150 TEMPORAL ORGANIZATION IN CELLS 



down rather than go faster, since the pulses would now be expected to have a 

 greater probability of increasing 6 than of decreasing it. If the estimate for 

 jS^ at about 20 molecules/min is anywhere near the correct value for the rate 

 of protein degradation, then it should be possible to bring about a switch in 

 the nature of the oscillations from continuous to discontinuous by altering 

 the ^-level of the cells. 



When an mRNA population oscillates in the manner of Fig. 10, then the 

 discontinuities will show up in the behaviour of the homologous protein species, 

 although the exact shape of its wave form will depend upon the mean life-time 

 of the mRNA population, X^, the mean interval between bursts, and the 

 stability of the protein. Kerner showed that the discontinuous bursts of an 

 oscillator such as we are considering, have a frequency which is appreciably 



Xr 



Pr 



Time 

 Figure 11. 



smaller than that of its continuous oscillations. On the basis of our estimates 

 in Chapter 6, concerning the mean periods of epigenetic oscillators (mean 

 value about 4 h), we might suggest that the discontinuous oscillation would 

 have a mean frequency of one every 6 or 8 h, the burst itself lasting for perhaps 

 2-3 h with a 4-6 h period of inactivity when the locus is shut off. Behaviour of 

 this kind in mRNA would produce an all-or-none oscillation in the homo- 

 logous protein species if our estimate for /3^ x 20 molecules/min is roughly 

 correct and if we assume that 200-300 messenger molecules are produced 

 during the burst, synthesizing some 5000-6000 protein molecules. In the 4-6 

 h between the appearance of mRNA in the system, the protein population 

 will have decayed. Once again these estimates are very crude, and in fact, 

 they are not in very good agreement with Stern's observations. The mean 

 period he observed between bursts of DNA-ase synthesis appears to have been 

 larger than 8 h. Our estimates could easily be recast to give such results; but 

 the main point of this discussion was to show that the same qualitative be- 

 haviour as that observed by Stern could arise in the biochemical control systems 

 of the class we are considering. The added non-linearity results in a new 

 statistical feature. The significance of this is that in systems composed of many 

 interacting components, discontinuities may arise which cannot be explained 



