A MODEL OF GROWTH AND GROWTH CONTROL IN MATHEMATICAL TERMS

Abstract

A practicable model of the growth process, which gives better definition to the problem of growth and growth regulation and greater precision to related experimental work than do earlier models, is developed on the basis of the following assumptions: "Growth" is the net balance of mass produced and retained over mass destroyed and otherwise lost, implying continual metabolic degradation and replacement. Terminal size represents stationary equilibrium between incremental and decremental components. The mass of an organic system consists of two functionally different components,—generative and differentiated. Generative mass increases by the catalytic action of key compounds ("templates") characteristic of each cell type. Each cell also produces specific freely diffusible compounds antagonistic to these templates ("antitemplates"). Growth regulation occurs automatically by a negative "feedback" in which increasing numbers of antitemplates progressively block the corresponding templates. Differential equations expressing these interrelationships are formulated, integrated, and the solutions evaluated for the case of chick growth. These specific solutions lead to descriptions of the normal growth of a biological system which are in good agreement with known facts, and to predictions of the course of automatic growth regulations after experimental or pathological disturbances which reproduce adequately biological observations in this domain.