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The French Flag model in developmental biology

Last modified: 2018-01-21 by ivan sache
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French Flag model - Image by António Martins, 8 October 2017

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Myers' rendition of the French Flag model

Noted biology professor and science popularizer P. Z. Myers designed a short video on the topic of "Positional information and morphogens".
It mentions the French flag model (timestamp: 00:01'40"), a conceptual definition of a morphogen, created by Lewis Wolpert in the 1960s. Myers says that "if a flag were a [pluricellular] organism, all a cell would need in order to determine the configuration of that particular flag is its distance from the flagpole". However (timestamp: 00:05'02") "this particular model" would yield a flag that is (timestamp: 00:05'29") "purplish, then pink, and then red".

António Martins, 8 October 2017

Wolpert's French Flag model

Lewis Wolpert (b. 1929; biography) is a British scientist of South African origin, widely engaged in popularization of sciences via books, interviews (Web of Stories), conferences, TV programs etc...

Wolpert presented the French Flag problem during the 3rd Meeting on Theoretical Biology held in 1968 at Villa Serbelloni, Bellagio, Lake Como (Italy). The four Serbelloni meetings were convened in 1966, 1967, 1968 and 1969 by Conrad Hal Waddington (1905-1975) to explore questions related to theoretical biology. Biologists, physicists and mathematicians raised many issues, identified relevant concepts and tools and stimulated the further developments of theoretical biology.
[The Waddington Centennial; C.H. Waddington. 1968. Towards a Theoretical Biology. Nature, 218, 525-527]

Wolpert's lecture was the source of the seminal paper "Positional information and the spatial pattern of cellular differentiation", published in 1969 in Journal of Theoretical Biology 25, 1-47.
Wolpert introduces the French Flag problem as follows:

I have formalized the problem of the regulative development of axial patterns, whose pattern is size invariant, in terms of the French Flag problem (Wolpert, 1968). This problem is concerned with the necessary properties and communications between units arranged in a line, each with three possibilities for molecular differentiation--blue, white and red-such that system always forms a French Flag irrespective of the number of units or which parts are removed; that is the left-hand third is always blue, the middle third is always white and the right-hand third always red. This abstraction of the problem corresponds quite well with experimental observations on the early development of sea urchin embryos, and regeneration of hydroids as well as a large variety of other systems.
It is perhaps also worth pointing out that all solutions to the French Flag problem appear to require three basic elements: (i) a mechanism for specifying polarity; (ii) a mechanism for the differential response of the cells, such as thresholds; and (iii) at least one spontaneous self-limiting reaction (Wolpert, 1968).

A more reader-friendly explanation of Wolpert's work, with emphasis on the scientific context of the time and subsequent legacy in the field of theoretical biology is provided by Jack Resnik (The French Flag Model. Embryo Project Encyclopedia, 2011)
Wolpert himself explains the French Flag problem in less than 80 seconds in the aforementioned series Web of Stories, April 2010.

Wolpert's French Flag model is still paradigmatic four decades after its publication, and still the matter of new developments. For instance, Patrick Hillenbrand, Ulrich Gerland and Gašper Tkačik proposed in 2016 "a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic 'French Flag' model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise."
[P. Hillenbrand, U. Gerland, G. Tkačik. 2016. Beyond the French Flag model: Exploiting spatial and gene regulatory interactions for positional information. PLoS ONE 11(9): e0163628]

Ivan Sache, 10 December 2017