A SUGGESTION OF A NEW APPROACH TO THEORY OF SOME BIOLOGICAL PERIODICITIES

Previous studies of L. Danziger and G. Elmergreen (Bull. Math. Biophysics, 16, 15-21, 1954;18, 1-13, 1956) of possible biochemical periodicities in organisms assumed non-linear biochemical interaction between different metabolites, because linear systems do not lead to undamped ocsillations. They treated homogeneous systems. Later N. Rashevsky generalized their results to a more realistic case where the non-homogeneity due to the histological structure is considered. (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1964;Bull. Math. Biophysics, 29, 389-393, 1967.) As long as the histological structure remains constant, the existence of sustained periodicities requires the assumption of non-linearity of biochemical interactions. If, however, the secretions of an endocrine gland affect the histological structure of the target organ, notably as in the menstrual cycle, and if there is a feed-back, the equations become non-linear and may admit sustained periodic solutions even if the purely biochemical interactions are linear. © 1968 N. Rashevsky.