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Table 1 Extended requirements in validation of computer CACO models

From: Computational modeling of the cell-autonomous mammalian circadian oscillator

Criterion Expected behavior of the circadian oscillator system
1. Circadian period close to 24 h Without external influences, molecular oscillations of concentrations of RNA and proteins in CACO genes occur with a period close to 24 h. In diurnal animals, in general free-running period is slightly greater than 24 h, whereas, in nocturnal animals one is shorter than 24 h.
2. The phase concordance a) Under autonomous (free running) conditions, the phases of oscillations of RNA and protein levels are concordant with each other and with experimental data.
b) Circadian oscillations of the molecular concentrations occur with appropriate phase shifts to each other and to the light–dark cycle
3. The entrainment of circadian clock by incoming stimulus There have to be a possibility to regulate the rhythms in response to external stimuli, a process called entrainment. Under influence of some periodic changes in environment (incoming stimulus) circadian rhythms can be delayed in frequency and phase. All circadian rhythms are synchronized by 24-h light–dark cycles. The closer period of the entrainment factor to the period of a free-running autonomous rhythm, the easier it entrained.
4. The reaction to the shift of daily rhythm Rhythms can be adapted for concordance with local time. Under condition of phase shift of daily rhythm or constant lighting for daily light–dark cycle a new stable state of rhythm always comes after transition phenomena (the transition period), their duration is species-specific and can last several days. The closer the phase of the entrainment factor to the phase of initial rhythm, the easier and faster the delay occurs.
5. The reaction to a single light stimulus (phase synchronization) (a) Single stimuli alter the phase of molecular oscillation.
(b) The reaction of the circadian system to an external stimulus depends on the phase in which it is administered. This property describes the phase response curve.
In diurnal species, exposure to light soon after wakening causes that the animal will tend to wake up earlier on the following day(s), whereas exposure before sleeping delays the rhythm, i.e. the animal will tend to wake up later on the following day(s).
(c) The length and consistency of light exposure influences entrainment:
- longer light exposures have more effect than shorter ones;
- continuous exposure has a greater effect than intermittent exposure.
(d) For wild-type mice, the phase shift after light stimulus can be equal to several hours (acceleration or delay). For mice with Clock−/+ mutation phase shift can reach 12 h.
6. Temperature compensation The rhythms exhibit temperature compensation in mammalian. The period of circadian rhythms changes only slightly under different temperatures within the organism’s physiological range. If in enzymatic reaction Q10 value is usually changed from 2 to 3 (reaction rate increases 2–3 times as much under the increase of temperature on 10Co), then the circadian period does not change (Q10 ≈ 1) or even decreases (Q10 < 1) in mammalian.
The temperature coefficient was calculated in the following equation: Q10 = (R2/R1)10/(T2-T1), where R is rate and T is temperature.
7. Change of rhythm in gene mutations Effect of mutations on the activity of circadian genes in vivo should be reproduced in the CACO model.