A model for the establishment of pattern by positional differentiation with memory.

A new model for the establishment of a pattern in a developing organism by means of positional differentiation is proposed. The model is capable of regenerating pattern in an amputated organism. The model uses a short range inductor and a long range inhibitor as signal carriers, as in many earlier works, but the following properties are different from previous (explicit) models: the processes of establishment of chemical and differentiated patterns proceed simultaneously; memory is included; there is no direct interaction between morphogens. Formulation of the model is in terms of linear differential equations, which are ordinary in the one dimensional case. Application to the slime mold Dictyostelium discoideum is discussed.