concentrations of substrate. When most of the enzyme is combined with substrate b is smaller, but still positive. [beta] must remain negative for equilibrium to be possible, but we can change the sign of [epsilon] by supposing Y to be formed (like trypsin, for example) by an autocatalytic process. Another simple model is:- [Diagram] It is assumed that A and B are formed irreversibly from large stores of P and Q, and pass over irreversibly into D and E by quasi- unimolecular reactions. They also form a small amount of a compound C by rapid reversible reaction. C catalyses both the reactions P[forward arrow]A and Q[forward arrow p]B, which, however, may also proceed in the absence of C. For example, A might be a substance like a cozymase and B an enzyme with which it acts as a coenzyme. Then if X and Y are the concentra- tions of A and B dX/dt = [alpha] - [beta]X + [gamma]XY dY/dt = [delta] - [epsilon]Y + [xi]XY all constants being positive. Hence a = [alpha]/h, b = [gamma]/h, c = [xi]k, d = [delta]/k. I am, of course, aware that these equations will only be nearly linear over a short range, but until some concrete examples which are linear over a wide range are known, it is, to my mind, confusing to postulate them <u>ad hoc<\u>. It will certainly make the whole theory appear implausible to many readers. The conclusion regarding case (d) in p.35 is important. It might be possible to state it is [sic] words, for the benefit of non-mathematical readers. In fact, the inequalities are not even given a number, and must be searched for. I am quite unable to understand the reactions postulated on p.46. The substance C appears to be removed by the reaction Y + C[forward arrow]C’, and is not regenerated. Thus C would be irreversibly destroyed, and I cannot see how the remaining argument follows, (particularly as “C” appears to be omitted on p.50 1.4).
Please login to transcribe
Referee report by J. B. S. Haldane on 'On the Chemical basis of Morphogenesis' by A. M. Turing, 1951. From The Royal Society, RR/1950-51/B62/2
Please login to comment