24
JACK COHEN
Fig. 7C). Occasionally, cells may line up as very narrow "ridges"; these
are ephemeral (but see Fig. IIB) and usually break up into islands of
epithelial cells.
These results must be regarded as only preliminary to a much fuller
investigation of the problem. Above all, some means must be found
either of obtaining expiants of constant size or of measuring the size in
a way which is relevant to the system under consideration. Because the
cultures show a little outgrowth, it is very difficult to see how this can
be done at the moment; it is hoped that taking the expiants from the
collars with a standard tool will minimize errors, and that this standardization may help to make meaningful correlations between temperature,
size of expiant, and number of barb ridges, as well as their periodicity.
Attempts to correlate variation in barb-ridge number at a given temperature with dimensions of the tissue involved have so far met with no
success at all. If, as Turing suggested, the final number of units for
systems of this kind is the nearest integer to one of the roots of his
equations (which are complex numbers), then one of two situations may
arise upon change of the parameters with temperature: either, for a
given dimension of the tissue, the wavelength will decrease steadily with
increase of temperature [with either similar or disparate increases in
Turing's a, b, c, d (the marginal reaction rates) and in the diffusion
rates] ; or, as the temperature increases and the parameters change, the
roots will come close to integers which are not consecutive and, indeed,
may be widely spaced. Dr. David Wishart of Birmingham University
Mathematics Department is investigating the properties of such systems,
and we hope to publish jointly in the near future.
However, our results to date do not enable us to say more than that
the production of feather barb ridges is not likely to be a simple Turing
system. Before experimental variation was tried, this system did have
all the properties that would lead one to anticipate a system of the
Turing kind; we now feel very much less confident about the other
systems suggested by Turing (e.g., tentacle number in Hydra, but see
Berrill, 1961, p. 193). This is referred to again in Section VII.
IV. Pigmentation—General
Of prime interest here is the interaction between cells of alien derivation (the neural crest) with the tissues of the skin and its appendages.
There is now no question as to the origin or history of these pigment
cells (melanoblasts -» melanocytes) ; some confusion in terminology has
resulted in difficulties of communication (e.g., Gordon, 1953; T. B. FitzPatrick and W. Quevedo, unpublished data, 1965), but the underlying
principles have not been found at fault since Willier (1952).
JACK COHEN
Fig. 7C). Occasionally, cells may line up as very narrow "ridges"; these
are ephemeral (but see Fig. IIB) and usually break up into islands of
epithelial cells.
These results must be regarded as only preliminary to a much fuller
investigation of the problem. Above all, some means must be found
either of obtaining expiants of constant size or of measuring the size in
a way which is relevant to the system under consideration. Because the
cultures show a little outgrowth, it is very difficult to see how this can
be done at the moment; it is hoped that taking the expiants from the
collars with a standard tool will minimize errors, and that this standardization may help to make meaningful correlations between temperature,
size of expiant, and number of barb ridges, as well as their periodicity.
Attempts to correlate variation in barb-ridge number at a given temperature with dimensions of the tissue involved have so far met with no
success at all. If, as Turing suggested, the final number of units for
systems of this kind is the nearest integer to one of the roots of his
equations (which are complex numbers), then one of two situations may
arise upon change of the parameters with temperature: either, for a
given dimension of the tissue, the wavelength will decrease steadily with
increase of temperature [with either similar or disparate increases in
Turing's a, b, c, d (the marginal reaction rates) and in the diffusion
rates] ; or, as the temperature increases and the parameters change, the
roots will come close to integers which are not consecutive and, indeed,
may be widely spaced. Dr. David Wishart of Birmingham University
Mathematics Department is investigating the properties of such systems,
and we hope to publish jointly in the near future.
However, our results to date do not enable us to say more than that
the production of feather barb ridges is not likely to be a simple Turing
system. Before experimental variation was tried, this system did have
all the properties that would lead one to anticipate a system of the
Turing kind; we now feel very much less confident about the other
systems suggested by Turing (e.g., tentacle number in Hydra, but see
Berrill, 1961, p. 193). This is referred to again in Section VII.
IV. Pigmentation—General
Of prime interest here is the interaction between cells of alien derivation (the neural crest) with the tissues of the skin and its appendages.
There is now no question as to the origin or history of these pigment
cells (melanoblasts -» melanocytes) ; some confusion in terminology has
resulted in difficulties of communication (e.g., Gordon, 1953; T. B. FitzPatrick and W. Quevedo, unpublished data, 1965), but the underlying
principles have not been found at fault since Willier (1952).