57 research outputs found

    Multiscale Modeling of Skeletal Muscle Active Contraction in Relation to Mechanochemical Coupling of Molecular Motors

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    In this work, a mathematical model was developed to relate the mechanochemical characterizations of molecular motors with the macroscopic manifestation of muscle contraction. Non-equilibrium statistical mechanics were used to study the collective behavior of myosin molecular motors in terms of the complex conformation change and multiple chemical states in one working cycle. The stochastic evolution of molecular motor probability density distribution during the contraction of sarcomere was characterized by the Fokker-Planck Equation. Quick muscle contraction was demonstrated by the collective dynamic behavior of myosin motors, the muscle contraction force, and the muscle contraction velocity-force relation. Our results are validated against published experiments, as well as the predictions from the Hill’s model. The quantitative relation between myosin molecular motors and muscle contraction provides a novel way to unravel the mechanism of force generation

    Molecular Biomechanics: The Molecular Basis of How Forces Regulate Cellular Function

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    Recent advances have led to the emergence of molecular biomechanics as an essential element of modern biology. These efforts focus on theoretical and experimental studies of the mechanics of proteins and nucleic acids, and the understanding of the molecular mechanisms of stress transmission, mechanosensing and mechanotransduction in living cells. In particular, single-molecule biomechanics studies of proteins and DNA, and mechanochemical coupling in biomolecular motors have demonstrated the critical importance of molecular mechanics as a new frontier in bioengineering and life sciences. To stimulate a more systematic study of the basic issues in molecular biomechanics, and attract a broader range of researchers to enter this emerging field, here we discuss its significance and relevance, describe the important issues to be addressed and the most critical questions to be answered, summarize both experimental and theoretical/computational challenges, and identify some short-term and long-term goals for the field. The needs to train young researchers in molecular biomechanics with a broader knowledge base, and to bridge and integrate molecular, subcellular and cellular level studies of biomechanics are articulated.National Institutes of Health (U.S.) (grant UO1HL80711-05 to GB)National Institutes of Health (U.S.) (grant R01GM076689-01)National Institutes of Health (U.S.) (grant R01AR033236-26)National Institutes of Health (U.S.) (grant R01GM087677-01A1)National Institutes of Health (U.S.) (grant R01AI44902)National Institutes of Health (U.S.) (grant R01AI38282)National Science Foundation (U.S.) (grant CMMI-0645054)National Science Foundation (U.S.) (grant CBET-0829205)National Science Foundation (U.S.) (grant CAREER-0955291

    Cardiac myosin contraction and mechanotransduction in health and disease

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    Cardiac myosin is the molecular motor that powers heart contraction by converting chemical energy from ATP hydrolysis into mechanical force. The power output of the heart is tightly regulated to meet the physiological needs of the body. Recent multiscale studies spanning from molecules to tissues have revealed complex regulatory mechanisms that fine-tune cardiac contraction, in which myosin not only generates power output but also plays an active role in its regulation. Thus, myosin is both shaped by and actively involved in shaping its mechanical environment. Moreover, these studies have shown that cardiac myosin-generated tension affects physiological processes beyond muscle contraction. Here, we review these novel regulatory mechanisms, as well as the roles that myosin-based force generation and mechanotransduction play in development and disease. We describe how key intra- and intermolecular interactions contribute to the regulation of myosin-based contractility and the role of mechanical forces in tuning myosin function. We also discuss the emergence of cardiac myosin as a drug target for diseases including heart failure, leading to the discovery of therapeutics that directly tune myosin contractility. Finally, we highlight some of the outstanding questions that must be addressed to better understand myosin\u27s functions and regulation, and we discuss prospects for translating these discoveries into precision medicine therapeutics targeting contractility and mechanotransduction

    Bridging spatiotemporal scales in biomechanical models for living tissues : from the contracting Esophagus to cardiac growth

