On integrability of (2+1)-dimensional quasilinear systems

A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants. Exact solutions described by these reductions, known as nonlinear interactions of planar simple waves, can be viewed as natural dispersionless analogs of n-gap solutions. It is demonstrated that the requirement of the existence of 'sufficiently many' n-component reductions provides the effective classification criterion. As an example of this approach we classify integrable (2+1)-dimensional systems of conservation laws possessing a convex quadratic entropy.Comment: 23 page

Aspectos estructurales y metabólicos de la multicelularidad en una cianobacteria formadora de heterocistos

Multicellularity appears to have arisen several times during the course of evolution and has evolved in different phylogenetic groups, including cyanobacteria, a highly diverse group of oxygenic photosynthetic prokaryotes that exhibit a wide range of developmental processes. Cyanobacteria represent one of the most diverse prokaryotic phyla, with morphotypes ranging from unicellular to multicellular filamentous forms. Some filamentous cyanobacteria can produce different types of cells, each one with specific functions. In some cases, cell differentiation allows the filament to carry out tasks that are functionally incompatible, such as oxygenic photosynthesis and the fixation of atmospheric nitrogen. The general plan in this thesis was to address the study of some structural and metabolic aspects of multicellularity in the model heterocyst-forming cyanobacterium Anabaena sp. PCC 7120. Heterocyst-forming cyanobacteria grow as chains of cells (trichomes or filaments), and septal proteins, such as SepJ, are important for cell-cell contact and filament formation. From a structural point of view, cyanobacteria are diderm bacteria, bearing two cellular membranes: the cytoplasmatic membrane and an outer membrane, the latter residing outside of the peptidoglycan layer (or murein sacculus). Filamentous cyanobacteria present a continuous outer membrane along the filament, determining the presence of a continuous periplasmic space that contains the peptidoglycan layer. Although the cell envelope from cyanobacteria has been studied in some detail, the role of this structure in multicellularity has not been addressed until recently. Chapter 1 of this thesis focuses on the possible role of cell envelope components in filamentation, the process of producing and maintaining filaments, thus contributing to the growth of Anabaena forming long trichomes. In order to address this structural aspect of multicellularity in Anabaena sp. PCC 7120, a set of available peptidoglycan- and outer membrane-related gene mutants and strains with mutations in two genes encoding class B penicillin-binding proteins isolated in this work have been used to study filament length and the response of their filaments to mechanical fragmentation. The results obtained indicate that alteration of both the peptidoglycan layer and the outer membrane influence filamentation, although none of these elements is as important as the septal protein SepJ. Because of the compartmentalization of photosynthetic CO2 fixation and N2 fixation processes in different cell types, an intercellular exchange of nutrients takes place in the cyanobacterial filament. Vegetative cells donate products of CO2 fixation, such as sucrose, glutamate and alanine to the heterocysts. Heterocysts, in turn, provide N2 fixation products to the vegetative cells, being glutamine a previously identified metabolite. However, the nitrogenous metabolites that are transferred from heterocysts to vegetative cells are still not fully known. The work presented in Chapter 2 aimed to study the role of cyanophycin, a biopolymer that serves as a dynamic nitrogen cellular reserve material, in the diazotrophic physiology, and of its derivative products as possible nitrogen vehicles in the diazotrophic filament of Anabaena. The results confirmed that ORF all3922 of Anabaena sp. PCC 7120 is the gene encoding isoaspartyl dipeptidase, the enzyme involved in the second step of cyanophycin degradation. Under diazotrophic conditions, the enzyme accumulates in vegetative cells, implying that the β-aspartyl-arginine dipeptide produced by cyanophycinase in heterocysts is transferred intercellularly to the vegetative cells, where it would be hydrolysed releasing aspartate and arginine. Thus, the β-aspartyl-arginine dipeptide has been identified as a nitrogen vehicle in the diazotrophic filament. Arginine appears to be an important metabolite in the physiology of cyanobacteria, not only because it is found in cyanophycin, but also because it might function as a nitrogen vehicle for intercellular molecular exchange, at least in part as β-aspartyl-arginine. However, arginine catabolism is not well understood in these microorganisms and only few studies have been published regarding arginine catabolic enzymes. In Chapter 3 and Annex II of this thesis, the study of two genes, alr2310, encoding an ureohydrolase family protein, and alr4995, encoding a protein belonging to the guanidine-group modifying enzymes superfamily, has been addressed in order to investigate their possible roles in arginine catabolism. The results showed that Alr2310 is the speB gene of Anabaena sp. PCC 7120, encoding an agmatinase, which accumulates preferentially in vegetative cells during diazotrophic growth, and that its inactivation leads to a severe toxic effect that could result from interference of accumulated agmatine with heterocyst differentiation. On the other hand, Alr4995 is a novel enzyme that generates proline from arginine in a two-step reaction, with ornithine (or citrulline) as intermediate metabolite. The concluding remarks of this work is that the heterocyst-forming cyanobacteria present highly coordinated and unique features of compartmentalized metabolic pathways as a strategy of multicellular behavior.La multicelularidad ha surgido numerosas veces a lo largo de la evolución, habiendo aparecido en diferentes grupos filogenéticos, incluidas las cianobacterias, un grupo de procariotas que realizan la fotosíntesis oxigénica y exhiben un amplio rango de procesos de desarrollo. Las cianobacterias representan uno de los grupos más diversos del mundo bacteriano, incluyendo organismos con distintas morfologías, desde estirpes unicelulares hasta otras que forman filamentos multicelulares. Algunas cianobacterias filamentosas pueden presentar células especializadas en distintas funciones fisiológicas. En algunos casos, esta diferenciación celular permite que el filamento cianobacteriano lleve a cabo simultáneamente procesos que son funcionalmente incompatibles, como la fotosíntesis oxigénica y la fijación del nitrógeno atmosférico. El objetivo general de esta tesis ha sido el estudio de algunos aspectos estructurales y metabólicos de la multicelularidad en la cianobacteria formadora de heterocistos modelo Anabaena sp. PCC 7120. Las cianobacterias filamentosas formadoras de heterocistos crecen formando cadenas de células (filamentos o tricomas), y presentan proteínas septales, como SepJ, que son elementos importantes para la adhesión celular y la filamentación (el proceso de formación y mantenimiento de los filamentos). Desde un punto de vista estructural, las cianobacterias son organismos didérmicos, presentando dos membranas celulares: la membrana citoplasmática y la membrana externa, esta última rodeando externamente a la capa de peptidoglicano (o saco de mureina). En el caso de las cianobacterias filamentosas, la membrana externa es continua a lo largo del filamento, determinando así un espacio periplásmico continuo que contiene la capa de peptidoglicano. A pesar de que la envuelta celular de las cianobacterias se ha estudiado en detalle recientemente, el papel de esta estructura en la multicelularidad no se había planteado previamente. El Capítulo 1 de esta tesis aborda el posible papel de los componentes de la envuelta celular en la filamentación. Para ello, se ha estudiado la longitud de los filamentos y la respuesta a la fragmentación mecánica de una colección de mutantes de genes relacionados con la formación del peptidoglicano y de la membrana externa, incluyendo dos estirpes con mutaciones en genes que determinan penicillin-binding proteins (proteínas de unión a la penicilina) de clase B generados en este trabajo. Los resultados obtenidos indican que la alteración tanto de los componentes de la capa de peptidoglicano como de la membrana externa afectan a la filamentación, contribuyendo así al crecimiento de Anabaena formando largos tricomas, aunque ninguno de estos elementos de la envuelta celular es tan relevante para la filamentación como la proteína septal SepJ. Los procesos de la fotosíntesis y la fijación del N2 están compartimentados en el filamento diazotrófico, lo que conlleva un intercambio de nutrientes entre las células vegetativas y los heterocistos. Las células vegetativas exportan a los heterocistos productos derivados de la fijación del CO2, como la sacarosa, el glutamato y la alanina, y a su vez los heterocistos aportan a las células vegetativas productos de la fijación del N2 atmosférico. Previamente se había identificado la glutamina como un vehículo de nitrógeno, pero se consideraba que podía haber otros metabolitos nitrogenados adicionales que se transfiriesen de los heterocistos a las células vegetativas. El Capítulo 2 de esta tesis aborda el papel de la cianoficina, un polímero de aspartato y arginina que funciona como reservorio dinámico de nitrógeno, en la fisiología cianobacteriana, y de sus productos derivados como posibles vehículos nitrogenados en el filamento diazotrófico. Los resultados confirman que en Anabaena la ORF all3922 es el gen que determina la isoaspartil dipeptidasa, enzima implicada en el segundo paso de la degradación de cianoficina. En condiciones diazotróficas, la enzima se expresa en las células vegetativas, lo cual implica que el dipéptido β-aspartilarginina producido por la cianoficinasa en los heterocistos se transfiere intercelularmente a las células vegetativas, donde se hidroliza liberando aspartato y arginina. De este modo, se ha identificado el dipéptido β-aspartil-arginina como vehículo nitrogenado en el filamento diazotrófico. La arginina es un metabolito importante en la fisiología de las cianobacterias, no sólo porque es un constituyente de la cianoficina sino también porque puede servir como vehículo intercelular de nitrógeno, al menos como parte del dipéptido β-aspartil-arginina. Sin embargo, el catabolismo de la arginina en las cianobacterias no se conoce en detalle, y sólo se han publicado unos pocos estudios acerca de las enzimas relacionadas con el mismo. En el Capítulo 3 y el Anexo II de esta tesis se han caracterizado dos genes, alr2310, que determina una proteína de la familia de las ureohidrolasas, y alr4995, que determina una proteína perteneciente a la familia de enzimas modificadoras del grupo guanidino, investigándose sus posibles funciones en el catabolismo de la arginina. Los resultados muestran que alr2310 es el gen speB de Anabaena, que determina una agmatinasa cuya inactivación causa un efecto tóxico severo que puede ser consecuencia de una interferencia de la agmatina acumulada en el mutante con la diferenciación de los heterocistos. Se encontró asimismo que la agmatinasa se acumula preferentemente en las células vegetativas durante el crecimiento diazotrófico. Por otra parte, Alr4995 es una nueva enzima que genera prolina a partir de arginina en dos pasos, siendo la ornitina (o la citrulina) un metabolito intermediario de dicha reacción. Los resultados de este trabajo indican que la envuelta celular es esencial para la filamentación en las cianobacterias formadoras de heterocistos, y que éstas presentan características únicas y altamente coordinadas de compartimentación celular de vías metabólicas como estrategia de organización multicelular

