Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up

We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free energy written in Lagrangian coordinates. We focus on the description of the blow-up of the particle system, namely: the number of particles involved in the first aggregate, and the limiting profile of the rescaled system. We exhibit basins of stability for which the number of particles is critical, and we prove a weak rigidity result concerning the rescaled dynamics. This work is complemented with a detailed analysis of the case where only three particles interact

Mathematical modelling for health systems research: a systematic review of system dynamics and agent-based models.

BACKGROUND: Mathematical modelling has been a vital research tool for exploring complex systems, most recently to aid understanding of health system functioning and optimisation. System dynamics models (SDM) and agent-based models (ABM) are two popular complementary methods, used to simulate macro- and micro-level health system behaviour. This systematic review aims to collate, compare and summarise the application of both methods in this field and to identify common healthcare settings and problems that have been modelled using SDM and ABM. METHODS: We searched MEDLINE, EMBASE, Cochrane Library, MathSciNet, ACM Digital Library, HMIC, Econlit and Global Health databases to identify literature for this review. We described papers meeting the inclusion criteria using descriptive statistics and narrative synthesis, and made comparisons between the identified SDM and ABM literature. RESULTS: We identified 28 papers using SDM methods and 11 papers using ABM methods, one of which used hybrid SDM-ABM to simulate health system behaviour. The majority of SDM, ABM and hybrid modelling papers simulated health systems based in high income countries. Emergency and acute care, and elderly care and long-term care services were the most frequently simulated health system settings, modelling the impact of health policies and interventions such as those targeting stretched and under resourced healthcare services, patient length of stay in healthcare facilities and undesirable patient outcomes. CONCLUSIONS: Future work should now turn to modelling health systems in low- and middle-income countries to aid our understanding of health system functioning in these settings and allow stakeholders and researchers to assess the impact of policies or interventions before implementation. Hybrid modelling of health systems is still relatively novel but with increasing software developments and a growing demand to account for both complex system feedback and heterogeneous behaviour exhibited by those who access or deliver healthcare, we expect a boost in their use to model health systems

Testing avoidability on sets of partial words is hard

We prove that the problem of deciding whether a finite set of partial words is unavoidable is NP-hard for any alphabet of size larger than or equal to two, which is in contrast with the well-known feasability results for unavoidability of a set of full words. We raise some related questions on avoidability of sets of partial words. (C) 2008 Elsevier B.V. All rights reserved

Evidence of a Large Diversity of <i>N</i>-acyl-Homoserine Lactones in Symbiotic <i>Vibrio fischeri</i> Strains Associated with the Squid <i>Euprymna scolopes</i>

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Characterization of N-Acyl Homoserine Lactones in Vibrio tasmaniensis LGP32 by a Biosensor-Based UHPLC-HRMS/MS Method

International audienceSince the discovery of quorum sensing (QS) in the 1970s, many studies have demonstrated that Vibrio species coordinate activities such as biofilm formation, virulence, pathogenesis, and bioluminescence, through a large group of molecules called N-acyl homoserine lactones (AHLs). However, despite the extensive knowledge on the involved molecules and the biological processes controlled by QS in a few selected Vibrio strains, less is known about the overall diversity of AHLs produced by a broader range of environmental strains. To investigate the prevalence of QS capability of Vibrio environmental strains we analyzed 87 Vibrio spp. strains from the Banyuls Bacterial Culture Collection (WDCM911) for their ability to produce AHLs. This screening was based on three biosensors, which cover a large spectrum of AHLs, and revealed that only 9% of the screened isolates produced AHLs in the defined experimental conditions. Among these AHL-producing strains, Vibrio tasmaniensis LGP32 is a well-known pathogen of bivalves. We further analyzed the diversity of AHLs produced by this strain using a sensitive bioguided UHPLC-HRMS/MS approach (Ultra-High-Performance Liquid Chromatography followed by High-Resolution tandem Mass Spectrometry) and we identified C10-HSL, OH-C12-HSL, oxo-C12-HSL and C14:1-HSL as QS molecules. This is the first report that documents the production of AHL by Vibrio tasmaniensis LGP32. View Full-Tex

Bacterial–Fungal Interactions in the Kelp Endomicrobiota Drive Autoinducer-2 Quorum Sensing

International audienceBrown macroalgae are an essential component of temperate coastal ecosystems and a growing economic sector. They harbor diverse microbial communities that regulate algal development and health. This algal holobiont is dynamic and achieves equilibrium via a complex network of microbial and host interactions. We now report that bacterial and fungal endophytes associated with four brown algae (Ascophyllum nodosum, Pelvetia canaliculata, Laminaria digitata, and Saccharina latissima) produce metabolites that interfere with bacterial autoinducer-2 quorum sensing, a signaling system implicated in virulence and host colonization. Additionally, we performed co-culture experiments combined to a metabolomic approach and demonstrated that microbial interactions influence production of metabolites, including metabolites involved in quorum sensing. Collectively, the data highlight autoinducer-2 quorum sensing as a key metabolite in the complex network of interactions within the algal holobiont

Quorum Sensing and Quorum Quenching in the Mediterranean Seagrass Posidonia oceanica Microbiota

Posidonia oceanica (L.) Delile is an endemic Mediterranean seagrass angiosperm. The taxonomic diversity of the Posidonia-associated microbiota has previously been inventoried using culture-based and culture-independent approaches. However, little is known about the type of chemical interactions that occur between the cells within this microbiota. In this study, we isolated 60 bacterial strains from the leaves and rhizomes of P. oceanica and evaluated their capacity to communicate through quorum sensing. We found 6 strains able to emit 8 different types of quorum sensing acyl homoserine lactones, identified through UHPLC-HRMS/MS after bioguided fractionation of large cultures. We also identified 19 strains able to produce furanosyl diester borate, another type of quorum sensing autoinducer. Also, 5 strains were found to produce quorum quenching compounds. Finally, as quorum sensing is known to be involved in biofilm production, we also tested whether strains positive to our biotests were able to produce biofilms. Collectively, these data reveal the importance of examining chemical interactions within this bacterial consortium associated with P. oceanica that could have an impact on the physiology of this key Mediterranean seagrass