Modelización de las propiedades radiativas e interacción de láseres ultraintensos con la materia

Desde el año 2004 el código ARWEN ha sido utilizado con éxito para simular y diseñar experimentos relacionados con blancos para fusión por confinamiento inercial [146], astrofísica de laboratorio [145], plasmas como amplificadores de láseres de rayos X [107] o plasmas creados por láser para la medición de espectros de transmisión. Para la realización de estas simulaciones es necesario, además de métodos de alto orden precisos y que presenten buenas propiedades conservativas, conocer ciertas propiedades de los plasmas. En el caso de la fluidodinámica y la conducción electrónica necesitaremos conocer la ecuación de estado [94, 49, 36], y para el transporte de la radiación será preciso disponer de los datos de absorción y emisión [104, 95, 40]. Hasta el año 2009 ARWEN dependía de códigos externos para la generación de estas tablas de opacidad, careciendo de control sobre los métodos empleados para su generación. Además estos códigos asumían equilibrio local termodinámico (LTE), limitando su validez a rangos de alta densidad y baja temperatura. En el marco de esta tesis se ha desarrollado el código BIGBART para la generación de tablas detalladas de opacidad y emisividad para su uso en el módulo de transporte de radiación. De esta forma el grupo dispondrá de su propia herramienta de generación de propiedades radiativas. El código desarrollado es capaz de tratar plasmas en estado fuera de equilibrio (non-LTE) mediante el modelo colisional-radiativo, extendiendo así el rango de validez de las tablas generadas. El trabajo desarrollado para implementar un código LTE/non-LTE estacionario es el siguiente Cálculo de estructura y datos atómicos. Se ha acoplado en código FAC a BIGBART, incorporando la capacidad para generar potenciales atómicos para una configuración y el cálculo de funciones de onda de electrones en orbitales ligados y libres. Aproximaciones y métodos para la obtención de tasas y secciones eficaces de procesos. Se han incluido y programado los modelos implementados en FAC para el cálculo de secciones eficaces de fotoionización, y tasas de decaimiento de emisión espontánea y autoionización. Además se ha incluido el modelo Plane-Wave Born (PWBA) para el cálculo de las secciones eficaces de ionización y excitación colisional. Modelos para la obtención de la distribución de estados iónicos dentro del plasma. Se ha programado un solver LTE basado en la ecuación de Saha-Boltzmann con efectos de ionización por presión debida a los iones adyacentes. También se ha implementado un modelo non-LTE colisionalradiativo para la resolución del sistema de ecuaciones que nos permite obtener la densidad de estados iónicos fuera de equilibrio. Modelo non-LTE RADIOM. Se ha implementado el modelo RADIOM para aproximar efectos de no-equilibrio mediante cálculos LTE a una temperatura equivalente, menor o igual que la temperatura electrónica real. Cálculo de las propiedades espectrales de absorción y emisión. Se han implementado los modelos para el cálculo de los perfiles espectrales de absorción y emisión para procesos entre niveles ligados, ligado-libre y librelibre. Aprovechando el trabajo realizado en este sentido, durante el transcurso de esta tesis se amplió el código BIGBART para tratar problemas con dependencia temporal. La extensión para tratar este tipo de problemas se orientó a la simulación numérica de la interacción de láseres ultra intensos en el rango XUV/rayos X. Para ello, además de adaptar el modelo non-LTE colisionalradiativo se incluyeron procesos adicionales asociados a la interacción de la materia con fotones altamente energéticos. También se han incluido modelos para el cálculo de las propiedades ópticas, y por ende las propiedades dieléctricas de la materia irradiada, de gran interés en algunas aplicaciones novedosas de estos láseres intensos. Debido a la naturaleza fuertemente fuera de equilibrio en la interacción de fotones de alta energía con la materia, se incluyó el tratamiento de la distribución de electrones libres fuera de equilibrio en la aproximación de Fokker-Planck, tanto para condiciones degeneradas como no degeneradas. El trabajo desarrollado en el código non-LTE con dependencia temporal es el siguiente Procesos asociados a láseres intensos XUV/rayos X. Se ha implementado el cálculo de procesos radiativos estimulados de absorción y emisión por el láser. También se han incluido procesos asociados a la creación de vacantes en capas internas electrónicas (Shake), además de doble autoionización y doble fotoionización. Cálculo de propiedades ópticas y dieléctricas en blancos sólidos. Se ha implementado un modelo para la absorción por bremsstrahlung inverso en blancos en estado sólido. Con el coeficiente de extinción debido a procesos de fotoabsorción resonante, fotoionización y bremsstrahlung inverso se obtiene el ´ındice de refracción mediante la relación de Kronig-Kramers. Electrones fuera de equilibrio. Se ha tratado la evolución de la distribución de electrones, cuando no está justificado asumir que es Maxwelliana o de Fermi-Dirac, mediante la aproximación de