The Dynamics of Feedback Control Circuits in Biochemical Pathways

[1]  P E Rapp,et al.  Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms. , 1977, Journal of theoretical biology.

[2]  H. Schweiger,et al.  The effect of different inhibitors of transcription and translation on the expression and control of circadian rhythm in individual cells of Acetabularia. , 1975, Experimental cell research.

[3]  J. Monod,et al.  Genetic regulatory mechanisms in the synthesis of proteins. , 1961, Journal of molecular biology.

[4]  H. Gainer.  Electrophysiological behavior of an endogenously active neurosecretory cell. , 1972, Brain research.

[5]  B. Lavenda.  The Theory of Multi-Stationary State Transitions and Biosynthetic Control Processes , 1972, Quarterly Reviews of Biophysics.

[6]  N. Macdonald,et al.  Time delay in simple chemostat models , 1976, Biotechnology and bioengineering.

[7]  H. Othmer.  The qualitative dynamics of a class of biochemical control circuits , 1976, Journal of mathematical biology.

[8]  R. V. von Baumgarten,et al.  Pacemaker properties of completely isolated neurones in Aplysia californica. , 1971, Nature: New biology.

[9]  J. Changeux,et al.  The feedback control mechanisms of biosynthetic L-threonine deaminase by L-isoleucine. , 1961, Cold Spring Harbor symposia on quantitative biology.

[10]  P. E. Rapp,et al.  A theoretical investigation of a large class of biochemical oscillators , 1975 .

[11]  A. Morley,et al.  Computer simulation of granulopoiesis: normal and impaired granulopoiesis. , 1970, Blood.

[12]  M Morales,et al.  Biochemical oscillations in "controlled" systems. , 1967, Biophysical journal.

[13]  T. Wheldon,et al.  Mathematical models of oscillatory blood cell production , 1975 .

[14]  C. Walter.  The occurrence and the significance of limit cycle behavior in controlled biochemical systems. , 1970, Journal of theoretical biology.

[15]  P. Rapp.  Biochemical oscillators—a search procedure , 1975 .

[16]  H. E. Umbarger,et al.  Evidence for a negative-feedback mechanism in the biosynthesis of isoleucine. , 1956, Science.

[17]  J. Cronin,et al.  The Danziger-Elmergreen theory of periodic catatonic schizophrenia. , 1973, Bulletin of mathematical biology.

[18]  D. E. Atkinson,et al.  Biological feedback control at the molecular level. , 1965, Science.

[19]  B. Hess,et al.  Allosteric kinetics of pyruvate kinase of Saccharomyces carlsbergensis. , 1973, Journal of molecular biology.

[20]  D. G. Aronson.  A Comparison Method for Stability Analysis of Nonlinear Parabolic Problems , 1978 .

[21]  N. Kazarinoff,et al.  An applicable Hopf bifurcation formula and instability of small periodic solutions of the field-Noyes model , 1976 .

[22]  John J. Tyson,et al.  Existence of periodic solutions for negative feedback cellular control systems , 1977 .

[23]  L E Scriven,et al.  Instability and dynamic pattern in cellular networks. , 1971, Journal of theoretical biology.

[24]  G. Yagil,et al.  On the relation between effector concentration and the rate of induced enzyme synthesis. , 1971, Biophysical journal.

[25]  B. Goodwin,et al.  An Entrainment Model for Timed Enzyme Syntheses in Bacteria , 1966, Nature.

[26]  A Robertson,et al.  Control of developing fields. , 1972, Annual review of biophysics and bioengineering.

[27]  T. Mansour.  Studies on Heart Phosphofructokinase: Purification, Inhibition, and Activation , 1963 .

[28]  N. Macdonald,et al.  Birfurcation theory applied to a simple model of a biochemical oscillator. , 1977, Journal of theoretical biology.

[29]  S. P. Hastings,et al.  On the uniqueness and global asymptotic stability of periodic solutions for a third order system , 1977 .

[30]  Leon Glass,et al.  Limit cycle oscillations in compartmental chemical systems , 1974 .

[31]  L. E. Scriven,et al.  Interactions of reaction and diffusion in open systems , 1969 .

[32]  I. Williams,et al.  Verification of Aizerman's conjecture for a class of third-order systems , 1962 .

[33]  W. Donachie,et al.  Repression and the Control of Cyclic Enzyme Synthesis in Bacillus subtilis , 1966, Nature.

[34]  B. Goodwin,et al.  A phase-shift model for the spatial and temporal organization of developing systems. , 1969, Journal of theoretical biology.

[35]  D. Ingwerson.  A modified Lyapunov method for nonlinear stability analysis , 1961 .

[36]  H. Othmer.  Nonlinear wave propagation in reacting systems , 1975 .

[37]  L. Danziger,et al.  Mathematical theory of periodic relapsing catatonia , 1954 .

[38]  E. Noldus.  A Frequency Domain Approach to the Problem of the Existence of Periodic Motion in Autonomous Nonlinear Feedback Systems , 1969 .

[39]  P. Schürmann,et al.  A regulatory mechanism for CO2 assimilation in plant photosynthesis: Activation of ribulose‐1,5‐diphosphate carboxylase by fructose 6‐phosphate and deactivation by fructose 1,6‐diphosphate , 1972, FEBS letters.

[40]  J. L. Kavanau,et al.  A MODEL OF GROWTH AND GROWTH CONTROL IN MATHEMATICAL TERMS , 1957, The Journal of general physiology.

[41]  U. Heiden.  Stability properties of neural and cellular control systems , 1976 .

[42]  L Glass,et al.  Co-operative components, spatial localization and oscillatory cellular dynamics. , 1972, Journal of theoretical biology.

[43]  Stability and enzyme separation: Integral representation of the solutions , 1974 .

[44]  P. Rapp,et al.  Analysis of biochemical phase shift oscillators by a harmonic balancing technique , 1976, Journal of mathematical biology.

[45]  J. Tyson.  On the existence of oscillatory solutions in negative feedback cellular control processes , 1975 .

[46]  J. Changeux,et al.  ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. , 1965, Journal of molecular biology.

[47]  A. Pardee,et al.  Sequence of enzyme synthesis and gene replication during the cell cycle of Bacillus subtilis. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[48]  J. Griffith.  Mathematics of cellular control processes. II. Positive feedback to one gene. , 1968, Journal of theoretical biology.

[49]  B. B. Edelstein.  The dynamics of cellular differentiation and associated pattern formation. , 1972, Journal of theoretical biology.

[50]  A. Mees,et al.  Spurious predictions of limit cycles in a non-linear feedback system by the describing function method , 1977 .

[51]  F. Takens,et al.  On the nature of turbulence , 1971 .

[52]  D. J. Allwright,et al.  A global stability criterion for simple control loops , 1977 .

[53]  D. Luss,et al.  The influence of end effects on the behavior and stability of catalytic wires , 1972 .

[54]  N. Macdonald.  Application of the describing function of the Danziger-Elmergreen equations. , 1976, Bulletin of mathematical biology.

[55]  B. Goodwin.  Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.

[56]  Aubrey B. Poore,et al.  On the theory and application of the Hopf-Friedrichs bifurcation theory , 1976 .