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Literature DB >> 1022823

The qualitative dynamics of a class of biochemical control circuits.

Abstract

The dynamical behavior of a class of biochemical control circuits that regulate enzyme or protein synthesis by end-product feedback is analyzed. Both inducible and repressible systems are studied and it is proven that in the former unique steady states are globally asymptotically stable. This precludes periodic solutions in these systems. A similar result holds for repressible systems under certain constraints on kinetic parameters and binding contants. However, when the reaction sequence is sufficiently long, or when a large enough number of effector molecules bind to each repressor molecule, repressible systems can show zero-amplitude ("soft") bifurcations: these are predicted by Hopf's bifurcation theorem.

Mesh：

Substances：
Enzymes

Year: 1976 PMID： 1022823 DOI： 10.1007/BF00307858

Source DB: PubMed Journal: J Math Biol ISSN： 0303-6812 Impact factor: 2.259

13 in total

1. Control of pyrimidine biosynthesis in Escherichia coli by a feed-back mechanism.

Authors: A B PARDEE; R A YATES
Journal: J Biol Chem Date: 1956-08 Impact factor: 5.157

2. Control of specific gene expression in higher organisms. Expression of mammalian genes may be controlled by repressors acting on the translation of messenger RNA.

Authors: G M Tomkins; T D Gelehrter; D Granner; D Martin; H H Samuels; E B Thompson
Journal: Science Date: 1969-12-19 Impact factor: 47.728

8. Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion.

Authors: W R Smith
Journal: Bull Math Biol Date: 1980 Impact factor: 1.758

9. On the stability of equilibria in metabolic feedback systems.

Authors: C Berding; G Haubs
Journal: J Math Biol Date: 1985 Impact factor: 2.259

10. Periodic metabolic systems: oscillations in multiple-loop negative feedback biochemical control networks.

Authors: A I Mees; P E Rapp
Journal: J Math Biol Date: 1978-03-03 Impact factor: 2.259

The qualitative dynamics of a class of biochemical control circuits.

1. Control of pyrimidine biosynthesis in Escherichia coli by a feed-back mechanism.

2. Control of specific gene expression in higher organisms. Expression of mammalian genes may be controlled by repressors acting on the translation of messenger RNA.

3. Chemical oscillations in membrane.

4. Limit-cycles in enzyme-systems with nonlinear negative feedback.

5. Co-operative components, spatial localization and oscillatory cellular dynamics.

Review 6. Biological feedback control at the molecular level.

7. Mathematics of cellular control processes. I. Negative feedback to one gene.

8. Stability of controlled biological systems.

9. The absolute stability of certain types of controlled biological systems.

10. Oscillatory behavior in enzymatic control processes.

1. Oscillations in a model of repression with external control.

2. The limiting dynamics of a bistable molecular switch with and without noise.

3. Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one.

4. The interaction graph structure of mass-action reaction networks.

5. Boolean versus continuous dynamics in modules with two feedback loops.

6. On the dynamics of a simple biochemical control circuit.

7. Models of genetic control by repression with time delays and spatial effects.

8. Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion.

9. On the stability of equilibria in metabolic feedback systems.

10. Periodic metabolic systems: oscillations in multiple-loop negative feedback biochemical control networks.