Genes, Morphogenesis, Evolution: Life and ALife Aspects

Pattern and Form in Morphogenesis

Reaction-Diffusion Models

One of the most interesting and widely studied topic in modern theoretical biology is the structure formation from more or less homogeneous egg. Here some global field models of such processes are represented. A characteristic feature of these models is that they consider autonomous growth (autocatalysis) coupled to dissipative processes, such as diffusion.
In some cases one can consider these models as Turing's systems of the first kind, what is represented by differential equation:

More rarely Turing's systems of second kind are used

As was noticed, before the stable pattern can be generated two conditions have to be fulfilled: a local deviation from an average concentration of a pattern forming substance should furher increase (1) and this increase should not go to infinity (2).
In supposition that increase in one part of the field is necessarily conected with a decrease in another part of it, i.e. that the total amount of substances is roughly conserved, the process of the pattern formation should reach the stable steady state.
Thus the mechanism underlying pattern formation should be similar to local autocatalysis with strong positive feedback and lateral inhibition.
We separately consider

the model with diffusion (class1 models) and
without it (class2 models)

References

Reaction-Diffusion Models of Morphogenesis

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