The Kinetics of Growth

Abstract

The relationship between the increase in size of a growing organism and the period of time occupied in the process largely depends upon the nature of the environment in which the growing cells are placed. If a bacterium or a fibroblast is isolated in a suitable culture medium, the cell will divide and grow at a constant rate as long as the external conditions remain the same. If, on the other hand, the environment is changed, the rate of growth also changes, being accelerated in some cases and retarded in others. As far as is known, the rate of growth of isolated cells does not change with the age of the culture but for any particular species remains fixed in any given set of external conditions. In marked contrast to this is the behaviour of cells occupying their normal position in the body of an animal. In this case, the rate of growth of individual cells and of the whole population of cells forming the organism exhibits a marked decline with the advancing age or size of the organism, and this decline is, partially at any rate, independent of the external conditions of the animal’s environment. It is possible to imagine that if we were able to adjust the medium surrounding isolated cells in vitro so that the chemical and physical conditions were precisely the same as in the body, we would observe a course of growth identical in quantity, if not in form, with that observed in vivo. Conversely, from a knowledge of those factors which influence growth in vitro we ought to be able to deduce the nature and distribution of the factors which control the growth of the whole body. Unfortunately we know very little of the factors controlling growth in vivo and we cannot, as a rule, interfere with the normal growth rate except by varying the amount and type of foodstuffs available for conversion into new tissue, or in certain cases by altering the temperature of the organism. It is quite clear that the organised growth of a whole organism is controlled by a series of factors which have not yet been isolated, and which play no obvious part when a homogeneous tissue is excised from the body and grown in vitro. For example, the rôles played by the “organiser” and by the hypophysis are not yet fully understood, and as yet we are unable to reproduce in vitro a type of biological environment for our homogeneous cultures in vitro which approximates in any real way to the internal environment of an animal’s body. For this reason we tend to fall back on less direct methods of attack and endeavor to define the nature of the factors controlling the rate (if not the form) of normal growth by a careful observation of the way in which the rate changes during the life of a normal animal. The results of such enquiry are curious in that the highly complex changes going on in the body appear to receive an adequate quantitative expression by algebraic equations of a comparatively simple type. If the course of growth in vivo can be expressed by a curve of a particular geometrical form and by no other curve, it is obvious that we have established a fact of fundamental importance, and can proceed at once to give quantitative expression to the factors controlling the growth rate at every instance during the life of the growing organism although we may be unable to isolate these factors as definite physical or chemical entities. Since, at present, it is impossible to isolate these factors experimentally, and since it is comparatively easy to construct an ordinary growth curve, it becomes of immediate importance to know precisely how far the deductions drawn from this curve are really valid, and how far they are fallacious.