The Kinetics of Growth

Abstract

A quantitative expression for the growth rate of living systems can only be obtained when the systems are homogeneous (or of known heterogeneity), and when the external conditions are constant. When more than one type of cell is present, or when the external conditions are varying, the known data (concerning even unorganised growth), are insufficient for the construction of a real equation defining the rate of growth in a given set of conditions existing at a particular instant of time. An equation representing the size of a population of cells or of an organism in terms of age, yields, on differentiation, a quantitative but empirical representation of the factors controlling the rate of growth, but since more than one equation can always represent a typical growth curve within the limits of probable error, a selection of one particular equation rests solely on the intrinsic probability of its differentiated form. The degree of probability can only be established by direct experiment. In the growing body of a metazoon the conditions of growth are extremely complex, and it is difficult to express the growth rate of the whole organism in terms of rational units. Graphical treatment of the data underlying a typical growth curve is liable to produce errors of considerable magnitude, and often tends to confuse the facts. The units which compose a metazoon's body form a very heterogeneous system, in which the rate of growth of one organ is dependent on that of others. It is, therefore, intrinsically improbable that the behaviour of such a system should conform to that of a simple chemical system in which the variables are few in number and capable of accurate analysis. The conception of growth as a simple physico-chemical process should not be accepted in the absence of very rigid and direct proof; at present, it rests on the results of a process of graphical analysis which is often, if not always, of a relatively inaccurate nature.