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A mathematical approach to the concepts of copolymerization of microtubules in the presence of anti-mitotic drugs is presented in this work. A general feature of the mathematical equations is presented. The possibility of having analytical steady state solutions of dynamic equations is investigated. The structure of equations is narrowed down for the specific brand of anti-mitotic drug, colchicine. The behavior of total T-tubulin concentration in the steady state in a regeneration system is investigated and analyzed through the numerical calculations. / Ph. D.

The tubulin/FtsZ superfamily contains a large set of proteins that spans through all kingdoms of life, with αβ-tubulins being the eukaryotic representatives and FtsZ being the best studied prokaryotic homologue. It is believed that all tubulin/FtsZ-related proteins have evolved from a common ancestor, however, members from this superfamily have diverged in many aspects. αβ-tubulins polymerise into giant and hollow microtubules in the presence of GTP. Despite the size of around 25 nm wide, microtubules display sophisticated dynamics. In particular, dynamic instability, the stochastic change between fast growth and rapid shrinkage, is a hallmark of microtubules. In contrast to αβ-tubulins, FtsZ lacks the C-terminal domain of tubulins and it probably functions as single homopolymeric protofilaments, possibly through treadmilling dynamics. There is strong divergence of the biological functions in the tubulin/FtsZ superfamily. Microtubules are involved in fundamental processes such as motility, transport and chromosomal segregation, whereas FtsZ is involved in bacterial cytokinesis (bacterial cell division), and the equivalent role of FtsZ is carried out by actin-based and ESCRTIII-based systems in eukaryotes. It seems that there is a big evolutionary gap between αβ-tubulins and FtsZ, and the only properties that are conserved within the tubulin/FtsZ superfamily are fold, protofilament formation and GTPase activity. In 2002, a pair of tubulin-like genes, btuba and btubb were identified in Prosthecobacter bacteria, with higher sequence homology to eukaryotic tubulins than FtsZ or any other bacterial homologues. The crystal structures solved later revealed, again, a closer similarity to αβ-tubulins than to their prokaryotic equivalents. It has been known for a while that BtubAB form filaments in the presence of GTP, however, little knowledge has been available regarding the filament architecture. In this project, I determined the near atomic resolution structure of the in vitro BtubAB filament using cryoEM and cryoET, revealing a hollow tube that consists of four protofilaments. A closer look showed that BtubAB filaments have many conserved microtubule features including: an overall polarity, similar longitudinal contacts, M-loops in lateral interfaces, and the presence of the seam, a structural hallmark of microtubules. My study also shows that BtubC, a protein with a TPR fold, binds to the BtubAB filaments in a stoichiometric manner, similar to some MAPs on microtubules. Based on this work, I concluded that BtubAB from Prosthecobacter form bacterial ‘mini microtubules’, and my work provided interesting insight into the evolution of tubulin/FtsZ-related proteins.

In simulation of closely- or separately-joined rock masses, stability of rock blocks is of primary concern. However, there seems to be no approach that can handle general modes of simultaneous sliding and truly large rotation under general forces, including non-conservative forces such as water forces. General causes of failure for rock blocks, such as limit points, bifurcation points, and dynamic instability (divergence and flutter), have never been addressed. This research implements a formulation, called BS3D(an incremental-iterative algorithm introduced by Tonon), for analyzing general failure modes of rock blocks under conservative and non-conservative forces. Among the constitutive models for rock fractures developed over the years, Barton's empirical model has been widely used because it is easy to apply and includes several important factors associated with fracture characteristics. Although Barton's failure criterion predicts peak shear strength of rock fractures with acceptable precision, it has some weaknesses in estimating the peak shear displacement, post-peak shear strength, dilation, and surface degradation in unloading and reloading. In this dissertation, modifications are made to Barton's original model in order to address these weaknesses. The modified Barton’s model is validated by a series of direct shear tests on rock fractures and implemented in BS3D to consider the dilatant behavior of fractures. The mechanical behavior of a rock block formed in the roof of a tunnel is governed by its geometry, the mechanical characteristics and the deformability of the fractures forming the block, the deformability of the block and that of the surrounding rock mass, and the stresses within the rock. BS3D, after verification and validation, is used to investigate the effect of dilatancy on stability of rock blocks formed in the roof of a circular tunnel. High-velocity plunging jets, issuing from hydraulic artificial or natural structures, can result in scouring of the rock riverbed or the dam toe foundation. Assessment of the extent of scour is necessary to ensure the safety of the dam and to guarantee the stability of its abutments. BS3D is used to investigate effect of high-velocity jet impact on stability of rock blocks in plunge pools. / text

