Evolution of uni- and bifactorial sexual compatibility systems in fungi.

Mating systems, that is, whether organisms give rise to progeny by selfing, inbreeding or outcrossing, strongly affect important ecological and evolutionary processes. Large variations in mating systems exist in fungi, allowing the study of their origin and consequences. In fungi, sexual incompatibility is determined by molecular recognition mechanisms, controlled by a single mating-type locus in most unifactorial fungi. In Basidiomycete fungi, however, which include rusts, smuts and mushrooms, a system has evolved in which incompatibility is controlled by two unlinked loci. This bifactorial system probably evolved from a unifactorial system. Multiple independent transitions back to a unifactorial system occurred. It is still unclear what force drove evolution and maintenance of these contrasting inheritance patterns that determine mating compatibility. Here, we give an overview of the evolutionary factors that might have driven the evolution of bifactoriality from a unifactorial system and the transitions back to unifactoriality. Bifactoriality most likely evolved for selfing avoidance. Subsequently, multiallelism at mating-type loci evolved through negative frequency-dependent selection by increasing the chance to find a compatible mate. Unifactoriality then evolved back in some species, possibly because either selfing was favoured or for increasing the chance to find a compatible mate in species with few alleles. Owing to the existence of closely related unifactorial and bifactorial species and the increasing knowledge of the genetic systems of the different mechanisms, Basidiomycetes provide an excellent model for studying the different forces that shape breeding systems.

Self construction, cognitive conflicts and polarization in bulimia nervosa

This study explores the cognitive structures, understood as construct systems, of patients suffering from bulimia nervosa (BN). Previous studies investigated the construct systems of disordered eaters suggesting that they had a higher distance between their construction of the self and the «ideal self», and also more rigidity. In addition to these aspects, this study explored the presence of implicative dilemmas (ID). Thirty two women who met criteria for BN and were treated in a specialized center were compared to a non clinical group composed by 32 women matched by age. All participants were assessed using Repertory Grid Technique (RGT). In BN patients it was more common (71.9%) to find IDs than in controls (18.8%). They also showed higher polarization and higher self-ideal discrepancies (even more for those with a long history of BN). The measures provided by the RGT can be useful for the assessment of self-construction and cognitive conflicts in BN patients and to appreciate their role in this disorder. In addition, this technique could be helpful for clinicians to explore the patient"s constructs system, and specially to identify IDs that could be maintaining the symptoms or hindering change in order to focus on them to facilitate improvement.

Bond strength of orthodontic brackets using different light and self-curing cements

The purpose of the study was to evaluate the shear bond strength of stainless steel orthodontic brackets directly bonded to extracted human premolar teeth. Fifty teeth were randomly divided into ¿ve groups: (1) System One (chemically cured composite resin), (2) Light Bond (light-cured composite resin), (3) Vivaglass Cem (self-curing glass ionomer cement), (4) Fuji Ortho LC (light-cured glass ionomer cement) used after 37% orthophosphoric acid¿etching of enamel (5) Fuji Ortho LC without orthophosphoric acid¿etching. The brackets were placed on the buccal and lingual surfaces of each tooth, and the specimens were stored in distilled water (24 hours) at 378C and thermocycled. Teeth were mounted on acrylic block frames, and brackets were debonded using an Instron machine. Shear bond strength values at fracture (Nw)were recorded. ANOVA and Student-Newman-Keuls multiple comparison tests were performed (P , .05). Bonding failure site was recorded by stereomicroscope and analyzed by Chi-square test, selected specimens of each group were observed by scanning electron microscope. System One attained the highest bond strength. Light Bond and Fuji Ortho LC, when using an acid-etching technique, obtained bond strengths that were within the range of estimated bond strength values for successful clinical bonding. Fuji Ortho LC and Vivaglass Cem left an almost clean enamel surface after debracketing.

