A New Approach to Modeling Morphogenesis Using Control Theory

Abstract

It has been proposed that biological structures termed fractones may govern morphogenic events of cells; that is, fractones may dictate when a cell undergoes mitosis by capturing and concentrating certain chemical growth factors created by cells in their immediate vicinity. Based on this hypothesis, we present a model of cellular growth that incorporates these fractones, freely-diffusing growth factor, their interaction with each other, and their effect on cellular mitosis. The question of how complex biological cell structures arise from single cells during development can now be posed in terms of a mathematical control problem in which the activation and deactivation of fractones determines how a cellular mass forms. Stated in this fashion, several new questions in the field of control theory emerge. We present this new class of problems, as well as an initial analysis of some of these questions. Also, we indicate an extension of the proposed control method to layout optimization.