[pt] Estruturas offshore têm demandado, em função do aumento da profundidade da lâminha de água e da severidade do ambiente, análises de vibração cada vez mais confiáveis. Em face de oscilações com grandes deslocamentos, torna-se imprescindível uma análise não linear dessas estruturas. Métodos numéricos como os elementos finitos constituem-se numa tarefa computacionalmente custosa, uma vez que os acoplamentos modais tornam necessários modelos com muitos graus de liberdade. Isso dificulta as análises paramétricas e prolonga os ciclos de projeto para estruturas offshore. Uma alternativa a esses problemas é o uso de modelos de ordem reduzida. Os modos normais não lineares têm-se mostrado uma ferramenta eficiente na derivação de modelos de ordem reduzida para análises de vibrações não lineares. Isso ocorre porque um número menor de modos não lineares, em relação aos modelos com modos lineares, é necessário para se obter o mesmo nível de precisão num modelo reduzido. Esse trabalho utiliza modelos de ordem reduzida, obtidos por meio de análise modal não linear, para o estudo de vibração de modelos simplificados de estruturas offshore. Três exemplos de aplicação são utilizados: pêndulo invertido, torre articulada e plataforma spar. Além dos métodos baseado no procedimento de Galerkin e o assintótico, um procedimento numérico alternativo é proposto para obtenção dos modos, podendo ser utilizado para construção dos modos essencialmente não lineares. As vibrações livres e forçadas são estudadas. A estabilidade das soluções é analisada utilizando-se a teoria de Floquet, diagramas de bifurcação e de Mathieu e seções de Poincaré. As seções de Poincaré são também utilizadas para identificar a multiplicidade dos modos não lineares e a existência de multimodos. Os resultados são comparados com a solução obtida da integração numérica do sistema original de equações, mostrando uma boa precisão dos modelos reduzidos. / [en] The increasing water depth and the ocean adverse environment demand more accurate vibration analysis of offshore structures. Due to large amplitude oscillations, a nonlinear vibration analysis becomes necessary. Numerical methods such as finite element constitute a computationally expensive task when applied to these problems, since the occurrence of modal coupling demands a high number of degrees-of-freedom. A feasible possibility to overcome these difficulties is the use of low order models. The nonlinear normal modes have been shown to be an effective tool in the derivation of reduced order models in nonlinear dynamics. In the use of nonlinear modal analysis fewer modes are required to achieve a given level of accuracy in comparison to the use of linear modes. This work uses the nonlinear normal modes to derive low dimensional models to study the vibration of simplified models of offshore structures. Three examples are considered: an inverted pendulum, an articulated tower and a spar platform. Both free and forced vibrations are studied. The asymptotic and Galerkin-based methods are used to derive the normal modes. In addition, an alternative numerical procedure to construct such modes is proposed, which can be used to derive coupled modes. The solution stability is determined by the use of the Floquet theory, bifurcation and Mathieu diagrams, and Poincaré sections. The Poincaré sections are also used to investigate the multiplicity of modes and multimodes. The results obtained from the numerical integration of the original system are favourably compared with those of the reduced order models, showing the accuracy of the reduced models.

Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws.

