The Diversity of Biochemical Time Patterns

The effects of coupling of oscillating glycolysis and oscillating substrate supply are investigated with a two-enzyme model using detailed two-substrate rate laws for both enzymes. Under a sinusoidal substrate supply rate, a profusion of entrained, quasiperiodic and chaotic regimes is obtained. Periodic modulation of the sinusoidal supply rate may lead to a considerable enhancement of the degree of randomness in the chaotic regime. Up to four coexisting attractors are found in phase space for a given set of control parameters, having complicatedly interleaved basins of attraction. Switching between such coexisting attractors is accomplished by pulsed substrate fluctuations that drive the system from one basin of attraction to the other. The effect of a series of substrate fluctuations with randomly distributed amplitudes is investigated, allowing the following distinction of cases: 1. For small fluctuations, the system stays within a given basin thus preserving the initial time pattern. 2. For larger fluctuations, an evolution takes place by which the system reaches a basin that cannot be left, thus displaying a time pattern that is fittest to withstand the external stochasticity. 3. For even larger fluctuations, the system is driven back and forth between the basins, displaying an intermittent switching between time patterns. 4. For still larger fluctuations, the system is switched between the basins, staying always so far from the attractors that it can be considered as an amplifier of random fluctuations.

[1]  V. Hamburger,et al.  Observations and experiments on spontaneous rhythmical behavior in the chick embryo. , 1963, Developmental biology.

[2]  L. Passano,et al.  Co-Ordinating Systems and Behaviour In Hydra : I. Pacemaker System of the Periodic Contractions , 1964 .

[3]  Robert L. DeHaan,et al.  Regulation of spontaneous activity and growth of embryonic chick heart cells in tissue culture , 1967 .

[4]  H. Buc,et al.  Kinetics of the allosteric interactions of phosphofructokinase from Escherichia coli. , 1968, Journal of molecular biology.

[5]  B. Hess,et al.  Oscillatory phenomena in biochemistry. , 1971, Annual review of biochemistry.

[6]  B. Hess,et al.  Cyclic-AMP-controlled oscillations in suspended Dictyostelium cells: their relation to morphogenetic cell interactions. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[7]  A. Goldbeter,et al.  Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: a model and experimental study. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[8]  C. Pittendrigh,et al.  Mutual entrainment of bilaterally distributed circadian pacemaker. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[9]  B Hess,et al.  Analysis of progress curves. Rate law of pyruvate kinase type I from Escherichia coli. , 1980, The Biochemical journal.

[10]  J. Ross,et al.  Oscillations and efficiency in glycolysis. , 1980, Biophysical chemistry.

[11]  C. Sparrow,et al.  Frequency encoded biochemical regulation is more accurate than amplitude dependent control. , 1981, Journal of theoretical biology.

[12]  B. Hess,et al.  Design of glycolysis. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[13]  A Goldbeter,et al.  Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[14]  G. Gerisch Chemotaxis in Dictyostelium. , 1982, Annual review of physiology.

[15]  B. Hess,et al.  Analysis of progress curves. Interaction of pyruvate kinase from Escherichia coli with fructose 1,6-bisphosphate and calcium ions. , 1983, The Biochemical journal.

[16]  B. Hess Non-equilibrium dynamics of biochemical processes. 8. Fritz Lipmann-Vorlesung. , 1983, Hoppe-Seyler's Zeitschrift fur physiologische Chemie.

[17]  B. Hess,et al.  Quasiperiodic, Entrained and Chaotic Responses of Yeast Extracts Under Periodic Substrate Input Flux: Model and Experiments , 1984 .

[18]  B. Hess,et al.  Dynamic Coupling and Time-Patterns of Glycolysis , 1984 .

[19]  B. Hess,et al.  Transitions between oscillatory modes in a glycolytic model system. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[20]  B. Hess,et al.  Time Pattern Transitions in Biochemical Processes , 1984 .

[21]  B Hess,et al.  Chaotic dynamics in yeast glycolysis under periodic substrate input flux , 1984, FEBS letters.

[22]  Stefan Müller,et al.  Observation of Entrainment, Quasiperiodicity and Chaos in Glycolyzing Yeast Extracts under Periodic Glucose Input , 1985 .