This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.

An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.

This book addresses the molecular bases of some of the most important biochemical rhythms known at the cellular level. The approach rests on the analysis of theoretical models closely related to experimental observations. Among the main rhythms considered are glycolytic oscillations observed in yeast and muscle, oscillations of cyclic AMP in Dictyostelium amoebae, intracellular calcium oscillation observed in a variety of cell types, the mitotic oscillator that drives the cell division cycle in eukaryotes, pulsatile hormone signaling, and circadian rhythms in Drosophila. This book will be of interest to life scientists such as biochemists, cell biologists, chronobiologists, medical scientists and pharmacologists. In addition, it will appeal to scientists studying nonlinear phenomena, including oscillations and chaos, in chemistry, physics, mathematics and theoretical biology.

This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas. .

Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation. It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different type of expertise. Instead certain classes of biological oscillators are described, and then only in as much detail as required for the study of their dynamics. The opening chapter reviews fundamental mathematical concepts and techniques which will be used in the remainder of the book. These include phase plane techniques; asymptotic techniques of Krylov, Bogoliubov, and Mitopolski; and the describing function. Subsequent chapters discuss examples of biological oscillators; phase shifts and phase response curves; the entrainment of oscillators by external inputs; the dynamics of circadian oscillators; effects of changing environment on the dynamics of biological oscillators; the features peculiar to populations of interacting oscillators; and biological phenomena attributable to populations of oscillators.

Written for intermediate-level undergraduates pursuing any science or engineering major, Physical Models of Living Systems helps students develop many of the competencies that form the basis of the new MCAT2015. The only prerequisite is first-year physics. With the more advanced "Track-2" sections at the end of each chapter, the book can be used in graduate-level courses as well.

The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of interdisciplinary concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals and chaos. It comprises 18 chapters written by leading figures in the field and covers experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. This book will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.

We present examples of familiar phenomena found in nonequilibrium systems, including oscillatory phenomena, order-formation processes, and pattern formation. In particular, we introduce commonly used mathematical methods to analyze their characteristics. First, we present oscillations described by the Lotka–Volterra and van der Pol equations, the Brusselator, the Oregonator, and relaxation oscillations as examples of oscillatory phenomena. Second, we investigate the order-formation process in colloidal crystals and present an experimental observation of 2D array formation. Third, we demonstrate pattern formation in crystals on the basis of the Mullins–Sekerka instability, and in chemical and biological systems on the basis of the Turing instability. In particular, we describe the optical properties and development of sophisticated structural patterns that directly interact with light. Finally, we briefly describe a theoretical phase-transition analogy that might clarify the concept of order formation in nonequilibrium systems.

As stated by Buckminster Fuller in Operation Manual for Spaceship Earth, "Synergy is the behavior of whole systems unpredicted by separately observed behaviors of any of the system's separate parts". In a similar vein, one might define an intellectual synergy as "an improvement in our understanding of the behavior of a system unpredicted by separately acquired viewpoints of the activities of such a system". Such considerations underlie, and provide a motivation for, an interdisciplinary approach to the problem of unraveling the deeper mysteries of cellular metabolism and organization, and have led a number of pioneering spirits, many represen ted in the pages which follow, to consider biological systems from an elec trochemical standpoint. is itself, of course, an interdisciplinary branch of Now electrochemistry science, and there is no doubt that many were introduced to it via Bockris and Reddy's outstanding, wide-ranging and celebrated textbook Modern Electrochemistry. If I am to stick my neck out, and seek to define bioelec trochemistry, I would take it to refer to "the study of the mutual interac tions of electrical fields and biological materials, including living systems".

The articles in this volume are based on papers presented at the International Symposium in Bad Neuenahr November 29 - December 1, 1982. The meeting was directed by H. Frohlich and was sponsored by IBM Deutschland through its Science and Education Programs Department. Contents Coherence in Biology H. Frohlich . Coherent Excitations and Raman Effect F. Drissler and L. Santo (With 4 Figures) 6 The Non-thermal Effect of Millimeter Wave Radiation on the Puffing of Giant Chromosomes F. Kremer, C. Koschnitzke, L. Santo, P. Quick, and A. Poglitsch (With 4 Figures) 10 Nonthermal Resonant Effects of 42 GHz Microwaves on the Growth of Yeast Cultures W. Grundler, F. Keilmann, V. Putterlik, L. Santo, D. Strube, and I. Zimmermann (With 15 Figures) 21 On the Microwave Response of the Drosophila Melanogaster G. Nimtz (With 5 Figures) 38 Effects of Low-level Millimeter Waves on Cellular and Subcellular Systems S. M. Motzkin, L. Benes, N. Block, B. Israel, N. May, J. Kuriyel, L. Birenbaum, S. Rosenthal, and Q. Han (With 12 Figures). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Millimeter-wave and Far-infrared Spec roscopy on Biological Macromolecules L. Genzel, F. Kremer, A. Poglitsch, and G. Bechtold (With 10 Figures). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Excitation of Proteins by Electric Fields J. B. Hasted, S. K. Husain, A. Y. Ko, D. Rosen, E. Nicol, and J. R. Birch (With 8 Figures) 71 Isotope Effects and Collective Excitations M. U. Palma (With 3 Figures) 84 Long-range Energy Continua in the Living Cell: Protochemical Considerations G. R. Welch and M. N. Berry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .