Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included. TOC:On the Mathematical Works of S.L. Sobolev in the 1930s, V. Babich.- Sobolev in Siberia, Y. Reshetnyak.- Boundary Harnack Principle and the Quasihyperbolic Boundary Condition, H. Aikawa.- Sobolev Spaces and their Relatives: local Polynomial Approximation Approach, Y. Brudnyi.- Spectral Stability of Higher Order Uniformly Elliptic Operators, V. Burenkov, P.D. Lamberti.- Conductor Inequalities and Criteria for Sobolev - Lorentz Two - Weight Inequalities, S. Costea, V. Maz'ya.- Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones, S. Dahlke, W. Sickel.- Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations, V. Galaktionov et al.- Lq,p-Cohomology of Riemannian Manifolds with Negative Curvature, V. Gol'dshtein, M. Troyanov.- Volume Growth and Escape Rate of Brownian Motion on a Cartan-Hadamard Manifold, A. Grigor'yan, E. Hsu.- Sobolev Estimates for the Green Potential Associated with the Robin-Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition, T. Jakab et al.- Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains, S. Nazarov.- Estimates for Completeley Integrable Systems of Differential Operators and Applications, Y. Reshetnyak.- Counting Schrödinger Boundstates: Semiclassics and Beyond, G. Rozenblum, M. Solomyak.- Function Spaces on Cellular Domains, H. Triebel.
Cellular domains play vital roles in a wide range of cellularfunctions. Defining cellular domains and understanding themolecular basis of their formation is essential to the study ofcell functionality. This authoritative reference provides the mostcomprehensive analysis available on cellular domains, with emphasison the definition and molecular composition of the domain as wellas the functional implications of domain organization.
When one is immersed in the fascinating world of neuroscience findings, the brain might start to seem like a collection of 'modules,' each specializes in a specific mental feat. But just like in other domains of Nature, it is possible that much of the brain and mind's operation can be explained with a small set of universal principles. Given exciting recent developments in theory, empirical findings and computational studies, it seems that the generation of predictions might be one strong candidate for such a universal principle. This is the focus of Predictions in the brain. From the predictions required when a rat navigates a maze to food-caching in scrub-jays; from predictions essential in decision-making to social interactions; from predictions in the retina to the prefrontal cortex; and from predictions in early development to foresight in non-humans. The perspectives represented in this collection span a spectrum from the cellular underpinnings to the computational principles underlying future-related mental processes, and from systems neuroscience to cognition and emotion. In spite of this diversity, they share some core elements. Memory, for instance, is critical in any framework that explains predictions. In asking 'what is next?' our brains have to refer to memory and experience on the way to simulating our mental future. But as much as this collection offers answers to important questions, it raises and emphasizes outstanding ones. How are experiences coded optimally to afford using them for predictions? How do we construct a new simulation from separate memories? How specific in detail are future-oriented thoughts, and when do they rely on imagery, concepts or language? Therefore, in addition to presenting the state-of-the-art of research and ideas about predictions as a universal principle in mind and brain, it is hoped that this collection will stimulate important new research into the foundations of our mental lives.
Examines new research on the role of cholesterol inregulating ion channels and receptors and its effect onhealth Drawing together and analyzing all the latest research findings,this book explores the role of cholesterol in the regulation of ionchannels and receptors, including its pathological effects. It isthe first book to comprehensively describe the complex mechanismsby which cholesterol regulates two major classes of membraneproteins. Moreover, it sheds new light on how cholesterol affectsessential cellular functions such as the contraction of the heart,propagation of nerve impulses, and regulation of blood pressure andkidney function. Written and edited by leading pioneers in the field,Cholesterol Regulation of Ion Channels and Receptors isdivided into three parts: * Part I, Cholesterol Regulation of Membrane Properties,introduces the heterogeneity of cholesterol distribution inbiological membranes and the physical and biological implicationsof the formation of cholesterol-rich membrane domains. * Part II, Cholesterol Regulation of Ion Channels,examines the mechanisms underlying cholesterol sensitivities of ionchannels, including the regulation of ion channels by cholesterolas a boundary lipid. * Part III, Cholesterol Regulation of Receptors, exploresthe latest discoveries concerning how cholesterol regulatesdistinct types of receptors, including G-protein coupled receptors,LDL and scavenger receptors, and innate immune systemreceptors. Increased levels of cholesterol represent a major health risk.Understanding cholesterol regulation of ion channels and receptorsis essential for facilitating the development of new therapeuticstrategies to alleviate the impact of pathological cholesterolconditions. With this book as their guide, readers have access tothe most current knowledge in the field.
What does it mean to find a gene or set of genes that are associated with ADHD, schizophrenia, or autism? Could we eradicate such diseases from our species through gene therapy? Is it possible to eradicate from our genome the genetic material that predisposes us to be too aggressive, too shy, less intelligent, or not active enough? Who has the political power and/or moral authority to make these decisions? The premise of Nature and Nurture is that the complexity of the transactions between nature and nurture--between genes and the environment from the cellular to the cultural level--make these questions incredibly complex and in need of careful attention by educators, scientists, the public, and policymakers. A product of the conference held at Brown University in 2001, this book suggests that genes and environments work together interactively in a complex and closely intertwined fashion. The contributors to this book--biologists, psychologists, psychiatrists, and economists--present knowledge that enables research and application to transcend the traditional question of whatever variance or significance is attributed to genetics versus environment in the development of a particular behavioral trait. This book presents a variety of views on the current status of knowledge about the ways in which dynamic, developmental, mutually interactive systems in the genetic and environmental domains operate. The chapters represent contributions from different perspectives.
