624 J. M. REINER 
the same protein and also other proteins, the term M;E’ should actually be (X2M;)E’, 
where the summation is over all occurrences. Consequently, at the step (in the steady- 
state treatment) where we solve for /,E’, we must write the equation as B,E, = 
M,E’(&M,)/M,. The final result will then be, instead of (3): 
(3’) d(Protein) /dt = w(H,P, + H,’/Py’) 
where w is an abbreviation for M,/2’M,. Formally, the effect is to give all the results 
as before, but with a factor w incorporated into each permease efficiency factor — not 
only the E and F factors, but the H, and H,’, the factor w being characteristic for 
each amino acid, provided that it appears terminally in some protein. 
Inasmuch as amounts of protein and rates of synthesis are, in a general way, 
determined by efficiency factors, the result of these considerations is that amounts 
and rates will be lowered according to the intensities of competition denoted by the 
various w’s. 
To see a little of what is involved, let us take a closer look at w. Since, in the steady 
state, M, = M, —... for a given protein, the summation of the M terms for each 
protein may be written as M, multipled by the number of times the terminal amino 
acid occurs in that protein. If we denote this number, for protein a, by mq, and so 
forth, we may write the wg of protein a (and of its terminal amino acid) as 
M,(a)/[maMi(a) + noMi(b) + ...]. 
If we were to assume that the M, factors for all proteins are nearly the same (which 
implhes that the rates of synthesis are the same, and is certainly not strictly true) 
as an approximation, this expression would be simply 1I/(#q + mp» + ...). That is, 
the competitive factor for any terminal amino acid will be inversely proportional 
to its total number of occurrences in the proteins of the system. 
More generally, recalling that dPr/dt = M,E’, and multiplying numerator and 
denominator of wg by E’, it appears as 
(dPrq|dt) |(na(dPra/dt) + ny(dPrp|dt) + ...]. 
That is, the competition factor is the rate of terminal incorporation in the given 
protein as a fraction of the total rate of incorporation into all its occurrences in all 
proteins. 
We get a particularly interesting view of the situation if we take account of the 
fact that, for a given terminal amino acid, the sum 2’M,E’ = LnjdPr;/dt is equal 
to the permeation rate for that amino acid and its precursor, an expression of the 
form HP + H’P’. Abbreviating this expression by 0, we have a linear equation 
LnjdPr;,/dt = o for the rates of synthesis of the various proteins. For each different 
kind of terminal amino acid, we can write a similar linear equation. If exactly x 
amino acids are terminal in all proteins, there will be « equations in the unknown 
rates of synthesis. 
There are more than x proteins, even if x = 20 (the number of different kinds of 
amino acids); and this introduces an indeterminacy into the system of equations. 
However, this may be removed by an approximate procedure as follows. 
For two proteins, a and b, with the same terminal amino acid, (dPr»/dt) /(dPrq/dt) = 
M,(b)/M,(a) = To(b)/T,(a). We can show that this ratio is proportional to the ratio 
of total template material for the respective proteins. For if we use the linear approxi- 
References p. 632 
