Referee report by J. B. S. Haldane on 'On the Chemical basis of Morphogenesis' by A. M. Turing

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                                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).

                            
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Manuscript details

Author
Alan Turing
Reference
RR/1950-51/B62/2
Series
RR
Date
1951
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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

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