Foundations Of Mathematical Biology Supercellular Systems

Subcellular systems; The nature of hierarchical control in living matter; Chemical kinetics and enzyme kinetics; Quantum genetics; Excitability phenomena in membranes; Cellular systems; Morphogenesis; Mechanics of epigenetic control; Automata theory in the context of theoretical embryology; Some relational cell models: the metabolism-repair systems; Compartments; Supercellular systems; Physiological regulation and control; Mathematical aspects of some cardiovascular phenomena; A unified approach to physics, biology, and sociology; Automata theory in the context of theoretical neurophysiology; The deterministic theory of population dynamics; Is there a unified mathematical biology?

Foundations of Mathematical Biology, Volume 1, Subcellular Systems, provides an introduction the place of mathematical biology in relation to the other biological, physical, and organizational sciences. It discusses the use of mathematical tools and techniques to solve biological problems. The book contains four chapters and begins with a discussion of the nature of hierarchical control in living matter. This is followed by a chapter on chemical kinetics and enzyme kinetics, covering the physicomathematical principles, models, and approximations underlying transition-state theory and the unimolecular reaction. Subsequent chapters deal with quantum genetics and membrane excitability.

Foundations of Mathematical Biology, Volume II: Cellular Systems describes the properties of cellular systems and their relationship to the development of multicellular organisms. This volume is composed of five chapters that present the mathematical tools applied in evaluating these systems. Chapters 1 illustrates the use of continuous time systems to examine the relationship between the properties of individual cells and the general problems of morphogenesis in developing systems, specifically how these properties could manifest themselves in morphological terms. Chapter 2 demonstrates the systems of rate equations or first-order differential equations to deal with the regulation of individual chemical processes and sequences of such processes, at both the genetic and metabolic levels. Chapter 3 discusses the application of the theory of automata to the evaluation of the concept and principles of embryology, while Chapter 4 presents some relational cell models to study the metabolism-repair cellular systems. Chapter 5 looks into the concept and systems of a compartment. This book will prove useful to mathematical and cell biologists and researchers.