A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Ab initio modeling and molecular dynamics simulation of the alpha 1b-adrenergic receptor activation.

This work describes the ab initio procedure employed to build an activation model for the alpha 1b-adrenergic receptor (alpha 1b-AR). The first version of the model was progressively modified and complicated by means of a many-step iterative procedure characterized by the employment of experimental validations of the model in each upgrading step. A combined simulated (molecular dynamics) and experimental mutagenesis approach was used to determine the structural and dynamic features characterizing the inactive and active states of alpha 1b-AR. The latest version of the model has been successfully challenged with respect to its ability to interpret and predict the functional properties of a large number of mutants. The iterative approach employed to describe alpha 1b-AR activation in terms of molecular structure and dynamics allows further complications of the model to allow prediction and interpretation of an ever-increasing number of experimental data.

Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling.

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

Estimating dormant and active hematopoietic stem cell kinetics through extensive modeling of bromodeoxyuridine label-retaining cell dynamics.

Bone marrow hematopoietic stem cells (HSCs) are responsible for both lifelong daily maintenance of all blood cells and for repair after cell loss. Until recently the cellular mechanisms by which HSCs accomplish these two very different tasks remained an open question. Biological evidence has now been found for the existence of two related mouse HSC populations. First, a dormant HSC (d-HSC) population which harbors the highest self-renewal potential of all blood cells but is only induced into active self-renewal in response to hematopoietic stress. And second, an active HSC (a-HSC) subset that by and large produces the progenitors and mature cells required for maintenance of day-to-day hematopoiesis. Here we present computational analyses further supporting the d-HSC concept through extensive modeling of experimental DNA label-retaining cell (LRC) data. Our conclusion that the presence of a slowly dividing subpopulation of HSCs is the most likely explanation (amongst the various possible causes including stochastic cellular variation) of the observed long term Bromodeoxyuridine (BrdU) retention, is confirmed by the deterministic and stochastic models presented here. Moreover, modeling both HSC BrdU uptake and dilution in three stages and careful treatment of the BrdU detection sensitivity permitted improved estimates of HSC turnover rates. This analysis predicts that d-HSCs cycle about once every 149-193 days and a-HSCs about once every 28-36 days. We further predict that, using LRC assays, a 75%-92.5% purification of d-HSCs can be achieved after 59-130 days of chase. Interestingly, the d-HSC proportion is now estimated to be around 30-45% of total HSCs - more than twice that of our previous estimate.

Modeling resting-state functional networks when the cortex falls asleep: local and global changes.

The transition from wakefulness to sleep represents the most conspicuous change in behavior and the level of consciousness occurring in the healthy brain. It is accompanied by similarly conspicuous changes in neural dynamics, traditionally exemplified by the change from "desynchronized" electroencephalogram activity in wake to globally synchronized slow wave activity of early sleep. However, unit and local field recordings indicate that the transition is more gradual than it might appear: On one hand, local slow waves already appear during wake; on the other hand, slow sleep waves are only rarely global. Studies with functional magnetic resonance imaging also reveal changes in resting-state functional connectivity (FC) between wake and slow wave sleep. However, it remains unclear how resting-state networks may change during this transition period. Here, we employ large-scale modeling of the human cortico-cortical anatomical connectivity to evaluate changes in resting-state FC when the model "falls asleep" due to the progressive decrease in arousal-promoting neuromodulation. When cholinergic neuromodulation is parametrically decreased, local slow waves appear, while the overall organization of resting-state networks does not change. Furthermore, we show that these local slow waves are structured macroscopically in networks that resemble the resting-state networks. In contrast, when the neuromodulator decrease further to very low levels, slow waves become global and resting-state networks merge into a single undifferentiated, broadly synchronized network.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Treeline and climate change : analyzing and modeling patterns and shifts in the Swiss Alps

