We present ten insights that can be gained from computational models based on molecular mechanisms for the mammalian circadian clock. These insights range from the conditions in which circadian rhythms occur spontaneously to their entrainment by the light-dark (LD) cycle and to clock-related disorders of the sleep-wake cycle. Endogenous oscillations originate spontaneously from transcription-translation feedback loops involving clock proteins such as PER, CRY, CLOCK and BMAL1. Circadian oscillations occur in a parameter domain bounded by critical values. Outside this domain the circadian network ceases to oscillate and evolves to a stable steady state. This conclusion bears on the nature of arrhythmic behavior of the circadian clock, which may not necessarily be due to mutations in clock genes. Entrainment by the LD cycle occurs in a certain range of parameter values, with a phase that depends on the endogenous period of the circadian clock. A decrease in PER phosphorylation is accompanied by a decrease in endogenous period and a phase advance of the clock; this situation accounts for the familial, advanced sleep phase syndrome (FASPS). The mirror delayed sleep phase syndrome (DSPS) can be accounted for, similarly, by an increase in PER phosphorylation and a rise in autonomous period. Failure of entrainment by the LD cycle in the model corresponds to the non-24 h sleep-wake cycle syndrome, in which the phase of the circadian clock drifts in the course of time. Quasi-periodic oscillations that develop in these conditions sometimes correspond to long-period patterns in which the circadian clock is nearly entrained for long bouts of time before its phase rapidly drifts until a new regime of quasi-entrainment is re-established. In regard to jet lag, the computational approach accounts for the two modes of re-entrainment observed after an advance or delay which correspond, respectively, to an eastward or westward flight: the clock adjusts in a direction similar (orthodromic) or opposite (antidromic) to that of the shift in the LD cycle. Computational modeling predicts that in the vicinity of the switch between orthodromic and antidromic re-entrainment the circadian clock may take a very long time to resynchronize with the LD cycle. Repetitive perturbations of the circadian clock due, for example, to chronic jet lag -a situation somewhat reminiscent of shift work- may lead to quasi-periodic or chaotic oscillations. The latter irregular oscillations can sometimes be observed in normal LD cycles, raising the question of their possible relevance to fragmented sleep patterns observed in narcolepsy. The latter condition, however, appears to originate from disorders in the orexin neural circuit, which promotes wakefulness, rather than from an irregular operation of the circadian clock.
