[Lineage tracing of epicardial cells during development and regeneration].

Tracing the history of individual cells during embryonic morphogenesis in a structure as complex as the cardiovascular system is one of the major challenges of developmental biology. It involves determining the relationships between the various lineages of cells forming an organ at different stages, describing the topological rearrangements tissues undergo during morphogenesis, and characterizing the interactions between cells in different structures. However, despite the great expectations raised in the field of regenerative medicine, only limited progress has been made in using regenerative therapy to repair the cardiovascular system. Recent research has highlighted the role of the epicardium during cardiac regeneration, but it is still unclear whether it is important for molecular signaling or acts as a source of progenitor cells during this process. Consequently, increasing knowledge about the origin, diversification and potential of epicardial cells during development and homeostasis and under pathological conditions is of fundamental importance both for basic research and for the development of effective cellular therapies. The aims of this article were to provide a general overview of the classical techniques used for tracing cell lineages, including their potential and limitations, and to describe novel techniques for studying the origin and differentiation of the epicardium and its role in cardiac regeneration.

Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.

Derivation of Change from Sequences of Snapshots

Current research in the domain of geographic information science considers possibilities of including another dimension, time, which is generally missing to this point. Users interested in changes have few functions available to compare datasets of spatial configurations at different points in time. Such a comparison of spatial configurations requires large amounts of manual labor. An automatic derivation of changes would decrease amounts of manual labor. The thesis introduces a set of methods that allows for an automatic derivation of changes. These methods analyze identity and topological states of objects in snapshots and derive types of change for the specific configuration of data. The set of change types that can be computed by the methods presented includes continuous changes such as growing, shrinking, and moving of objects. For these continuous changes identity remains unchanged, while topological relations might be altered over time. Also discrete changes such as merging and splitting where both identity and topology are affected can be derived. Evaluation of the methods using a prototype application with simple examples suggests that the methods compute uniquely and correctly the type of change that applied in spatial scenarios captured in two snapshots.

A Framework for Realistic and Systematic Multicast Performance Evaluation

Previous multicast research often makes commonly accepted but unverifed assumptions on network topologies and group member distribution in simulation studies. In this paper, we propose a framework to systematically evaluate multicast performance for different protocols. We identify a series of metrics, and carry out extensive simulation studies on these metrics with different topological models and group member distributions for three case studies. Our simulation results indicate that realistic topology and group membership models are crucial to accurate multicast performance evaluation. These results can provide guidance for multicast researchers to perform realistic simulations, and facilitate the design and development of multicast protocols.

Role of phosphatidylethanolamine in the function and assembly of phenylalanine-specific permease of Escherichia coli

Transmembrane segments of polytopic membrane proteins once inserted are generally considered stably oriented due to the large free energy barrier for topological reorientation of adjacent extra-membrane domains. However, proper topology and function of the polytopic membrane protein lactose permease (LacY) of Escherichia coli is dependent on the membrane phospholipid composition revealing topological dynamics of transmembrane domains (Bogdanov, M., Heacock, P. N., and Dowhan, W. (2002) EMBO J. 21, 2107–2116). The high affinity phenylalanine permease PheP shares many topological similarities with LacY. In this study, mutant E. coli cells lacking phosphatidylethanolamine (PE) as a membrane component were used to evaluate the role of PE in the function and assembly of PheP. Active transport of phenylalanine by cells lacking PE was severely inhibited (both Vmax and Km were altered), whereas the PheP protein level in membranes was unaffected. Cysteine residues were introduced into predicted periplasmic or cytoplasmic segments of cysteine-less PheP, and the topology of the protein was explored using a membrane-impermeable thiol-specific biotinylated probe. Based on the biotinylation patterns of PheP in whole cells, the N-terminus and adjoining transmembrane hairpin of PheP adopted an inverted topological orientation in PE-lacking cells. Introduction of PE following the assembly of PheP triggered a reorientation of the N-terminus and adjacent hairpin to their native orientation associated with regain of wild type transport function. These results coupled with the results for LacY support a specific role for membrane lipid composition in determining topological organization and function of membrane proteins. Several other secondary symporters are compromised for activity in PE-lacking cells suggesting that lipid-assisted topogenesis is a general property of such transporters. The reversible orientation of these secondary transport proteins in response to a change of phospholipid composition might be a result of inherent conformational flexibility necessary for transport function or during protein assembly. ^

Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production

This paper provides new sufficient conditions for the existence, computation via successive approximations, and stability of Markovian equilibrium decision processes for a large class of OLG models with stochastic nonclassical production. Our notion of stability is existence of stationary Markovian equilibrium. With a nonclassical production, our economies encompass a large class of OLG models with public policy, valued fiat money, production externalities, and Markov shocks to production. Our approach combines aspects of both topological and order theoretic fixed point theory, and provides the basis of globally stable numerical iteration procedures for computing extremal Markovian equilibrium objects. In addition to new theoretical results on existence and computation, we provide some monotone comparative statics results on the space of economies.

