What type of empirically verifiable predictions can topological biology make?

Abstract

It has been shown previously (Bull. Math. Biophysics,17, 207–218, 1955) that within the framework of the general principle of biotopological mapping a number of different specific hypotheses can be made about the topological structure of the primordial organism and the transformation which lead to the description of higher organisms. Each set of such hypotheses leads to different conclusions and different predictions of specific biological relations. In the present paper it is shown that while the specific predictions depend on the specific assumptions within the framework of the general principle of biotopological mapping, the type of the predicted relation is characteristic of the general topological approach. Relations of this kind would hardly ever be considered in the usual metric approach to mathematical biology. As specific examples it is shown how topological considerations lead to the problem of the total number of possible organisms, the problem of relations between number of organs and number of cell types in an organism, the problem of the number of cell types in different organs, a possible approach to the problem of the number of different endocrine secretions in different organisms, and other similar problems. All this shows the predictive value of topological biology.