Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Proteins unfold in steps

I present results from an experiment on the dynamics of folding of a globular protein (bovine serum albumin). Employing a micro-mechanical technique, I perform the measurements on very few molecules (1–100). I observed a sequence of steps in time for both unfolding and refolding. The overall characteristic time of the process is thus built up of waiting times between successive steps. The pattern of steps is reproducible, demonstrating the existence of deterministic pathways for folding and unfolding. Certain symmetries in the patterns of steps may reflect the architecture of the protein’s structure.

Direct interaction of flagellin termini essential for polymorphic ability of flagellar filament

We report the structures of flagellar filaments reconstituted from various flagellins with small terminal truncations. Flagellins from Salmonella typhimurium strains SJW1103 (wild type), SJW1660, and SJW1655 were used, which form a left-handed supercoil, the L- and R-type straight forms, respectively. Structure analyses were done by electron cryomicroscopy and helical image reconstruction with a help of x-ray fiber diffraction for determining precise helical symmetries. Truncation of either terminal region, irrespective of the original flagellin species, results in a straight filament having a helical symmetry distinct either from the L- or R-type. This filament structure is named Lt-type. Although the local subunit packing is similar in all three types, a close comparison shows that the Lt-type packing is almost identical to the R-type but distinct from the L-type, which demonstrates the strong two-state preference of the subunit interactions. The structure clearly suggests that both termini are located in the inner tube of the concentric double-tubular structure of the filament core, and their proper interaction is responsible for the correct folding of fairly large terminal regions that form the inner tube. The double tubular structure appears to be essential for the polymorphic ability of flagellar filaments, which is required for the swimming–tumbling of bacterial taxis.

Gel catalysts that switch on and off

We report development of a polymer gel with a catalytic activity that can be switched on and off when the solvent composition is changed. The gel consists of two species of monomers. The major component, N-isopropylacrylamide, makes the gel swell and shrink in response to a change in composition of ethanol/water mixtures. The minor component, vinylimidazole, which is capable of catalysis, is copolymerized into the gel network. The reaction rate for catalytic hydrolysis of p-nitrophenyl caprylate was small when the gel was swollen. In contrast, when the gel was shrunken, the reaction rate increased 5 times. The activity changes discontinuously as a function of solvent composition, thus the catalysis can be switched on and off by an infinitesimal change in solvent composition. The kinetics of catalysis by the gel in the shrunken state is well described by the Michaelis–Menten formula, indicating that the absorption of the substrate by the hydrophobic environment created by the N-isopropylacrylamide polymer in the shrunken gel is responsible for enhancement of catalytic activity. In the swollen state, the rate vs. active site concentration is linear, indicating that the substrate absorption is not a primary factor determining the kinetics. Catalytic activity of the gel is studied for substrates with various alkyl chain lengths; of those studied the switching effect is most pronounced for p-nitrophenyl caprylate.

PMD fundamentals: Polarization mode dispersion in optical fibers

This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Self-organized phase transitions in neural networks as a neural mechanism of information processing.

Transitions between dynamically stable activity patterns imposed on an associative neural network are shown to be induced by self-organized infinitesimal changes in synaptic connection strength and to be a kind of phase transition. A key event for the neural process of information processing in a population coding scheme is transition between the activity patterns encoding usual entities. We propose that the infinitesimal and short-term synaptic changes based on the Hebbian learning rule are the driving force for the transition. The phase transition between the following two dynamical stable states is studied in detail, the state where the firing pattern is changed temporally so as to itinerate among several patterns and the state where the firing pattern is fixed to one of several patterns. The phase transition from the pattern itinerant state to a pattern fixed state may be induced by the Hebbian learning process under a weak input relevant to the fixed pattern. The reverse transition may be induced by the Hebbian unlearning process without input. The former transition is considered as recognition of the input stimulus, while the latter is considered as clearing of the used input data to get ready for new input. To ensure that information processing based on the phase transition can be made by the infinitesimal and short-term synaptic changes, it is absolutely necessary that the network always stays near the critical state corresponding to the phase transition point.

Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories.

Randomly distributed Dictyostelium discoideum cells form cooperative territories by signaling to each other with cAMP. Cells initiate the process by sending out pulsatile signals, which propagate as waves. With time, circular and spiral patterns form. We show that by adding spatial and temporal noise to the levels of an important regulator of external cAMP levels, the cAMP phosphodiesterase inhibitor, we can explain the natural progression of the system from randomly firing cells to circular waves whose symmetries break to form double- and single- or multi-armed spirals. When phosphodiesterase inhibitor is increased with time, mimicking experimental data, the wavelength of the spirals shortens, and a proportion of them evolve into pairs of connected spirals. We compare these results to recent experiments, finding that the temporal and spatial correspondence between experiment and model is very close.

From local to global in quasiconformal structures.

We exhibit a large class of metric spaces whose infinitesimal quasiconformal structure is strong enough to capture the global quasiconformal structure. A sufficient condition for this to happen is described in terms of a Poincaré-type inequality.

Cell cycling and patterned cell proliferation in the wing primordium of Drosophila.

The pattern of cell proliferation in the Drosophila imaginal wing primordium is spatially and temporally heterogeneous. Direct visualization of cells in S, G2, and mitosis phases of the cell cycle reveals several features invariant throughout development. The fraction of cells in the disc in the different cell cycle stages is constant, the majority remaining in G1. Cells in the different phases of the cell cycle mainly appear in small synchronic clusters that are nonclonally derived but result from changing local cell-cell interactions. Cluster synchronization occurs before S and in the G2/M phases. Rates of cell division are neither constant nor clonal features. Cell cycle progression is linear rather than concentric. Clusters appear throughout the disc but with symmetries related to presumptive wing patterns, compartment boundaries, and vein clonal restrictions.

