94 TEMPORAL ORGANIZATION IN CELLS 



the non-essential amino acid, proline, from ornithine or from glutamic acid 

 via glutamic semialdehyde, then such a feed-back repression circuit could be 

 operating and we would then expect that the prohne pool size will oscillate. 

 A small amount of hot proline entering such an oscillating pool at a steady or 

 smoothly-decaying rate will result in cyclic variations in the specific activity of 

 the pool as the hot proline is periodically diluted by endogenously-formed 

 proline. If now the cells are flooded with cold proline, then the control circuit 

 will be saturated with co-repressor, the biosynthetic pathway will be " shut-off", 

 and the system will stop oscillating. It should actually be possible to damp out 

 the oscillations in any epigenetic control circuit in this manner, providing 

 always that the cell is sufficiently permeable to the feed-back metaboHte to 

 allow for saturation of the control circuit. Whether or not this is the correct 

 interpretation of the observations made by Tanzerand Gross (in press, 1963) is 

 not yet clear. The observed damping with cortisone, on the other hand, 

 remains unexplained. However, perhaps the most important aspect of these 

 results is the demonstration that it is possible to ehminate the periodic fluctua- 

 tions in the prohne pool by well-defined modifications in the experimental 

 procedure, thus suggesting that the variations represent a real ceUular variable. 

 Another feature of these observations deserves consideration, and that is 

 the fact that once again, as with Stern's work, the experimental analysis was 

 performed not on single cefls but on cell masses or even on whole embryos. 

 Thus if the observations do indeed reveal primary oscillations in intracellular 

 proline pools, then large populations of cells are in synchrony with one another 

 with respect to the dynamics of their metabolic pools ; and, most extraordinary 

 of ah, a whole group of embryos is in synchrony, for in the case of the chick 

 studies each experimental point on the oscillating curve represents one 

 embryo. If this conclusion is correct, then it has the greatest implications for 

 future experimental work, for it means that direct observations on intracellular 

 dynamics can be made without recourse to techniques whose resolution 

 reaches the single cell. In any event, the studies of Stern, Gross, Jackson, and 

 Tanzer have certainly broken new experimental ground which promises an 

 extremely rich harvest for the understanding of temporal organization in the 

 developing embryo, and also off'ers some experimental support for the theory 

 presented here. 



The Relaxation Time and Irreversible Processes 



Returning to our discussion of the relaxation time of the epigenetic system, 

 the importance of having an estimate for this quantity in a statistical mechanics 

 is the following. The macroscopic variables such as 6, G, S, etc., which are 

 used to define the "thermodynamic" state, exist only for equihbrium states of 

 the system. In the present theory these equilibrium states are steady states, 

 defined by particular values of the quantities Pi and ^,-. It is meaningful to 

 speak of the talandic temperature of the epigenetic system, for example, only if 

 the system has been at a particular steady state long enough for G to become 

 uniformly distributed over all the parts of the system, so that 6 is the same 

 throughout. If some microscopic parameter such as ^, or ^'/ changes to a new 



