Emergence of Recursivity through Isologous Diversification

Abstract

A scheme of inter-intra dynamics is presented for the study of biological systems. The dynamics consists of internal dynamics of a unit, interaction among the units, and the replication (and death) of units according to their internal states. Applying the dynamics to cell biology, isologous diversification theory is proposed for cell differentiation. Through several simulations and theoretical considerations, the cell differentiation is shown to proceed through the following steps: (1) Up to some number, cells, created by divisions, are almost identical, whose intracellular chemical oscillations are synchronized. (2)As the number exceeds some number, the oscillations lose the synchrony, and cells split into groups of different phases of oscillations. (3)Few distinct gropes of cell types are formed, with different (average) chemical compositions and different types of intra-cellular oscillations. (4) The differentiated behavior of states is transmitted by divisions to daughter cells. Recursivity is formed so that the daughter cells keep the identical chemical character. (5) Hierarchical differentiation proceeds, leading to the generation of the rule of differentiation. Relevance of the theory to cell biology is discussed.