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    Appropriate functioning of our body is determined by the mechanical behavior of our organs. An improved understanding of the biomechanical functioning of the soft tissues making up these organs is therefore crucial for the choice for, and development of, efficient clinical treatment strategies focused on patient-specific pathophysiology. This doctoral dissertation describes the passive and active biomechanical behavior of gastrointestinal and cardiovascular tissue, both in the short and long term, through computer models that bridge the cell, tissue and organ scale. Using histological characterization, mechanical testing and medical imaging techniques, virtual esophagus and heart models are developed that simulate the patient-specific biomechanical organ behavior as accurately as possible. In addition to the diagnostic value of these models, the developed modeling technology also allows us to predict the acute and chronic effect of various treatment techniques, through e.g. drugs, surgery and/or medical equipment. Consequently, this dissertation offers insights that will have an unmistakable impact on the personalized medicine of the future.Het correct functioneren van ons lichaam wordt bepaald door het mechanisch gedrag van onze organen. Een verbeterd inzicht in het biomechanisch functioneren van deze zachte weefsels is daarom van cruciale waarde voor de keuze voor, en ontwikkeling van, efficiënte klinische behandelingsstrategieën gefocust op de patiënt-specifieke pathofysiologie. Deze doctoraatsthesis brengt het passieve en actieve biomechanisch gedrag van gastro-intestinaal en cardiovasculair weefsel, zowel op korte als lange termijn, in kaart via computermodellen die een brug vormen tussen cel-, weefsel- en orgaanniveau. Aan de hand van histologische karakterisering, mechanische testen en medische beeldvormingstechnieken worden virtuele slokdarm- en hartmodellen ontwikkeld die het patiënt-specifieke orgaangedrag zo accuraat mogelijk simuleren. Naast de diagnostische waarde van deze modellen, laat de ontwikkelde modelleringstechnologie ook toe om het effect van verschillende behandelingstechnieken, via medicatie, chirurgie en/of medische apparatuur bijvoorbeeld, acuut en chronisch te voorspellen. Bijgevolg biedt deze doctoraatsthesis inzichten die een onmiskenbare impact zullen hebben op de gepersonaliseerde geneeskunde van de toekomst

    UNCOVERING FUNDAMENTAL MECHANISMS OF ACTOMYOSIN CONTRACTILITY USING ANALYTICAL THEORY AND COMPUTER SIMULATION

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    Actomyosin contractility is a ubiquitous force-generating function of almost all eukaryotic organisms. While more understanding of its dynamic non-equilibrium be- havior has been uncovered in recent years, little is known regarding its self-emergent structures and phase transitions that are observed in vivo. With this in mind, this thesis aims to develop a state-of-the-art computational model for the simulation of actomyosin assemblies, containing detailed cytosolic reaction-diffusion processes such as actin filament treadmilling, cross-linker (un)binding, and molecular motor walking. This is explicitly coupled with novel mechanical potentials for semi-flexible actin filaments. Then, using this simulation framework combined with other ana- lytical approaches, we propose a novel mechanism of contractility in a fundamental actomyosin structural element, derived from a thermodynamic free energy gradi- ent favoring overlapped actin filament states when passive cross-linkers are present. With this spontaneous cross-linking, transient motors such as non-muscle myosin II can generate robust network contractility in a collective myosin II-cross-linker ratcheting mechanism. Finally, we map the phases of contractile behavior of disor- dered actomyosin using this theory, showing explicitly the cross-linking, motor and boundary conditions required for geometric collapse or tension generation in a net- work comprised of those elements. In this theory, we move away from the sarcomeric contractility mechanism typically reconciled in disordered non-muscle structures. It is our hope that this study adds theoretical knowledge as well as computational tools to study the diverse contractile assemblies found in non-muscle actomyosin networks

    Modeling the interplay of mechanics and self-assembly in the actin cytoskeleton

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    Many cellular processes such as cell migration or division require a trade-off between structural integrity and dynamic reorganization of the load-bearing elements. The actin cytoskeleton has evolved to provide this function for animal cells, but a physical understanding of the interplay between its mechanics and self-assembly is missing. Here I model theoretically two paradigmatic situations of this kind. First, I consider the self-assembly of non-muscle myosin II minifilaments, with a special focus on the stochastic effects that arise due to the small system size of around 30 load bearing elements that turn-over simultaneously to producing contractile force. The self-assembly model follows a consensus architecture, thereby relating the geometrical neighborhood relations of the myosin II monomers with associated binding energies. I find that the turn-over of monomers depends on the mechanochemistry of the cross-bridge cycle by simulating the associated master equation explicitly and by a mean-field approach that maps the complex assembly structure to a simple monomer-addition scheme. Using a rheological framework, I characterize the distinct mechanical properties of non-muscle myosin II minifilaments that arise due to differences in the cross-bridge cycle of the different myosin II isoforms, that can co-assemble in one hetero-filament. Quantitative analysis of the frequency dependent response by a complex modulus, reveals a cross over from viscous to elastic behavior as the ratio of slow to fast isoforms working together is increased. Second I consider the dynamical stability of a peripheral stress fiber, that depends on the interplay of contraction by myosin II minifilaments, self-assembly of new actin filaments at both ends of the fiber and cortical tension. In collaboration with an experimental group, we could show how the myosin II isoform content is differentially reflected by the phenotype of peripheral stress fibers and show their position in a stability phase diagram of the stress fiber. These results demonstrate quantitatively how mechanics and self-assembly interact on different scales in the actin cytoskeleton