The endoplasmic reticulum (ER), called 'the mother of all membranes,' is spotlighted in this timely new book. The work presented here is especially exciting since GFP-technology has provided new ways of looking at the dynamics of the ER and its relationship to other organelles, particularly the Golgi apparatus and peroxisomes. This book provides in-depth knowledge of the ER and the diverse roles it plays, for instance, in protein trafficking, homeostasis of cellular calcium, plant hormone and lipid synthesis. These manifold activities are reflected in the great plasticity of the ER as a structure, with more than a dozen specialized domains recognized for this organelle. TOC:The Morphology and Dynamics of the ER.- Targeting of RNAs to ER Subdomains and its Relationship to Protein Localization.- The ER Folding Helpers: A Connection Between Protein Maturation, Stress Responses and Plant Development.- Endoplasmic Reticulum-associated Protein Degradation in Plant Cells.- ER-to-Golgi Transport: The COPII-Pathway.- Transport of Proteases to the Vacuole: ER Export Bypassing Golgi?.- Induction of Specialized Compartments from the ER.- Synthesis of Structural and Storage Lipids by the ER.- Oleosins and Endoplasmic Reticulum in Seeds and Anthers.- Participation of the Plant ER in Peroxisomal Biogenesis.- The ER and Plant Hormones.- The ER and Cell Calcium.- The ER Within Plasmodesmata.- The ER in Replication of Positive-Strand RNA Viruses.
Fluorescence reporter is the key element of any sensing or imaging technology. Its optimal choice and implementation is very important for increasing the sensitivity, precision, multiplexing power, and also the spectral, temporal, and spatial reso- tion in different methods of research and practical analysis. Therefore, design of ?uorescence reporters with advanced properties is one of the most important problems. In this volume, top experts in this ?eld provide advanced knowledge on the design and properties of ?uorescent dyes. Organic dyes were the ?rst ?uorescent materials used for analytical purposes, and we observe that they retain their leading positions against strong competition of new materials - conjugated polymers, semiconductor nanocrystals, and metal chelating complexes. Recently, molecular and cellular biology got a valuable tool of organic ?uorophores synt- sized by cell machinery and incorporated into green ?uorescent protein and its analogs. Demands of various ?uorescence techniques operating in spectral, anisotropy, and time domains require focused design of ?uorescence reporters well adapted to these techniques. Near-IR spectral range becomes more and more attractive for various applications, and new dyes emitting in this range are strongly requested. Two-photonic ?uorescence has become one of the major tools in bioimaging, and ?uorescence reporters well adapted to this technique are in urgent need. These problems cannot be solved without the knowledge of fundamental principles of dye design and of physical phenomena behind their ?uorescence response.
A step-by-step guide to using computational tools to solve problems in cell biology Combining expert discussion with examples that can be reproduced by the reader, this text introduces an array of informatics tools that are available for analyzing biological data and modeling cellular processes. You learn to fully leverage public databases and create your own computational models. All that you need is a working knowledge of algebra and cellular biology; the author provides all the other tools you need to understand the necessary statistical and mathematical methods. Coverage is divided into two main categories: * Molecular sequence database chapters are dedicated to gaining an understanding of tools and strategies-including queries, alignment methods, and statistical significance measures-needed to improve searches for sequence similarity, protein families, and putative functional domains. Discussions of sequence alignments and biological database searching focus on publicly available resources used for background research and the characterization of novel gene products. * Modeling chapters take you through all the steps involved in creating a computational model for such basic research areas as cell cycle, calcium dynamics, and glycolysis. Each chapter introduces a new simulation tooland is based on published research. The combination creates a rich context for ongoing skill and knowledge development in modeling biological research systems. Students and professional cell biologists can develop the basic skills needed to learn computational cell biology. This text, with its step-by-step instruction, enables you to test and develop your new bioinformatics and modeling skills. References are provided to help you take advantage of more advanced techniques, technologies, and training.
This book deals with the role of water in cell function. Though long recognized to be central to cell function, water's role has not received the attention lately that it deserves. This book brings the role of water front and central. It presents the most recent work of the leading authorities on the subject, culminating in a series of sometimes astonishing observations. Water is a subject of interest to virtually everyone. It is becoming increasingly important in health therapy, in the environment, in chemistry and physics, and certainly in cells. Thus, this groundbreaking volume will be of great interest to a broad audience, well beyond those in biology alone. The reader will be richly awarded with insights difficult or impossible to obtain in current textbooks, which generally treat water merely as a background carrier with limited significance. TOC:Preface.- A Convergence of Experimental and Theoretical Breakthroughs Affirms the PM theory of Dynamically Structures Cell Water on the Theory's 40th Birthday.- Molecular Basis of Articular Disk Biomechanics: Fluid Flow and Water Content in the Temporomandibular Disk as related to distribution of sulfur.- Coherent domains in the streaming of cytoplasm of a giant algal cell.- The glassy state of water: A 'stop and go' device for biological processes.- Information exchange within intracellular water.- Biology's unique phase transition drives cell function.- The effects of static magnetic fields, low frequency electromagnetic field and mechanical vibration on some physicochemical properties of water.- Solute exclusion and potential distribution near hydrophilic surfaces.- Vicinal Hydration of Biopolymers: Cell Biological Consequences.- The Liquid Crystalline organism and biological water.- The unfolded protein state revisited.- Some properties of interfacial water: determinant for cell architecture and function?- Domain potential in hydrogels of Poly(methacryic acid) and its potassium salt.- Biological significance of active oxygen-dependent processes in aqueous systems.- The comprehensive Experimental Research on the Autothixotropy of water.- Non-bulk-like water in cellular interfaces.- The physical nature of the biological signal, a puzzling phenomenon: The critical contribution of Jaques Beveniste.- Index.