Quantisation of the bosonic string

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied.

A gauge theory for continuous spin particles

In this dissertation we explore the features of a Gauge Field Theory formulation for continuous spin particles (CSP). To make our discussion as self-contained as possible, we begin by introducing all the basics of Group Theory - and representation theory - which are necessary to understand where the CSP come from. We then apply what we learn from Group Theory to the study of the Lorentz and Poincaré groups, to the point where we are able to construct the CSP representation. Finally, after a brief review of the Higher-Spin formalism, through the Schwinger-Fronsdal actions, we enter the realm of CSP Field Theory. We study and explore all the local symmetries of the CSP action, as well as all of the nuances associated with the introduction of an enlarged spacetime, which is used to formulate the CSP action. We end our discussion by showing that the physical contents of the CSP action are precisely what we expected them to be, in comparison to our Group Theoretical approach.

El vínculo sustancial y las mónadas en Leibniz

El vínculo sustancial es para Leibniz la relación en donde las sustancias simples (mónadas) se unen para integrarse en un compuesto del que surge una sustancialidad colectiva, y no es la mera adición de sustancialidades individuales. El vínculo es fundamental, determinante para el compuesto, pero no para lo simple. Lo conectivo se vuelve definitorio en lo compuesto, de manera que la ontología leibniziana apuesta fuertemente por lo simple, por lo individual, como actualización de lo infinitesimal.

O papel simbólico da língua na construção das identidades nacionais : o caráter identitário da discussão sobre o AO90 em Portugal

Tese de doutoramento, Estudos de Literatura e de Cultura (Cultura e Comunicação), Universidade de Lisboa, Faculdade de Letras, 2016

Modularisation épistatique des loci à trait quantitatif associés à la pression artérielle et identification de gènes candidats pour l’hypertension

Problématique: L’hypertension artérielle essentielle, facteur de risque majeur dans le développement des maladies cardiovasculaires, est un trait multigénique complexe dont les connaissances sur le déterminisme génétique nécessitent d’être approfondies. De nombreux loci à trait quantitatif (QTLs); soit des gènes responsables de faire varier la pression artérielle (PA), ont été identifiés chez l’humain et le modèle animal. Cependant, le mystère plane encore sur la façon dont ces gènes fonctionnent ensemble pour réguler la PA. Hypothèse et objectif: Plutôt qu’une addition de QTLs ayant chacun une action infinitésimale sur la PA, une interaction épistatique entre les gènes serait responsable du phénotype hypertendu. Ainsi, l’étude de cette épistasie entre les gènes impliqués, directement ou indirectement, dans l’homéostasie de la PA nous permettrait d’explorer de nouvelles voies de régulation moléculaire en cause dans cette maladie. Méthodes: Via la réalisation de souches congéniques de rats, où un segment chromosomique provenant d’une souche receveuse hypertendue (Dahl Salt Sensitive, SS/Jr) est remplacé par son homologue provenant d’une souche donneuse normotendue (Lewis, LEW), des QTLs peuvent être mis en évidence. Dans ce contexte, la combinaison de QTLs via la création de doubles ou multiples congéniques constitue la première démonstration fonctionnelle des interactions intergéniques. Résultats: Vingt-sept combinaisons au total nous ont menés à l’appréciation d’une modularisation des QTLs. Ces derniers ont été catégorisés selon deux principaux modules épistatiques (EMs) où les QTLs appartenant à un même EM sont épistatiques entre eux et participent à une même voie régulatrice. Les EMs/cascades agissent alors en parallèle pour réguler la PA. Grâce à l’existence de QTLs ayant des effets opposés sur la PA, nous avons pu établir l’ordre hiérarchique entre trois paires de QTLs. Cependant, lorsque cette suite régulatrice ne peut être déterminée, d’autres approches sont nécessaires. Nos travaux nous ont mené à l’identification d’un QTL situé sur le chromosome 16 du rat (C16QTL), appartenant au EM1 et qui révélerait une nouvelle voie de l’homéostasie de la PA. Le gène retinoblastoma-associated protein 140 (Rap140)/family with sequence similarity 208 member A (Fam208a), présentant une mutation non synonyme entre SS/Jr et LEW est le gène candidat le plus plausible pour représenter C16QTL. Celui-ci code pour un facteur de transcription et semblerait influencer l’expression de Solute carrier family 7 (cationic amino acid transporter, y+ system) member 12 (Slc7a12), spécifiquement et significativement sous exprimé dans les reins de la souche congénique portant C16QTL par rapport à la souche SS/Jr. Rap140/Fam208a agirait comme un inhibiteur de la transcription de Slc7a12 menant à une diminution de la pression chez Lewis. Conclusions: L’architecture complexe de la régulation de la PA se dévoile mettant en scène de nouveaux acteurs, pour la plupart inconnus pour leur implication dans la PA. L’étude de la nouvelle voie de signalisation Rap140/Fam208a - Slc7a12 nous permettra d’approfondir nos connaissances quant à l’homéostasie de la pression artérielle et de l’hypertension chez SS/Jr. À long terme, de nouveaux traitements anti-hypertenseurs, ciblant plus d’une voie de régulation à la fois, pourraient voir le jour.