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

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                                <u>The Chemical Basis of Morphogenesis</u>
by A.M. Turing, F.R.S.

Before the paper is accepted, I consider that the whole mathematical part should be re-written. In the first place, some 
passages assuming ignorance in readers might be omitted without 
much loss. Secondly, much of the biology, e.g. pp 56-58, can be 
found in elementary textbooks, and often stated more accurately 
(e.g. exceptional flowers with abnormal petal numbers are found in 
nature). A biologist does not need to be told that men and snails 
are asymmetrical, nor does he need a description of Hydra. Similarly, 
the gist of p.9 will be found in any good textbook of biochemistry, 
illustrated by concrete examples, and perhaps stated more clearly.
I am sure that the general results would be more readily accepted 
if the author did not postulate hypothetical (and to my mind most 
improbable) reactions such as those of pp. 14 and 46.
As I see it all his later results up to p.44 follow from equation 
(6.2). This states that within each cell (considered for the moment 
as isolated)
dX/dt = f(X,Y), dY/dt = g(X,Y).
Further f(h,k) = g(h,k) = 0, and neither f nor g has a stationary 
point near the equilibrium point. If this is so equation (6.3) 
follow so long as x and y are small. Now concrete examples can be 
given of substances of biochemical interest behaving in this way.
For example, a number of enzymes (X) destroy their substrates (Y) 
and are protected from destruction by other agencies while combined 
with the substrate. If then X and Y are produced at constant rates, 
and removed by quasi-uni-molecular reactions, we have 
dX/dt = [alpha] - [beta]X + [gamma]XY 
dY/dt = [delta] - [epsilon]Y - [xi]XY (all constants positive).
Then if [alpha] - [beta]h + [gamma]hk = [delta] - [epsilon]k - [xi]hk = [theta]
dx/dt = ([gamma]k - [beta])x + [gamma]hy 
dy/dt = - [xi]kx - ([epsilon] + [xi]h)y 
approximately. So a = -[alpha]/h, b = [gamma]h, c = -[xi]k, d = -[delta]/k. Hence by 
the formulae of p.35 it should be possible to choose [mu]’ and [nu]’ 
so as to give case (d). The above equations only hold at low 
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Alan Turing
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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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