Febs Letters Volume 75, Number 1./Volume 76, Number 1-2. [antikvár]

Volume 75, number 1 FEBS LETTERS March 1977 Meeting Report OSCILLATORY PHENOMENA IN BIOLOGICAL SYSTEMS A. BOITEUX, B. HESS and Th. PLESSER Max-Planck-lmtitut für Ernähningsphysiologie, D-4600 Dortmund, FRC and J. D. MURRAY University of Oxford, Oxford, England Reeeived 17 January 1977 Recently, under the auspices of the European Molecular Biology Organization (EMBO) and supported by the Max-Planck-Gesellschaft and the Deutsche Forschungsgemeinschaft, a workshop on oscillatory phenomena was held, 3-6 October 1976, covering the thermodynamic and kinetic requirements for the generation of periodic phenomena, mathematical methods as well as specific chemical, biochemical and biological systems. 1. General aspects In a fresh look at the fundamentals of oscillatory phenomena, P. H. Richter (Gottingen) discussed general aspects of stability from a fluctuation theory point of view. It was shown how the concept of time reversal could be useful in the study of such phenomena. Using fluctuation theory the onset of periodic behaviour related to symmetry breaking and limit cycle invariance was discussed from the point of view of breaking of time translation invariance. U. F. Franck (Aachen), in a comprehensive survey of experimentally observed oscillations, showed how all of the examples illustrated could be understood on the basis of simultaneous feedback mechanisms. Positive feedback could result in propagation phenomena while negative feedback could initiate recovery and overshoot reactions. J. J. Tyson (Innsbruck) discussed the end-product feedback control in certain biochemical pathways as a general system of «-species. The model system of reaction equations, all of which are linear except that one in which the feedback directly acts, can be represented by an «th-order differential equation of the form where the fc,-, / = 1, . . ., « are related to the rate constants and f{x) is the non-linear feedback term. Useful general results were found and proved for this system with particular emphasis on the existence of periodic solutions. Also presented were some general results on the character and stabihty (both linear and global) of the steady-states: a sound knowledge of these is a necessary prerequisite to establish the presence of periodic solutions. In a methods paper B. L. Clarke (Alberta) presented a method for the study of chemical networks, the basis of which is geometrical in character. It provides useful steady-state stabihty results, which are obtained by a simple computer algorithm. Results, which can be deduced from the application of this approach for feedback cycles of a general character, were illustrated. Simple pedagogic models were described by J. D. Murray (Oxford) for kinematic (diffusionless) waves which have been observed with the Belousov-Zhabotinskii reaction. Some of the pitfalls were noted that can exist in making mathematical and chemical deductions from computed travelling wave solutions North-Holland Publishing Company - Amsterdam 1