Nonlinear dynamical model for tissue control growth

Cancer research deals mainly with the study of genoma alterations associated with tumour apparition. This approach has been fruitful leading to the discovery of oncogenes. The study of tumour formation, however, cannot be limited to the genome. It is necessary to study collective behaviour of cells in the tissue. Recent results strongly suggest that many kinds of cancer can be caused by disfunctions in the communication mechanisms between cells. On the other hand, it is known that almost everything that has been measured in the cell, shows periodic oscillations (proteins, DNA, RNA, transmembrane potentials, etc.). Thus, early has been hypothesized that some kind of biochemical clock underlies the control of the mitotic cell cycle. In this paper we present a model for the control of tissue growth which bound together the two ingredients before mentioned, that is, we propose that a control substance is exchanged which affect the dynamical parameters of the biochemical clocks attaining in this way the homeostatic control of tissue growth. In our point of view, the tissue can be considered as a set of nonlinear coupled oscillators, being the global dynamical behaviour of the system, the crucial factor in the growth regulation strategy. Numerical simulations of the model for different parameters values, show distinct asymptotic behaviours which can be associated with normal and pathological conditions of the tissue.