New Mathematical Methods in the Life Sciences

Abstract

Haldane stated only way of real advance in biology lies in taking as our starting point, not the separated parts of an organism and its environment, but the whole organism in its actual relation to environment, and defining the parts and in this whole implying their existing relationships to the other parts and activities [1]. Recognizing the dangers inherent in oversimplification, we might nevertheless say that in medicine we are dealing functionally with highly complex systems of chemical reactions and with control mechanisms that affect the varying rates of these reactions. A living animal is perhaps the most complex chemical factory that will ever be devised. Its highly dynamic character has been brought into even sharper focus by the recent introduction of isotope techniques. It is clear that new approaches should be sought for viewing the human body as a whole and to make it possible to integrate and evaluate the information that has been accumulated but not necessarily interrelated about thousands of parameters developed in the study of living systems. Indeed it is interesting to note that the most recent developments have evolved out of the analogy between the automation and control of complex industrial processes (and decision making in general) and the complex metabolic and control processes of the human body. We appear to be at that point in human understanding when the greatest progress will be made if many processes are considered in relation to each other. Mathematical models of biochemical processes should now be undertaken that view the human body as a whole, as well as consider a particular organ which may incorporate a number of such processes. The idea of building mathematical models of biological systems is, of course, not new. Lotka, Rashevsky, Henderson, Michaelis, and others were early investigators who proposed mathematical models of biological systems or who pioneered in the quantification of parts of such systems. But it is only in recent years that the field has attracted a great deal of attention because now better tools are at hand to develop the basic ideas. The emerging nuclear and space age presents an especially difficult challenge to biological science and medical art. The stresses that may be placed on organisms by the completely new and stringent environments associated with these technologies are largely unknown. To understand the effects of these environments on the whole organism, especially on the human system, will be difficult and slow, if not impossible, within the present state of the biological arts and sciences. The reason is partly our lack of knowledge of individual biological phenomena, and partly the present lack of a technique for integrating a very large number of environmental effects. We should not try to decide in advance which lack is more important. Mathematical techniques and computing facilities