Fokker-Planck para la colisión entre electrones libres. En la resolución de la ecuación de Fokker-Planck se han incluido los procesos inelásticos por colisiones con iones y términos fuente por interacción con el láser y otros procesos. ABSTRACT Since 2004 the ARWEN code has been successfully used to simulate and design targets for inertial confinement fusion experiments [146], laboratory astrophysics [145], plasmas as X-ray lasers amplifiers [107] or laser created plasmas for measuring transmission spectra. To perform these simulations it is necessary, in addition to high order precise methods with good conservative properties, to know certain properties of plasmas. For fluid dynamic and electronic conduction we need to know the equation of state [94, 49, 36], and for radiation transport it will be necessary to have the data of the absorption and emission [104, 95, 40]. Until 2009 ARWEN depended on external codes to generate these opacity tables, lacking of control over the methods used for their generation. Besides, these codes assumed local thermodynamic equilibrium (LTE), limiting their validity ranges to high densities and low temperatures. As part of this thesis it has been developed the BIGBART code for generating detailed opacity and emissivity tables for use in the radiation transport module. This group will have its own tool for the generation of radiative properties. The developed code is capable of treating plasmas out of equilibrium (non-LTE) by means of a collisional-radiative model, extending the range of validity of the generated tables. The work to implement an LTE/non-LTE steady-state code is as follows Calculation of structure and atomic data. the FAC code was coupled to BIGBART, incorporating the ability to generate atomic potentials for calculating configuration wave functions for bound and free electrons. Approaches and methods for obtaining cross sections and processes rates. We have included and reprogrammed in Fortran the models implemented in FAC for calculation of photoionization cross sections and decay rates of spontaneous emission and autoionization. We also included the Plane- Wave Born (PWBA) model to calculate the cross sections of ionization and collisional excitation. Models for the obtention of the distribution of ionic states within the plasma. We programmed a LTE solver based on the Saha-Boltzmann equation with pressure ionization effects due to adjacent ions. It has also been implemented a non-LTE collisional-radiative model for solving the system of equations that allows us to obtain the density of ionic states out of equilibrium. Non-LTE RADIOM model. We have implemented the non-LTE RADIOM model to approximate non-equilibrium effects with LTE data at an equivalent temperature, lower or equal to the actual electronic temperature. Calculation of the spectral absorption and emission properties. Models have been implemented for the calculation of the spectral profiles of absorption and emission processes between bound levels, free-bound and free-free. Taking advantage of the work done in this direction throughout the course of this thesis the code BIGBART was extended to treat time-dependent problems. The extension to treat such problems is oriented to the numerical simulation of the interaction of ultra intense lasers in the XUV/X-ray range. For this range, in addition to adapting the non-LTE collisional-radiative model, additional processes associated with the interaction of matter with high energy photons. We also included models for calculation of the optical properties, and therefore the dielectric properties of the irradiated material, of great interest in some novel applications of these intense lasers. Due to the strong non-equilibrium nature of the interaction of high energy photons with matter, we included the treatment of the distribution of free electrons out of equilibrium in the Fokker-Planck approximation for both degenerate and non-degenerate conditions. The work in the non-LTE time-dependent code is as follows Processes associated with intense XUV/X-ray lasers. We have implemented the calculation of stimulated radiative processes in absorption and emission. Also we included processes associated with the creation of electronic vacancies in inner shells (Shake), double autoionization and double photoionization. Calculation of optical and dielectric properties in solid targets. We have implemented a model for inverse bremsstrahlung absorption in solid targets. With the extinction coefficient from resonant photoabsorption, photoionization and inverse bremsstrahlung the refractive index is obtained by the Kramers-Kronig relation. Electrons out of equilibrium. We treat the evolution of the electron distribution, when it is not justified to assume a Maxwellian or Fermi-Dirac distribution, by the Fokker-Planck approximation for collisions between electrons. When solving the Fokker-Planck equation we included inelastic collision processes with ions and source terms by interaction with the laser and other processes.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Intermediate band to conduction band optical absorption in ZnTeO

