I have more many years worked on pattern in the developing embryo formation which is the development of spatial organization as seen, for example in the arm and hand. My main model for pattern formation is based on cells acquiring a positional value. The model proposes that cells have their position specified as in a co-ordinate system and this determines, depending on their developmental history and their genetic constitution what they do.
The development of the chick limb illustrates some of the problems. As the wing grows out from the flank up there is a thickened ridge of the covering sheet of cells that secretes special proteins which we think, and this is controversial, specifies a region in the cells beneath the ridge which we call the progress zone. At the posterior margin of the limb is the polarising region which secretes a protein, Sonic Hedgehog. This is a signaling molecule used again and again in the development of the embryo. The normal pattern of digits in the chick wing is 2, 3, and 4. If another polarising region is grafted to the anterior margin the pattern of digits is 4, 3, 2, 2, 3, 4.
The interpretation is that Sonic Hedgehog sets up a gradient which specifies position and with the graft there is a mirror image gradient and Crick suggested this was due to diffusion of a molecule like sonic hedgehog setting up a gradient. We have worked hard to show that this model is correct.
The best evidence that it maybe gradient is that if just a small amount of Sonic Hedgehog in the anterior margin then you just get an extra digit 2. If one increases it a bit put a little bit more and you get a 3, 2. But is there really a diffusible gradient in Sonic Hedgehog specifying position? The situation is much more complex.
We now think that the model is wrong as diffusion of a molecule is far too unreliable for reliably and accurately specifying positional values. The reasons why we think diffusion cannot work is that there is now good evidence that a diffusing molecule has to go between and even into cells, and interact with extracellular molecules making it totally unreliable. A more attractive model might be based on interactions at cell contacts as in the polarity models proposed by others. Position would be specified by cells talking to each other.
This is a serious change in my thinking.