Alan Turing

Alan Turing was born 100 years ago, today: June 23rd, 1912. He was a pioneer of computing, cryptography, artificial intelligence, and biology. His most influential work was launching computer science by the definition of computable, introduction of Turing-machine, and solution of the Entscheidungsproblem (Turing, 1936). He served his King and Country in WW2 as the leader of Hut 8 in the Government Code and Cypher School at Bletchley Park. With his genius the British were able to build a semi-automated system for cracking the Enigma machine used for German encryption. After the war he foresaw the connectionist-movement of Cognitive Science by developing his B-type neural network in 1948. He launched the field of artificial intelligence with Computing machinery and intelligence (1950), introducing the still discussed Turing test. In 1952 he published his most cited work: The Chemical Basis of Morphogenesis spurring the development of mathematical biology. Unfortunately, Turing did not leave to see his impact on biology.

In 1952, homosexuality was illegal in the United Kingdom and Turing’s sexual orientation was criminally prosecuted. As an alternative to prison he accepted chemical castration (treatement with female hormones). On June 8th, 1954, just two weeks shy of his 42nd birthday, Alan Turing was found dead in his apartment. He died of cyanide poisoning, and an inquire ruled the death a suicide. A visionary pioneer was taken and we can only wonder: how would Alan Turing develop biology?

In The Chemical Basis of Morphogenesis (1952) Turing asked: how does a spherically symmetric embryo develop into a non-spherically symmetric organism under the action of symmetry-preserving chemical diffusion of morphogens? Morphogens are abstract particles that Turing defined; they can stand in place for any molecules relevant to developmental biology. The key insight that Turing made is that very small stochastic fluctuations in the chemical distribution can be amplified by diffusion to produce stable patterns that break the spherical symmetry. These asymmetric patters are stable and can be time-independent (except a slow increase in intensity), although with three or more morphogens there is also the potential for time-varying patterns.

The beauty of Turing’s work was in its abstraction and simplicity. He modeled the question generally via Chemical diffusion equations and instantiated his model by considering specific arrangements of cells like a discrete cycle, and a continuous ring of tissue. He proved results that were general and qualitative in nature. On more complicated models he also encouraged a numeric quantitative approach to be carried out on the computer he helped develop. It is these rigorous qualitative statements that have become the bread-and-butter of theoretical computer science (TCS).

For me, rigorous qualitative statements (valid for various constants and parameters) instead of quantitative statements based on specific (in some fields: potentially impossible to measure) constant and parameters is one of the two things that sets TCS apart from theoretical physics. The other key feature is that TCS deals with discrete objects of arbitrarily large size, while (classical) physics assumes that the relevant behavior can be approximated by continuous variables. The differential equation approach of physics can provide useful approximations such as replicator dynamics (example applications: perception-deception and cost-of-agency), I think it is fundamentally limited. Differential equations should only be used for intuition in fields like theoretical biology. Although Turing did not get a chance to pursue this avenue, I think that he would have pushed biology into the direction of using more discrete models.

Shnerb et al. (2000) make a good point for the importance of discrete models. The model is of spatial diffusion with two populations: catalyst A that never expires and a population B — agents of which expire at a constant rate and use A to catalyze reproduction. The authors use the standard mean-field diffusion approach to look at the parameter range where the abundance of A is not high enough to counteract the death rate of B agents. The macro-dynamic differential equation approach predicts extinction of the B-population at an exponential rate. However, when the model is simulated at micro-dynamic level with discrete agents, then there is no extinction. Clumps of B agents form and follow individual A agents as they follow Brownian motion through the population. The result is an abundance of life (B agents) at the macro-scale in contrast to the continuous approximation. This is beautifully summarized by Shnerb et al. (2000) in the figure below.

Figure 1 from Shnerb et al. (2000) showing Log of B agent concentration versus time for discrete (solid blue line) and continues (dotted red line) models.

Like Turing’s (1952) approach, the discrete model also shows clumping and symmetry breaking. However, the requirements are not as demanding as what Turing developed. Thus, it is natural to expect that Turing would have found similar models if he continued his work on morphogenesis. This is made more likely by Turing’s exploration of discrete computer models of Artificial Life prior to his death. I think that he would have developed biology by promoting the approach of theoretical computer science: simple abstract models that lead to rigorous qualitative results about discrete structures; Alan Turing would view biology through algorithmic lenses. Since he is no longer with us, I hope that myself and others can carry on his vision.

References

Shnerb NM, Louzoun Y, Bettelheim E, & Solomon S (2000). The importance of being discrete: Life always wins on the surface. Proceedings of the National Academy of Sciences of the United States of America, 97 (19), 10322-4 PMID: 10962027

Turing, A. M. (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 2(42): 230–65.

