620 J. M. REINER 
We now write the stoichiometric equations for the reactions involved in syn- 
thesizing one particular protein—which one, for the moment, need not be specified: 
Ps Py Ey 
(A) Koi > Xj : Yi > Voi ; ti > VA 
Ej; 
Wwt+n> Ww 
joe 
Mi a resi = he ee 
Tn > Protein + T, 
It should be noted that we are treating all the reactions as irreversible. This is best 
viewed as an approximation adopted for the sake of mathematical simplicity; there 
may be occasions when we would like to investigate the consequences of the fact 
that some of the early reactions, at least, are in principle reversible. 
We may now write down the differential equations corresponding to the reactions 
of Scheme A. For abbreviation we will adopt one more notational convention with 
respect to enzymatic or permease reactions. We know" that enzymatic reactions 
involving one step may often have their rates expressed as k(Substrate) (Enzyme) / 
[Kk + (Substrate)], while bimolecular reactions will take the form 
k (Substrate 1) (Substrate 2) (Enzyme)/[K + aS, + bS, + cS,S,]. 
We will abbreviate such expressions, in a great deal of what follows, by such forms 
as A(Enzyme); and we will term the abbreviating symbol A the efficiency of the 
enzyme*. We shall in particular use the letter H, with suitable affixes, when referring 
to permeases. When it is desirable to express the efficiency of a step explicitly, we 
will frequently expand in a linear form, which would be a good approximation at low 
values of the concentrations—e.g., k(Substrate) or k(Substrate 1) (Substrate 2). 
However, the complete forms indicated above guarantee that every efficiency has a 
finite limiting value when the substrate concentration is sufficiently great. 
With these conventions, we may write: 
(1) dx;,/dt = H,P; — AjEy ; dy;{dt = Aj;Ey + Hi’ Pi’ — Bik; 
avi jdt = BEM Be Sata Se MORE’ 
(when 7 = I, 2, .... m — I) 
dT ,/dt = aTn — ME’ : dT,/dt = MnE’ — aTn 
d(Protein) /dt = aTp. 
* The efficiency is very nearly the same as what is usually termed the specific activity of an 
enzyme. However, we are talking about the activity per mole of protein, not the activity per 
milligram or per gram. Moreover, we want the term to cover permeases, for which we have as 
yet no clearcut evidence for an enzymatic function. Finally, the term specific activity already has 
a well-established usage in tracer isotope work. It seems preferable not to use the term in two 
ways. 
References p. 632 
