Pattern formation during mesophase growth in a homologous series

Remarkable differences in the shape of the nematic-smectic-B interface in a quasi-two-dimensional geometry have been experimentally observed in three liquid crystals of very similar molecular structure, i.e., neighboring members of a homologous series. In the thermal equilibrium of the two mesophases a faceted rectanglelike shape was observed with considerably different shape anisotropies for the three homologs. Various morphologies such as dendritic, dendriticlike, and faceted shapes of the rapidly growing smectic-B germ were also observed for the three substances. Experimental results were compared with computer simulations based on the phase field model. The pattern forming behavior of a binary mixture of two homologs was also studied.

Suppression of scroll wave turbulence by noise

Rotating scroll waves are dynamical spatiotemporal structures characteristic of three-dimensional active media. It is well known that, under low excitability conditions, scroll waves develop an intrinsically unstable dynamical regime that leads to a highly disorganized pattern of wave propagation. Such a ¿turbulent¿ state bears some resemblance to fibrillation states in cardiac tissue. We show here that this unstable regime can be controlled by using a spatially distributed random forcing superimposed on a control parameter of the system. Our results are obtained from numerical simulations but an explicit analytical argument that rationalizes our observations is also presented.

Pulse propagation sustained by noise in arrays of bistable electronic circuits

One-dimensional arrays of nonlinear electronic circuits are shown to support propagation of pulses when operating in a locally bistable regime, provided the circuits are under the influence of a global noise. These external random fluctuations are applied to the parameter that controls the transition between bistable and monostable dynamics in the individual circuits. As a result, propagating fronts become destabilized in the presence of noise, and the system self-organizes to allow the transmission of pulses. The phenomenon is also observed in weakly coupled arrays, when propagation failure arises in the absence of noise.

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges

We review recent results on dynamical aspects of viscous fingering. The Saffman¿Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman¿Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering

Application of fuzzy-rule-based postprocessing to correlation methods in pattern recognition

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

Regulation of Nav1.7 and Nav1.8 voltage-gated sodium channels by Nedd4-2 and β-subunits and its implication in neuropathic pain

