Stabilization in a two-species chemotaxis system with logistic source

We study a system of three partial differential equations modelling the spatiotemporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. For a range of the parameters the system possesses a uniquely determined spatially homogeneous positive equilibrium (u?, v?) globally asymptotically stable within a certain nonempty range of the logistic growth coefficients.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

On a two species chemotaxis model with slow chemical diffucion.

In this paper we consider a system of three parabolic equations modeling the behavior of two biological species moving attracted by a chemical factor. The chemical substance verifies a parabolic equation with slow diffusion. The system contains second order terms in the first two equations modeling the chemotactic effects. We apply an iterative method to obtain the global existence of solutions using that the total mass of the biological species is conserved. The stability of the homogeneous steady states is studied by using an energy method. A final example is presented to illustrate the theoretical results.

Reduction of critical mass in a chemotaxis system by external application of a chemoattractant

In this paper we study non-negative radially symmetric solutions of a parabolic-elliptic Keller-Segel system. The system describes the chemotactic movement of cells under the additional circumstance that an external application of a chemo attractant at a distinguished point is introduced.

On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.

Mecanismos implicados en las etapas iniciales de infección en la cancrosis de los cítricos provocada por Xanthomonas citri subsp. citri

La cancrosis o chancro bacteriano de los cítricos (CBC) causada por Xanthomonas citri subsp. citri (Xcc) y X. fuscans subsp. aurantifolii, afecta a un gran número de especies dentro de la familia de las rutáceas, especialmente cítricos. Esta enfermedad produce graves pérdidas económicas allí donde está presente, principalmente porque la comercialización de cítricos desde las zonas afectadas hacía zonas libres de cancrosis, está sujeta a fuertes medidas cuarentenarias. La cancrosis se encuentra distribuida a nivel mundial pero no se ha localizado ni en la Unión Europea ni en ningún área del Mediterráneo. Se han descrito tres tipos de cancrosis en función de la gama de huésped y de las características fenotípicas y genotípicas de las bacterias que las producen. La más extendida es la cancrosis tipo A producida por Xcc, dentro de la cual se distinguen los subtipos Aw y A*, originarios de Florida y Sudeste Asiático, respectivamente, que de forma natural solo son capaces de producir enfermedad en lima mejicana. En este trabajo se presentan estudios sobre mecanismos implicados en las primeras etapas de la infección, como la quimiotaxis y formación de biopelículas, en la cancrosis de los cítricos. La quimiotaxis es el proceso por el cual las bacterias se dirigen hacia zonas favorables para su supervivencia y desarrollo. Los perfiles quimiotácticos obtenidos frente a distintas fuentes de carbono, así como los estudios en relación al contenido de proteínas aceptoras de grupos metilo (MCPs), permitieron agrupar a las cepas de Xanthomonas estudiadas en este trabajo, de acuerdo a la enfermedad producida y a su gama de huésped. Todas las cepas mostraron quimiotaxis positiva frente a extractos de hoja y apoplasto de diferentes especies, sin embargo, Xcc 306, X. alfalfae subsp. citrumelonis (Xac) y X. campestris pv. campestris (Xc) manifestaron respuestas más específicas frente a extractos de apoplasto de hojas de naranjo dulce, lima y col china, respectivamente. Dicho resultado nos permite asociar el mecanismo de quimiotaxis con la capacidad de las cepas de Xanthomonas para colonizar estos huéspedes de forma específica. Las cepas estudiadas fueron capaces de realizar movimiento tipo swimming, twitching y sliding en distintos medios, siendo el movimiento swimming el único en el que se encontraron diferencias entre las cepas de Xcc con distinta gama de huésped. En este trabajo se ha estudiado además la formación de biopelículas en superficies bióticas y abióticas, un mecanismo importante tanto para la supervivencia en superficie vegetal como para el desarrollo de la infección. Las cepas de Xanthomonas estudiadas fueron capaces de formar biopelículas in vitro, siendo mayor en un medio que simula el