Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

CHARACTERIZATION OF NrsZ, A NOVEL SMALL REGULATORY NON-CODING RNA INVOLVED IN THE ADAPTATION OF PSEUDOMONAS AERUGINOSA PAO1

The opportunistic ubiquitous pathogen Pseudomonas aeruginosa strain PAOl is a versatile Gram-negative bacterium that has the extraordinary capacity to colonize a wide diversity of ecological niches and to cause severe and persistent infections in humans. To ensure an optimal coordination of the genes involved in nutrient utilization, this bacterium uses the NtrB/C and/or the CbrA/B two-component systems, to sense nutrients availability and to regulate in consequence the expression of genes involved in their uptake and catabolism. NtrB/C is specialized in nitrogen utilization, while the CbrA/B system is involved in both carbon and nitrogen utilization and both systems activate their target genes expression in concert with the alternative sigma factor RpoN. Moreover, the NtrB/C and CbrA/B two- component systems regulate the secondary metabolism of the bacterium, such as the production of virulence factors. In addition to the fine-tuning transcriptional regulation, P. aeruginosa can rapidly modulate its metabolism using small non-coding regulatory RNAs (sRNAs), which regulate gene expression at the post-transcriptional level by diverse and sophisticated mechanisms and contribute to the fast physiological adaptability of this bacterium. In our search for novel RpoN-dependent sRNAs modulating the nutritional adaptation of P. aeruginosa PAOl, we discovered NrsZ (Nitrogen regulated sRNA), a novel RpoN-dependent sRNA that is induced under nitrogen starvation by the NtrB/C two-component system. NrsZ has a unique architecture, formed of three similar stem-loop structures (SL I, II and II) separated by variant spacer sequences. Moreover, this sRNA is processed in short individual stem-loop molecules, by internal cleavage involving the endoribonuclease RNAse E. Concerning NrsZ functions in P. aeruginosa PAOl, this sRNA was shown to trigger the swarming motility and the rhamnolipid biosurfactants production. This regulation is due to the NrsZ-mediated activation of rhlA expression, a gene encoding for an enzyme essential for swarming motility and rhamnolipids production. Interestingly, the SL I structure of NrsZ ensures its regulatory function on rhlA expression, suggesting that the similar SLs are the functional units of this modular sRNA. However, the regulatory mechanism of action of NrsZ on rhlA expression activation remains unclear and is currently being investigated. Additionally, the NrsZ regulatory network was investigated by a transcriptome analysis, suggesting that numerous genes involved in both primary and secondary metabolism are regulated by this sRNA. To emphasize the importance of NrsZ, we investigated its conservation in other Pseudomonas species and demonstrated that NrsZ is conserved and expressed under nitrogen limitation in Pseudomonas protegens Pf-5, Pseudomonas putida KT2442, Pseudomonas entomophila L48 and Pseudomonas syringae pv. tomato DC3000, strains having different ecological features, suggesting an important role of NrsZ in the adaptation of Pseudomonads to nitrogen starvation. Interestingly the architecture of the different NrsZ homologs is similarly composed by SL structures and variant spacer sequences. However, the number of SL repetitions is not identical, and one to six SLs were predicted on the different NrsZ homologs. Moreover, NrsZ is processed in short molecules in all the strains, similarly to what was previously observed in P. aeruginosa PAOl, and the heterologous expression of the NrsZ homologs restored rhlA expression, swarming motility and rhamnolipids production in the P. aeruginosa NrsZ mutant. In many aspects, NrsZ is an atypical sRNA in the bacterial panorama. To our knowledge, NrsZ is the first described sRNA induced by the NtrB/C. Moreover, its unique modular architecture and its processing in similar short SL molecules suggest that NrsZ belongs to a novel family of bacterial sRNAs. -- L'agent pathogène opportuniste et ubiquitaire Pseudomonas aeruginosa souche PAOl est une bactérie Gram négative versatile ayant l'extraordinaire capacité de coloniser différentes niches écologiques et de causer des infections sévères et persistantes chez l'être humain. Afin