Lectures on Mathematics in the Life Sciences – serie

This volume contains 13 selected lectures from the International Workshop on Mathematical and Computational Biology subtitled 'Computational Morphogenesis, Hierarchical Complexity and Digital Evolution' held at the University of Aizu (Japan). This interdisciplinary workshop brought together researchers working on aspects of evolutionary, mathematical, and computational biology that are of particular interest for computer scientists, biologists, and mathematicians. Discussion topics include mathematical approaches for addressing evolutionary problems (such as replication, multicellularity, individuality, and morphogenesis), the theoretical tools for rigorously developing these questions, software systems and applications.Of special concern were self-replication, the evolution of individuality, symbiogenesis, evolutionary developmental biology, computational morphogenesis, interaction dynamics, the evolution and maintenance of sex, and properties of the digital genetic code. Lectures are organized roughly according to increase of biological scale in the order of themes presented at the workshop.

Currently the outstanding problem in muscle contraction is determining the mechanism for the sliding of actin and myosin filaments. This volume contains papers based on lectures presented at the Seventeenth Annual Symposium on Some Mathematical Questions in Biology which was held in conjunction with the Annual Meeting of the AAAS. The six papers deal with overlapping areas of muscle physiology: cross-bridge dynamics (the mechanism currently receiving most attention), as well as distinctions between striated and cardiac muscles and the control of muscular contractions by action potentials.Focusing on both experimental techniques and theoretical underpinnings, the authors present the recent technological advances that provide an improved database for obtaining a better understanding of the biochemical mechanics and developing better mathematical models. In the first article Dr. Hugh E. Huxley reviews current studies of muscle systems which use X-ray diffraction and electron-microscopic analysis.Dr. Even Eisenberg describes how ATP hydrolysis drives muscle contraction via the action of myosin cross-bridges. The next two papers contain mathematical studies of muscle contraction. Dr. Michael Propp uses a thermodynamic formalism to predict the physiological properties of muscle. Drs. H. Michael Lacker and Charles S. Peskin develop a mathematical method for working backwards to determine uniquely microscopic properties of the cross-bridges. Drs. John W. Krueger and Katsuhiko Tsujioka use light diffraction observations to develop a quantitative understanding of cardiac function from properties of the myofibril and elements of the cross-bridge cycle. In the concluding paper, Dr. Robert S. Eisenberg reviews the current work on the electrical control mechanisms in excitation-contraction coupling which lead to muscle contraction.

Several data banks around the world are accumulating DNA sequences at a feverish rate, with tremendous potential for furthering our knowledge of how biological systems code and pass on information. The sophisticated mathematical analysis of that data is just beginning. The Eighteenth Annual Symposium on Some Mathematical Questions in Biology was held in conjunction with the Annual Meeting of the AAAS and brought together speakers knowledgeable in both biology and mathematics to discuss these developments and to emphasize the need for rigorous, efficient computational tools.These computational tools include biologically relevant definitions of sequence similarity and string matching algorithms. The solutions for some of these problems have great generality; the string matching methods first developed for biological sequences have now been applied to areas such as geology, linguistics, and speech recognition. There is a great potential here for creating of new mathematics to handle this growing data base, with new applications for many areas of mathematics, computer science, and statistics.

Distinguishing itself among other books on mathematics in plant biology, this book is unique in that it presents a broad overview of how plant biologists are currently utilizing mathematics in their research, and the only one to particularly emphasize plant ecology. Each article is unified by an attempt to tie models at one level of organization to an understanding at other levels. This approach strengthens the connections between theoretical development and observable biology, facilitating the testing of new predictions. Intended for mathematicians, plant biologists and ecologists alike, this book requires only a basic knowledge of differential equations, linear algebra and mathematical modeling; a knowledge of plant biology is helpful. Readers will gain a perspective on what types of biological systems can benefit from mathematical treatment and an appreciation of the current important problems in plant biology.

The articles in this collection are based on lectures given at the 20th Annual Symposium on Some Mathematical Questions in Biology, held in May 1986, and sponsored jointly by the AMS, the Society for Industrial and Applied Mathematics, and Section A of the American Association for the Advancement of Science. For the past thirty years, due particularly to the fundamental work of Pittendrigh, Aschoff, and Wever, theoretical analysis of circadian rhythms and sleep have gone hand in hand with experimental and clinical studies.Circadian rhythms have been investigated at levels ranging from cell fragments to humans, from biochemistry to behavior. This experimental diversity is reflected in a diversity of modeling approaches, several of which are represented in this collection. One class of models focuses on the circadian sleep and activity cycles of humans, for which some investigators postulate pacemaker systems with two coupled oscillators, while others propose single oscillator models. Other analyses focus upon the activity patterns of small vertebrates or upon anatomical data and physiological recordings. The mathematical formulations and analyses utilize nonlinear dynamical systems, stochastic models, and computer simulations. The articles in this volume discuss, analyze, and compare these various experimental, theoretical, and mathematical approaches.

The seven articles in this volume are based on lectures presented at the annual symposium, Some Mathematical Questions in Biology, held in conjunction with the American Institute of Biological Sciences meeting in Toronto, Ontario in August 1989. Sexual selection, sex determination, and sex allocation have been at the center of evolutionary ecology since its inception and have played an important role in the development of many concepts. As this volume demonstrates, many key questions remain to be investigated through a combination of empirical and theoretical work. In addition, questions of sex provide a natural mechanism for crossing the great taxonomic divide by allowing plant and animal researchers to focus on similar kinds of questions using a wide variety of organisms.

This collection of papers addresses a variety of problems and approaches for predicting spatial effects in ecological systems. The central themes are the characterization of effects, exploration of mechanisms, and understanding of consequences of spatial heterogeneity on ecological systems. Discussed here are the spatial dynamics of natural systems and the impact of economic and sociological changes, as well as recent adaptation methods from statistical lattice physics.Progress in dealing with spatial effects in ecological systems is accelerating as faster computers access the extensive data sets available from remote sensing. The new mathematical approaches presented here will be especially useful for identifying the effect of landscape change on ecosystem productivity and sustainability. Balancing theoretical development and empirical testing, this book provides an excellent introduction to the scope and scale of issues to be addressed in predicting change in ecological systems. Mathematicians and ecologists interested in these issues will find this book useful, and individual chapters will be of interest to physicists, econometricians, landscape ecologists, and human ecologists.