[pt] O objetivo desta tese é estudar os mecanismos de escape em sistemas estruturais sensíveis a imperfeições quando submetidos a certas classes de carregamentos dinâmicos, identificar os parâmetros que controlam o escape e criar critérios capazes de prever a fronteira de escape e a perda de estabilidade da estrutura no espaço dos parâmetros de controle. Isto permitirá um melhor entendimento dos processos de perda de estabilidade e servirá de base para o cálculo e controle da integridade dessas estruturas. Após a descrição dos fenômenos que podem ocorrer na dinâmica dessa classe de estruturas, são testados e adaptados alguns critérios existentes na literatura, que verificam a estabilidade de uma estrutura a partir do conhecimento dos parâmetros de controle. Em seguida estuda-se a evolução da estabilidade global do conjunto das soluções medida pela área da bacia de atração, e pelas características de sua fronteira. Desenvolvem-se expressões gerais para o critério de Melnikov, e mostra-se, a partir de perturbações aleatórias nos parâmetros de controle e na força externa, que essas expressões podem ser tomadas como um limite inferior para o carregamento de escape e conseqüentemente como uma contribuição para o desenvolvimento de critérios de projeto. Verifica-se também que os valores obtidos pelos critérios de escape podem ser tomados como limites superiores para o valor da força de escape. / [en] The purpose of this thesis is to study the escape mechanisms in imperfection sensitive structural systems under certain dynamical loading conditions. Other objectives are to identify the parameters that control the escape phenomenon and to create some criteria capable of predicting the escape boundary and the structures stability in the control parameters space. This will allow a better understanding of the stability loss process and can serve as a basis to the integrity control and design of these structures. After a description of the phenomena that can occur in the dynamics of this class of structures, some predictive criteria, found in literature, that verify the structure stability based on the control parameters knowledge, are adapted and tested. Following is a study of the evolution of the global stability of the set of solutions measured by the basin of attraction area, and by the characteristics of its boundary. Some general expressions for the Melnikov criterion are developed, and it is shown by randomly perturbing the control parameters and the external force, that these expressions can be taken as a lower bound for the escape load, and consequently as a contribution to the development of design criteria. It is also observed that the values obtained by the escape criteria can be taken as an upper bound for the values of the escape force. / [es] EL objetivo de esta tesis es estudiar los mecanismos de escape en sistemas extructurales que son sensibles a imperfecciones cuando son sometidos a ciertas clases de cargas dinámicas. Outro objetivo es identificar los parámetros que controlan el escape y crear criterios capaces de preveer la frontera de escape y la pérdida de estabilidad de la extructura en el espacio de los parámetros de control. Esto permitirá una mejor comprensión de los procesos de pérdida de estabilidad y servirá de base para el cálculo y control de la integridad de esas extructuras. Después de describir los fenómenos que pueden ocurrir en la dinámica de esta clase de extructuras, se prueban y adaptan algunos criterios existentes en la literatura, que verifican la estabilidad de una extructura a partir del conocimiento de los parámetros de control. Seguidamente, se estudia la evolución de la estabilidad global del conjunto de las soluciones, se dearrollan expresiones generales para el criterio de Melnikov, y se muestra, a partir de perturbaciones aleatorias en los parámetros de control y en la fuerza externa, que esas expresiones pueden ser tomadas como límite inferior para la carga de escape y conseqüentemente como una contribución para el desarrollo de criterios de proyecto. Se verifica también que los valores obtenidos por los criterios de escape pueden ser tomados como límites superiores para el valor de la fuerza de escape.