Photonic characteristics of Langmuir-Blodgett self-assembled monolayers of colloidal silica particles

Monodispersed colloidal crystals based on silica sub-micrometric particles were synthesized using the Stöber-Fink-Bohn process. The control of nucleation and coalescence result in improved characteristics such as high sphericity and very low size dispersion. The resulting silica particles show characteristics suitable for self-assembling across large areas of closely-packed 2D crystal monolayers by an accurate Langmuir-Blodgett deposition process on glass, fused silica and silicon substrates. Due to their special optical properties, colloidal films have potential applications in fields including photonics, electronics, electro-optics, medicine (detectors and sensors), membrane filters and surface devices. The deposited monolayers of silica particles were characterized by means of FESEM, AFM and optical transmittance measurements in order to analyze their specific properties and characteristics. We propose a theoretical calculation for the photonic band gaps in 2D systems using an extrapolation of the photonic behavior of the crystal from 3D to 2D. In this work we show that the methodology used and the conditions in self-assembly processes are decisive for producing high-quality two-dimensional colloidal crystals by the Langmuir-Blodgett technique.

Qualitative modeling identifies IL-11 as a novel regulator in maintaining self-renewal in human pluripotent stem cells.

Pluripotency in human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) is regulated by three transcription factors-OCT3/4, SOX2, and NANOG. To fully exploit the therapeutic potential of these cells it is essential to have a good mechanistic understanding of the maintenance of self-renewal and pluripotency. In this study, we demonstrate a powerful systems biology approach in which we first expand literature-based network encompassing the core regulators of pluripotency by assessing the behavior of genes targeted by perturbation experiments. We focused our attention on highly regulated genes encoding cell surface and secreted proteins as these can be more easily manipulated by the use of inhibitors or recombinant proteins. Qualitative modeling based on combining boolean networks and in silico perturbation experiments were employed to identify novel pluripotency-regulating genes. We validated Interleukin-11 (IL-11) and demonstrate that this cytokine is a novel pluripotency-associated factor capable of supporting self-renewal in the absence of exogenously added bFGF in culture. To date, the various protocols for hESCs maintenance require supplementation with bFGF to activate the Activin/Nodal branch of the TGFβ signaling pathway. Additional evidence supporting our findings is that IL-11 belongs to the same protein family as LIF, which is known to be necessary for maintaining pluripotency in mouse but not in human ESCs. These cytokines operate through the same gp130 receptor which interacts with Janus kinases. Our finding might explain why mESCs are in a more naïve cell state compared to hESCs and how to convert primed hESCs back to the naïve state. Taken together, our integrative modeling approach has identified novel genes as putative candidates to be incorporated into the expansion of the current gene regulatory network responsible for inducing and maintaining pluripotency.

Development of Self-Cleaning Box Culvert Designs, TR-545, 2009

The main function of a roadway culvert is to effectively convey drainage flow during normal and extreme hydrologic conditions. This function is often impaired due to the sedimentation blockage of the culvert. This research sought to understand the mechanics of sedimentation process at multi-box culverts, and develop self-cleaning systems that flush out sediment deposits using the power of drainage flows. The research entailed field observations, laboratory experiments, and numerical simulations. The specific role of each of these investigative tools is summarized below: a) The field observations were aimed at understanding typical sedimentation patterns and their dependence on culvert geometry and hydrodynamic conditions during normal and extreme hydrologic events. b) The laboratory experiments were used for modeling sedimentation process observed insitu and for testing alternative self-cleaning concepts applied to culverts. The major tasks for the initial laboratory model study were to accurately replicate the culvert performance curves and the dynamics of sedimentation process, and to provide benchmark data for numerical simulation validation. c) The numerical simulations enhanced the understanding of the sedimentation processes and aided in testing flow cases complementary to those conducted in the model reducing the number of (more expensive) tests to be conducted in the laboratory. Using the findings acquired from the laboratory and simulation works, self-cleaning culvert concepts were developed and tested for a range of flow conditions. The screening of the alternative concepts was made through experimental studies in a 1:20 scale model guided by numerical simulations. To ensure the designs are effective, performance studies were finally conducted in a 1:20 hydraulic model using the most promising design alternatives to make sure that the proposed systems operate satisfactory under closer to natural scale conditions.

