The Amplitude Problem

If you are one of the few of my readers who actually slogged through my Clock Tutorials, especially the difficult series on Entrainment and Phase Response Curves, you got to appreciate the usefulness of the oscillator theory from physics in its application to the study of biological clocks. Use of physics models in the study of biological rhythms, pioneered by Colin Pittendrigh, is an immensely useful tool in the understanding of the process of entrainment to environmental cycles.

Yet, as I warned several times, a Clock is a metaphor and, as such, has to be treated with thought and caution. Is the physics model always applicable? Is it sometimes deceptive? How much does it oversimplify the behavior out in the natural environment?

The few tests of the theory conducted in the field demonstrate that the models of entrainment (the PRCs) work quite well, though not always perfectly. Use of Limit Cycles (something that is, IMHO, too complex for me to try to explain on a blog) is also useful. The theory appears to work quite well in regard to period and phase, but the effects of amplitude of the oscillation are not as well tested, although a number of studies, especially regarding photoperiodism in non-mammalian vertebrates and invertebrates, suggests that the amplitude is an important parameter of a biological rhythm.

The main problem with the amplitude is that it is not clear if the measured amplitude of the overt rhythms (e.g., activity, body temperature, melatonin release, etc.) faithfully reflects the amplitude of the underlying oscillator. It is not even certain that the amplitude of the expression of core clock genes and proteins is the equivalent of the amplitude of the idealized physical system.

In a recent paper (provisional PDF) in the Journal of Circadian Rhythms (an Open Access journal, where you can also comment on the papers, just like on PLoS ONE), Daniel Kripke, Jeffrey Elliott, Shawn Youngstedt and Katharine Rex, using that most difficult laboratory model of all - the human - tried to kill two birds with one stone: test if the physical oscillatory models apply for the amplitude of circadian clocks and test if the amplitude of the overt rhythms is a good reflection of the amplitude of the underlying biological oscillator. The medical implicaitons of their work, no matter what the results, is quite obvious as well.

It is well known that the amplitude of overt rhythms (activity, sleep-wake cycle, temperature, melatonin, cortisol, etc.) gets a little smaller with advanced age in humans. Measuring simultaneously several overt rhythms (always a good thing!) while constructing a Phase-Response Curve to light pulses in two groups - young and old people - they excpected, from theory, to see a change in the shape and size of the PRC. According to theory, an oscillator with a higher amplitude (young) would be more difficult to shift, i.e., the size of phase-shifts would be smaller than in the old cohort (for some odd reason - typo perhaps? - they state they expected the opposite, i.e., smaller shifts in the older group).

If they got positive results, i.e., if the size of phase-shifts differed between the two age groups, they would have demonstrated that a) physical model of oscillatons applies to biological clocks in respect to amplitude, and b) that the amplitude of overt rhythms faithfully reflects the amplitude of the underlying biological oscillator.

But, their results were negative, i.e., there was no difference in the size of phase-shifts between young and old cohorts (or, for that matter, between women and men), though the phase of all rhythms (except temperature and the offset of melatonin metabolites in the urine - likely due to the slower metabolism itself) was advanced and the PRCs, as expected, moved somewhat to the left to reflect this.

This unfortunate result suggests one (or both) of the two possibilities:

- Oscillator models borrowed from physics do not apply to biology in regard to amplitude, or
- Amplitude of overt rhythms does not reflect the amplitude of the underlying oscillator

As they say, more work needs to be done.