Quantitative modeling and biology: the multivariate approach.

Even though elegant examples of mathematical modeling of biological problems exist, such approaches still remain outside the domain of most biologists. It is proposed that, for a wider and more systematic use of mathematical models in biology, the soft modeling approaches, which are applicable to phenomena with a limited level of definition, should be investigated and preferred. In particular, multivariate data analysis (MDA) is indicated as an important tool toward fulfilling this goal. This paper reviews the general principles of MDA and examines in detail principal component analysis and cluster analysis, which are two of the most important MDA techniques. A number of applications to real biological problems are presented. These examples show how the construction of classifications corresponds to the generation of new knowledge and new concepts, which are hierarchically on a higher level than the initial information. This new form of knowledge is obtained without superimposing a priori theories on the data. It is demonstrated how the MDA can lead to the identification of biological systems; also shown is their ability to describe multiple scale phenomena, a typical feature of biological systems. Moreover, the multivariate analyses provide new descriptors for a given biological system; these descriptors are quantitative, thus allowing the system to be described in a "metric space," where it then becomes possible to use any other mathematical tool.