Controlling anomalous stresses in soft field-responsive systems

We report a phenomenon occurring in field-responsive suspensions: shear-induced anomalous stresses. Competition between a rotating field and a shear flow originates a multiplicity of anomalous stress behaviors in suspensions of bound dimers constituted by induced dipoles. The great variety of stress regimes includes nonmonotonic behaviors, multiresonances, negative viscosity effect, and blockades. The reversibility of the transitions between the different regimes and the self-similarity of the stresses make this phenomenon controllable and therefore applicable to modify macroscopic properties of soft condensed matter phases.

Multi-scale systems analysis of plant development : beyond cellular signaling and tissue morphodynamics

Les plantes sont essentielles pour les sociétés humaines. Notre alimentation quotidienne, les matériaux de constructions et les sources énergétiques dérivent de la biomasse végétale. En revanche, la compréhension des multiples aspects développementaux des plantes est encore peu exploitée et représente un sujet de recherche majeur pour la science. L'émergence des technologies à haut débit pour le séquençage de génome à grande échelle ou l'imagerie de haute résolution permet à présent de produire des quantités énormes d'information. L'analyse informatique est une façon d'intégrer ces données et de réduire la complexité apparente vers une échelle d'abstraction appropriée, dont la finalité est de fournir des perspectives de recherches ciblées. Ceci représente la raison première de cette thèse. En d'autres termes, nous appliquons des méthodes descriptives et prédictives combinées à des simulations numériques afin d'apporter des solutions originales à des problèmes relatifs à la morphogénèse à l'échelle de la cellule et de l'organe. Nous nous sommes fixés parmi les objectifs principaux de cette thèse d'élucider de quelle manière l'interaction croisée des phytohormones auxine et brassinosteroïdes (BRs) détermine la croissance de la cellule dans la racine du méristème apical d'Arabidopsis thaliana, l'organisme modèle de référence pour les études moléculaires en plantes. Pour reconstruire le réseau de signalement cellulaire, nous avons extrait de la littérature les informations pertinentes concernant les relations entre les protéines impliquées dans la transduction des signaux hormonaux. Le réseau a ensuite été modélisé en utilisant un formalisme logique et qualitatif pour pallier l'absence de données quantitatives. Tout d'abord, Les résultats ont permis de confirmer que l'auxine et les BRs agissent en synergie pour contrôler la croissance de la cellule, puis, d'expliquer des observations phénotypiques paradoxales et au final, de mettre à jour une interaction clef entre deux protéines dans la maintenance du méristème de la racine. Une étude ultérieure chez la plante modèle Brachypodium dystachion (Brachypo- dium) a révélé l'ajustement du réseau d'interaction croisée entre auxine et éthylène par rapport à Arabidopsis. Chez ce dernier, interférer avec la biosynthèse de l'auxine mène à la formation d'une racine courte. Néanmoins, nous avons isolé chez Brachypodium un mutant hypomorphique dans la biosynthèse de l'auxine qui affiche une racine plus longue. Nous avons alors conduit une analyse morphométrique qui a confirmé que des cellules plus anisotropique (plus fines et longues) sont à l'origine de ce phénotype racinaire. Des analyses plus approfondies ont démontré que la différence phénotypique entre Brachypodium et Arabidopsis s'explique par une inversion de la fonction régulatrice dans la relation entre le réseau de signalisation par l'éthylène et la biosynthèse de l'auxine. L'analyse morphométrique utilisée dans l'étude précédente exploite le pipeline de traitement d'image de notre méthode d'histologie quantitative. Pendant la croissance secondaire, la symétrie bilatérale de l'hypocotyle est remplacée par une symétrie radiale et une organisation concentrique des tissus constitutifs. Ces tissus sont initialement composés d'une douzaine de cellules mais peuvent aisément atteindre des dizaines de milliers dans les derniers stades du développement. Cette échelle dépasse largement le seuil d'investigation par les moyens dits 'traditionnels' comme l'imagerie directe de tissus en profondeur. L'étude de ce système pendant cette phase de développement ne peut se faire qu'en réalisant des coupes fines de l'organe, ce qui empêche une compréhension des phénomènes cellulaires dynamiques sous-jacents. Nous y avons remédié en proposant une stratégie originale nommée, histologie quantitative. De fait, nous avons extrait l'information contenue dans des images de très haute résolution de sections transverses d'hypocotyles en utilisant un pipeline d'analyse et de segmentation d'image à grande échelle. Nous l'avons ensuite combiné avec un algorithme de reconnaissance automatique des cellules. Cet outil nous a permis de réaliser une description quantitative de la progression de la croissance secondaire révélant des schémas développementales non-apparents avec une inspection visuelle classique. La formation de pôle de phloèmes en structure répétée et espacée entre eux d'une longueur constante illustre les bénéfices de notre approche. Par ailleurs, l'exploitation approfondie de ces résultats a montré un