Thermodynamic Network Analysis of Biological Systems This book is devoted to the question: What fundamental ideas and concepts can phys­ ics contribute to the analysis of complex systems like those in biology and ecolo­ gy The book originated from two lectures which I gave during the winter term 1974 75 and the summer term 1976 at the Rheinisch Westfalische Technische Hoch­ schule in Aachen. The wish for a lecture with this kind of subject was brought forward by students of physics as well as by those from other disciplines like biology physiology and engineering sciences. The students of physics were look­ ing for ways which might lead them from their monodisciplinary studies into the interdisciplinary field between physics and life sciences. The students from the other disciplines suspected that there might be helpful physical concepts and ideas for the analysis of complex systems they ought to become acquainted with. It is clear that a lecture or a book which tries to realize the expectations of both these groups will meet with difficulties arising from the different train­ ings and background knowledge of physicists and nonphysicists. For the physicists I have tried to give a brief description of the biological aspect and significance of a problem wherever it seems necessary and appropriate and as far as a physicist like me feels authorized to do so. 1. Introduction 2. Models 2.1 The Purpose and Nature of Models 2.2 Enzyme Catalyzed Reactions and the Michaelis Menten Kinetics 2.3 Transport Across Membranes: A Black Box Approach 2.4 Excitation of the Nervous Membrane: Hodgkin Huxley Equations 2.5 A Cooperative Model for Nerve Excitation 2.6 The Volterra Lotka Model 2.7 A Model for the Control of Metabolic Reaction Chains 3. Thermodynamics 3.1 Thermodynamics Systems 3.2 The First Law of Thermodynamics 3.3 The Second Law of Thermodynamics 3.4 Temperature and Transfer of Heat 3.5 Chemical Potential and the Transfer of Matter 3.6 Chemical Reactions 3.7 Some Basic Relations of Equilibrium Thermodynamics 3.8 Perfect Gases and Ideal Mixtures 3.9 Linear Irreversible Thermodynamics 4. Networks 4.1 Network Language and Its Processes 4.2 Storage Elements: Generalized Capacitances 4.3 Kirchhoff’s Current Law and the 0 Junction 4.4 Unimolecular Reactions 4.5 Higher Order Reactions Kirchhoff’s Voltage Law and the 1 Junction 4.6 Diffusion 5. Networks for Transport Across Membranes 5.1 Pore Models 5.2 Pore Blocking 5.3 Self Blocking of Pores 5.4 Carrier Models 5.5 Active Transport 5.6 Hodgkin Huxley Equations and the Coupling of Material and Electric Flux 5.7 Nernst Planck Equations 6. Feedback Networks 6.1 Autocatalytic Feedback Loops 6.2 An Autocatalytic Excitation Model 6.3 Networks of Al Elements 6.4 Limit Cycle Networks 7. Stability 7.1 Capacitances as Thermodynamic Equilibrium Systems 7.2 Stability of the Equilibrium State 7.3 Tellegen’s Theorem and Liapunov Stability of the EquilibriumH 7.4 Glansdorff Prigogine Criterion for the Stability of Nonequilibrium Steady States 7.5 Uniqueness of Steady States 7.6 Globally and Asymptotically Stable Networks 7.7 Global Stability Techniques References.