Turing, A. M. (1950) Computing Machinery and Intelligence. Mind.

Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London 237 (641): 37–72. DOI:10.1098/rstb.1952.0012

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Alan Turing: morphogenesis

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Impact of Alan Turing’s approach to morphogenesis
embryology history development

Shortly before his untimely passing, the computing pioneer Alan Turing published his most cited paper The Chemical Basis of Morphogenesis (1952).

The central question for Turing was: how does a spherically symmetric embryo develop into a non-spherically symmetric organism under the action of symmetry-preserving chemical diffusion of morphogens (as Turing calls them, an abstract term for arbitrary molecules relevant to development)? The insight that Turing made is that very small stochastic fluctuations in the chemical distribution can be amplified by diffusion to produce stable (i.e. not time varying except slow increases in intensity; although also potentially time-varying with 3 or more morphogens) patterns that break the spherical symmetry.

The theory is beautifully simple and abstract, and produces very important qualitative results (and also quantitative results through computer simulation, which unfortunately Turing did not get to fully explore). However, even in the definition Turing discusses some potential limitations such as ignoring mechanical factors, and the inability to explain preferences in handedness. The particular models he considers — a cycle of discrete cells and a circular tissue — do not seem particularly relevant. As far as I understand, the key feature is his observation of symmetry breaking through small stochastic noise and instability.

What was the most important contribution of Turing’s paper to developmental biology? Is his approach still used, or has the field moved on to other models? If his approach is used, how was the handedness problem resolved?

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asked Jun 23 ’12 at 9:43

Artem Kaznatcheev
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our current understanding of plant morphogenesis seems close to this idea (and there’s no problem of handedness). See my answer here. – Richard Smith Jun 23 ’12 at 11:56
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This is a very interesting question. Many people have researched this topic, and many still are. But regardless, I had never heard of Alan Turing’s contributions, so thank you!

First of all, I cannot actually find who first coined the term morphogen. Though people had hypothesized that chemicals could play a critical role in development through much of the 20th century, I cannot actually find the first person to use morphogen. But the most important paper really came from a guy named Lewis Wolpert, who came up with the model of a gradient of morphogens leading to differential cell fates. The idea being that if some area of an embryo produces a morphogen at a very high concentration, then as you move away from that area, the concentration goes down. So if this morphogen is required at or above a certain threshold for activity, then only those cells with that concentration will have a certain cell fate, while at lower concentrations, the cells can become something different.

But this does not really answer your question. You are asking how a single cell, which is spherically symmetrical, can determine a particular axis. Though most organisms do this is in slightly different ways, the most common feature is that sperm entry point breaks the symmetry. The best way to explain this is to show you a diagram of Xenopus (frog) eggs.

Image from: http://studentreader.com/nieuwkoop-center/

The Xenopus egg, first of all, is inherently not spherically symmetrical. There is a black animal pole, and a white vegetal pole. The sperm can only enter a marrow region of the egg about 30˚ north of the animal/vegetal line. Upon fertilization, an event occurs where the pigmented areas turn toward the sperm entry point, leaving a gray crescent. Nearby the gray crescent, in the vegetal pole, a structure called the organiser develops. This organiser creates many of the morphogens that then pattern the rest of the embryo.

Researchers have studied this a lot in many different organisms, but a few things really remain constant: eggs are not exactly spherically symmetrical, and the sperm entry point provides asymmetry.

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answered Aug 27 ’12 at 20:26

atomadam2
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Thank you for the answer. Any thoughts on the issue of handed-ness? Because a sperm entry point would still leave the egg achiral. – Artem Kaznatcheev Aug 27 ’12 at 21:03
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I would think this is very much still “used.” 60 years later, we finally have the first experimental support for it:

In this blog article about this journal piece the authors studied the ridges that form on the roof of mouse mouths. They manipulated the signaling molecules that induce their formation and observed changes in line with Turing’s theory. Of course, this doesn’t preclude other mechanisms from occurring, but supports that of Turing.

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edited Aug 28 ’12 at 18:31
Rory M♦
answered Aug 28 ’12 at 13:57

jmerkin
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Welcome to Bio.SE! When linking to articles you should summarise the content in your answer in case the article isn’t available in the future. – Rory M♦ Aug 28 ’12 at 14:30

Thanks. It’s not my field of biology (so I’m not an expert) but the authors studied the ridges that form on the roof of mouse mouths. They manipulated the signaling molecules that induce their formation and observed changes in line with Turing’s theory. Of course, this doesn’t preclude other mechanisms from occurring, but supports that of Turing. – jmerkin Aug 28 ’12 at 18:12
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