6. THE RELAXATION TIME OF THE EPIGENETIC SYSTEM 81 



bacterial cell which is growing logarithmically with a division time of about 

 one hour. About 13-7% of these ribosomes are active, so that there are some 

 2 X 10^ ribosomes which are engaged in protein synthesis. This does not 

 necessarily imply that there are 2000 mRN A molecules present in the cell at any 

 one time, since studies by Warner, Rich, and Hall (1962) have suggested that 

 two or more ribosomes may be "reading" one messenger molecule of high 

 molecular weight ( ~ 10^) simultaneously. These latter observations were made 

 on material from rabbit reticulocytes, and it is not yet known if the same 

 phenomenon occurs in bacteria. Let us assume, however, that there are about 

 2 X 10^ messenger RNA molecules present at any one moment in a bacterial 

 cell. An estimate by Davis (1961) suggests that there may be 400-500 different 

 species of protein in a cell growing exponentially on rich medium (so that it 

 does not need to synthesize amino acids or nucleotides). 



The estimate that we arrive at for the average number of messenger mole- 

 cules per protein species is of the order of 4-5. This is a very small number, 

 surprisingly so. However, protein synthesis in bacteria takes about 4 sec 

 according to Byrne's calculations (McQuillan, Roberts and Britten (1959), 

 estimated 5 sec as the protein synthetic time in bacteria). Therefore one 

 messenger can produce 15 protein molecules per minute, and for exponentially 

 growing cells these proteins are very stable (Mandelstam, 1960). In one hour 

 2 X 10^ messenger molecules producing protein at the above rate can synthesize 

 2 X 103 X 15 X 60 = 18 X jq^ protein molecules, which is about the number of 

 molecules required for a new bacterial cell (Guild, 1956). 



Obviously these calculations are very rough and we cannot put much 

 confidence in them except as order of magnitude estimates. What is revealing is 

 the very small average size of the messenger RNA populations in bacterial cells. 

 Under certain conditions these can be greatly changed. Thus when the alkaline 

 phosphatase locus is fully induced in E. coli it has been estimated by Byrne that 

 there are some 840 active ribosomes engaged in the synthesis of this enzyme, 

 which enzyme accounts for about 20% of the total protein manufactured by 

 the cell. In the fully induced state, the alkaline phosphatase locus must be 

 producing mRNA at the rate of approximately 1-2 molecules/sec, since the life- 

 time of these messengers is only about 2 min (Levinthal et al., 1962). A single 

 locus can then maintain a messenger population of about 120-240 molecules, 

 and a single bacterium will have 2-3 such loci. Therefore the messenger popu- 

 lation of an inducible enzyme may be in the hundreds under conditions of full 

 induction. 



The condition for induction of alkaline phosphatase in E. coli is phosphate 

 deprivation, and under these conditions the rate of enzyme synthesis decreases 

 to about one molecule every 60 sec, a value 15 times slower than the synthetic 

 time of 4 sec observed during exponential growth with a division time of 1 h 

 (Byrne, 1963). It is thus clear that different environmental conditions can 

 produce very different epigenetic states in bacteria, with populations of differ- 

 ent messenger RNA and protein species varying greatly. Whether or not all 

 loci in bacteria have such a high potential for messenger synthesis as inducible 

 loci is not known, although it seems unlikely. If this were the case, however, 