d'assurer une coordination optimale des gènes impliqués dans l'utilisation de différents nutriments, cette bactérie se sert de systèmes à deux composants tel que NtrB/C et CbrA/B afin de détecter la disponibilité des ressources nutritives, puis de réguler en conséquence l'expression des gènes impliqués dans leur importation et leur catabolisme. Le système NtrB/C régule l'utilisation des sources d'azote alors que le système CbrA/B est impliqué à la fois dans l'utilisation des sources de carbone et d'azote. Ces deux systèmes activent l'expression de leurs gènes-cibles de concert avec le facteur sigma alternatif RpoN. En outre, NtrB/C et CbrA/B régulent aussi le métabolisme secondaire, contrôlant notamment la production d'importants facteurs de virulence. En plus de toutes ces régulations génétiques fines ayant lieu au niveau transcriptionnel, P. aeruginosa est aussi capable de moduler son métabolisme en se servant de petits ARNs régulateurs non-codants (ARNncs), qui régulent l'expression génétique à un niveau post- transcriptionnel par divers mécanismes sophistiqués et contribuent à rendre particulièrement rapide l'adaptation physiologique de cette bactérie. Au cours de nos recherches sur de nouveaux ARNncs dépendant du facteur sigma RpoN et impliqués dans l'adaptation nutritionnelle de P. aeruginosa PAOl, nous avons découvert NrsZ (Nitrogen regulated sRNA), un ARNnc induit par la cascade NtrB/C-RpoN en condition de carence en azote. NrsZ a une architecture unique, composée de trois structures en tige- boucle (TB I, II et III) hautement similaires et séparées par des « espaceurs » ayant des séquences variables. De plus, cet ARNnc est clivé en petits fragments correspondant au trois molécules en tige-boucle, par un processus de clivage interne impliquant l'endoribonucléase RNase E. Concernant les fonctions de NrsZ chez P. aeruginosa PAOl, cet ARNnc est capable d'induire la motilité de type « swarming » et la production de biosurfactants, nommés rhamnolipides. Cette régulation est due à l'activation par NrsZ de l'expression de rhlA, un gène essentiel pour la motilité de type swarming et pour la production de rhamnolipides. Étonnamment, la structure TB I est capable d'assurer à elle seule la fonction régulatrice de NrsZ sur l'expression de rhlA, suggérant que ces molécules TBs sont les unités fonctionnelles de cet ARNnc modulaire. Cependant, le mécanisme moléculaire par lequel NrsZ active l'expression de rhlA demeure à ce jour incertain et est actuellement à l'étude. En plus, le réseau de régulations médiées par NrsZ a été étudié par une analyse de transcriptome qui a indiqué que de nombreux gènes impliqués dans le métabolisme primaire ou secondaire seraient régulés par NrsZ. Pour accentuer l'importance de NrsZ, nous avons étudié sa conservation dans d'autres espèces de Pseudomonas. Ainsi, nous avons démontré que NrsZ est conservé et exprimé en situation de carence d'azote par les souches Pseudomonas protegens Pf-5, Pseudomonas putida KT2442, Pseudomonas entomophila L48, Pseudomonas syringae pv. tomato DC3000, quatre espèces ayant des caractéristiques écologiques très différentes, suggérant que NrsZ joue un rôle important dans l'adaptation du genre Pseudomonas envers la carence en azote. Chez toutes les souches étudiées, les différents homologues de NrsZ présentent une architecture similaire faite de TBs conservées et d'espaceurs. Cependant, le nombre de TBs n'est pas identique et peut varier de une à six copies selon la souche. Les différentes versions de NrsZ sont clivées en petites molécules dans ces quatre souches, comme il a été observé chez P. aeruginosa PAOl. De plus, l'expression hétérologue des différentes variantes de NrsZ est capable de restaurer l'expression de rhlA, la motilité swarming et la production de rhamnolipides dans une souche de P. aeruginosa dont nrsZ a été inactivé. Par bien des aspects, NrsZ est un ARNnc atypique dans le monde bactérien. À notre connaissance, NrsZ est le premier ARNnc décrit comme étant régulé par le système NtrB/C. De plus, son unique architecture modulaire et son clivage en petites molécules similaires suggèrent que NrsZ appartient à une nouvelle famille d'ARNncs bactériens.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Intercellular calcium waves in primary cultured rat mesenteric smooth muscle cells are mediated by connexin43.

