Tooth eruption: the phase transition theory on biological formation of an orderly structure.

The mechanism of the formation of an orderly structure from random elements in organ development was clarified by studying the maturation of the dental arch in the human mandible. First, an application of methods established in statistical physics to a system of organ development was made possible, and then, the mathematical procedures for quantitative study of the structure and development of the dental arch were established in relation to radiographic data. The experimental results demonstrate that a parallel arrangement of the longitudinal axes of the lateral teeth is formed co-operatively in the dental arch. As formulation of the results to mathematical relations, the regulatory process was expressed by a non-linear Langevin equation of order parameter denoting an angle between longitudinal axes of the individual teeth. It follows that the orderly structure evolves with a change in thermodynamic potential; that is, the establishment of order in a phase transition. We propose the concept that organ differentiation is a phase transition in a dissipative system, with the decrease of gene activity substituted for temperature.