Ultradian Clock Research Articles

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

A mitotic oscillator with one slowly increasing variable (τ L of the order of hours) and one rapidly increasing variable (τ 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 quasiperiodic, 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.

Quantized cell cycle times: interaction between a relaxation oscillator and ultradian clock pulses

Control of the timing of cell division is considered to result from a relaxation cell cycle oscillator: this has one slow and one rapid component and obeys a system of two ordinary differential equations. Interactions of the slow component with an ultradian oscillator leads to quantization of cell cycle times when the free parameters of the cell cycle oscillator are chosen close to its bifurcation point. This model fits the experimental results previously reported.

Dynamics of nap sleep during a 40 hour period

Following 1 baseline night, the sleep of 8 adult males in equally spaced 1 h naps during a 40 h period was examined. Ten additional subjects were sleep-deprived for 40 h with 1 h periods of exercise given in place of naps. One recovery night followed the 40 h period for both groups. Total sleep time and the amount of stage REM during the naps were negatively related to the circadian-temperature cycle. Stage REM frequently appeared within 10 min of stage 1 onset and the normal sequence of stages REM and 4 were altered, demonstrating that the organization of sleep within a nap is quite different from that in monophasic nocturnal sleep. Auto-correlation and cross-correlation analyses showed that the relation of sleep stages from hour to hour in normal continuous baseline sleep was altered in nap-to-nap comparison. The timing of REM onset may be controlled by a sleep-dependent ultradian clock; the clock may stop upon awakening and resume at the next sleep onset. Naps had recuperative value in terms of maintaining the normal amounts of sleep stages on the recovery night; recovery sleep for the exercise group showed typical sleep-loss effects.