changement de croissance anisotropique des cellules du cambium et du phloème qui semble en phase avec l'expansion du xylème. Combinant des outils génétiques et de la modélisation biomécanique, nous avons démontré que seule la croissance plus rapide des tissus internes peut produire une réorientation de l'axe de croissance anisotropique des tissus périphériques. Cette prédiction a été confirmée par le calcul du ratio des taux de croissance du xylème et du phloème au cours de développement secondaire ; des ratios élevés sont effectivement observés et concomitant à l'établissement progressif et tangentiel du cambium. Ces résultats suggèrent un mécanisme d'auto-organisation établi par un gradient de division méristématique qui génèrent une distribution de contraintes mécaniques. Ceci réoriente la croissance anisotropique des tissus périphériques pour supporter la croissance secondaire. - Plants are essential for human society, because our daily food, construction materials and sustainable energy are derived from plant biomass. Yet, despite this importance, the multiple developmental aspects of plants are still poorly understood and represent a major challenge for science. With the emergence of high throughput devices for genome sequencing and high-resolution imaging, data has never been so easy to collect, generating huge amounts of information. Computational analysis is one way to integrate those data and to decrease the apparent complexity towards an appropriate scale of abstraction with the aim to eventually provide new answers and direct further research perspectives. This is the motivation behind this thesis work, i.e. the application of descriptive and predictive analytics combined with computational modeling to answer problems that revolve around morphogenesis at the subcellular and organ scale. One of the goals of this thesis is to elucidate how the auxin-brassinosteroid phytohormone interaction determines the cell growth in the root apical meristem of Arabidopsis thaliana (Arabidopsis), the plant model of reference for molecular studies. The pertinent information about signaling protein relationships was obtained through the literature to reconstruct the entire hormonal crosstalk. Due to a lack of quantitative information, we employed a qualitative modeling formalism. This work permitted to confirm the synergistic effect of the hormonal crosstalk on cell elongation, to explain some of our paradoxical mutant phenotypes and to predict a novel interaction between the BREVIS RADIX (BRX) protein and the transcription factor MONOPTEROS (MP),which turned out to be critical for the maintenance of the root meristem. On the same subcellular scale, another study in the monocot model Brachypodium dystachion (Brachypodium) revealed an alternative wiring of auxin-ethylene crosstalk as compared to Arabidopsis. In the latter, increasing interference with auxin biosynthesis results in progressively shorter roots. By contrast, a hypomorphic Brachypodium mutant isolated in this study in an enzyme of the auxin biosynthesis pathway displayed a dramatically longer seminal root. Our morphometric analysis confirmed that more anisotropic cells (thinner and longer) are principally responsible for the mutant root phenotype. Further characterization pointed towards an inverted regulatory logic in the relation between ethylene signaling and auxin biosynthesis in Brachypodium as compared to Arabidopsis, which explains the phenotypic discrepancy. Finally, the morphometric analysis of hypocotyl secondary growth that we applied in this study was performed with the image-processing pipeline of our quantitative histology method. During its secondary growth, the hypocotyl reorganizes its primary bilateral symmetry to a radial symmetry of highly specialized tissues comprising several thousand cells, starting with a few dozens. However, such a scale only permits observations in thin cross-sections, severely hampering a comprehensive analysis of the morphodynamics involved. Our quantitative histology strategy overcomes this limitation. We acquired hypocotyl cross-sections from tiled high-resolution images and extracted their information content using custom high-throughput image processing and segmentation. Coupled with an automated cell type recognition algorithm, it allows precise quantitative characterization of vascular development and reveals developmental patterns that were not evident from visual inspection, for example the steady interspace distance of the phloem poles. Further analyses indicated a change in growth anisotropy of cambial and phloem cells, which appeared in phase with the expansion of xylem. Combining genetic tools and computational modeling, we showed that the reorientation of growth anisotropy axis of peripheral tissue layers only occurs when the growth rate of central tissue is higher than the peripheral one. This was confirmed by the calculation of the ratio of the growth rate xylem to phloem throughout secondary growth. High ratios are indeed observed and concomitant with the homogenization of cambium anisotropy. These results suggest a self-organization mechanism, promoted by a gradient of division in the cambium that generates a pattern of mechanical constraints. This, in turn, reorients the growth anisotropy of peripheral tissues to sustain the secondary growth.