ZnTe doped with high concentrations of oxygen has been proposed in previous works as an intermediate band (IB) material for photovoltaic applications. The existence of extra optical transitions related to the presence of an IB has already been demonstrated in this material and it has been possible to measure the absorption coefficient of the transitions from the valence band (VB) to the IB. In this study, we present the first measurement of the absorption coefficient associated with transitions from the IB to the conduction band (CB) in ZnTeO. The samples used are 4-mum-thick ZnTe layers with or without O in a concentration ~10 19 cm -3, which have been grown on semiinsulating GaAs substrates by molecular beam epitaxy (MBE). The IB-CB absorption coefficient peaks for photon energies ~0.4 eV. It is extracted from reflectance and transmittance spectra measured using Fourier transform infrared (FTIR) spectroscopy. Under typical FTIR measurement conditions (low light intensity, broadband spectrum), the absorption coefficient in IB-to-CB transitions reaches 700 cm -1. This is much weaker than the one observed for VB-IB absorption. This result is consistent with the fact that the IB is expected to be nearly empty of electrons under equilibrium conditions in ZnTe(O).

Modified Gutenberg-Richter coefficient for damage evaluation in reinforced concrete structures subjected to seismic simulations on a shaking table

This paper presents analysis and discussion of the b- and ib-values calculated from the acoustic emission (AE) signals recorded during dynamic shake-table tests conducted on a reinforced concrete (RC) frame subjected to several uniaxial seismic simulations of increasing intensity until collapse. The intensity of shaking was controlled by the peak acceleration applied to the shake-table in each seismic simulation, and it ranged from 0.08 to 0.47 times the acceleration of gravity. The numerous spurious signals not related to concrete damage that inevitably contaminate AE measurements obtained from complex dynamic shake-table tests were properly filtered with an RMS filter and the use of guard sensors. Comparing the b- and ib-values calculated through the tests with the actual level of macro-cracking and damage observed during testing, it was concluded that the limit value of 0.05 proposed in previous research to determine the onset of macro-cracks should be revised in the case of earthquake-type dynamic loading. Finally, the b- and ibvalues were compared with the damage endured by the RC frame evaluated both visually and quantitatively in terms of the inter-story drift index.

Comparative analysis of measurement techniques of the sound absorption coefficient of a material

Las tendencias actuales apuntan al desarrollo de nuevos materiales económicos y ecológicos con óptimas propiedades mecánicas, acústicas y térmicas. En la caracterización acústica del material es habitual medir su coeficiente de absorción sonora. Las dos técnicas usuales de medida de este parámetro son en cámara reverberante y en tubo de Kundt. No obstante, existen técnicas de medida “in situ” del coeficiente de absorción que permiten una comprobación del comportamiento real en la forma definitiva de colocación del material. En este trabajo se presenta un estudio comparativo del coeficiente de absorción sonora medido en un material usando distintas técnicas de medida.

