Control of Metabolic Oscillations: Unpredictability, Critical Slowing Down, Optimal Stability and Hysteresis
Control analysis can be divided into three main areas. The first deals with systems in the steady state and is discussed in most of the contributions to the present volume. The second deals with time-dependent sensitivity coefficients of the first and second order (Larter et al., 1984; Edelson & Rabitz, 1985), sensitivity densities (Larter et al., 1983, 1984), as well as control and elasticity coefficients (Kohn et al., 1979; see also Chapter 25 by Acerenza in this book). The third is concerned with time-independent coefficients of time-dependent (oscillatory) processes, such as period sensitivities (Larter et al., 1984; Edelson & Rabitz, 1985) or control coefficients, as discussed by Acerenza in Chapter 25 of this book. We shall deal with this third area in the present contribution.
KeywordsPyruvate Kinase Chaotic Oscillation Maximum Lyapunov Exponent Control Coefficient Optimal Stability
Unable to display preview. Download preview PDF.
- Acerenza, L., Sauro, H. M. & Kacser, H. (1989) J. Theor. Biol.,in pressGoogle Scholar
- Edelson, D. & Rabitz, H. (1985) in Oscillations and Travelling Waves in Chemical Systems (Field, R. J. & Burger, M., eds.), pp. 193–222, J. Wiley, New YorkGoogle Scholar
- Hess, B. (1966) Studia Biophysica sl,s41-s63Google Scholar
- Hess, B. & Markus, M. (1984) in Synergetics — From Microscopic to Macroscopic Order (Frehland, E., ed.), pp. 6–16, Springer-Verlag, BerlinGoogle Scholar
- Hess, B. & Markus, M. (1985a) in Temporal Order (Rensing, L. & Jaeger, N.I., eds.), pp. 179–190, Springer-Verlag, BerlinGoogle Scholar
- Hess, B. & Markus, M. (19856) Ber. Bunsenges. Phys. Chem. 89,642–651Google Scholar
- L’vov, V.S., Predtechensky, A.A. & Chemikh, A.I. (1981) Soviet Physics JETP 53, 562–581Google Scholar
- Markus, M. & Hess, B. (1985a) in Temporal Order (Rensing, L. & Jaeger, N.I., eds.), pp. 191–193, Springer-Verlag, BerlinGoogle Scholar
- Markus, M., Kuschmitz, D. & Hess, B. (1985b)Biophys. Chem. 22,95–105Google Scholar
- Markus, M. & Hess, B. (1986) in Dynamics of Biochemical Systems (Damjanovich, S., Keleti, T. & Trion, L., eds.), pp. 11–25, Akadémiai Kiad6, BudapestGoogle Scholar
- Schuster, H. G. (1984) Deterministic Chaos, Physik-Verlag, WeinheimGoogle Scholar
- Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. (1985) Physica 16D, 285–317Google Scholar