a clinical isolate (E/CS88), before and after one-year of serial in vitro passaging (up to 3500 bacterial generations). We observed a slow adaptation of C. trachomatis to the in vitro environment, which was essentially governed by four mutations for L2/434/Bu and solely one mutation for E/CS88, corresponding to estimated mutation rates from 3.84 × 10(-10) to 1.10 × 10(-9) mutations per base pair per generation. In a speculative basis, the mutations likely conferred selective advantage as: (i) mathematical modeling showed that selective advantage is mandatory for frequency increase of a mutated clone; (ii) transversions and non-synonymous mutations were overrepresented; (iii) two non-synonymous mutations affected the genes CTL0084 and CTL0610, encoding a putative transferase and a protein likely implicated in transcription regulation respectively, which are families known to be highly prone to undergone laboratory-derived advantageous mutations in other bacteria; and (iv) the mutation for E/CS88 is located likely in the regulatory region of a virulence gene (CT115/incD) believed to play a role in subverting the host cell machinery. Nevertheless, we found no significant differences in the growth rate, plasmid load, and attachment/entry rate, between strains before and after their long-term laboratory propagation. Of note, from the mixture of clones in E/CS88 initial population, an inactivating mutation in the virulence gene CT135 evolved to 100% prevalence, unequivocally indicating that this gene is superfluous for C. trachomatis survival in vitro. Globally, C. trachomatis revealed a slow in vitro adaptation that only modestly modifies the in vivo-derived genomic evolutionary landscape.

Remarks on Lagrangian intersections in toric manifolds

I will consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. The remarks address the fact that one can use simple cartesian product and symplectic reduction considerations to go from basic examples to much more sophisticated ones. I will show in particular how rigidity results for the above Lagrangian intersection problems in weighted projective spaces can be combined with these considerations to prove analogous results for all monotone toric symplectic manifolds. We also discuss non-monotone and/or non-Fano examples, including some with a continuum of non-displaceable torus orbits. This is joint work with Leonardo Macarini.

Compatible complex structures on symplectic rational ruled surfaces

In this article, we study the topology of the spaceIω of complex structures compatible with a fixed symplectic form ω, using the framework of Donaldson. By comparing our analysis of the spaceIω with results of McDuff on the spaceJω of compatible almost complex structures on rational ruled surfaces, we find that Iω is contractible in this case. We then apply this result to study the topology of the symplectomorphism group of a rational ruled surface, extending results of Abreu and McDuff.

Displacing Lagrangian toric fibers by extended probes

In this paper we introduce a new way of displacing Lagrangian fibers in toric symplectic manifolds, a generalization of McDuff’s original method of probes. Extended probes are formed by deflecting one probe by another auxiliary probe. Using them, we are able to displace all fibers in Hirzebruch surfaces except those already known to be nondisplaceable, and can also displace an open dense set of fibers in the weighted projective space P.1;3;5/ after resolving the singularities. We also investigate the displaceability question in sectors and their resolutions. There are still many cases in which there is an open set of fibers whose displaceability status is unknown. 53D12; 14M25, 53D40

Kähler–Sasaki geometry of toric symplectic cones in action-angle coordinates

In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents a symplectic action-angle coordinates approach to toric Kahler geometry and how it was recently generalized, by Burns-Guillemin-Lerman and Martelli-Sparks-Yau, to toric Kahler-Sasaki geometry. It also describes, as an application, how this approach can be used to relate a recent new family of Sasaki-Einstein metrics constructed by Gauntlett-Martelli-Sparks-Waldram in 2004, to an old family of extremal Kahler metrics constructed by Calabi in 1982.

Multiplicity of periodic orbits for dynamically convex contact forms

We give a sharp lower bound for the number of geometrically distinct contractible periodic orbits of dynamically convex Reeb flows on prequantizations of symplectic manifolds that are not aspherical. Several consequences of this result are obtained, like a new proof that every bumpy Finsler metric on

Kahler Geometry of Toric Varieties and Extremal Metrics

S^n

Kahler geometry of toric manifolds in symplectic coordinates

Sn carries at least two prime closed geodesics, multiplicity of elliptic and non-hyperbolic periodic orbits for dynamically convex contact forms with finitely many geometrically distinct contractible closed orbits and precise estimates of the number of even periodic orbits of perfect contact forms. We also slightly relax the hypothesis of dynamical convexity. A fundamental ingredient in our proofs is the common index jump theorem due to Y. Long and C. Zhu.