Determinación de la higroscopicidad y comportamiento termodinámico de la madera juvenil y madura a través de sus isotermas de sorción

La respuesta higroscópica de la madera varía a lo largo de la dirección radial del árbol. El aumento de corta de ejemplares jóvenes y el uso de troncos de pequeños diámetros en la industria de los productos forestales, hacen preciso estudiar el comportamiento higroscópico tanto de la madera juvenil como de la madura. Su determinación proporciona información para comprender los mecanismos de sorción. Asimismo, la obtención de las propiedades termodinámicas de ambos tipos de madera facilita la modelización de procesos industriales como el secado o el encolado. En el presente trabajo, se ha comparado el comportamiento higroscópico y las propiedades termodinámicas de la madera juvenil y madura de Abies pinsapo Boissier, Abies alba Mill., Pinus canariensis C. Sm. ex DC., Pinus nigra Arnold, Pinus uncinata Mill. ex Mirb. y Pinus pinea L. Para este propósito se han utilizado las isotermas de sorción obtenidas mediante el método tradicional de sales saturadas descrito por COST Action E8 a 15, 35 y 50ºC en Abies pinsapo, Abies alba, Pinus nigra, Pinus uncinata y Pinus pinea, y a 35 y 50ºC en Pinus canariensis. Igualmente, se ha empleado el equipo dynamic vapor sorption (DVS) en la obtención de las isotermas de Pinus pinea a 35 y 50ºC. El ajuste de las curvas se ha realizado mediante el modelo Guggenheim, Anderson y de Boer-Dent (GAB), cumpliendo todas las muestras los criterios de aceptación establecidos. En el estudio de las isotermas se ha calculado el coeficiente y área de histéresis entre el proceso de adsorción y desorción para cada una de las muestras. Con el fin de comprender el comportamiento higroscópico experimentado por cada madera se ha determinado la composición química, espectros de infrarrojos (FTIR) y difractogramas de rayos X de cada una. Los parámetros termodinámicos - calor isostérico neto y total heat of wetting - se han obtenido a partir de las isotermas de sorción mediante el método de integración de la ecuación de Clausius-Clapeyron. Finalmente, se han comparado los datos obtenidos con el método tradicional de sales saturadas y con dynamic vapor sorption con el propósito de conocer la existencia de similitudes entre ambas metodologías. Los resultados mostraron que los puntos de equilibrio son, en la mayor parte de los casos, superiores en la madera madura frente a la juvenil, y por tanto las isotermas de la madera madura se encuentran siempre por encima de las de la juvenil, debido principalmente a la composición química. Respecto a las propiedades termodinámicas, se ha determinado que la energía involucrada en los procesos de sorción es superior en la madera madura que en la madera juvenil, siendo mayor en el proceso de desorción frente al de adsorción. En la comparación de las metodologías de sales saturadas y dynamic vapor sorption no se han detectado casi diferencias significativas en el proceso de adsorción, mientras que sí se han obtenido en el de desorción. ABSTRACT The hygroscopic response of wood varies throughout the radial direction of the tree. The longer cut of young trees and the use of small-diameter trunks in the forest product industry make it necessary to study the hygroscopic behaviour of both juvenile and mature wood. Determining this behaviour in both types of wood provides information for understanding the sorption mechanisms. Similarly, obtaining the thermodynamic properties of juvenile and mature wood facilitates modelling of industrial processes such as drying and bonding. In this study a comparison was made of the hygroscopic behaviour and thermodynamic properties of juvenile and mature wood of Abies pinsapo Boissier, Abies alba Mill., Pinus canariensis C. Sm. ex DC., Pinus nigra Arnold, Pinus uncinata Mill. ex Mirb. and Pinus pinea L. This was done by obtaining the sorption isotherms using the traditional saturated salt method described by COST Action E8 at 15, 35 and 50ºC in Abies pinsapo, Abies alba, Pinus nigra, Pinus uncinata and Pinus pinea, and at 35 and 50ºC in Pinus canariensis. In addition, dynamic vapour sorption (DVS) was used to obtain the isotherms of Pinus pinea at 35 and 50ºC. The curves were fitted using the Guggenheim, Anderson and de Boer- Dent (GAB) model and all samples met the established acceptance criteria. In the study of the isotherms, the hysteresis coefficient and area of the hysteresis loop between adsorption and desorption were calculated for each sample. To understand the hygroscopic behaviour of juvenile and mature wood, the chemical composition, infrared spectra (FTIR) and X-ray diffractograms of each type of wood were determined. The thermodynamic parameters - net isosteric heat and total heat of wetting - were obtained from the sorption isotherms by applying the integration method of the Clausius-Clapeyron equation. The data obtained using the traditional saturated salt method and with dynamic vapour sorption were compared to determine the similarities between the two methods. The results showed that the equilibrium points are greater in the mature wood than in the juvenile wood in most cases, and therefore the mature wood isotherms are always above the juvenile wood isotherms, mainly because of the chemical composition. As regards the thermodynamic properties, it was determined that the energy involved in the sorption processes is greater in the mature wood than in the juvenile wood, and is greater in the desorption process than in the adsorption process. On comparing the saturated salt and dynamic vapour sorption methods, almost no significant differences were detected in the adsorption process, but significant differences were obtained in the desorption process.

