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.

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.

The Biological Clock describes the rhythmic processes in a great variety of plants and animals. This book is an outgrowth of the 1969 James Arthur Lecture Series on "Time and its Mysteries" held at New York University. This three-chapter work begins with the basic principles of biological rhythms and clocks, along with various diagrams to illustrate some aspects of circadian rhythms in animals. The second chapter discusses the hypothesis of environmental timing of the clock. This chapter explores numerous research studies on phenomenon of biological rhythms, the nature of the rhythmic mechanism, and hormonal regulation. The third chapter examines the cellular-biochemical clock hypothesis and its contribution in the progress of understanding the complexity of biological rhythm. This book is intended primarily for biologists, behaviorists, and researchers.

Popular science at its most exciting: the breaking new world of chronobiology - understanding the rhythm of life in humans and all plants and animals. The entire natural world is full of rhythms. The early bird catches the worm -and migrates to an internal calendar. Dormice hibernate away the winter. Plants open and close their flowers at the same hour each day. Bees search out nectar-rich flowers day after day. There are cicadas that can breed for only two weeks every 17 years. And in humans: why are people who work anti-social shifts more illness prone and die younger? What is jet-lag and can anything help? Why do teenagers refuse to get up in the morning, and are the rest of us really 'larks' or 'owls'? Why are most people born (and die) between 3am-5am? And should patients be given medicines (and operations) at set times of day, because the body reacts so differently in the morning, evening and at night? The answers lie in our biological clocks the mechanisms which give order to all living things. They impose a structure that enables us to change our behaviour in relation to the time of day, month or year. They are reset at sunrise and sunset each day to link astronomical time with an organism's internal time.

This book is a concise, comprehensive and up-to-date account of fundamental concepts and potential applications of biological timekeeping mechanisms in animals and humans. It also discusses significant aspects of the organization and importance of timekeeping mechanisms in both groups. Divided into seven sections, it addresses important aspects including fundamental concepts; animal and human clocks; clock interactions; clocks and metabolism and immune functions; pineal, melatonin and timekeeping; and clocks, photoperiodism and seasonal behaviours. The book also focuses on biological clock applications in a 24x7 human society, particularly in connection with life-style associated disorders like obesity and diabetes. It is a valuable resource for advanced undergraduates, researchers and professionals engaged in the study of the science of biological timekeeping.

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.

With the invitation to edit this volume, I wanted to take the opportunity to assemble reviews on different aspects of circadian clocks and rhythms. Although most c- tributions in this volume focus on mammalian circadian clocks, the historical int- duction and comparative clocks section illustrate the importance of various other organisms in deciphering the mechanisms and principles of circadian biology. Circadian rhythms have been studied for centuries, but only recently, a mole- lar understanding of this process has emerged. This has taken research on circadian clocks from mystic phenomenology to a mechanistic level; chains of molecular events can describe phenomena with remarkable accuracy. Nevertheless, current models of the functioning of circadian clocks are still rudimentary. This is not due to the faultiness of discovered mechanisms, but due to the lack of undiscovered processes involved in contributing to circadian rhythmicity. We know for example, that the general circadian mechanism is not regulated equally in all tissues of m- mals. Hence, a lot still needs to be discovered to get a full understanding of cir- dian rhythms at the systems level. In this respect, technology has advanced at high speed in the last years and provided us with data illustrating the sheer complexity of regulation of physiological processes in organisms. To handle this information, computer aided integration of the results is of utmost importance in order to d- cover novel concepts that ultimately need to be tested experimentally.