34 TEMPORAL ORGANIZATION IN CELLS 



to assume that messenger RNA populations must be increased by at least a 

 factor of 100, and probably by 1000. With mRNA populations of 100-1000 per 

 species we are in a range where continuous variables can be used, fluctuations 

 being a relatively small percentage of their mean values. Such a representation 

 is even more valid if messenger stability is greater in protozoa than in bacteria, 

 and if protein and mRNA synthesis is slower. Both these factors tend to 

 smooth out the dynamics of the system. Furthermore, we will see that the 

 rates for macromolecular synthesis must be lower than in bacteria if circadian 

 rhythms are to be generated. This is because, according to what is currently 

 known about the properties of non-linear oscillators, it would be difficult to 

 produce strong, stable oscillations with a 24-h period from an oscillator which 

 has a frequency of 2-3 c/h (Krylov and BogoUubov, 1937), unless cells have 

 a rather unusual " cascading " mechanism for generating slow oscillations from 

 fast ones, one having a frequency of some 50-75 times the other. This question 

 will not be treated in detail until Chapter 7. 



If we turn now to the cells of higher organisms we find a great diversity of 

 cell size, but very few cells are smaller than about 10 /x in diameter. This means 

 that cell volumes are at least 100 times those of bacteria and usually 10^ or 

 greater. To this we add the observation that in cells of metazoon organisms the 

 total number of different protein species present in any cell type is usually 

 considerably smaller than in bacteria, due to cell specialization or differentia- 

 tion. Since the higher the turnover rate of a protein species the larger the 

 messenger RNA population required to maintain it at a particular level, 

 another factor tending to increase mean mRNA population levels in the cells of 

 higher organisms over those in bacteria, is the fact that the average turnover 

 rate of proteins in the former cells is always about 1 % per hour (Mandelstam, 

 1960). This is considerably larger than the value observed in exponentially 

 growing bacteria, where proteins are very stable. Since many of the protein 

 species play a structural role in the cell and will turn over at a considerably 

 lower rate than this, we may expect that metabolically active proteins such as 

 the enzymes forming part of the closed feed-back control loops which we are 

 studying, may be turning over at rates of 5-10% per hour and even higher for 

 enzymes such as ascorbic acid oxidase which appear to be inactivated in the 

 course of catalytic activity. 



For the protein synthetic time in higher organisms we will assume an 

 average value of 5 min, which is the time observed by Loftfield and Eigner 

 (1958) in their study of ferritin synthesis in rat liver. Dintzis (1961) has 

 observed a rather smaller biosynthetic time than this for the case of the poly- 

 peptide chains of haemoglobin in rabbit reticulocytes, his studies giving the 

 value of 1 1 min for the completion of the polypeptide units. However, we shall 

 keep to the value of 5 min because the time period which is required for our 

 purposes is that for amino acid assembly, secondary and tertiary folding of the 

 polypeptide chains, and their aggregation into functionally complete macro- 

 molecules. The time required for messenger RNA synthesis is not known, but 

 we may estimate that its lower limit is about 1 min if the same relative rates hold 

 in higher organisms as in bacteria where mRNA synthesis is 4-10 times faster 



