This textbook provides an introduction to dynamic modeling in molecular cell biology, taking a computational and intuitive approach. Detailed illustrations, examples, and exercises are included throughout the text. Appendices containing mathematical and computational techniques are provided as a reference tool.

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.

Biological and Biochemical Oscillators compiles papers on biochemical and biological oscillators from a theoretical and experimental standpoint. This book discusses the oscillatory behavior, excitability, and propagation phenomena on membranes and membrane-like interfaces; two-dimensional analysis of chemical oscillators; and chemiluminescence in oscillatory oxidation reactions catalyzed. The problems associated with the computer simulation of oscillating systems; mechanism of single-frequency glycolytic oscillations; excitation wave propagation during heart fibrillation; and biochemical cycle of excitation are also elaborated. This compilation likewise covers the physiological rhythms in Saccharomyces cerevisiae populations; integral and indissociable property of eukaryotic gene-action systems; and role of actidione in the temperature jump response of the circadian rhythm in Euglena gracilis. This publication is valuable to biochemists interested in biochemical and biological oscillations.

As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.

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.

How can we understand the complexity of genes, RNAs, and proteins and the associated regulatory networks? One approach is to look for recurring types of dynamical behavior. Mathematical models prove to be useful, especially models coming from theories of biochemical reactions such as ordinary differential equation models. Clever, careful experiments test these models and their basis in specific theories. This textbook aims to provide advanced students with the tools and insights needed to carry out studies of signal transduction drawing on modeling, theory, and experimentation. Early chapters summarize the basic building blocks of signaling systems: binding/dissociation, synthesis/destruction, and activation/inactivation. Subsequent chapters introduce various basic circuit devices: amplifiers, stabilizers, pulse generators, switches, stochastic spike generators, and oscillators. All chapters consistently use approaches and concepts from chemical kinetics and nonlinear dynamics, including rate-balance analysis, phase plane analysis, nullclines, linear stability analysis, stable nodes, saddles, unstable nodes, stable and unstable spirals, and bifurcations. This textbook seeks to provide quantitatively inclined biologists and biologically inclined physicists with the tools and insights needed to apply modeling and theory to interesting biological processes. Key Features: Full-color illustration program with diagrams to help illuminate the concepts Enables the reader to apply modeling and theory to the biological processes Further Reading for each chapter High-quality figures available for instructors to download