The in vivo and in vitro formation of sticky DNA and the GAA.TTC trinucleotide repeat associated with Friedreich's ataxia

Friedreich's ataxia is caused by the expansion of the GAA•TTC trinucleotide repeat sequence located in intron 1 of the frataxin gene. The long GAA•TTC repeats are known to form several non-B DNA structures including hairpins, triplexes, parallel DNA and sticky DNA. Therefore it is believed that alternative DNA structures play a role in the loss of mRNA transcript and functional frataxin protein in FRDA patients. We wanted to further elucidate the characteristics for formation and stability of sticky DNA by evaluating the structure in a plasmid based system in vitro and in vivo in Escherichia coli. The negative supercoil density of plasmids harboring different lengths of GAA•TTC repeats, as well as either one or two repeat tracts were studied in E. coli to determine if plasmids containing two long tracts (≥60 repeats) in a direct repeat orientation would have a different topological effect in vivo compared to plasmids that harbored only one GAA•TTC tract or two tracts of < 60 repeats. The experiments revealed that, in fact, sticky DNA forming plasmids had a lower average negative supercoil density (-σ) compared to all other control plasmids used that had the potential to form other non-B DNA structures such as triplexes or Z-DNA. Also, the requirements for in vitro dissociation and reconstitution of the DNA•DNA associated region of sticky DNA were evaluated. Results conclude that the two repeat tracts associate in the presence of negative supercoiling and MgCl 2 or MnCl2 in a time and concentration-dependent manner. Interaction of the repeat sequences was not observed in the absence of negative supercoiling and/or MgCl2 or in the presence of other monovalent or divalent cations, indicating that supercoiling and quite specific cations are needed for the association of sticky DNA. These are the first experiments studying a more specific role of supercoiling and cation influence on this DNA conformation. To support our model of the topological effects of sticky DNA in plasmids, changes in sticky DNA band migration was measured with reference to the linear DNA after treatment with increasing concentrations of ethidium bromide (EtBr). The presence of independent negative supercoil domains was confirmed by this method and found to be segregated by the DNA-DNA associated region. Sequence-specific polyamide molecules were used to test the effect of binding of the ligands to the GAA•TTC repeats on the inhibition of sticky DNA. The destabilization of the sticky DNA conformation in vitro through this binding of the polyamides demonstrated the first conceptual therapeutic approach for the treatment of FRDA at the DNA molecular level. ^ Thus, examining the properties of sticky DNA formed by these long repeat tracts is important in the elucidation of the possible role of sticky DNA in Friedreich's ataxia. ^

Lipid-dependent topogenesis and function of membrane proteins

Membranes are essential for the integrity and function of the cell. The collective property of the lipid bilayer is critical in providing an optimal functioning environment for membrane proteins. The simple yet well-characterized bacterium Escherichia coli serves an ideal model system to study the function of specific lipids since its lipid content can be easily manipulated. The most abundant lipid in E. coli membrane is phosphatidylethanolamine (PE, 70-80%). A PE-lacking E. coli mutant displays a complex mixture of deficient phenotypes, suggesting a profound role for PE in different aspects of cell function. A novel role of PE as a topological and functional determinant for membrane proteins has been established using lactose permease (LacY) as a model protein. PE is found to be required for energy-dependent uphill transport process of LacY. In PE-lacking membranes, LacY undergoes a dramatic conformational change, and the first half of the protein adopts an inverted topology with respect to the bilayer plane. ^ The work reported here was initiated to understand the molecular properties of lipids that enable their function as topological and functional determinants for membrane proteins. A glycolipid, monoglucosyldiacylglycerol (MGlcDAG) which shares physicochemical similarities with PE, was introduced to PE-lacking E. coli membranes. The introduction of MGlcDAG suppresses many of the PE-deficient phenotypes, and in particular supports the function and native topology of LacY. ^ The lipid-sensitive topogenic signals encoded in the amino acid sequence of LacY were also identified. Native LacY adopts an inverted topology when synthesized without PE, but mutation of specific acidic residues in the cytoplasmic extra-membrane domains can prevent this inversion and supports a native topological organization of LacY in PE-lacking membranes. These results suggest that it is the interplay between the collective charge properties of the lipid bilayer and extra-membrane loops of protein that determines the final orientation of transmembrane domains. By comparing the similarities as well as differences between these two lipids, we established how specific physical and chemical properties of lipids influence various cell functions and elucidated the molecular basis for the novel role of lipids in determining membrane protein topology. ^

