deodands

Approaching The Chemical Basis of Morphogenesis

From: R ...
To: jonathan@swintons.net

Subject: RE: morphogenesis

Hi Jonathan,
I'm a PhD student in ...

... my supervisor has asked me to understand the morphogenesis paper completely so that I know how these people came up with these equations and especially understand how and why Turing came up with the idea.
... I did pure mathematics many years ago but no applied maths so I know I can understand it with some help

Dear R,

If you want to approach Turing's 1952 morphogenesis paper from a technical point of view, you do need some applied mathematics. I would suggest you start with JD Murray, Mathematical Biology. It's written from a discipline very much in the shadow of the Turing paper. It has split from one to two volumes since I read it so I may be a bit out of date, but it certainly in the old edition the reaction-diffusion sections (half the book) cover most of the technical material in the Turing paper at an undergraduate level. It will be hard work if you have done no applied mathematics at all, but actually it's pretty straightforward stuff.

From a non-technical point of view, there are probably ten billion descriptions of the Turing instability around, so I will only recommend my own, which forms a section in an upcoming book chapter. That also points to a good few more references.

For a relentlessly optimistic view of the value of the Turing instability in understanding biological form, almost any exposition of mathematical biology will do, but Ian Stewart's Life's Other Secret is non-technical, well written and relentlessly optimistic. After reading one, though, I would strongly recommend anyone enthused by (great) books like Stewart's also to read Evelyn Fox Keller's Making Sense of Life for an insight into why biologists are much more indifferent to these theories than mathematicians think they ought to be (it's not technical ignorance: it's about what counts as an explanation).

In terms of 'how and why Turing came up with the idea', the 'why' is relatively well documented. There are several sections of Andrew Hodges' superb and readable biography devoted to Turing's early interests in pattern in nature, his growing interest in the neurophysiological construction of the brain, and the general problem of morphogenesis. As to the 'how' we have little concrete idea. I do have some mild speculations about this in the chapter mentioned above