In mammals, the presence of excitable cells in muscles, heart and nervous system is crucial and allows fast conduction of numerous biological information over long distances through the generation of action potentials (AP). Voltage-gated sodium channels (Navs) are key players in the generation and propagation of AP as they are responsible for the rising phase of the AP. Navs are heteromeric proteins composed of a large pore-forming a-subunit (Nav) and smaller ß-auxiliary subunits. There are ten genes encoding for Navl.l to Nav1.9 and NaX channels, each possessing its own specific biophysical properties. The excitable cells express differential combinations of Navs isoforms, generating a distinct electrophysiological signature. Noteworthy, only when anchored at the membrane are Navs functional and are participating in sodium conductance. In addition to the intrinsic properties of Navs, numerous regulatory proteins influence the sodium current. Some proteins will enhance stabilization of membrane Navs while others will favour internalization. Maintaining equilibrium between the two is of crucial importance for controlling cellular excitability. The E3 ubiquitin ligase Nedd4-2 is a well-characterized enzyme that negatively regulates the turnover of many membrane proteins including Navs. On the other hand, ß-subunits are known since long to stabilize Navs membrane anchoring. Peripheral neuropathic pain is a disabling condition resulting from nerve injury. It is characterized by the dysregulation of Navs expressed in dorsal root ganglion (DRG) sensory neurons as highlighted in different animal models of neuropathic pain. Among Navs, Nav1.7 and Nav1.8 are abundantly and specifically expressed in DRG sensory neurons and have been recurrently incriminated in nociception and neuropathic pain development. Using the spared nerve injury (SNI) experimental model of neuropathic pain in mice, I observed a specific reduction of Nedd4-2 in DRG sensory neurons. This decrease subsequently led to an upregulation of Nav1.7 and Nav1.8 protein and current, in the axon and the DRG neurons, respectively, and was sufficient to generate neuropathic pain-associated hyperexcitability. Knocking out Nedd4-2 specifically in nociceptive neurons led to the same increase of Nav1.7 and Nav1.8 concomitantly with an increased thermal sensitivity in mice. Conversely, rescuing Nedd4-2 downregulation using viral vector transfer attenuated neuropathic pain mechanical hypersensitivity. This study demonstrates the significant role of Nedd4-2 in regulating cellular excitability in vivo and its involvement in neuropathic pain development. The role of ß-subunits in neuropathic pain was already demonstrated in our research group. Because of their stabilization role, the increase of ßl, ß2 and ß3 subunits in DRGs after SNI led to increased Navs anchored at the membrane. Here, I report a novel mechanism of regulation of a-subunits by ß- subunits in vitro; ßl and ß3-subunits modulate the glycosylation pattern of Nav1.7, which might account for stabilization of its membrane expression. This opens new perspectives for investigation Navs state of glycosylation in ß-subunits dependent diseases, such as in neuropathic pain. - Chez les mammifères, la présence de cellules excitables dans les muscles, le coeur et le système nerveux est cruciale; elle permet la conduction rapide de nombreuses informations sur de longues distances grâce à la génération de potentiels d'action (PA). Les canaux sodiques voltage-dépendants (Navs) sont des participants importants dans la génération et la propagation des PA car ils sont responsables de la phase initiale de dépolarisation du PA. Les Navs sont des protéines hétéromériques composées d'une grande sous-unité a (formant le pore du canal) et de petites sous-unités ß accompagnatrices. Il existe dix gènes qui codent pour les canaux sodiques, du Nav 1.1 au Nav 1.9 ainsi que NaX, chacun possédant des propriétés biophysiques spécifiques. Les cellules excitables expriment différentes combinaisons des différents isoformes de Navs, qui engendrent une signature électrophysiologique distincte. Les Navs ne sont fonctionnels et ne participent à la conductibilité du Na+, que s'ils sont ancrés à la membrane plasmique. En plus des propriétés intrinsèques des Navs, de nombreuses protéines régulatrices influencent également le courant sodique. Certaines protéines vont favoriser l'ancrage et la stabilisation des Navs exprimés à la membrane, alors que d'autres vont plutôt favoriser leur internalisation. Maintenir l'équilibre des deux processus est crucial pour contrôler l'excitabilité cellulaire. Dans ce contexte, Nedd4-2, de la famille des E3 ubiquitin ligase, est une enzyme bien caractérisée qui régule l'internalisation de nombreuses protéines, notamment celle des Navs. Inversement, les sous-unités ß sont connues depuis longtemps pour stabiliser l'ancrage des Navs à la membrane. La douleur neuropathique périphérique est une condition débilitante résultant d'une atteinte à un nerf. Elle est caractérisée par la dérégulation des Navs exprimés dans les neurones sensoriels du ganglion spinal (DRG). Ceci a été démontré à de multiples occasions dans divers modèles animaux de douleur neuropathique. Parmi les Navs, Nav1.7 et Nav1.8 sont abondamment et spécifiquement exprimés dans les neurones sensoriels des DRG et ont été impliqués de façon récurrente dans le développement de la douleur neuropathique. En utilisant le modèle animal de douleur neuropathique d'épargne du nerf sural (spared nerve injury, SNI) chez la souris, j'ai observé une réduction spécifique des Nedd4-2 dans les neurones sensoriels du DRG. Cette diminution avait pour conséquence l'augmentation de l'expression des protéines et des courants de Nav 1.7 et Nav 1.8, respectivement dans l'axone et les neurones du DRG, et était donc suffisante pour créer l'hyperexcitabilité associée à la douleur neuropathique. L'invalidation pour le gène codant pour Nedd4-2 dans une lignée de souris génétiquement modifiées a conduit à de similaires augmentations de Nav1.7 et Nav1.8, parallèlement à une augmentation à la sensibilité thermique. A l'opposé, rétablir une expression normale de Nedd4-2 en utilisant un vecteur viral a eu pour effet de contrecarrer le développement de l'hypersensibilité mécanique lié à ce modèle de douleur neuropathique. Cette étude démontre le rôle important de Nedd4-2 dans la régulation de l'excitabilité cellulaire in vivo et son implication dans le développement des douleurs neuropathiques. Le rôle des sous-unités ß dans les douleurs neuropathiques a déjà été démontré dans notre groupe de recherche. A cause de leur rôle stabilisateur, l'augmentation des sous-unités ßl, ß2 et ß3 dans les DRG après SNI, conduit à une augmentation des Navs ancrés à la membrane. Dans mon travail de thèse, j'ai observé un nouveau mécanisme de régulation des sous-unités a par les sous-unités ß in vitro. Les sous-unités ßl et ß3 régulent l'état de glycosylation du canal Nav1.7, et stabilisent son expression membranaire. Ceci ouvre de nouvelles perspectives dans l'investigation de l'état de glycosylation des Navs dans des maladies impliquant les sous-unités ß, notamment les douleurs neuropathiques.

Propagation in a thermal graviton background

It is well known that radiative corrections evaluated in nontrivial backgrounds lead to effective dispersion relations which are not Lorentz invariant. Since gravitational interactions increase with energy, gravity-induced radiative corrections could be relevant for the trans-Planckian problem. As a first step to explore this possibility, we compute the one-loop radiative corrections to the self-energy of a scalar particle propagating in a thermal bath of gravitons in Minkowski spacetime. We obtain terms which originate from the thermal bath and which indeed break the Lorentz invariance that possessed the propagator in the vacuum. Rather unexpectedly, however, the terms which break Lorentz invariance vanish in the high three-momentum limit. We also found that the imaginary part, which gives the rate of approach to thermal equilibrium, vanishes at one loop.

