ON THE MECHANICAL THEORY FOR BIOLOGICAL PATTERN-FORMATION

We investigate the pattern-forming potential of mechanical models in embryology proposed by Oster, Murray and their coworkers. We show that the presence of source terms in the tissue extracellular matrix and cell density equations give rise to spatio-temporal oscillations. An extension of one such model to include 'biologically realistic long range effects induces the formation of stationary spatial patterns. Previous attempts to solve the full system were in one dimension only. We obtain solutions in one dimension and extend our simulations to two dimensions. We show that a single mechanical model alone is capable of generating complex but regular spatial patterns rather than the requirement of model interaction as suggested by Nagorcka et al. and Shaw and Murray. We discuss some biological applications of the models among which are wound healing and formation of dermatoglyphic (fingerprint) patterns.