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The notion of phase transitions as a characterization of a change in physical properties pervades modern physics. Such abrupt and fundamental changes in the behavior of physical systems are evident in condensed matter system and also occur in nuclear and subatomic settings. While this concept is less prevalent in the field of biology, recent advances have pointed to its relevance in a number of settings. Recent studies have modeled both the cell cycle and cancer as phase transition in physical systems. In this dissertation we construct simplified models for two biological systems. As described by those models, both systems exhibit phase transitions. The first model is inspired by the shape transition in the nuclei of neutrophils during differentiation. During differentiation the nucleus transitions from spherical to a shape often described as "beads on a string." As a simplified model of this system, we investigate the spherical-to-wrinkled transition in an elastic core bounded to a fluid shell system. We find that this model exhibits a first-order phase transition, and the shape that minimizes the energy of the system scales as ( r 3 / ). The second system studied is motivated by the dynamics of globular proteins. These proteins may undergoes conformational changes with large displacements relative to their size. Transitions between conformational states are not possible if the dynamics are governed strictly by linear elasticity. We construct a model consisting of an predominantly elastic region near the energetic minimum of the system and a non-linear softening of the system at a critical displacement. We find that this simple model displays very rich dynamics include a sharp dynamical phase transition and driving-force-dependent symmetry breaking.
This IMA Volume in Mathematics and its Applications MODELING OF SOFT MATTER contains papers presented at a very successful workshop with the same ti tle. The event, which was held on September 27-October 1, 2004, was an integral part of the 2004-2005 IMA Thematic Year on "Mathematics of Ma terials and Macromolecules: Multiple Scales, Disorder, and Singularities. " We would like to thank Maria-Carme T. Calderer (School of Mathematics, University of Minnesota) and Eugene M. Terentjev (Cavendish Laboratory, University of Cambridge) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE The physics of soft matter in particular, focusing on such materials as complex fluids, liquid crystals, elastomers, soft ferroelectrics, foams, gels and particulate systems is an area of intense interest and contemporary study. Soft matter plays a role in a wide variety of important processes and application, as well as in living systems. For example, gel swelling is an essential part of many biological processes such as motility mecha nisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switch ing devices. Experiments of the last decade have provided a great deal of detailed information on structures and properties of soft matter.
Current Topics in Membranes provides a systematic, comprehensive, and rigorous approach to specific topics relevant to the study of cellular membranes. Each volume is a guest edited compendium of membrane biology. Discusses the current state of electrostatics in biomolecular simulations and future directions Includes information on time and length scales in lipid bilayer simulations Includes a chapter on the nature of lipid rafts
Computational modeling is emerging as a powerful new approach to study and manipulate biological systems. Multiple methods have been developed to model, visualize, and rationally alter systems at various length scales, starting from molecular modeling and design at atomic resolution to cellular pathways modeling and analysis. Higher time and length scale processes, such as molecular evolution, have also greatly benefited from new breeds of computational approaches. This book provides an overview of the established computational methods used for modeling biologically and medically relevant systems.
The workshop "Biologically Inspired Physics" was organized, with the support of the NATO Scientific Affairs Division and the Directorate-General for Science, Research and Development of the Commission of the European Communities, in order to review some subjects of physics of condensed matter which are inspired by biological problems or deal with biological systems, but which address physical questions. The main topics discussed in the meeting were: 1. Macromolecules: In particular, proteins and nucleic acids. Special emphasis was placed on modelling protein folding, where analogies with disordered systems in con densed matter (glasses, spin glasses) were suggested. It is not clear at this point whether such analogies will help in solving the folding problem. Interesting problems in nucleic acids (in particular DNA) deal with the dynamics of semiflexible chains with torsion and the relationship between topology and local structure. They arise from such biological problems as DNA packing or supercoiling. 2. Membranes: This field has witnessed recent progress in the understanding of the statistical mechanics of fluctuating flexible sheets, such as lipid bilayers. It appears that one is close to understanding shape fluctuations in red blood cells on a molec ular basis. Open problems arise from phenomena such as budding or membrane fusion. Experiments on model systems, such as vesicle systems or artificial lipids, have great potential. Phenomena occurring inside the membrane (protein diffusion, ionic pumps) were only discussed briefly.
Soft matter and biological systems pose many challenges for theoretical, experimental and computational research. From the computational point of view, these many-body sytems cover variations in relevant time and length scales over many orders of magnitude. Indeed, the macroscopic properties of materials and complex fluids are ultimately to be deduced from the dynamics of the microsopic, molecular level. In these lectures, internationally renowned experts offer a tutorial presentation of novel approaches for bridging these space and time scales in realistic simulations. This volume addresses graduate students and nonspecialist researchers from related areas seeking a high-level but accessible introduction to the state of the art in soft matter simulations.
The development of a proper description of the living world today stands as one of the most significant challenges to physics. A variety of new experimental techniques in molecular biology, microbiol ogy, physiology and other fields of biological research constantly expand our knowledge and enable us to make increasingly more detailed functional and structural descriptions. Over the past decades, the amount and complexity of available information have multiplied dramatically, while at the same time our basic understanding of the nature of regulation, behavior, morphogenesis and evolution in the living world has made only modest progress. A key obstacle is clearly the proper handling of the available data. This requires a stronger emphasis on mathematical modeling through which the consistency of the adopted explanations can be checked, and general princi ples may be extracted. As an even more serious problem, however, it appears that the proper physical concepts for the development of a theoretically oriented biology have not hitherto been available. Classical mechanics and equilibrium thermody namics, for instance, are inappropriate and useless in some of the most essen tial biological contexts. Fortunately, there is now convincing evidence that the concepts and methods of the newly developed fields of nonlinear dynam ics and complex systems theory, combined with irreversible thermodynamics and far-from-equilibrium statistical mechanics will enable us to move ahead with many of these problems.
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
This handbook will provide the reader with a profound introduction to the key subjects comprising the relatively new topic of Soft Condensed Matter. It will provide students and researchers with an authoritative overview of the field, identify key principles at play, and the most prominent ways of further development.