The effects of DNA cytosine methylation on H -ras promoter structure and function

The effect of DNA cytosine methylation on H-ras promoter activity was assessed using a transient expression system employing the plasmid H-rasCAT (NaeI H-ras promoter linked to the chloramphenicol acetyltransferase (CAT) gene). This 551 bp promoter is 80% GC rich, enriched with 168 CpG dinucleotides, and contains six functional GC box elements which represent major DNA methylation target sites. Prokaryotic methyltransferases HhaI (CGm$\sp5$CG) and HpaII (Cm$\sp5$CGG) alone or in combination with a human placental methyltransferase (HP MTase) were used to introduce methyl groups at different CpG sites within the promoter. To test for functional promoter activity, the methylated plasmids were introduced into CV-1 cells and CAT activity assessed 48 h post-transfection. Methylation at specific HhaI and HpaII sites reduced CAT expression by 70%, whereas more extensive methylation at generalized CpG sites with HP MTase inactivated the promoter $>$95%. The inhibition of H-ras promoter activity was not attributable to methylation-induced differences in DNA uptake or stability in the cell, topological form of the plasmid, or methylation effects in nonpromoter regions. We also observed that DNA cytosine methylation of a 360 bp promoter fragment by HP MTase induced a local change in DNA conformation. Using three independent methodologies (nitrocellulose filter binding assays, gel mobility shifts, and Southwestern blots), we determined that this change in promoter conformation affected the interaction of nuclear proteins with cis-regulatory sequences residing in the promoter region. The results provide evidence to suggest that DNA methylation may regulate gene expression by inducing changes in local promoter conformation which in turn alters the interactions between DNA and protein factors required for transcription. The results provide supportive evidence for the hypothesis of Cedar and Riggs, who postulated that DNA methylation may regulate gene expression by altering the binding affinities of proteins for DNA. ^

Analysis of VirB4, a membrane-associated ATPase subunit essential for T -complex transport in Agrobacterium tumefaciens

Agrobacterium tumefaciens is a plant pathogen with the unique ability to export oncogenic DNA-protein complexes (T-complexes) to susceptible plant cells and cause crown gall tumors. Delivery of the T-complexes across the bacterial membranes requires eleven VirB proteins and VirD4, which are postulated to form a transmembrane transporter. This thesis examines the subcellular localization and oligomeric structure of the 87-kDa VirB4 protein, which is one of three essential ATPases proposed to energize T-complex transport and/or assembly. Results of subcellular localization studies showed that VirB4 is tightly associated with the cytoplasmic membrane, suggesting that it is a membrane-spanning protein. The membrane topology of VirB4 was determined by using a nested deletion strategy to generate random fusions between virB4 and the periplasmically-active alkaline phosphatase, $\sp\prime phoA$. Analysis of PhoA and complementary $\beta$-galactosidase reporter fusions identified two putative periplasmically-exposed regions in VirB4. A periplasmic exposure of one of these regions was further confirmed by protease susceptibility assays using A. tumefaciens spheroplasts. To gain insight into the structure of the transporter, the topological configurations of other VirB proteins were also examined. Results from hydropathy analyses, subcellular localization, protease susceptibility, and PhoA reporter fusion studies support a model that all of the VirB proteins localize at one or both of the bacterial membranes. Immunoprecipitation and Co$\sp{2+}$ affinity chromatography studies demonstrated that native VirB4 (87-kDa) and a functional N-terminally tagged HIS-VirB4 derivative (89-kDa) interact and that the interaction is independent of other VirB proteins. A $\lambda$ cI repressor fusion assay supplied further evidence for VirB4 dimer formation. A VirB4 dimerization domain was localized to the N-terminal third of the protein, as judged by: (i) transdominance of an allele that codes for this region of VirB4; (ii) co-retention of a His-tagged N-terminal truncation derivative and native VirB4 on Co$\sp{2+}$ affinity columns; and (iii) dimer formation of the N-terminal third of VirB4 fused to the cI repressor protein. Taken together, these findings are consistent with a model that VirB4 is topologically configured as an integral cytoplasmic membrane protein with two periplasmic domains and that VirB4 assembles as homodimers via an N-terminal dimerization domain. Dimer formation is postulated to be essential for stabilization of VirB4 monomers during T-complex transporter assembly. ^

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

Free dense subgroups of holomorphic automorphisms

We show the existence of free dense subgroups, generated by two elements, in the holomorphic shear and overshear group of complex-Euclidean space and extend this result to the group of holomorphic automorphisms of Stein manifolds with the density property, provided there exists a generalized translation. The conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms.

