Formative capacities of mechanically stressed networks: developmental and evolutionary implications.

We present a biomechanical model of morphogenesis highlighting the extensive formative capacities of stressed networks with a very simple initial geometry. They consist of a restricted number of kinematically independent elements exerting a pressure to each other and increasing thus the local curvatures. The pressure is applied as a series of periodic impulses and is opposed by a constant quasi-elastic resistance force. Single elements can be also regarded as the half wave-lengths of the undulations determined by the mechanical properties of a given body. All of the model parameters are assumed to be evenly spread throughout a body (no prepatterns are implied). On the other hand, the model parameters can be associated with genetic factors. Thus, our model relates to as yet unsolved problem of genetic regulation of shape formation. We classify the modeled shapes according to their symmetry orders and compare them with the ancient Echinodermata and with Arthropods. Possible evolutionary and developmental implications are discussed.