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

In Situ Determination of the Effects of Lead and Copper on Cyanobacterial Populations in Microcosms

BACKGROUND: Biomass has been studied as biomarker to evaluate the effect of heavy metals on microbial communities. Nevertheless, the most important methodological problem when working with natural and artificial microbial mats is the difficulty to evaluate changes produced on microorganism populations that are found in thicknesses of just a few mm depth. METHODOLOGY/PRINCIPAL FINDINGS: Here, we applied for first time a recently published new method based on confocal laser scanning microscopy and image-program analysis to determine in situ the effect of Pb and Cu stress in cyanobacterial populations. CONCLUSIONS/SIGNIFICANCE: The results showed that both in the microcosm polluted by Cu and by Pb, a drastic reduction in total biomass for cyanobacterial and Microcoleus sp. (the dominant filamentous cyanobacterium in microbial mats) was detected within a week. According to the data presented in this report, this biomass inspection has a main advantage: besides total biomass, diversity, individual biomass of each population and their position can be analysed at microscale level. CLSM-IA could be a good method for analyzing changes in microbial biomass as a response to the addition of heavy metals and also to other kind of pollutants

Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page

The functional cooperation of 5−HT1A5-HT_{1A} and mGlu4R in HEK-293 cell line

Background The serotonin 5-HT1A receptor (5-HT1AR) and metabotropic glutamate receptor 4 (mGlu4) have been implicated as sites of antipsychotic drug action. 5-HT1AR belongs to the A class of G protein-coupled receptors (GPCRs); mGlu4 is a representative of class C GPCRs. Both receptors preferentially couple with Gi protein to inhibit cAMP formation. The present work aimed to examine the possibility of mGlu4 and 5-HT1A receptor cross-talk, the phenomenon that could serve as a molecular basis of the interaction of these receptor ligands observed in behavioral studies. Methods First, in vitro studies were performed to examine the pharmacological modulation of interaction of the mGlu4 and 5-HT1A receptors in the T-REx 293 cell line using SNAP- or HALO-tag and cAMP accumulation assay. Next, the colocalization of these two receptors was examined in some regions of the mouse brain by applying RNAScope dual fluorescence in situ hybridization, immunohistochemical labeling, and proximity ligation assay (PLA). Results The ex vivo and in vitro results obtained in the present work suggest the existence of interactions between mGlu4 and 5-HT1A receptors. The changes were observed in cAMP accumulation assay and were dependent on expression and activation of mGlu4R in T-REx 293cell line. Moreover, the existence of spots with proximity expression of both receptors were showed by PLA, immunofluorescence labeling and RNAscope methods. Conclusion The existence of interactions between mGlu4 and 5-HT1A receptors may represent another signaling pathway involved in the development and treatment psychiatric disorders such as schizophrenia or depression

The Influence of Chemical Surface Treatment on the Corrosion Resistance of Titanium Castings Used in Dental Prosthetics

Abstract Air abrasion process is used for cleaning casting surface of prosthetic components, and to prepare the surface of these elements for the application of veneering items. Its side effect, however, is that abrasive particles are embedded in the treated surface, which can be up to 30% of the surface and it constitutes the side effect of this procedure. Such a significant participation of foreign material can not be indifferent to the properties of the surface. Embedded particles can be the place of stress concentration causing cracking of ceramics, and may deteriorate corrosion resistance by forming corrosive microlinks. In the latter cases, it would be advisable to remove elements embedded into the surface. The simplest method is chemical etching or electrochemical one. Nevertheless, these procedures should not significantly change the parameters of the surface. Among many possible reagents only a few fulfills all the above conditions. In addition, processing should not impair corrosion resistance of titanium, which is one of the most important factors determining its use as a prosthetic restoration in the mouth. The study presented results of corrosion resistance of titanium used to make prosthetic components by means of casting method, which were subjected to chemical processing designed to remove the embedded abrasive particles. The aim of the study was to investigate whether etching with selected reagents affects the corrosion resistance of titanium castings. For etching the following reagents were used: 30% HNO 3 + 3% HF + H 2 O, HNO 3 + HF+ glycerol (1:2:3), 4% HF in H 2 O 2 , 4% HF in H 2 O, with a control sandblasted sample, not subjected to etching. Tests demonstrated that the etching affected corrosion properties of test samples, in each case the reduction of the corrosion potential occurred -possibly due to the removal of particles of Al 2 O 3 from the surface and activation of the surface. None of the samples underwent pitting corrosion as a result of polarization to 9 V. Values of the polarization resistance, and potentiodynamic characteristics indicated that the best corrosion resistance exhibited the samples after etching in a mixture of 4% solution of HF in H 2 O 2 . They showed very good passivation of the surface