BIOSYNTHESIS OF MACROMOLECULES 625 
mation for the M; (M; = my,'T;_,, treating the rate constant m of peptide bond 
synthesis as being the same for all bonds), we can solve the recursive set of equations 
M, =M, = ..., gettmg 1; = Toy,’ /yi' +1, In = my, PoE ja. From the conservation 
equation 
— an \ 7, 
1 total = PB) yl is 
z7=0 
it then follows that 7, = cTyo;., where 
c= DS Wey’ tna + my1/E’ Ja |. 
Since the y,;’ is constant in the steady state, and the rate of unpeeling from the 
template, a, is either a universal constant or characteristic of the given protein, and 
constant with respect to time, we may consider the c for each protein as a charac- 
teristic constant. For our two proteins a and b, therefore, we may restore the affixes 
and write T9(b)/To(a) = [Ttot.(b)/Ttot.(a)](co/ca). Abbreviating this ratio by the 
symbol cap, we have (dPry/dt)/(dPrq/dt) = cay. Thus, in an equation containing the 
two terms 1qdPrq/dt andnypd Pry /dt,wemay merge the two terms as (%q + Capnp)dPrq/dt. 
This effectively reduces the number of unknown rates to the number of terminal 
amino acids x. It has the disadvantage that the ca» presently cannot be computed 
independently of rate measurements. They must be treated as empirical constants 
to be determined from rate data. There are compensations for the somewhat inelegant 
character of this procedure, however; inferences about the relative availability of 
templates for various proteins would not be without interest. 
The problem of indeterminacy arises from our assumption that a common pool 
of activated amino acids is formed, and fed to all proteins. If activation occurred in 
small units (e.g., nbosomes) where only a few proteins are made, this indeterminacy 
would be removed. But we would have a separate set of biosynthetic equations for 
each kind of particle, not one set for the cell as a whole. 
The system of linear equations could in principle be solved straightforwardly by 
determinants; and from our knowledge of the expansion of determinants we can 
say that the solutions will be linear functions of the o’s. Since these are linear func- 
tions of P and P’, we are led to predict that each dPy/dt will be a linear function of 
P and P’, just as in (3) and (3’), but with coefficients that are linear functions of 
the various H and H’ efficiency factors, multiplied by functions of the ; only. 
In principle, therefore, we could find exact equivalents of (3) and (3’), which 
would still lend themselves to the same elementary methods of integration as before. 
In practice, however, the evaluation of determinants of high order whose elements 
are algebraic, not numerical, is not an attractive procedure. It is satisfying, however, 
to see that competitive interaction in protein synthesis would not seem to change 
the basic pattern of the equations of synthesis, when compared with a simpler treat- 
ment where this interaction is neglected. It is also interesting to see that the coeffi- 
cients of P and P’ in the rigorous rate expressions will depend on the permeation 
rates and external supplies of all the amino acids, and on the composition of all the 
proteins, which seems like an eminently reasonable result. 
References p. 632 
