82 TEMPORAL ORGANIZATION IN CELLS 



then all loci might be in theory inducible, but the control mechanisms may be 

 much more complex than those which operate for hydrolytic enzymes such as 

 alkaline phosphatase and j8-galactosidase. 



What emerges from these estimates is the evidence that in bacteria a great 

 many of the messenger RNA species must have population sizes which are on 

 the average less than 10. These are certainly too small to be represented by a 

 continuous variable. Such a population will show an extremely irregular 

 behaviour in time, varying randomly between perhaps 5 and 15 messengers or 

 more. These fluctuations will produce variations in the population size of the 

 homologous protein species, although the "noise" produced in the protein 

 population will be somewhat less than that in the mRNA population. If, 

 for example, the messenger level changes from 10 to 20 molecules and back 

 again to 10 in the course of say 10 min, then these "extra " messenger molecules 

 could produce some 1200 "extra" protein molecules in this time interval. 

 With a mean protein population of about 4 x 10^ (18 x 10^ protein molecules 

 in all, 500 different species), the per cent variation in the population is 

 J-|^ = 30%, compared with a 50% fluctuation in the messenger popula- 

 tion. 



The conclusion which we must draw from this brief study of bacterial 

 systems, is that any continuing oscillations which might occur due to negative 

 feed-back in their biochemical control devices, would be very nearly obliterated 

 by the noise level which would exist in the populations of messenger RNA's 

 because of their small size. It is completely unreasonable to use differential 

 equations and continuous variables to represent the kinetics of molecular 

 species whose total population in the cell is less than 10 molecules, so that our 

 procedures cannot be applied to the study of temporal organization in bacteria. 

 There is one rather comforting observation which we can make at this point, 

 however, and that is that no rhythmic or cyclic behaviour has ever been obser- 

 ved in bacteria analogous to the tidal, diurnal, lunar, and other rhythms which 

 are such an obtrusive feature of behaviour in higher organisms, from the 

 protozoa up. It has been suggested (Ehret and Barlow, 1960) that the reason 

 for this may be the absence of a well-defined nucleus in bacteria, the "double- 

 envelope" structure of all higher cells being assumed to be an essential feature 

 for the generation of oscillations in the feed-back control circuits. The above 

 analysis suggests that another and possibly more fundamental reason, may 

 be the difficulty of producing and making use of a periodic signal when the 

 noise level in the very small mRNA populations in bacteria is, in all probability, 

 so high. 



However, there is one situation in which well-defined oscillations could 

 occur in bacteria according to our analysis, and that is when a locus is induced 

 sufficiently to bring the level of mRNA for the induced species to a mean value 

 of say 100-200 molecules. Considering again the case of alkaline phospha- 

 tase, control of messenger synthesis is regulated by the level of inorganic 

 phosphate in the cell, so that a closed feed-back loop of the type shown in Fig. 1 

 exists. Once the enzyme is induced and the messenger population is of the 

 order of a few hundred molecules, then the noise level will probably have 