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

A clinical pattern-based etiological diagnostic strategy for sensory neuronopathies: a French collaborative study.

Sensory neuronopathies (SNNs) encompass paraneoplastic, infectious, dysimmune, toxic, inherited, and idiopathic disorders. Recently described diagnostic criteria allow SNN to be differentiated from other forms of sensory neuropathy, but there is no validated strategy based on routine clinical investigations for the etiological diagnosis of SNN. In a multicenter study, the clinical, biological, and electrophysiological characteristics of 148 patients with SNN were analyzed. Multiple correspondence analysis and logistic regression were used to identify patterns differentiating between forms of SNNs with different etiologies. Models were constructed using a study population of 88 patients and checked using a test population of 60 cases. Four patterns were identified. Pattern A, with an acute or subacute onset in the four limbs or arms, early pain, and frequently affecting males over 60 years of age, identified mainly paraneoplastic, toxic, and infectious SNN. Pattern B identified patients with progressive SNN and was divided into patterns C and D, the former corresponding to patients with inherited or slowly progressive idiopathic SNN with severe ataxia and electrophysiological abnormalities and the latter to patients with idiopathic, dysimmune, and sometimes paraneoplastic SNN with a more rapid course than in pattern C. The diagnostic strategy based on these patterns correctly identified 84/88 and 58/60 patients in the study and test populations, respectively.

Early co-occurrence of a neurologic-psychiatric disease pattern in Niemann-Pick type C disease: a retrospective Swiss cohort study.

BackgroundNiemann-Pick disease type C (NP-C) is a rare autosomal recessive disorder of lysosomal cholesterol transport. The objective of this retrospective cohort study was to critically analyze the onset and time course of symptoms, and the clinical diagnostic work-up in the Swiss NP-C cohort.MethodsClinical, biochemical and genetic data were assessed for 14 patients derived from 9 families diagnosed with NP-C between 1994 and 2013. We retrospectively evaluated diagnostic delays and period prevalence rates for neurological, psychiatric and visceral symptoms associated with NP-C disease. The NP-C suspicion index was calculated for the time of neurological disease onset and the time of diagnosis.ResultsThe shortest median diagnostic delay was noted for vertical supranuclear gaze palsy (2y). Ataxia, dysarthria, dysphagia, spasticity, cataplexy, seizures and cognitive decline displayed similar median diagnostic delays (4¿5y). The longest median diagnostic delay was associated with hepatosplenomegaly (15y). Highest period prevalence rates were noted for ataxia, dysarthria, vertical supranuclear gaze palsy and cognitive decline. The NP-C suspicion index revealed a median score of 81 points in nine patients at the time of neurological disease onset which is highly suspicious for NP-C disease. At the time of diagnosis, the score increased to 206 points.ConclusionA neurologic-psychiatric disease pattern represents the most characteristic clinical manifestation of NP-C and occurs early in the disease course. Visceral manifestation such as isolated hepatosplenomegaly often fails recognition and thus highlights the importance of a work-up for lysosomal storage disorders. The NP-C suspicion index emphasizes the importance of a multisystem evaluation, but seems to be weak in monosymptomatic and infantile NP-C patients.

Evidence for catabolic pathway of propionate metabolism in CNS: expression pattern of methylmalonyl-CoA mutase and propionyl-CoA carboxylase alpha-subunit in developing and adult rat brain.

Methylmalonyl-CoA mutase (MCM) and propionyl-CoA carboxylase (PCC) are the key enzymes of the catabolic pathway of propionate metabolism and are mainly expressed in liver, kidney and heart. Deficiency of these enzymes leads to two classical organic acidurias: methylmalonic and propionic aciduria. Patients with these diseases suffer from a whole spectrum of neurological manifestations that are limiting their quality of life. Current treatment does not seem to effectively prevent neurological deterioration and pathophysiological mechanisms are poorly understood. In this article we show evidence for the expression of the catabolic pathway of propionate metabolism in the developing and adult rat CNS. Both, MCM and PCC enzymes are co-expressed in neurons and found in all regions of the CNS. Disease-specific metabolites such as methylmalonate, propionyl-CoA and 2-methylcitrate could thus be formed autonomously in the CNS and contribute to the pathophysiological mechanisms of neurotoxicity. In rat embryos (E15.5 and E18.5), MCM and PCC show a much higher expression level in the entire CNS than in the liver, suggesting a different, but important function of this pathway during brain development.