Spatial filtering for pilot-aided WCDMA systems: a semi-blind subspace approach

This paper proposes a spatial filtering technique forthe reception of pilot-aided multirate multicode direct-sequencecode division multiple access (DS/CDMA) systems such as widebandCDMA (WCDMA). These systems introduce a code-multiplexedpilot sequence that can be used for the estimation of thefilter weights, but the presence of the traffic signal (transmittedat the same time as the pilot sequence) corrupts that estimationand degrades the performance of the filter significantly. This iscaused by the fact that although the traffic and pilot signals areusually designed to be orthogonal, the frequency selectivity of thechannel degrades this orthogonality at hte receiving end. Here,we propose a semi-blind technique that eliminates the self-noisecaused by the code-multiplexing of the pilot. We derive analyticallythe asymptotic performance of both the training-only andthe semi-blind techniques and compare them with the actual simulatedperformance. It is shown, both analytically and via simulation,that high gains can be achieved with respect to training-onlybasedtechniques.

Functional independence within the self-memory system: new insights from two cases of developmental amnesia.

Neuropsychological and neuroimaging data suggest that the self-memory system can be fractionated into three functionally independent systems processing personal information at several levels of abstraction, including episodic memories of one's life (episodic autobiographical memory, EAM), semantic knowledge of facts about one's life (semantic autobiographical memory, SAM), and semantic knowledge of one's personality [conceptual self, (CS)]. Through the study of two developmental amnesic patients suffering of neonatal brain injuries, we explored how the different facets of the self-memory system develop when growing up with bilateral hippocampal atrophy. Neuropsychological evaluations showed that both of them suffered from dramatic episodic learning disability with no sense of recollection (Remember/Know procedure), whereas their semantic abilities differed, being completely preserved (Valentine) or not (Jocelyn). Magnetic resonance imaging, including quantitative volumetric measurements of the hippocampus and adjacent (entorhinal, perirhinal, and temporopolar) cortex, showed severe bilateral atrophy of the hippocampus in both patients, with additional atrophy of adjacent cortex in Jocelyn. Exploration of EAM and SAM according to lifetime periods covering the entire lifespan (TEMPAu task, Piolino et al., 2009) showed that both patients had marked impairments in EAM, as they lacked specificity, details and sense of recollection, whereas SAM was completely normal in Valentine, but impaired in Jocelyn. Finally, measures of patients' CS (Tennessee Self-Concept Scale, Fitts and Warren, 1996), checked by their mothers, were generally within normal range, but both patients showed a more positive self-concept than healthy controls. These two new cases support a modular account of the medial-temporal lobe with episodic memory and recollection depending on the hippocampus, and semantic memory and familiarity on adjacent cortices. Furthermore, they highlight developmental episodic and semantic functional independence within the self-memory system suggesting that SAM and CS may be acquired without episodic memories.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Mass transfer and particleinteractions in granular systems and suspension flows