    A coarse-grained approach to model the dynamics of the actomyosin cortex

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    Background: The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions. Results: Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin. Conclusions: We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell corte

    Multiscale computational modeling of single cell migration in 3D

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    La migración celular es un proceso complejo, orquestado por factores químicos y biológicos, por la microestructura y por las propiedades mecánicas de la matriz extracelular. Este fenómeno es fundamental para el desarrollo de tejidos en los organismos pluricelulares, y como seres humanos, nos acompaña durante toda la vida, desde el mismo momento de la concepción hasta la muerte. Juega un papel fundamental durante el desarrollo embrionario determinando la formación de los diferentes órganos (morfogénesis) y es clave en todos los procesos regenerativos como la renovación de la piel, la respuesta inflamatoria o la cicatrización de heridas. Sin embargo, también contribuye al desarrollo de procesos patológicos como la metástasis, el retraso mental, la osteoporosis o enfermedades vasculares entre otros. Es por ello de vital importancia el conocer los mecanismos fundamentales que controlan la migración celular con el fin de tratar de manera efectiva las diferentes patologías, así como avanzar en el trasplante de órganos y el desarrollo de tejidos artificiales. Así pues, el objetivo de esta Tesis es el desarrollo de modelos a distintas escalas y centrados en diversos aspectos de la migración, de manera que faciliten la compresión de fenómenos específicos y sirvan como guía para el diseño de experimentos. Dada la complejidad y las grandes diferencias respecto a la migración colectiva, todos los modelos y análisis de esta Tesis se centran en células individuales. En primer lugar se ha estudiado la migración tridimensional de una célula individual embebida en una matriz extracelular donde su velocidad y orientación se consideran reguladas por estímulos mecánicos. Para ello se ha desarrollado un modelo mecanosensor basado en elementos finitos y se ha analizado el comportamiento celular en función de diferentes rigideces y condiciones de contorno a escala celular. A medida que el trabajo ha progresado, los resultados del modelo unidos a nuevos avances científicos publicados en este ámbito, han reforzado la idea de que el mecansimo mecanosensor juega un papel crítico en los procesos que dirigen la migración celular. Por ello, se ha necesitado un estudio más profundo de este fenómeno para lo que se ha utilizado un modelo mucho más detallado a escala intracelular. Así pues, se ha explorado la estructura interna del citoesqueleto y su comportamiento ante cambios mecánicos en la matriz extracelular, utilizando un modelo discreto de partículas basado en dinámica Browniana con el que se ha simulado la formación de una red de actina (polimerización) entrecruzada con proteínas y motores moleculares. En concreto, se ha estudiado el comportamiento activo de estos motores y su papel como sensores de estímulos mecánicos externos (mecanosensores) de manera que los resultados obtenidos con este modelo “micro” han permitido validar las hipótesis del modelo previo. Consecuentemente, se ha revisado el modelo mecánico y se le ha añadido dependencia temporal, obteniendo un modelo continuo capaz de predecir respuestas celulares macroscópicas basadas en el comportamiento de los componentes microestructurales. En otras palabras, esta simplificación ha permitido la introducción de la respuesta macroscópica emergente obtenida del comportamiento dinámico de la microestructura, disminuyendo enormemente el coste computacional y por tanto permitiendo simulaciones a mayores escalas espacio-temporales. A continuación se han introducido las nuevas hipótesis en un modelo probabilístico de migración a escala celular basado en elementos finitos que permite al mismo tiempo el estudio de factores tanto a escala macroscópica (velocidades, trayectorias) como a escala celular (orientación, área de adhesión, tensiones celulares, desplazamientos de la matriz etc.). Adicionalmente, este modelo es sensible no sólo a la mecánica sino a las condiciones fluido-químicas del entorno, las cuales han sido analizadas igualmente mediante simulaciones por elementos finitos. Con todo esto, los modelos desarrollados todavía no incluyen una descripción detallada de procesos importantes envueltos en la migración celular como la protrusión de la membrana, la polimerización de actina en el frente celular o la formación de adhesiones focales. Por lo tanto, para completar la Tesis, se ha desarrollado un modelo continuo basado en diferencias finitas que permite el estudio del comportamiento dinámico del lamelipodio y el papel fundamental que juegan la polimerización de actina, los motores moleculares y las adhesiones focales (FAs) en el frente celular durante la migración. Cell migration is a complex process, orchestrated by biological and chemical factors, and by the microstructure and extracellular matrix (ECM) mechanical properties among others. It is essential for tissue development in multicellular organisms, and as human beings, it accompanies us throughout life, from conception to death. It plays a major role during embryonic development, defining organ formation (morphogenesis) and being crucial in all the regenerative processes such as skin renewal, inflammatory response or wound healing. However, it is also involved in several pathological processes e.g. metastasis, mental retardation, osteoporosis or vascular diseases. Therefore, understanding the fundamental mechanisms controling cell migration is vitally important to effectively treat different pathologies and to make progress in organ transplantation and tissue development. Thus, the main scope of this Thesis is the development of mathematical models at different scales and focused on different aspects of cell migration so that specific phenomena can be better understood, serving as a guide for the development of new experiments. All the models and analysis contained in this thesis are focused on single cells, firstly due to the complexity and marked differences with respect to collective cell migration, and secondly owing to the importance of individual migration in important processes such as metastatic tumor cell migration. In addition, since three- dimensional environments are physiologically more relevant, 3D approaches have been considered in most of the models here developed to better mimic in vivo conditions. Firstly, single cell migration of a cell embedded in a three-dimensional matrix was studied, regulating its velocity and polarization through mechanical clues. For this purpose, a finite element (FE) based mechanosensing model was developed, analyzing cell behavior according to different ECM rigidities and boundary conditions at the cell scale. As work advanced, results from the model together with recent findings from literature strengthened the idea that mechanosensing plays a critical role in cell motility driving processes. For this reason, a deeper understanting of this mechanism was needed, resulting in the development of a specific and more detailed model (at the intracellular scale). Hence, the cytoskeletal structure response to mechanical stimuli has been explored using a discrete particle-based Brownian dynamics model. This model was used to simulate the formation of actin networks (through actin polymerization) cross-linked with proteins (ACPs) and molecular motors. Specifically, the active role of molecular motors and their role as mechanosensors were studied, so that the results of the intracellular scale approach allowed the validation of the previous model main assumptions. As a consequence, the mechanical hypothesis were revised and a temporal dependence was incorporated, obtaining a new continuum model able to predict macroscopic cell responses based on microstructural components behavior. In other words, this simplification allowed introducing the emergent macroscopic response obtained from the active behavior of the microstructure, saving large amounts of computational time and permitting simulations at higher time and length scales. Next, the new hypotheses were incorporated into a probabilistic, FE-voxel-based cell-scale migration model, permitting simultaneously the study of macro-scale factors (velocities, trajectories) and cell-scale ones (polarization, adhesion area, cell stress, ECM displacements etc.). Additionally this model includes the effect of fluid-chemical stimuli, which was also analyzed by means of FE-simulations. With all this, the developed models still lacked a detailed description of important processes involved in cell migration such as membrane protrusion, actin polymerization or focal adhesion (FA) formation. As a result, a continuum model was designed to study the lamellipodium dynamics and the major role of actin polymerization and focal adhesions (FA) at the cell front during cell migration

