8. APPLICATIONS AND PREDICTIONS 135 



of the oscillation. But if the protein concentration is above the steady state 

 when the stimulus begins, then the shift is away from the steady state axis and 

 the amplitude of oscillation is increased. We come now to an observation 

 which is critical to the argument. The oscillations occurring in the feed-back 

 control mechanism studied in this work are distinctly asymmetrical, as has 

 been observed in connection with many different properties of the oscillators. 

 This asymmetry is particularly marked in the case of the oscillations in protein 

 concentrations, the different species of proteins spending considerably more 

 time above their steady state values than below. Therefore it follows that a 

 transient increase in protein synthesis will be more likely to occur on that part 

 of the cycle which is above the steady state axis, and hence cause the trajectory 

 to move away from this axis then vice versa. That is to say, the small pulse of 

 amino acids will have a greater probability of increasing the amplitude of the 

 oscillation, hence the talandic temperature, than of decreasing it. 



However, a single stimulus is not likely to cause a permanent change in the 

 talandic temperature. What is required to bring about such a change is a 

 repetition of the pulse at intervals of perhaps 2 h over a fairly long period of 

 time, say 2 days. It is better if the interval between the pulses is smaller than the 

 mean period of the oscillations, so that the pulses are staggered across the 

 trajectories and do not always arrive at the same part of the cycle, which might 

 be that below the steady state axis. An interval of 2 h should be sufficient for 

 the system to return to its initial condition with respect to the microscopic 

 parameters, but not long enough for the effect of the pulse on the talandic 

 temperature to have died away. The latter time we have estimated to be about 

 4 h, the relaxation time of the epigenetic system. Therefore the suggestion is 

 that pulses of amino acids given every 2 h or so in quantities which will be com- 

 pletely exhausted in about i h by the culture of organisms, should have the 

 effect of increasing the talandic temperature of the epigenetic system in the cells 

 without changing their microscopic state. The way to observe such a change is, 

 of course, through the rhythmic behaviour of the organisms. We have in 

 equation (57) a result which shows us that as d increases, the mean frequency 

 of the oscillation decreases. Therefore the effect of the above experimental 

 treatment should be that the biological "clock" in the organisms is slowed 

 down. 



The crucial part of this argument is not that an increased level of 9 results in 

 a decreased frequency of biochemical oscillations. It is a general characteris- 

 tic of non-linear oscillations that an increased amplitude results in a decrease 

 in frequency. The important prediction is that the experimental procedure 

 outlined above should cause an increase in 6, this increase being observed via a 

 change in the temporal behaviour of the organism. This result depends upon 

 the particular type of asymmetry that occurs in the oscillations, and this 

 asymmetry is due ultimately to the assumption that the kinetics of repression 

 are essentially those of adsorption isotherms, as is the case with enzyme 

 inhibition, antigen-antibody reactions, and other macromolecular phenomena 

 Therefore the experiment is a test of the validity of this assumption If the 

 oscillations were symmetrical, the disturbances should have no effect upon the 



