Mathematical Theory of Sedimentation Analysis deals with ultracentrifugal analysis. The book reviews flow equations for the ultracentrifuge, for two component systems, for multicomponent systems, and in chemically reacting systems. It explains the Svedberg equation and its extensions, and also the tests of the Onsager reciprocal relation. By employing a system consisting of two strong electrolytes and a solvent, the book illustrates that the sedimentation processes can be treated in terms of thermodynamics of irreversible processes. It also explains sedimentation-diffusion equilibrium and an approach to sedimentation equilibrium. It reviews the prediction of the time required to reach equilibrium, the estimates being made by Weaver (1926), and by Mason and Weaver (1924). The book employs sedimentation in a sector-shaped cell in a centrifugal field, of which the solutions of Mason and Weaver closely approximate the actual concentration distribution in the ultra-centrifuge cell. Other accurate solutions are by Fujita, Nazarian (1958), Yphantis, and Waugh. The book will prove valuable for mathematicians, physical chemists, biophysical chemists students, or professor of advanced mathematics.
Mathematical Theory of Sedimentation Analysis presents the flow equations for the ultracentrifuge. This book is organized into two parts encompassing six chapters that evaluate the systems of reacting components, the differential equations for the ultracentrifuge, and the case of negligible diffusion. The first chapters consider the Archibald method for molecular weight determination; pressure-dependent sedimentation; expressions for the refractive index and its gradient; relation between refractive index and concentration; and the analysis of Gaussian distribution. Other chapters deal with the basic equations for three-component systems, the extension of the Archibald method to multicomponent systems, and the case of independent sedimentation and diffusion. These topics are followed by a presentation of the extrapolation procedures due to Oth and Desreux. The last chapters are devoted to the examination of the Johnston-Ogston effect and sedimentation with a differential boundary. The book can provide useful information to chemists, physicists, students, and researchers.
The aim of this book is to present a rigorous phenomenological and mathematical formulation of sedimentation processes and to show how this theory can be applied to the design and control of continuous thickeners. The book is directed to stu dents and researchers in applied mathematics and engineering sciences, especially in metallurgical, chemical, mechanical and civil engineering, and to practicing en gineers in the process industries. Such a vast and diverse audience should read this book differently. For this reason we have organized the chapters in such a way that the book can be read in two ways. Engineers and engineering students will find a rigorous formulation of the mathematical model of sedimentation and the exact and approximate solutions for the most important problems encountered in the laboratory and in industry in Chapters 1 to 3, 7 and 8, and 10 to 12, which form a self-contained subject. They can skip Chapters 4 to 6 and 9, which are most important to applied mathematicians, without losing the main features of sedimentation processes. On the other hand, applied mathematicians will find special interest in Chapters 4 to 6 and 9 which show some known but many recent results in the field of conservation laws of quasilinear hyperbolic and degenerate parabolic equations of great interest today. These two approaches to the theory keep their own styles: the mathematical approach with theorems and proofs, and the phenomenological approach with its deductive technique.
"This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it." --Pierre C. Sabatier "This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today – optical, acoustical, radar, etc.... I believe it will find widespread use and value." --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics "The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging." --Mario Bertero, Professor, University of Geneva "a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications." --Prof. Ian Proudler, Loughborough University "a ‘must have’ for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion.... I strongly recommend it." --Michael A.? Fiddy, Professor, University of North Carolina at Charlotte This book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with "continuous" data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.
Analytical ultracentrifugation has become an increasingly important technique for monitoring the size and shape of biological macromolecules. Analytical Ultracentrifugation: Techniques and Methods contains contributions from experts in the field, bringing together the multitude of developments that have taken place in instrumentation and analysis over the past decade into a single volume. This book covers the latest methods in analysis along with an extensive introduction for the novice user. Analysis methods in both sedimentation velocity and sedimentation equilibrium are discussed at length. Protein, protein/DNA, membrane proteins and polymer systems are also explored, along with software developments and non-ideality.
