88 TEMPORAL ORGANIZATION IN CELLS 



per minute each, this nucleotide pool would have to be replaced every 30 sec, 

 so that 1000 activated nucleotides must be synthesized every second. This is 

 well within the capacity of nucleotide activating enzymes. 



Li is the equilibrium constant for the reaction between activated nucleo- 

 tides and the DNA templates. From equation (5) we have the relation 



.m - '^ 



The right-hand side of this relation is the ratio of templates engaged in mRNA 

 synthesis to those free of activated nucleotides, and we will assume that the 

 ratio is heavily in favour of messenger synthesis, taking it to be 100, Thus 

 LXA;\ = 100 so that Li=\, with units 



1 



molecules/cell 



Assuming a cell volume of 10^ cubic microns, which is about average for 

 the cells of higher organisms, the above value for L,- corresponds to a dissoci- 

 ation constant of about TTx 10~i2 moles/litre, in standard units. The free 

 energy involved in the combination between the activated nucleotides and the 

 DNA template which is thus obtained is about 16,000 calories/mole. This is 

 in the right range, but it is doubtful that this calculation really has very much 

 meaning. The state of macromolecules and molecules in the cell is hardly that 

 occurring in aqueous solution, and the effective volume of a cell with respect 

 to solutes is not the total cell volume. In view of these considerations it seems 

 best for the present purpose to express concentrations in the arbitrary units of 

 molecules per cell, without attempting to reduce them to moles per litre. 



With a 4 h mean life-time for mRNA and a steady state value of 100 mole- 

 cules, we get 25 molecules degraded every hour. Thus ^,=ff =^ofan 

 mRNA molecule degraded per minute. So far we have 



dXi 2100 



At the steady state 



dt l-M00+/:,[i?,] 12 

 200 5 _ 



\Q\+Ki{R^ 12 

 so that K{R;\ = 379 



[/?,] is here the size of the population of free repressor molecules when the 

 system is at the steady state. Any estimate for this quantity is sheer speculation. 

 We take it to be 100. This makes /f, = 3 79, so that the affinity of the repressor 

 for the DNA template is greater than that of the activated nucleotides (deter- 

 mined by L,), which seems a reasonable assumption. 



The quantity Q, can now be evaluated, since we have 



Qi = Ai+k;qi = 1+L,U] +/:,[/?,] = 480 