Summary: Global warming has led to an average earth surface temperature increase of about 0.7 °C in the 20th century, according to the 2007 IPCC report. In Switzerland, the temperature increase in the same period was even higher: 1.3 °C in the Northern Alps anal 1.7 °C in the Southern Alps. The impacts of this warming on ecosystems aspecially on climatically sensitive systems like the treeline ecotone -are already visible today. Alpine treeline species show increased growth rates, more establishment of young trees in forest gaps is observed in many locations and treelines are migrating upwards. With the forecasted warming, this globally visible phenomenon is expected to continue. This PhD thesis aimed to develop a set of methods and models to investigate current and future climatic treeline positions and treeline shifts in the Swiss Alps in a spatial context. The focus was therefore on: 1) the quantification of current treeline dynamics and its potential causes, 2) the evaluation and improvement of temperaturebased treeline indicators and 3) the spatial analysis and projection of past, current and future climatic treeline positions and their respective elevational shifts. The methods used involved a combination of field temperature measurements, statistical modeling and spatial modeling in a geographical information system. To determine treeline shifts and assign the respective drivers, neighborhood relationships between forest patches were analyzed using moving window algorithms. Time series regression modeling was used in the development of an air-to-soil temperature transfer model to calculate thermal treeline indicators. The indicators were then applied spatially to delineate the climatic treeline, based on interpolated temperature data. Observation of recent forest dynamics in the Swiss treeline ecotone showed that changes were mainly due to forest in-growth, but also partly to upward attitudinal shifts. The recent reduction in agricultural land-use was found to be the dominant driver of these changes. Climate-driven changes were identified only at the uppermost limits of the treeline ecotone. Seasonal mean temperature indicators were found to be the best for predicting climatic treelines. Applying dynamic seasonal delimitations and the air-to-soil temperature transfer model improved the indicators' applicability for spatial modeling. Reproducing the climatic treelines of the past 45 years revealed regionally different attitudinal shifts, the largest being located near the highest mountain mass. Modeling climatic treelines based on two IPCC climate warming scenarios predicted major shifts in treeline altitude. However, the currently-observed treeline is not expected to reach this limit easily, due to lagged reaction, possible climate feedback effects and other limiting factors. Résumé: Selon le rapport 2007 de l'IPCC, le réchauffement global a induit une augmentation de la température terrestre de 0.7 °C en moyenne au cours du 20e siècle. En Suisse, l'augmentation durant la même période a été plus importante: 1.3 °C dans les Alpes du nord et 1.7 °C dans les Alpes du sud. Les impacts de ce réchauffement sur les écosystèmes - en particuliers les systèmes sensibles comme l'écotone de la limite des arbres - sont déjà visibles aujourd'hui. Les espèces de la limite alpine des forêts ont des taux de croissance plus forts, on observe en de nombreux endroits un accroissement du nombre de jeunes arbres s'établissant dans les trouées et la limite des arbres migre vers le haut. Compte tenu du réchauffement prévu, on s'attend à ce que ce phénomène, visible globalement, persiste. Cette thèse de doctorat visait à développer un jeu de méthodes et de modèles pour étudier dans un contexte spatial la position présente et future de la limite climatique des arbres, ainsi que ses déplacements, au sein des Alpes suisses. L'étude s'est donc focalisée sur: 1) la quantification de la dynamique actuelle de la limite des arbres et ses causes potentielles, 2) l'évaluation et l'amélioration des indicateurs, basés sur la température, pour la limite des arbres et 3) l'analyse spatiale et la projection de la position climatique passée, présente et future de la limite des arbres et des déplacements altitudinaux de cette position. Les méthodes utilisées sont une combinaison de mesures de température sur le terrain, de modélisation statistique et de la modélisation spatiale à l'aide d'un système d'information géographique. Les relations de voisinage entre parcelles de forêt ont été analysées à l'aide d'algorithmes utilisant des fenêtres mobiles, afin de mesurer les déplacements de la limite des arbres et déterminer leurs causes. Un modèle de transfert de température air-sol, basé sur les modèles de régression sur séries temporelles, a été développé pour calculer des indicateurs thermiques de la limite des arbres. Les indicateurs ont ensuite été appliqués spatialement pour délimiter la limite climatique des arbres, sur la base de données de températures interpolées. L'observation de la dynamique forestière récente dans l'écotone de la limite des arbres en Suisse a montré que les changements étaient principalement dus à la fermeture des trouées, mais aussi en partie à des déplacements vers des altitudes plus élevées. Il a été montré que la récente déprise agricole était la cause principale de ces changements. Des changements dus au climat n'ont été identifiés qu'aux limites supérieures de l'écotone de la limite des arbres. Les indicateurs de température moyenne saisonnière se sont avérés le mieux convenir pour prédire la limite climatique des arbres. L'application de limites dynamiques saisonnières et du modèle de transfert de température air-sol a amélioré l'applicabilité des indicateurs pour la modélisation spatiale. La reproduction des limites climatiques des arbres durant ces 45 dernières années a mis en évidence des changements d'altitude différents selon les régions, les plus importants étant situés près du plus haut massif montagneux. La modélisation des limites climatiques des arbres d'après deux scénarios de réchauffement climatique de l'IPCC a prédit des changements majeurs de l'altitude de la limite des arbres. Toutefois, l'on ne s'attend pas à ce que la limite des arbres actuellement observée atteigne cette limite facilement, en raison du délai de réaction, d'effets rétroactifs du climat et d'autres facteurs limitants.

