Identification of the lactococcal exonuclease/recombinase and its modulation by the putative Chi sequence

Studies of RecBCD–Chi interactions in Escherichia coli have served as a model to understand recombination events in bacteria. However, the existence of similar interactions has not been demonstrated in bacteria unrelated to E. coli. We developed an in vivo model to examine components of dsDNA break repair in various microorganisms. Here, we identify the major exonuclease in Lactococcus lactis, a Gram-positive organism evolutionarily distant from E. coli, and provide evidence for exonuclease–Chi interactions. Insertional mutants of L. lactis, screened as exonuclease-deficient, affected a single locus and resulted in UV sensitivity and recombination deficiency. The cloned lactococcal genes (called rexAB) restored UV resistance, recombination proficiency, and the capacity to degrade linear DNA, to an E. coli recBCD mutant. In this context, DNA degradation is specifically blocked by the putative lactococcal Chi site (5′-GCGCGTG-3′), but not by the E. coli Chi (5′-GCTGGTGG-3′) site. RexAB-mediated recombination was shown to be stimulated ≈27-fold by lactococcal Chi. Our results reveal that RexAB fulfills the biological roles of RecBCD and indicate that its activity is modulated by a short DNA sequence. We speculate that exonuclease/recombinase enzymes whose activities are modulated by short DNA sequences are widespread among bacteria

Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

Viscosity solutions of systems of PDEs with interconnected obstacles and Multi modes switching problems

This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is connected with the valuation of a power plant in the energy market. The main tool is the notion of systems of reflected BSDEs with oblique reflection.Comment: 36 page

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

Systematic determination of the mosaic structure of bacterial genomes: species backbone versus strain-specific loops

BACKGROUND: Public databases now contain multitude of complete bacterial genomes, including several genomes of the same species. The available data offers new opportunities to address questions about bacterial genome evolution, a task that requires reliable fine comparison data of closely related genomes. Recent analyses have shown, using pairwise whole genome alignments, that it is possible to segment bacterial genomes into a common conserved backbone and strain-specific sequences called loops. RESULTS: Here, we generalize this approach and propose a strategy that allows systematic and non-biased genome segmentation based on multiple genome alignments. Segmentation analyses, as applied to 13 different bacterial species, confirmed the feasibility of our approach to discern the 'mosaic' organization of bacterial genomes. Segmentation results are available through a Web interface permitting functional analysis, extraction and visualization of the backbone/loops structure of documented genomes. To illustrate the potential of this approach, we performed a precise analysis of the mosaic organization of three E. coli strains and functional characterization of the loops. CONCLUSION: The segmentation results including the backbone/loops structure of 13 bacterial species genomes are new and available for use by the scientific community at the URL:

Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

Inf-convolution of G-expectations

In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.Comment: 23 page

Dry Markets and Superreplication Bounds of American Derivatives

This paper studies the impact of dry markets for underlying assets on the pricing of American derivatives, using a discrete time framework. Dry markets are characterized by the possibility of non-existence of trading at certain dates. Such non-existence may be deterministic or probabilistic. Using superreplicating strategies, we derive expectation representations for the range of arbitrage-free values of the dervatives. In the probabilistic case, if we consider an enlarged filtration induced by the price process and the market existence process, ordinary stopping times are required. If not, randomized stopping times are required. Several comparisons of the ranges obtained with the two market restrictions are performed. Finally, we conclude that arbitrage arguments are not enough to define the optimal exercise policy.N/

Mechanical slowing-down of cytoplasmic diffusion allows in vivo counting of proteins in individual cells.

Many key regulatory proteins in bacteria are present in too low numbers to be detected with conventional methods, which poses a particular challenge for single-cell analyses because such proteins can contribute greatly to phenotypic heterogeneity. Here we develop a microfluidics-based platform that enables single-molecule counting of low-abundance proteins by mechanically slowing-down their diffusion within the cytoplasm of live Escherichia coli (E. coli) cells. Our technique also allows for automated microscopy at high throughput with minimal perturbation to native physiology, as well as viable enrichment/retrieval. We illustrate the method by analysing the control of the master regulator of the E. coli stress response, RpoS, by its adapter protein, SprE (RssB). Quantification of SprE numbers shows that though SprE is necessary for RpoS degradation, it is expressed at levels as low as 3-4 molecules per average cell cycle, and fluctuations in SprE are approximately Poisson distributed during exponential phase with no sign of bursting