Intercellular Ca(2+) wave propagation between vascular smooth muscle cells (SMCs) is associated with the propagation of contraction along the vessel. Here, we characterize the involvement of gap junctions (GJs) in Ca(2+) wave propagation between SMCs at the cellular level. Gap junctional communication was assessed by the propagation of intercellular Ca(2+) waves and the transfer of Lucifer Yellow in A7r5 cells, primary rat mesenteric SMCs (pSMCs), and 6B5N cells, a clone of A7r5 cells expressing higher connexin43 (Cx43) to Cx40 ratio. Mechanical stimulation induced an intracellular Ca(2+) wave in pSMC and 6B5N cells that propagated to neighboring cells, whereas Ca(2+) waves in A7r5 cells failed to progress to neighboring cells. We demonstrate that Cx43 forms the functional GJs that are involved in mediating intercellular Ca(2+) waves and that co-expression of Cx40 with Cx43, depending on their expression ratio, may interfere with Cx43 GJ formation, thus altering junctional communication.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

High-density collagen gel tubes as a matrix for primary human bladder smooth muscle cells.

Tissue-engineered grafts for the urinary tract are being investigated for the potential treatment of several urologic diseases. These grafts, predominantly tubular-shaped, usually require in vitro culture prior to implantation to allow cell engraftment on initially cell-free scaffolds. We have developed a method to produce tubular-shaped collagen scaffolds based on plastic compression. Our approach produces a ready cell-seeded graft that does not need further in vitro culture prior to implantation. The tubular collagen scaffolds were in particular investigated for their structural, mechanical and biological properties. The resulting construct showed an especially high collagen density, and was characterized by favorable mechanical properties assessed by axial extension and radial dilation. Young modulus in particular was greater than non-compressed collagen tubes. Seeding densities affected proliferation rate of primary human bladder smooth muscle cells. An optimal seeding density of 10(6) cells per construct resulted in a 25-fold increase in Alamar blue-based fluorescence after 2 wk in culture. These high-density collagen gel tubes, ready seeded with smooth muscle cells could be further seeded with urothelial cells, drastically shortening the production time of graft for urinary tract regeneration.

Role of major histocompatibility complex class II expression by non-hematopoietic cells in autoimmune and inflammatory disorders: facts and fiction.

It is well established that interactions between CD4(+) T cells and major histocompatibility complex class II (MHCII) positive antigen-presenting cells (APCs) of hematopoietic origin play key roles in both the maintenance of tolerance and the initiation and development of autoimmune and inflammatory disorders. In sharp contrast, despite nearly three decades of intensive research, the functional relevance of MHCII expression by non-hematopoietic tissue-resident cells has remained obscure. The widespread assumption that MHCII expression by non-hematopoietic APCs has an impact on autoimmune and inflammatory diseases has in most instances neither been confirmed nor excluded by indisputable in vivo data. Here we review and put into perspective conflicting in vitro and in vivo results on the putative impact of MHCII expression by non-hematopoietic APCs-in both target organs and secondary lymphoid tissues-on the initiation and development of representative autoimmune and inflammatory disorders. Emphasis will be placed on the lacunar status of our knowledge in this field. We also discuss new mouse models-developed on the basis of our understanding of the molecular mechanisms that regulate MHCII expression-that constitute valuable tools for filling the severe gaps in our knowledge on the functions of non-hematopoietic APCs in inflammatory conditions.

Endogenous cannabinoid receptor CB1 activation promotes vascular smooth-muscle cell proliferation and neointima formation.

Percutaneous transluminal angioplasty is frequently used in patients with severe arterial narrowing due to atherosclerosis. However, it induces severe arterial injury and an inflammatory response leading to restenosis. Here, we studied a potential activation of the endocannabinoid system and the effect of FA amide hydrolase (FAAH) deficiency, the major enzyme responsible for endocannabinoid anandamide degradation, in arterial injury. We performed carotid balloon injury in atherosclerosis-prone apoE knockout (apoE(-/-)) and apoE(-/-)FAAH(-/-) mice. Anandamide levels were systemically elevated in apoE(-/-) mice after balloon injury. ApoE(-/-)FAAH(-/-) mice had significantly higher baseline anandamide levels and enhanced neointima formation compared with apoE(-/-) controls. The latter effect was inhibited by treatment with CB1 antagonist AM281. Similarly, apoE(-/-) mice treated with AM281 had reduced neointimal areas, reduced lesional vascular smooth-muscle cell (SMC) content, and proliferating cell counts. The lesional macrophage content was unchanged. In vitro proliferation rates were significantly reduced in CB1(-/-) SMCs or when treating apoE(-/-) or apoE(-/-)FAAH(-/-) SMCs with AM281. Macrophage in vitro adhesion and migration were marginally affected by CB1 deficiency. Reendothelialization was not inhibited by treatment with AM281. In conclusion, endogenous CB1 activation contributes to vascular SMC proliferation and neointima formation in response to arterial injury.

Cis interactions of immunoreceptors with MHC and non-MHC ligands

The conventional wisdom is that cell-surface receptors interact with ligands expressed on other cells to mediate cell-to-cell communication (trans interactions). Unexpectedly, it has recently been found that two classes of receptors specific for MHC class I molecules not only interact with MHC class I molecules expressed on opposing cells, but also with those on the same cell. These cis interactions are a feature of immunoreceptors that inhibit, rather than activate, cellular functions. Here, we review situations in which cis interactions have been observed, the characteristics of receptors that bind in trans and cis, and the biological roles of cis recognition.

GAP-independent functions of DLC1 in metastasis.