Funicularity and equilibrium for high-performance conceptual structural design

Las estructuras que trabajan por forma se caracterizan por la íntima e indisociable relación entre geometría y comportamiento estructural. Por consiguiente, la elección de una apropiada geometría es el paso previo indispensable en el diseño conceptual de dichas estructuras. En esa tarea, la selección de las posibles geometrías antifuniculares para las distribuciones de cargas permanentes más habituales son más bien limitadas y, muchas veces, son criterios no estructurales (adaptabilidad funcional, estética, proceso constructivo, etc.) los que no permiten la utilización de dichas geometrías que garantizarían el máximo aprovechamiento del material. En este contexto, esta tesis estudia la posibilidad de obtener una estructura sin momentos flectores incluso si la geometría no es antifunicular para sus cargas permanentes. En efecto, esta tesis presenta un procedimiento, basado en la estática gráfica, que demuestra cómo un conjunto de cargas adicionales, introducidas a través de un sistema de pretensado exterior con elementos post-tesos, puede eliminar los momentos flectores debidos a cargas permanentes en cualquier geometría plana. Esto se traduce en una estructura antifunicular que proporciona respuestas innovadoras a demandas conjuntas de versatilidad arquitectónica y optimización del material. Dicha metodología gráfica ha sido implementada en un software distribuido libremente (EXOEQUILIBRIUM), donde el análisis estructural y la variación geométrica están incluidos en el mismo entorno interactivo y paramétrico. La utilización de estas herramientas permite más versatilidad en la búsqueda de nuevas formas eficientes, lo cual tiene gran importancia en el diseño conceptual de estructuras, liberando al ingeniero de la limitación del propio cálculo y de la incomprensión del comportamiento estructural, facilitando extraordinariamente el hecho creativo a la luz de una metodología de este estilo. Esta tesis incluye la aplicación de estos procedimientos a estructuras de cualquier geometría y distribución inicial de cargas, así como el estudio de diferentes posibles criterios de diseño para optimizar la posición del sistema de post-tesado. Además, la metodología ha sido empleada en el proyecto de maquetas a escala reducida y en la construcción de un pabellón hecho enteramente de cartón, lo que ha permitido obtener una validación física del procedimiento desarrollado. En definitiva, esta tesis expande de manera relevante el rango de posibles geometrías antifuniculares y abre enormes posibilidades para el diseño de estructuras que combinan eficiencia estructural y flexibilidad arquitectónica.Curved structures are characterized by the critical relationship between their geometry and structural behaviour, and selecting an appropriate shape in the conceptual design of such structures is important for achieving materialefficiency. However, the set of bending-free geometries are limited and, often, non-structural design criteria (e.g., usability, architectural needs, aesthetics) prohibit the selection of purely funicular or antifunicular shapes. In response to this issue, this thesis studies the possibility of achieving an axial-only behaviour even if the geometry departs from the ideally bending-free shape. This dissertation presents a new design approach, based on graphic statics that shows how bending moments in a two-dimensional geometry can be eliminated by adding forces through an external post-tensioning system. This results in bending-free structures that provide innovative answers to combined demands on versatility and material optimization. The graphical procedure has been implemented in a free-downloadable design-driven software (EXOEQUILIBRIUM) where structural performance evaluations and geometric variation are embedded within an interactive and parametric working environment. This provides greater versatility in finding new efficient structural configurations during the first design stages, bridging the gap between architectural shaping and structural analysis. The thesis includes the application of the developed graphical procedure to shapes with random curvature and distribution of loads. Furthermore, the effect of different design criteria on the internal force distribution has been analyzed. Finally, the construction of reduced- and large-scale models provides further physical validation of the method and insights about the structural behaviour of these structures. In summary, this work strongly expands the range of possible forms that exhibit a bending-free behaviour and, de facto, opens up new possibilities for designs that combine high-performing solutions with architectural freedom.