The purpose of this study was to investigate some important features of granular flows and suspension flows by computational simulation methods. Granular materials have been considered as an independent state ofmatter because of their complex behaviors. They sometimes behave like a solid, sometimes like a fluid, and sometimes can contain both phases in equilibrium. The computer simulation of dense shear granular flows of monodisperse, spherical particles shows that the collisional model of contacts yields the coexistence of solid and fluid phases while the frictional model represents a uniform flow of fluid phase. However, a comparison between the stress signals from the simulations and experiments revealed that the collisional model would result a proper match with the experimental evidences. Although the effect of gravity is found to beimportant in sedimentation of solid part, the stick-slip behavior associated with the collisional model looks more similar to that of experiments. The mathematical formulations based on the kinetic theory have been derived for the moderatesolid volume fractions with the assumption of the homogeneity of flow. In orderto make some simulations which can provide such an ideal flow, the simulation of unbounded granular shear flows was performed. Therefore, the homogeneous flow properties could be achieved in the moderate solid volume fractions. A new algorithm, namely the nonequilibrium approach was introduced to show the features of self-diffusion in the granular flows. Using this algorithm a one way flow can beextracted from the entire flow, which not only provides a straightforward calculation of self-diffusion coefficient but also can qualitatively determine the deviation of self-diffusion from the linear law at some regions nearby the wall inbounded flows. Anyhow, the average lateral self-diffusion coefficient, which was calculated by the aforementioned method, showed a desirable agreement with thepredictions of kinetic theory formulation. In the continuation of computer simulation of shear granular flows, some numerical and theoretical investigations were carried out on mass transfer and particle interactions in particulate flows. In this context, the boundary element method and its combination with the spectral method using the special capabilities of wavelets have been introduced as theefficient numerical methods to solve the governing equations of mass transfer in particulate flows. A theoretical formulation of fluid dispersivity in suspension flows revealed that the fluid dispersivity depends upon the fluid properties and particle parameters as well as the fluid-particle and particle-particle interactions.

Design and optimization of selfnanoemulsifying drug delivery systems for enhanced dissolution of gemfibrozil

Self-nanoemulsifying drug delivery systems of gemfibrozil were developed under Quality by Design approach for improvement of dissolution and oral absorption. Preliminary screening was performed to select proper components combination. BoxBehnken experimental design was employed as statistical tool to optimize the formulation variables, X1 (Cremophor® EL), X2 (Capmul® MCM-C8), and X3 (lemon essential oil). Systems were assessed for visual characteristics (emulsification efficacy), turbidity, droplet size, polydispersity index and drug release. Different pH media were also assayed for optimization. Following optimization, the values of formulation components (X1, X2, and X3) were 32.43%, 29.73% and 21.62%, respectively (16.22% of gemfibrozil). Transmission electron microscopy demonstrated spherical droplet morphology. SNEEDS release study was compared to commercial tablets. Optimized SNEDDS formulation of gemfibrozil showed a significant increase in dissolution rate compared to conventional tablets. Both formulations followed Weibull mathematical model release with a significant difference in td parameter in favor of the SNEDDS. Equally amodelistic parameters were calculated being the dissolution efficiency significantly higher for SNEDDS, confirming that the developed SNEDDS formulation was superior to commercial formulation with respect to in vitro dissolution profile. This paper provides an overview of the SNEDDS of the gemfibrozil as a promising alternative to improve oral absorption.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.