Metastases are responsible for most cancer-related deaths. One of the hallmarks of metastatic cells is increased motility and migration through extracellular matrixes. These processes rely on specific small GTPases, in particular those of the Rho family. Deleted in liver cancer-1 (DLC1) is a tumor suppressor that bears a RhoGAP activity. This protein is lost in most cancers, allowing malignant cells to proliferate and disseminate in a Rho-dependent manner. However, DLC1 is also a scaffold protein involved in alternative pathways leading to tumor and metastasis suppressor activities. Recently, substantial information has been gathered on these mechanisms and this review is aiming at describing the potential and known alternative GAP-independent mechanisms allowing DLC1 to impair migration, invasion, and metastasis formation.

Non-viral gene therapy for GDNF production in RCS rat: the crucial role of the plasmid dose.

Glial cell line-derived neurotrophic factor (GDNF) is one of the candidate molecules among neurotrophic factors proposed for a potential treatment of retinitis pigmentosa (RP). It must be administered repeatedly or through sustained releasing systems to exert prolonged neuroprotective effects. In the dystrophic Royal College of Surgeon's (RCS) rat model of RP, we found that endogenous GDNF levels dropped during retinal degeneration time course, opening a therapeutic window for GDNF supplementation. We showed that after a single electrotransfer of 30 μg of GDNF-encoding plasmid in the rat ciliary muscle, GDNF was produced for at least 7 months. Morphometric, electroretinographic and optokinetic analyses highlighted that this continuous release of GDNF delayed photoreceptors (PRs) as well as retinal functions loss until at least 70 days of age in RCS rats. Unexpectedly, increasing the GDNF secretion level accelerated PR degeneration and the loss of electrophysiological responses. This is the first report: (i) demonstrating the efficacy of GDNF delivery through non-viral gene therapy in RP; (ii) establishing the efficacy of intravitreal administration of GDNF in RP associated with a mutation in the retinal pigment epithelium; and (iii) warning against potential toxic effects of GDNF within the eye/retina.

Single cell analysis reveals similar functional competence of dominant and non-dominant CD8 T-cell clonotypes

The properties of CD8 T-cells requiredfor protection from infectiousdisease and cancer are only partiallycharacterized, and only limited data isavailable regarding T-cell clonotypes.It has been proposed that dominantT-cell clonotypes may have higherprotective potential than their nondominantcounterparts. Our objectiveswere to assess memory andeffector functions, stage of differentiationand clonotype selection of tumor-reactive T lymphocytes followingpeptide vaccination in melanomapatients.We also characterized dominantversus non-dominant clonotypesto further understand the in vivo functionof these T-cells based on theirprevalence. Using a novel single-cellapproach for simultaneous ex vivomolecular and functional analysis, wereport the preferential selection andexpansion of several tumor-specificco-dominant clonotypes of intermediateto high frequencies, irrespectiveof whether native or analog peptidewas used for vaccination. Theseclonotypes made up 40 - 95% of thedifferentiated "effector-like" T-cells,but only 25% of the less-differentiated"effector-memory" cells. Bothsubsets also contained non-dominantT-cell clonotypes, but these were significantlymore frequent in the lessdifferentiatedcells. Thus, cell differentiationwas clonotype-dependent.Surprisingly however, the acquisitionof memory and effector T-cell propertieswas clonotype independent, as wefound similar functional profiles indominant and low/ non-dominantT-cell clonotypes. In contrast to analogpeptide vaccination, native peptidevaccination induced T-cell functionsthat were more comprehensive,with more pronounced effector functionscombined with memory cellproperties. In summary, this study revealsthat T-cell functions are determinedprimarily by the antigen andthe stage of T-cell differentiation, butare similar in dominant and non-dominantclonotypes participating in aCD8 T-cell response. The identifiedclonotypic basis of T-cell responsescontributes to the rational developmentof vaccines.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

The nuclear hormone receptor PPARγ counteracts vascular calcification by inhibiting Wnt5a signalling in vascular smooth muscle cells.

Vascular calcification is a hallmark of advanced atherosclerosis. Here we show that deletion of the nuclear receptor PPARγ in vascular smooth muscle cells of low density lipoprotein receptor (LDLr)-deficient mice fed an atherogenic diet high in cholesterol, accelerates vascular calcification with chondrogenic metaplasia within the lesions. Vascular calcification in the absence of PPARγ requires expression of the transmembrane receptor LDLr-related protein-1 in vascular smooth muscle cells. LDLr-related protein-1 promotes a previously unknown Wnt5a-dependent prochondrogenic pathway. We show that PPARγ protects against vascular calcification by inducing the expression of secreted frizzled-related protein-2, which functions as a Wnt5a antagonist. Targeting this signalling pathway may have clinical implications in the context of common complications of atherosclerosis, including coronary artery calcification and valvular sclerosis.