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Biomedical subjects

A L Lloyd

Publications and source records attributed to A L Lloyd.

21 records · Page 2Linked to original sources

Hypothesis: the central oscillator of the circadian clock is a controlled chaotic attractor.

Controlled chaos may be important for the generation of rhythmic behaviour in living systems. A model is proposed in which the central circadian oscillator is a chaotic attractor. Whereas a limit cycle mechanism (previously invoked to explain circadian clocks as well as ultradian clocks and cell division cycles) can provide only a single stable periodic orbit, a chaotic attractor can generate rich dynamic behaviour. Control by feedback makes accessible a selected stabilized orbit; this can be chosen so as to optimize system performance. Such a system can accommodate a wide variety of requirements, e.g. that a single clock mutation can affect both period and temperature compensation, and the generation of higher periods from an ultradian oscillator. Simultaneous operation of more than one clock (with differing periods) may require a high-dimension chaotic attractor. Attractive features of such a model include versatility of period selection (e.g. as in the per mutants of Drosophila) and the use of control elements of the type already well known in metabolic circuitry.

Animals↗

The cell division cycle: a physiologically plausible dynamic model can exhibit chaotic solutions.

A mitotic oscillator with one slowly increasing variable (tau L of the order of hours) and one rapidly increasing variable (tau R of the order of minutes) modulated by a timer (ultradian clock) gives an auto-oscillating solution: cells divide when this relaxation oscillator reaches a critical threshold to initiate a rapid phase of the limit cycle. Increasing values of the velocity constant in the slow equation give quasi-periodic, chaotic and periodic solutions. Thus dispersed and quantized cell cycle times are consequences of a chaotic trajectory and have a purely deterministic basis. This model of the dispersion of cell cycle times contrasts with many previous ones in which cell cycle variability is a consequence of stochastic properties inherent in a sequence of many thousands of reactions or the random nature of a key transition step.

Activity Cycles↗