Arquitectura cognitiva basada en el gradiente sensorial y su aplicación a la robótica móvil

El objetivo de esta tesis es el desarrollo de un sistema completo de navegación, aprendizaje y planificación para un robot móvil. Dentro de los innumerables problemas que este gran objetivo plantea, hemos dedicado especial atención al problema del conocimiento autónomo del mundo. Nuestra mayor preocupación ha sido la de establecer mecanismos que permitan, a partir de información sensorial cruda, el desarrollo incremental de un modelo topológico del entorno en el que se mueve el robot. Estos mecanismos se apoyan invariablemente en un nuevo concepto propuesto en esta tesis: el gradiente sensorial. El gradiente sensorial es un dispositivo matemático que funciona como un detector de sucesos interesantes para el sistema. Una vez detectado uno de estos sucesos, el robot puede identificar su situación en un mapa topológico y actuar en consecuencia. Hemos denominado a estas situaciones especiales lugares sensorialmente relevantes, ya que (a) captan la atención del sistema y (b) pueden ser identificadas utilizando la información sensorial. Para explotar convenientemente los modelos construidos, hemos desarrollado un algoritmo capaz de elaborar planes internalizados, estableciendo una red de sugerencias en los lugares sensorialmente relevantes, de modo que el robot encuentra en estos puntos una dirección recomendada de navegación. Finalmente, hemos implementado un sistema de navegación robusto con habilidades para interpretar y adecuar los planes internalizados a las circunstancias concretas del momento. Nuestro sistema de navegación está basado en la teoría de campos de potencial artificial, a la que hemos incorporado la posibilidad de añadir cargas ficticias como ayuda a la evitación de mínimos locales. Como aportación adicional de esta tesis al campo genérico de la ciencia cognitiva, todos estos elementos se integran en una arquitectura centrada en la memoria, lo que pretende resaltar la importancia de ésta en los procesos cognitivos de los seres vivos y aporta un giro conceptual al punto de vista tradicional, centrado en los procesos. The general objective of this thesis is the development of a global navigation system endowed with planning and learning features for a mobile robot. Within this general objective we have devoted a special effort to the autonomous learning problem. Our main concern has been to establish the necessary mechanisms for the incremental development of a topological model of the robot’s environment using the sensory information. These mechanisms are based on a new concept proposed in the thesis: the sensory gradient. The sensory gradient is a mathematical device which works like a detector of “interesting” environment’s events. Once a particular event has been detected the robot can identify its situation in the topological map and to react accordingly. We have called these special situations relevant sensory places because (a) they capture the system’s attention and (b) they can be identified using the sensory information. To conveniently exploit the built-in models we have developed an algorithm able to make internalized plans, establishing a suggestion network in the sensory relevant places in such way that the robot can find at those places a recommended navigation direction. It has been also developed a robust navigation system able to navigate by means of interpreting and adapting the internalized plans to the concrete circumstances at each instant, i.e. a reactive navigation system. This reactive system is based on the artificial potential field approach with the additional feature introduced in the thesis of what we call fictitious charges as an aid to avoid local minima. As a general contribution of the thesis to the cognitive science field all the above described elements are integrated in a memory-based architecture, emphasizing the important role played by the memory in the cognitive processes of living beings and giving a conceptual turn in the usual process-based approach.

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map

Community Structure in Soil Porous System

Diffusion controls the gaseous transport process in soils when advective transport is almost null. Knowledge of the soil structure and pore connectivity are critical issues to understand and modelling soil aeration, sequestration or emission of greenhouse gasses, volatilization of volatile organic chemicals among other phenomena. In the last decades these issues increased our attention as scientist have realize that soil is one of the most complex materials on the earth, within which many biological, physical and chemical processes that support life and affect climate change take place. A quantitative and explicit characterization of soil structure is difficult because of the complexity of the pore space. This is the main reason why most theoretical approaches to soil porosity are idealizations to simplify this system. In this work, we proposed a more realistic attempt to capture the complexity of the system developing a model that considers the size and location of pores in order to relate them into a network. In the model we interpret porous soils as heterogeneous networks where pores are represented by nodes, characterized by their size and spatial location, and the links representing flows between them. In this work we perform an analysis of the community structure of porous media of soils represented as networks. For different real soils samples, modelled as heterogeneous complex networks, spatial communities of pores have been detected depending on the values of the parameters of the porous soil model used. These types of models are named as Heterogeneous Preferential Attachment (HPA). Developing an exhaustive analysis of the model, analytical solutions are obtained for the degree densities and degree distribution of the pore networks generated by the model in the thermodynamic limit and shown that the networks exhibit similar properties to those observed in other complex networks. With the aim to study in more detail topological properties of these networks, the presence of soil pore community structures is studied. The detection of communities of pores, as groups densely connected with only sparser connections between groups, could contribute to understand the mechanisms of the diffusion phenomena in soils.