Formal grammars and the regeneration capability of biological systems

摘要

A biological experiment to measure regeneration capability often involves cutting out a part or parts of an organism, and comparing the subsequent development of the damaged organism with that of a normal specimen of the same kind. Outside the laboratory, the natural environment of some organisms during development and adulthood can inflict a sequence of accidents from which, providing the accidents are not unusually severe, the organism is able to recover, at least partially.A definition is proposed to place such damage and regeneration in the framework of an existing formal model for biological growth and development.Some results linking the stable adult configurations of such models with the languages of the Chomsky hierarchy are reviewed. Then it is shown that, while the stable adult configurations which can be achieved by models without cellular interactions in the absence of damage correspond exactly to the context-free languages, the analogous sets of configurations obtained when damage is inflicted are regular languages. It is also shown that, in spite of the simplicity of the models without cellular interactions, there is no algorithm which will decide for any such model whether or not it is capable of complete regeneration. Finally, it is shown that cell death and replacement plays an important role in regeneration.