    COMPUTATIONAL MECHANOBIOLOGY OF FILAMENTOUS PROTEINS: ALPHA-HELICAL COILED COILS AND F-ACTIN

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    This dissertation sits at the intersection of mechanics and biology. Specifically, we devise mesoscopic mechanochemical models to study biofilaments, very ubiquitous cellular protein structures. Since they undergo functional bending, twisting, buckling and stretching motions, understanding the mechanical response of biofilaments is crucial for a correct description of the conformational states of these proteins. Our models contribute to the better understanding of the nonlinearities in the mechanical response of biofilaments to the environmental perturbations, without resorting to computationally costly full atomistic simulations. Two important filamentous structures coiled-coil and actin make up the main concentration of our work. Coiled coils are a rope-like protein motif formed by two or more alpha helices. The energetic of a coiled coil involves a competition between elastic deformation and hydrophobic interaction of residues of each helix. The model treats alpha helices as elastic rods where each rod interacts with another exclusively through beads representing the hydrophobic residues. We validate our model using steered molecular dynamics simulations and compare it with continuum thin rod model. We analyze the bending, buckling and twisting behavior of coiled coil molecules of various lengths and conclude that a coiled coil molecule cannot be fully characterized by a simple single-parameter mechanical model. The second filamentous biological structure we study is filamentous actin, F-actin, which is an important player in eukaryotic cellular processes including motility, morphogenesis, and mechanosensation. Actin monomer, G-actin, polymerizes to form F-actin. G-actin is an ATP hydrolase and at any time it is bound to either an ATP or ADP molecule. Mechanical and chemical properties of actin filaments are strongly coupled to each other through the bound nucleotide type. In our model of F-actin, each monomer is treated as a spherical particle with a bound molecule identity. The particles are connected by a set of springs with changing mechanical properties that depend on the bound molecule. Using this model, we study and explain the behavior of actin filaments under various external mechanical stimuli introduced by actin binding proteins. Finally, we discuss the coupling of monomer chemical state changes to the global mechanical response of actin
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