apoplasto y que contiene una baja concentración de nutrientes en comparación con medios que contenían alta concentración de nutrientes. La formación de biopelículas en superficie vegetal se encontró relacionada, en las cepas patógenas de cítricos, con la capacidad para infectar un tejido o huésped determinado. Se han caracterizado algunos de los componentes de la matriz extracelular producida por Xcc, que compone hasta un 90% de las bipoelículas. Entre ellos destaca el ADN extracelular, que tiene un papel como adhesina en las primeras etapas de formación de biopelículas y estructural en biopelículas maduras. Además, se han identificado el pilus tipo IV como componente importante en las biopelículas, que también participa en motilidad. Finalmente, se han realizado estudios sobre la expresión de genes implicados en motilidad bacteriana y formación de biopelículas que han confirmado las diferencias existentes entre cepas de Xcc de amplia y limitada gama de huésped, así como el papel que juegan elementos como el pilus tipo IV o el flagelo en estos procesos. ABSTRACT Xanthomonas citri subsp. citri (Xcc) and X. fuscans subsp. aurantifolii are the causal agents of Citrus Bacterial Canker (CBC) which is one of the most important citrus diseases. CBC affects all Citrus species as well as other species from Rutaceae family. CBC produces strong economic losses; furthermore the commercialization of plants and fruits is restricted from infested to citrus canker free areas. The disease is worldwide distributed in tropical and subtropical areas, however it is not present in the European Union. Three types of CBC have been described according to the host range and phenotypic and genotypic characteristics. CBC type A caused by Xcc is he widest distributed. Within CBC A type two subtypes Aw and A* were described from Florida and Iran respectively, both infecting only Mexican lime. Herein mechanisms connected to early events in the citrus bacterial canker disease such as chemotaxis and biofilm formation, were studied. Chemotaxis allows bacteria to move towards the more suitable environments for its survival, host colonization and infection. Studies performed on citrus pathogenic Xanthomonas and X. campestris pv. campestris (Xc), a crucifer pathogen, have shown different chemotactic profiles towards carbon compound as well as different MCPs profile, which clustered strains according to host range and disease caused. Every strain showed positive chemotaxis toward leaf extracts and apoplastic fluids from sweet orange, Mexican lime and Chinese cabbage leaves. However, a more specific response was found for strains Xcc 306, X. alfalfae subsp. citrumelonis and Xc towards sweet orange, Mexican lime and Chinese cabbage apoplastic fluids, respectively. These results relate chemotaxis with the higher ability of those strains to specifically colonize their proper host. Xanthomonas strains studied were able to perform swimming, sliding and twitching motilities. The ability to swim was variable among CBC strains and seemed related to host range. Biofilm formation is an important virulence factor for Xcc because it allows a better survival onto the plant surface as well as facilitates the infection process. The studied Xanthomonas strains were able to form biofilm in vitro, on both nutrient rich and apoplast mimicking media, furthermore the biofilm formation by all the strains was higher in the apoplast mimicking media. The ability to form biofilm in planta by Xcc and Xac strains was dependent of the host and the tissue colonized. The wide host range CBC strain was able to form biofilm onto several citrus leaves and fruits, however the limited host range CBC strain produced biofilm solely onto Mexican lime leaves and fruits. Furthermore Xac strain, which solely infects leaves of young plants, was not able to develop biofilms on fruits. Some components of the extracellular matrix produced by Xcc strains have been characterized. Extracellular DNA acted as an adhesin at the very early stages of biofilm formation and as structural component of mature biofilm for citrus pathogenic Xanthomonas. Furthermore type IV pilus has been identified as a component of the extracellular matrix in biofilm and motility. Transcriptional studies of genes related with biofilm formation and motility have confirmed the differential behavior found among wide and limited host range CBC strains as well as the role of type IV pili and flagellum on those processes.