146 TEMPORAL ORGANIZATION IN CELLS 



pulsing experiments described earlier in the chapter. It would certainly be of 

 great interest to be able to interfere with the timing mechanisms involved 

 in differentiation, thus approaching development through the phenomenon 

 of competence rather than through the more commonly employed study 

 of induction and the nature of inducers. However, the present theory can offer 

 no specific predictions in this field, and we must conclude that except for rather 

 special cases, it cannot be used as it now stands in the analysis of temporal 

 organization in developing cells. 



The importance of a temporal structure in cellular activities during develop- 

 ment may prove to be of importance not only in relation to competence but also 

 in relation to the generation and continuous remodelling of morphogenetic 

 structure which is so obviously a part of epigenesis. Especially in the construc- 

 tion of bone, muscle, and connective tissue it would seem that a certain plasticity 

 of the structuring process is necessary in order that optimal design be achieved 

 in relation to the stresses which develop as the embryo attains its adult mor- 

 phology. A periodic laying down of new structual materials followed by their 

 partial degradation may provide the embryo with the plasticity required for 

 morphogenetic modelling. The results of Gross, Tanzer, and Jackson on the 

 periodicities in proline pool sizes and collagen synthesis are of particular 

 relevance to this viewpoint. Gross (1961) has discussed how a periodicity in 

 the synthesis and release of collagen from differentiating cells in a developing 

 embryo could explain the remarkable orthogonal layering of collagen fibres 

 in connective tissue. The interactions of non-linear oscillators, discussed in 

 the last chapter, could provide the dynamic basis for establishing this type of 

 spatial structure from time structure. 



Statistical Discontinuities 



In this final section we will consider in some detail the observations made by 

 Stern (1961) on the rather remarkable all-or-none fluctuations in the DNA-ase 

 activity of developing lily anthers. So far the oscillations which we have been 

 studying show no evidence of all-or-none behaviour, and the question arises 

 how this might occur. Can we obtain a biochemical control circuit of the class 

 we are considering which shows an oscillation in 7,- with discontinuous 

 characteristics, 7, vanishing or nearly vanishing from the system between large 

 bursts of synthesis? We will now show that such behaviour can, in fact, arise 

 when a small change is made in the differential equations (14). The result by 

 no means proves that the kinetics of control of DNA-ase synthesis in lily 

 anthers are necessarily those of the system to be derived below. But the 

 interesting feature of the modified control system is that the discontinuity 

 arises as a consequence of weak interaction through metabolic pools and would 

 not occur in an isolated control circuit; i.e. the all-or-none behaviour is a 

 property of the whole system described by the statistical mechanics and is not a 

 property of a single component. The result therefore suggests that Stern's 

 observation need not necessarily find an explanation in terms of a special 

 microscopic switching system which turns the DNA-ase locus on and off 



