8. APPLICATIONS AND PREDICTIONS 139 



Now bi is the rate of degradation of niRNA, and it should have a positive 

 temperature coetVicient, increasing with increased temperature. In order to get 

 temperature compensation, it is thus necessary that the denominator also 

 should increase. This means either that the amplitude of the oscillations should 

 increase so that (A',-/j,) is larger, or that the steady state value p,- should 

 increase so that X; is larger, or both. 



If increased physical temperature does cause an increase in the amplitude of 

 the oscillation, then it should be possible to observe this effect by an experi- 

 mental procedure similar to the one described for altering 6 by means of pulses 

 of amino acids. The pulse would now be mild heat shocks, lasting perhaps 15 

 min every 2 h and involving a temperature increment of say, 4-5°C. The object 

 of the treatment would be to increase 6 without altering permanently the micro- 

 scopic parameters (the rate and equilibrium constants). If such an effect is 

 produced the clock should slow down. Providing it is possible to keep the 

 microscopic parameters unchanged by such treatment, there should be no tem- 

 perature compensation effect because only the denominator of the expression 

 (91) is being changed. Since the cell is very seldom, if ever, subjected to a 

 natural temperature regime of this kind, with a periodicity which is too small to 

 allow the temperature compensation mechanism to work, there seems some 

 chance that excited G-levels might be produced by mild transient heat treat- 

 ment. This would certainly be a simpler experimental procedure than the ones 

 involving transient changes in chemical environment, and it may be another 

 way of testing the idea that the epigenetic system of a cell can exist in one of 

 many different G-levels when the microscopic parameters remain constant. 



It is perhaps a little unrealistic to suppose that the mechanism of tempera- 

 ture compensation in cells will be revealed by an equation for the mean fre- 

 quency of oscillation of a simple uncoupled biochemical oscillator. This has 

 given one suggestion, but in the strongly-coupled oscillators it will certainly be 

 the case that the mean frequency function involves ratios of microscopic 

 parameters which would indicate a much stronger natural "buffering" of the 

 system against temperature fluctuations than is apparent in equation (57). 

 There is the possibility that at different physical temperatures different orders 

 of subharmonic resonance or frequency demultiplication are stable, as dis- 

 cussed earlier in the chapter. This latter mechanism would involve disconti- 

 nuities in the circadian period as the ambient temperature is changed, a pheno- 

 menon which is not uncommon in these studies. However, the temperature 

 compensation device usually seems to work rather more smoothly than this, 

 and it would be of interest to see if changes in the amplitude of the oscil- 

 lators are involved, with their resultant effects upon frequency. 



At this point, it is of some interest to pursue a purely speculative line of 

 reasoning which illustrates how a thermodynamic law of a quantitative nature 

 might be derived from our theory and applied to the behaviour of cells. The 

 importance of physical temperature as an external parameter for the study of 

 temporal organization in cells has already been noted. In thermodynamic 

 terms it might be looked upon as an experimental variable, somewhat ana- 

 logous to pressure in the case of gases. What we want to suggest now, is how 



