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 It has split from one to two volumes since I read it so I may be a bit out of date, but it certainly in the old edition the reaction-diffusion sections (half the book) cover most of the technical material in the Turing paper at an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
Alan Turing: the Enigma
Andrew Hodges, Alan Turing: the Enigma.
A great read; don't forget the website.
Mathematical Biology
JD Murray, Mathematical Biology. (My local bookshelf has an apparently new edition of this in two volumes, but Amazon still thinks there is a single edition.)
See Jim with the cheetah. See the spots of the cheetah. Do you like spots? Jim likes spots. The cheetah likes spots. Jim likes the cheetah. See Jim with the model. See the spots of the model. The model has spots. Jim likes the model.
See Jim with the zebra. See the stripes of the zebra. Do you like stripes? Jim likes stripes. The zebra likes stripes. Jim likes the zebra...
See Jim with the butterfly...
Or, this book taught me all I know about the mathematics of morphogenesis. Oddly, no mention of Hox in the index.
Making Sense of Life
Evelyn Fox Keller, Making Sense of Life
One of those books that expresses things you knew but couldn't express. Plus a whole lot more that I didn't know (and some that I didn't read because I had to take it back to the library, but I will have another go at it soon).
Fox Keller argues, with scholarship and the force of personal experience, that there are good reasons that working developmental biologists are uninterested in D'Arcy Thompson, Turing, and the mathematical biology project, and those reasons are not technical ignorance. It's because the nature of what counts for an explanation differs between the mathematically and the biologically trained.
A couple of quotations:
D'Arcy Thompson is sometimes claimed as the father of mathematical biology, but as is so often the case with the granting of retrospective paternity, such claims may have more to do with legitimization than actual kinship.
The voice of a woman has been there:
Anyone who has observed encounters between experimental biologists and theoretical physicists (or applied mathematicians) will surely have noticed the bristling of the biologists when faced with the discplinary hubris of physicists that is so familiar on their own turf as to go unnoticed. Elsewhere, however (Is there an organism in this text?, pp273-290 of PR Sloan, ed, Controlling our destinies, Notre Dame, 2000) I have argued that misunderstanding and frustration typical of such encounters is not due only to hubris but also to deep differences in understanding between the two disciplines regarding, first, the nature of theory, and, second, its relation to practice.
Life's Other Secret
Ian Stewart, Life's Other Secret.
Ian Stewart argues that mathematical explanations will be as important to future biology as genetic ones. Full of great examples, written in characteristically fluent Stewart style, and in the tradition of D'Arcy Thompson. But without some deeper understanding (pace Fox Keller) of why biologists haven't yet actually signed up to D'Arcy Thompson either, perhaps these mathematical hypotheses will remain comfort tales for our mathematics students and unemployed (sorry, newly interdisciplinary) physics postdocs.