Homology modeling and metabolism prediction of human carboxylesterase-2 using docking analyses by GriDock: a parallelized tool based on AutoDock 4.0.

Metabolic problems lead to numerous failures during clinical trials, and much effort is now devoted to developing in silico models predicting metabolic stability and metabolites. Such models are well known for cytochromes P450 and some transferases, whereas less has been done to predict the activity of human hydrolases. The present study was undertaken to develop a computational approach able to predict the hydrolysis of novel esters by human carboxylesterase hCES2. The study involved first a homology modeling of the hCES2 protein based on the model of hCES1 since the two proteins share a high degree of homology (congruent with 73%). A set of 40 known substrates of hCES2 was taken from the literature; the ligands were docked in both their neutral and ionized forms using GriDock, a parallel tool based on the AutoDock4.0 engine which can perform efficient and easy virtual screening analyses of large molecular databases exploiting multi-core architectures. Useful statistical models (e.g., r (2) = 0.91 for substrates in their unprotonated state) were calculated by correlating experimental pK(m) values with distance between the carbon atom of the substrate's ester group and the hydroxy function of Ser228. Additional parameters in the equations accounted for hydrophobic and electrostatic interactions between substrates and contributing residues. The negatively charged residues in the hCES2 cavity explained the preference of the enzyme for neutral substrates and, more generally, suggested that ligands which interact too strongly by ionic bonds (e.g., ACE inhibitors) cannot be good CES2 substrates because they are trapped in the cavity in unproductive modes and behave as inhibitors. The effects of protonation on substrate recognition and the contrasting behavior of substrates and products were finally investigated by MD simulations of some CES2 complexes.

Modeling the biophysical impacts of global change in mountain biosphere reserves

Mountains and mountain societies provide a wide range of goods and services to humanity, but they are particularly sensitive to the effects of global environmental change. Thus, the definition of appropriate management regimes that maintain the multiple functions of mountain regions in a time of greatly changing climatic, economic, and societal drivers constitutes a significant challenge. Management decisions must be based on a sound understanding of the future dynamics of these systems. The present article reviews the elements required for an integrated effort to project the impacts of global change on mountain regions, and recommends tools that can be used at 3 scientific levels (essential, improved, and optimum). The proposed strategy is evaluated with respect to UNESCO's network of Mountain Biosphere Reserves (MBRs), with the intention of implementing it in other mountain regions as well. First, methods for generating scenarios of key drivers of global change are reviewed, including land use/land cover and climate change. This is followed by a brief review of the models available for projecting the impacts of these scenarios on (1) cryospheric systems, (2) ecosystem structure and diversity, and (3) ecosystem functions such as carbon and water relations. Finally, the cross-cutting role of remote sensing techniques is evaluated with respect to both monitoring and modeling efforts. We conclude that a broad range of techniques is available for both scenario generation and impact assessments, many of which can be implemented without much capacity building across many or even most MBRs. However, to foster implementation of the proposed strategy, further efforts are required to establish partnerships between scientists and resource managers in mountain areas.

Habitat-quality effects on metapopulation dynamics in greater white-toothed shrews, Crocidura russula.

The effects of patch size and isolation on metapopulation dynamics have received wide empirical support and theoretical formalization. By contrast, the effects of patch quality seem largely underinvestigated, partly due to technical difficulties in properly assessing quality. Here we combine habitat-quality modeling with four years of demographic monitoring in a metapopulation of greater white-toothed shrews (Crocidura russula) to investigate the role of patch quality on metapopulation processes. Together, local patch quality and connectivity significantly enhanced local population sizes and occupancy rates (R2 = 14% and 19%, respectively). Accounting for the quality of patches connected to the focal one and acting as potential sources improved slightly the model explanatory power for local population sizes, pointing to significant source-sink dynamics. Local habitat quality, in interaction with connectivity, also increased colonization rate (R2 = 28%), suggesting the ability of immigrants to target high-quality patches. Overall, patterns were best explained when assuming a mean dispersal distance of 800 m, a realistic value for the species under study. Our results thus provide evidence that patch quality, in interaction with connectivity, may affect major demographic processes.

Identification of optimal structural connectivity using functional connectivity and neural modeling.

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.