Determination of a refractive index and an extinction coefficient of standard production of CVD-graphene

The refractive index and extinction coefficient of chemical vapour deposition grown graphene are determined by ellipsometry analysis. Graphene films were grown on copper substrates and transferred as both monolayers and bilayers onto SiO2/Si substrates by using standard manufacturing procedures. The chemical nature and thickness of residual debris formed after the transfer process were elucidated using photoelectron spectroscopy. The real layered structure so deduced has been used instead of the nominal one as the input in the ellipsometry analysis of monolayer and bilayer graphene, transferred onto both native and thermal silicon oxide. The effect of these contamination layers on the optical properties of the stacked structure is noticeable both in the visible and the ultraviolet spectral regions, thus masking the graphene optical response. Finally, the use of heat treatment under a nitrogen atmosphere of the graphene-based stacked structures, as a method to reduce the water content of the sample, and its effect on the optical response of both graphene and the residual debris layer are presented. The Lorentz-Drude model proposed for the optical response of graphene fits fairly well the experimental ellipsometric data for all the analysed graphene-based stacked structures.

Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Tubulin Polyglycylation: Differential Posttranslational Modification of Dynamic Cytoplasmic and Stable Axonemal Microtubules in Paramecium

Polyglycylation, a posttranslational modification of tubulin, was discovered in the highly stable axonemal microtubules of Paramecium cilia where it involves the lateral linkage of up to 34 glycine units per tubulin subunit. The observation of this type of posttranslational modification mainly in axonemes raises the question as to its relationship with axonemal organization and with microtubule stability. This led us to investigate the glycylation status of cytoplasmic microtubules that correspond to the dynamic microtubules in Paramecium. Two anti-glycylated tubulin monoclonal antibodies (mAbs), TAP 952 and AXO 49, are shown here to exhibit different affinities toward mono- and polyglycylated synthetic tubulin peptides. Using immunoblotting and mass spectrometry, we show that cytoplasmic tubulin is glycylated. In contrast to the highly glycylated axonemal tubulin, which is recognized by the two mAbs, cytoplasmic tubulin reacts exclusively with TAP 952, and the α- and β- tubulin subunits are modified by only 1–5 and 2–9 glycine units, respectively. Our analyses suggest that most of the cytoplasmic tubulin contains side chain lengths of 1 or 2 glycine units distributed on several glycylation sites. The subcellular partition of distinct polyglycylated tubulin isoforms between cytoplasmic and axonemal compartments implies the existence of regulatory mechanisms for glycylation. By following axonemal tubulin immunoreactivity with anti-glycylated tubulin mAbs upon incubation with a Paramecium cellular extract, the presence of a deglycylation enzyme is revealed in the cytoplasm of this organism. These observations establish that polyglycylation is reversible and indicate that, in vivo, an equilibrium between glycylating and deglycylating enzymes might be responsible for the length of the oligoglycine side chains of tubulin.

Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Equilibration rates in lipid monolayers

A theoretical analysis is given for the rate of change of domain sizes in lipid monolayers at the air–water interface. The calculation is applicable to liquid domains formed from binary mixtures of lipids that form two coexisting liquid phases. Under conditions where the two lipid molecules have approximately equal areas, the equilibration rate does not involve macroscopic hydrodynamic flow in the subphase but rather depends on the diffusion coefficient of the lipid molecules. The calculation shows that the equilibration rate in binary mixtures of cholesterol and phosphatidylcholine is remarkably slow, the radius of a typical 20-μm diameter domain changing by as little as a part in a million per second. Under these circumstances, equilibration times of the order of days or weeks are expected. Even with such long times, the final state reached by the monolayer will in general be a state of metastable equilibrium, rather than true equilibrium.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.