Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

Characterization of cytotoxic ribonucleases: from the internalization pathway to the importance of dimeric structures

En aquesta tesi s'ha caracteritzat la ruta d'internalització de l'onconasa, una RNasa citotòxica. Els resultats indiquen que l'onconasa entra a les cèl·lules per la via dependent de clatrina i del complex AP-2. Seguidament es dirigeix als endosomes de reciclatge i es a través d'aquesta ruta que la proteïna exerceix la citotoxicitat. Per altra banda, els resultats d'aquest treball demostren que PE5, una variant citotòxica de la ribonucleasa pancreàtica humana (HP-RNasa), interacciona amb la importina  mitjançant diferents residus que tot i que no són seqüencials, es troben propers en l'estructura tridimensional d'aquesta proteïna. PM8 és una HP-RNasa amb estructura cristal·logràfica dimèrica constituïda per intercanvi de dominis N-terminals. En aquesta tesi s'han establert les condicions per estabilitzar aquest dimer en solució i també es proposa un mecanisme per la dimerització.

Les sHsps en surera: Estudis de funcionalitat

Aquesta tesi es centra en la caracterització funcional d'una proteïna de xoc de calor de baix pes molecular (Small Heat Shock Protein - sHSP) de classe I de surera pel que fa a la seva capacitat per protegir les cèl·lules de l'estrès i per estabilitzar les membranes. Les sHsps són proteïnes que s'expressen en condicions d'estrès cel·lular. Encara que certs aspectes funcionals de les sHsps són ben coneguts, el nostre treball aporta informacions noves sobre el paper de les diferents regions de la proteïna, especialment de la regió N-terminal. L'objectiu concret d'aquest treball és determinar la funció termoprotectora de QsHsp17.4-CI, una sHsp de classe I oobtinguda a partir de les cèl·lules de fel·lema d'alzina surera, en un model bacterià i analitzar la importància de les diferents regions de la proteïna en aquesta funció. Amb aquesta finalitat s'han dissenyat dues proteïnes parcials derivades de QsHsp17.4-CI: una a la que li falta la regió N-terminal (C105) i una altra amb pràcticament tot el domini -cristal·lí deleccionat (N61), i una tercera, derivada de QsHs10-CI, a la que li falta la meitat del domini -cristal·lí (Hsp10). També s'estudia la possible capacitat estabilitzadora de membranes i la capacitat de modificar l'expressió d'altres Hsps quan s'expressa de forma heteròloga. Els nostres resultats demostren que l'expressió de QsHsp17.4-CI protegeix a les cèl·lules d'E.coli de l'estrès tèrmic alhora que la regió N-terminal i la regió consens II del domini -cristal·lí són imprescindibles per aquesta funció de protecció. En relació a un possible paper en les membranes, els estudis de localització subcel·lular mostren que QsHsp17.4-CI colocalitza amb la fracció membranes i que la regió N-terminal de la proteïna és responsable d'aquesta colocalització. No s'ha pogut demostrar, però, que la localització amb la membrana estigui associada a un efecte protector d'aquesta: en cap cas la sobrexpressió de les proteïnes modifica la composició d'àcids grassos i només N61, que no té acció termoprotectora, altera l'estat fisico-químic de la membrana. En estudis d'expressió de novo en E.coli s'ha observat que, a diferència de les altres proteïnes heteròlogues, N61 activa l'expressió de la majoria de Hsps d'E.coli fent pensar en una possible relació entre l'estat físic de la membrana i l'activació de la resposta a l'estrès. En resum, en aquest treball hem provat la capacitat protectora de QsHsp17.4 i aportem noves dades sobre la importància de la regió N-terminal i la regió consens II del domini -cristal·lí en aquesta funció. Per altra banda, es suggereix que QsHsp17.4 podria interaccionar amb la membrana d'E.coli i que la regió N-terminal seria imprescindible per aquesta interacció. Finalment hem determinat que les proteïnes que provoquen variacions en l'estat de fluïdesa de la membrana poden activar la resposta al xoc de calor per part de la cèl·lula bacteriana.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.