Some Mathematical Questions In Biology Muscle Physiology

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.

As the techniques of modern molecular biology continue to revolutionize experimental design in cell biology, mathematical modeling and analysis become increasingly necessary and feasible. The papers in this collection expand on invited lectures presented at the Symposium on Some Mathematical Questions in Biology: Cell Biology, held in November 1992 in Denver, Colorado. The work reviewed in the papers demonstrates the power of combining mathematics and experiment to study a number of cell processes, including: protein transport in nerve axons, formation of transport vesicles at the Golgi, molecular motion in cell membranes, cell adhesion, T lymphocyte activation, and cellular responses to receptor aggregation. The volume is an important contribution to the literature, as it introduces mathematicians to a growing application area and cell biologists to new tools and results. The individual articles can be used as readings in a course on mathematical modeling.

Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review

The theory of blood circulation is the oldest and most advanced branch of biomechanics, with roots extending back to Huangti and Aristotle, and with contributions from Galileo, Santori, Descartes, Borelli, Harvey, Euler, Hales, Poiseuille, Helmholtz, and many others. It represents a major part of humanity's concept of itself. This book presents selected topics of this great body of ideas from a historical perspective, binding important experiments together with mathematical threads. The objectives and scope of this book remain the same as in the first edition: to present a treatment of circulatory biomechanics from the stand points of engineering, physiology, and medical science, and to develop the subject through a sequence of problems and examples. The name is changed from Biodynamics: Circulation to Biomechanics: Circulation to unify the book with its sister volumes, Biomechanics: Mechanical Properties of Living Tissues, and Biomechanics: Motion, Flow, Stress, and Growth. The major changes made in the new edition are the following: When the first edition went to press in 1984, the question of residual stress in the heart was raised for the first time, and the lung was the only organ analyzed on the basis of solid morphologic data and constitutive equations. The detailed analysis of blood flow in the lung had been done, but the physiological validation experiments had not yet been completed.

It is now widely recognized that fundamental progress in science is made not in a continuous manner but in a stepwise manner. In the field of the molecular mechanism of contraction in striated muscle, the stepwise progress was achieved by three great investigators in 1940's and 1950's. In the early 1940's, Albert Szent-Gyorgyi and his associates showed biochemically that muscle contraction is essentially an interaction between actin and myosin coupled with ATP hydrolysis. Then, in the 1950's, Hugh E. Huxley together with Jean Hanson demonstrated that striated muscle is composed of a hexagonal lattice of two kinds of interdigtating myofilaments consisting of action and myosin respectively, and made a monumental discovery that muscle contraction results from the relative sliding between the actin and myosin filaments. Andrew F. Huxley, who also participated in the discovery of the sliding filament mechanism of muscle contraction was attributed to the attachment-detachment cycle between the cross-bridges extending from the myosin filament and the complementary sites on the actin filament. After the above stepwise progress, however, muscle research appears to have entered into a period of so-called 'normal science' where detailed knowledge has been accumulating around the well established 'central dogmas' but without fundamental progress. More specifically, most experiments on muscle contraction mechanisms have been designed, carried out and interpreted on the basis of the Huxley's 1957 and the Huxley-Simmons' 1971 contraction models, as well as the kinetic scheme of actomyosin ATPase; but the molecular mechanism of contraction still remains to be a matter for debate and speculation. For further fundamental progress in this field of research, we feel it necessary to reconsider the validity of these dogmas and to interpret the results more freely. In 1978, one of us (H.S.) organized a symposium in Tokyo based on the above idea, and we published the proceedings under the title of "Cross-bridge Mechanism in Muscle Contraction" (ed. H. Sugi and G.H. Pollack, University of Tokyo Press/University Park Press, 1979). The unusual interest of muscle physiologists in this symposium encouraged us to organize a second symposium on muscle contraction in Seattle in 1982, and proceedings was again published under the title of "Contractile Mechanisms in Muscle" (ed. G.H. Pollack and H. Sugi, Plenum Publishing Corporation, 1984). We were again very much encouraged by the intense interest of the people at the symposium as well as by readers of the proceedings, and became convinced that the symposia of this kind would greatly accelerate the progress in this field. The present symposium was organized by one of us (H.S.) as the third "Cross-bride" symposium. Though most papers are concerned, as in the previous two symposia, with experiments on intact and demembranated muscle fibers and isolated myofibrils, where the three-Dimensional muofilament-lattice structures have been preserved, the results are frequently discussed in connection with the kinetics of actomyosin ATPase, reflecting the recent development of experimental methods connecting physiology and biochemistry. It has also become possible to obtain direct information about the orientation and configuration of the cross-bridges as various stages during muscle contraction.