Direct simulation of interface dynamics: linking capillary pressure, interfacial area and surface energy

We perform direct numerical simulations of drainage by solving Navier- Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and to model the transition from stable flow to viscous fingering, we focus on the definition of macroscopic capillary pressure. When the fluids are at rest, the difference between inlet and outlet pressures and the difference between the intrinsic phase average pressure coincide with the capillary pressure. However, when the fluids are in motion these quantities are dominated by viscous forces. In this case, only a definition based on the variation of the interfacial energy provides an accurate measure of the macroscopic capillary pressure and allows separating the viscous from the capillary pressure components.

Modeling the impact of lesions in the human brain.

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous ("resting-state") neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions.

Molecular modeling of peptide-MHC class I complexes : applications to peptide based immunotherapy

Summary The specific CD8+ T cell immune response against tumors relies on the recognition by the T cell receptor (TCR) on cytotoxic T lymphocytes (CTL) of antigenic peptides bound to the class I major histocompatibility complex (MHC) molecule. Such tumor associated antigenic peptides are the focus of tumor immunotherapy with peptide vaccines. The strategy for obtaining an improved immune response often involves the design of modified tumor associated antigenic peptides. Such modifications aim at creating higher affinity and/or degradation resistant peptides and require precise structures of the peptide-MHC class I complex. In addition, the modified peptide must be cross-recognized by CTLs specific for the parental peptide, i.e. preserve the structure of the epitope. Detailed structural information on the modified peptide in complex with MHC is necessary for such predictions. In this thesis, the main focus is the development of theoretical in silico methods for prediction of both structure and cross-reactivity of peptide-MHC class I complexes. Applications of these methods in the context of immunotherapy are also presented. First, a theoretical method for structure prediction of peptide-MHC class I complexes is developed and validated. The approach is based on a molecular dynamics protocol to sample the conformational space of the peptide in its MHC environment. The sampled conformers are evaluated using conformational free energy calculations. The method, which is evaluated for its ability to reproduce 41 X-ray crystallographic structures of different peptide-MHC class I complexes, shows an overall prediction success of 83%. Importantly, in the clinically highly relevant subset of peptide-HLAA*0201 complexes, the prediction success is 100%. Based on these structure predictions, a theoretical approach for prediction of cross-reactivity is developed and validated. This method involves the generation of quantitative structure-activity relationships using three-dimensional molecular descriptors and a genetic neural network. The generated relationships are highly predictive as proved by high cross-validated correlation coefficients (0.78-0.79). Together, the here developed theoretical methods open the door for efficient rational design of improved peptides to be used in immunotherapy. Résumé La réponse immunitaire spécifique contre des tumeurs dépend de la reconnaissance par les récepteurs des cellules T CD8+ de peptides antigéniques présentés par les complexes majeurs d'histocompatibilité (CMH) de classe I. Ces peptides sont utilisés comme cible dans l'immunothérapie par vaccins peptidiques. Afin d'augmenter la réponse immunitaire, les peptides sont modifiés de façon à améliorer l'affinité et/ou la résistance à la dégradation. Ceci nécessite de connaître la structure tridimensionnelle des complexes peptide-CMH. De plus, les peptides modifiés doivent être reconnus par des cellules T spécifiques du peptide natif. La structure de l'épitope doit donc être préservée et des structures détaillées des complexes peptide-CMH sont nécessaires. Dans cette thèse, le thème central est le développement des méthodes computationnelles de prédiction des structures des complexes peptide-CMH classe I et de la reconnaissance croisée. Des applications de ces méthodes de prédiction à l'immunothérapie sont également présentées. Premièrement, une méthode théorique de prédiction des structures des complexes peptide-CMH classe I est développée et validée. Cette méthode est basée sur un échantillonnage de l'espace conformationnel du peptide dans le contexte du récepteur CMH classe I par dynamique moléculaire. Les conformations sont évaluées par leurs énergies libres conformationnelles. La méthode est validée par sa capacité à reproduire 41 structures des complexes peptide-CMH classe I obtenues par cristallographie aux rayons X. Le succès prédictif général est de 83%. Pour le sous-groupe HLA-A*0201 de complexes de grande importance pour l'immunothérapie, ce succès est de 100%. Deuxièmement, à partir de ces structures prédites in silico, une méthode théorique de prédiction de la reconnaissance croisée est développée et validée. Celle-ci consiste à générer des relations structure-activité quantitatives en utilisant des descripteurs moléculaires tridimensionnels et un réseau de neurones couplé à un algorithme génétique. Les relations générées montrent une capacité de prédiction remarquable avec des valeurs de coefficients de corrélation de validation croisée élevées (0.78-0.79). Les méthodes théoriques développées dans le cadre de cette thèse ouvrent la voie du design de vaccins peptidiques améliorés.