The first purpose of this research is to investigate the effect of added viscous fluid dampers on a nine story special steel moment frame designed for strength in Seattle. At the initial stages of the work, knowing the fact that moment frames are almost always controlled by drift, it was thought that two different moment frames, controlled by strength or controlled by drift (stiffness), could be designed in Seattle and the effect of additional dampers on the structural behavior of the strength controlled design could be studied. However, since ASCE 7 permits determining the elastic drifts by using the seismic design forces based on the computed fundamental period of the structure, without the upper limit (CuTa), the strength controlled design satisfied the drift limit requirements of ASCE 7. Although the strength controlled design meets the drift requirements, the stability checks of both ASCE 7 and the AISC Seismic Design Manual were not satisfied. Thus, the strength controlled frame was redesigned to meet the stability requirements, and the process is called stability controlled design. By adding supplemental dampers to the strength controlled design, it was expected that the seismic drift would be controlled and a better structural behavior would be obtained in terms of dynamic stability. Incremental Dynamic Analysis (IDA) was implemented to investigate the benefits of the dampers on the structural behavior. Using ten different earthquakes scaled up to a maximum target multiplier two, with ten increments, damage measures such as interstory drift, residual displacement, IDA dispersion, base shear, and roof displacement were studied. Using IDA dispersion, the effect of dampers on dynamic instability was also investigated in this study. As a result, it was found that as the damping of the structure increases with the help of added dampers, the structural response gets better. Maximum and residual roof displacements, interstory drifts, and IDA dispersion decreases with increasing damping. In addition, by using supplemental damping, most of the collapses that occur for the inherently damped frames are prevented. The second purpose of this research is to develop an improved "Hybrid" moment frame without added damping but by controlling the inelastic behavior. Hybrid Frames were designed as the combination of three different moment frames: Special, Intermediate and Ordinary Moment Frames (SMF, IMF, OMF). The design procedure of each bay, which corresponds to different moment frame systems, follows the rules of the related moment frame for that bay. By varying the plastic hinge capacities across the same level stories, four different Hybrid Frame designs were obtained. Nonlinear static pushover analysis was applied to these frames, and as expected, the more reduction in the plastic capacity of the Hybrid Frame, the earlier the pushover curve starts yielding and the later the negative post yield stiffness of the pushover curve was reached. It was observed that the effect of early plastic hinge forming in the frame, which caused inelastic hysteretic damping, and the relatively late formation of negative post yield stiffness resulted in a better dynamic behavior. As a result of the IDA studies, as the frames become more "hybrid", the residual displacements decrease significantly and then collapses are even prevented. This is considered as the positive effect of reaching the negative post yield stiffness late. The residual displacement was reduced for low intensity gentle earthquakes. The ductility demand IDA study proves that as the frames become more hybrid, the ductility demand increases for the special detailing frame, where plastic capacity was reduced, and decreases for the ordinary detailing frame, where the plastic capacity was increased. The Hybrid Frame system is expected to perform better than the traditional special moment frame, and to be more economical than the special moment frame because of the limited amount of special detailing. / Master of Science

[pt] As estruturas com cargas não conservativas podem perder a estabilidade por divergência, quando a amplitude da resposta estática se incrementa monotonamente, ou por flutter, através de oscilações com amplitudes exponencialmente crescentes. Neste trabalho estudam-se vários aspectos sobre o efeito do amortecimento e da deformação cisalhante na estabilidade dinâmica de vigas e tubos. Um programa computacional que permite obter cargas críticas e respostas no domínio do tempo é implementado, formulando as equações através do método dos elementos finitos. Comparam-se os resultados de vigas de Euler-Bernoulli e vigas de Timoshenko, considerando várias alternativas para a aplicação do amortecimento proporcional e viscoelástico. Tubos são modelados com elementos tridimensionais enriquecidos com modos adicionais incompatíveis. O amortecimento viscoelástico é introduzido na relação constitutiva do material, atuando sobre as deformações desviadoras. As cargas críticas dinâmicas são calculadas a partir do problema de autovalor característico, obtido aplicando a transformada de Laplace às equações de conservação de momentum. Nas análises dinâmicas um método implícito é utilizado para a integração do tempo e um algoritmo de segunda ordem na integração das relações constitutivas viscoelásticas. Os resultados mostram que para algumas formas de amortecimento, as respostas obtidas considerando a deformação cisalhante mudam qualitativamente o comportamento da carga crítica dinâmica, incluindo alguns paradoxos, conforme o amortecimento é incrementado. / [en] Structures with non-conservative loads can lose stability either by divergence, when static response amplitude increases monotonically, or by flutter, through oscillations with exponentially increasing amplitudes. Several aspects concerning the influence of damping and shear on the dynamic stability of beams and tubes are studied. A special-purpose computer program has been developed, enabling critical loads and time history responses to be obtained applying the finite element method to formulation of the equations. Results of Euler-Bernoulli and Timoshenko beams are compared for a number of alternative formulations of proportional and viscoelastic damping. Tubes are modeled with tridimensional elements implemented with additional incompatible modes. Viscoelastic damping is introduced in the constitutive relations of the material, acting on deviatoric strains. Flutter loads are calculated through the characteristic eigenvalue problem obtained applying the Laplace’s transform to the momentum equation. In the dynamic analysis an implicit method is used for time integration and a second order algorithm is used in the integration of viscoelastic constitutive relations. The results show that, for some types of damping, the responses obtained taking into account shear strains change qualitatively the behavior of the flutter load, including certain paradoxical phenomena, as damping is increased.