136 TEMPORAL ORGANIZATION IN CELLS 



mean amplitude, since the stimuli would fall equally, in all probability, over 

 both positive and negative parts of the cycle (measured relative to the steady 

 state axis) On the other hand, if the asymmetry were in the other direction so 

 that protein levels were on the average less than the steady state values, then the 

 experimental procedure should result in a decreased 6 value. 



The theory implies not only that this treatment should result in a slowing 

 down of the clock, but that the changed clock period should be stable. That 

 is to say, the cell should continue to show a lengthened "day" even after the 

 pulsing is discontinued, and should not return to their normal diurnal period so 

 long as they continue to be kept under constant environmental conditions. If, 

 however, the treatment changes the period of the clock but this change is 

 unstable, the period returning to its normal one when the pulsing is discon- 

 tinued, then the circadian mechanism is much more deterministic then we have 

 assumed it to be and the present theory would not be a very useful one for des- 

 cribing its properties. It is true that attempts to impose upon circadian 

 systems a regime very different from a diurnal one have nearly always resulted 

 in an unstable state, the system slipping back into a daily cycle after completing 

 a few abnormal periods. However, we are looking for much smaller changes 

 in temporal characteristics than this, variations of perhaps 2-3 h on either 

 side of the normal period being the maximum that could reasonably be 

 expected. 



The observation of changes in 6 by means of changes in the period of a 

 circadian clock is perhaps questionable, although there should be a direct 

 correlation over some range of variation in d. If we are correct in suggesting 

 that the circadian rhythms are generated from shorter oscillations by means of 

 subharmonic resonance, then there is the possibility that as d increases and the 

 fundamental oscillations slow down, the order of the subharmonic decreases 

 so that 24-h rhythm continues to be generated even at elevated G-levels. This 

 is a conceivable compensation mechanism for eliminating environmental 

 variations from the diurnal clock. However, since subharmonics are always 

 integral fractions of the primary oscillations, a change from one order to 

 another would have to occur as a jump or discontinuity at some ^-level. 

 Between discontinuities of this kind, the clock should vary continuously so 

 that changes in 6 should be observable over a certain range of variation. The 

 occurrence of a discontinuity in the period of the circadian clock would actually 

 be evidence for the occurrence of subharmonics. 



Let us consider a specific example in order to see what order of variation 

 might be expected in a system organized temporally according to the assump- 

 tions of this study and subjected to an experimental treatment such as that 

 described above. Using equation (59) of the last chapter for very rough 

 estimates, it is readily calculated that when 6 = 9 the period of a fundamental 

 oscillation will be about 6 h. If such an oscillator is properly coupled to 

 another component there could arise a subharmonic of order ^ so that a 

 circadian rhythm would be generated. If now 6 is increased by periodic 

 pulsing of amino acids in the manner described, then by the time 6 = \2 

 the period of the fundamental or free-running oscillations will have increased 