Analytical Ultracentrifugation, the latest volume in Methods in Enzymology, focuses on analytical ultracentrifugation. The scope of this technique has greatly expanded in recent years due to advances in instrumentation, algorithms and software. This volume describes the latest innovations in the field and in the applications of analytical ultracentrifugation in the analysis of macromolecules, macromolecular assemblies, and biopharmaceuticals. - Timely contribution that describes a rapidly changing field - Leading researchers in the field - Broad coverage: instrumentation, basic theory, data analysis, and applications
As a distinct class of macromolecules, viruses are continually being studied in order to determine their properties. Following a knowledge of host-range infectivity, the particle mass-molecular weight of the virus and related properties - including size, shape, sedimentation, and diffusion coefficients - are also important characterizations. In the literature, these values have been determined for many viruses, and a variety of techniques are available by which such properties may be analyzed. Until now, there has been no single source for such information that the interested investigator may consult, and no databases provided this kind of information. CRC Handbook of Viruses: Mass-Molecular Weight Values and Related Properties corrects this deficiency by presenting such data for all classes of viruses; centering on viruses, their molecular weight, and their related properties; and acquainting the investigator to many methods for obtaining the mass-molecular weight value of viruses. This singular study explains the variety of methods available to the researcher as well as provides examples of each method. Molecular weight values are accessed directly from the book, saving the investigator a tedious search through the range of literature. Chapters discuss: Viruses as infectious agents and their role in establishing the relatively new discipline of molecular biology Essential components of viruses, protein, and nucleic acid - considering their discovery, nature, structural organization, and the forming of viruses from nucleoproteins Basic aspects of virus purification, preparative centrifuge, and various purification methods Basic aspects of crystallography, including procedures, x-ray analysis of the viral protein component, the arranging of subunits, and the composition of the intact virus Sedimentation experiments and studies used to obtain molecular weight Sedimentation and diffusion coefficients integral to the basic Svedberg equation Sedimentation equilibrium procedures The new Beckman Optima series of analytical ultracentrifuges Scattering studies, including small angle x-ray, small angle neutron, classical light scattering, and electron microscopy The renaissance of instrumentation in classical light scattering techniques Cold neutron facilities currently being set into operation by government laboratories Sizing and solvation of viruses in solution - their "natural environment" Critical modeling experiments Facilities and instrumentation for molecular weight studies - including the high voltage transmission electron microscope for obtaining mass values of viral inclusion bodies CRC Handbook of Viruses serves the: Researcher seeking values of virus molecular weight and related parameters Investigator getting started in virology and seeking information on physical chemical procedures Student interested in viruses as infectious agents
This book introduces analytical ultracentrifugation (AUC) as a whole, covering essential theoretical and practical aspects as well as its applications in both biological and non-biological systems. Comprehensive characterizations of macromolecules in a solution are now routinely required not only for understanding the solution system but also for producing a solution with better properties. Analytical ultracentrifugation is one of most powerful and reliable techniques for studying the biophysical behavior of solutes in solution. In the last few years, there have been steady advances made in hardware, software, and applications for AUC. This book provides chapters that cover everything essential for beginners to the most advanced users and also offer updated knowledge of the field on advances in hardware, software, and applications. Recent development of hardware described in this book covers new detection systems that give added dimensions to AUC. Examples of data analysis with essential theoretical explanations for advanced and recently updated software are also introduced. Besides AUC of biological systems including membrane proteins and biopharmaceuticals, AUC applications for non-biological questions are included. AUC studies under non-ideal conditions such as highly concentrated solutions and solutions with high salt concentration are also included. The contributors to this book are leading researchers in the fields of solution biophysics and physical chemistry who extensively employ AUC analysis for their research. From this published work, one can gain new and comprehensive knowledge of recent AUC analysis.
There are numerous examples in the history of science when the parallel develop ments of two or more disciplines, methodologies, technologies or theoretical in sights have converged to produce significant scientific advances. The decades following the 1950s have produced several such significant advances, as a result of a convergence of developments in molecular biology and in solid state-based electronics instrumentation. Since one of these areas of significant advancement, analytical ultracentrifu gation, has been undergoing a renaissance, we thought it would be a useful activity to call upon a group of researchers who have been developing either the experi mental or theoretical aspects of the methodology and gather in one place a group of articles summarizing the current status of the field. The success of recombinant DNA methodologies at producing biologically active macromolecules of commer cial interest has evoked interests in mechanisms of function. Pursuit of the related questions has emphasized the importance of studies of macromolecular binding and interaction. Several contributions to this volume remind us that analytical ultra centrifugation is rigorously based on solid thermodynamic theory and, as such, is fully capable of providing comprehensive quantitative descriptions of molecular interactions in solution. Furthermore, a number of the chapters provide examples, along with innovative methods for carrying out these characterizations. The past decade has seen several developments that reflect the rebirth of interest in analytical ultracentrifugation.
