"The time needed to set up a gradient: detailed calculations"

Date:: 1970-1971

Reference:: PP/CRI/H/4/25

Catalogue details

Licence: In copyright

Credit: "The time needed to set up a gradient: detailed calculations". Source: Wellcome Collection.

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Introduction In embryological development there are many cells which acquire positional information (see, for example, Wolpert, 1969) and it is plausible that this is obtained from the concentration of certain unknown chemicals (called here morphogens) which are diffusing down concen tration gradients set up by sources and sinks at special places in the embryo. It is therefore important to be able to calculate how much time is needed to set up a steady concentration gradient. This problem has been discussed in a recent paper (Crick, 1970) which suggests that the times available are roughly what might be expected on theoretical grounds. Here we give the details of various calculations quoted in that paper. The physics and mathematics of diffusion are fairly straight forward. The classic references are two books: The Conduction of Heat in Solids by Carslaw and Jaeger, 2nd Edition, 1959, (here referred to as C. and J. ) and The Mathematics of Diffusion by J. Crank, 1956. Results which could not be obtained easily in an algebraical form were calculated by computer. Although a tissue consists of discrete cells, we have often found it convenient to treat it as a continuous medium, in which the morphogen has a diffusion constant D cm^/s. On the other hand, in calculations on

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