Cooperative regulation of cellular proliferation by intercellular diffusion.

A theoretical model for the cooperative control of cellular kinetics is investigated. A critical substance A is produced by the cells whose concentration in a given cell determines whether that cell can divide. The substance A can leak out of the cells into the surrounding medium as well as be reabsorbed by the cells. This feature then implies communication between the cells since all concentrations will be functions of the population density. The substance A also has a lifetime, i.e. decays, for example, by denaturation. This system can be described by three coupled nonlinear differential equations which can be solved analytically in certain limiting cases and can, of course, be studied in detail by computer techniques. Our investigations have shown that (a) there is a critical initial cell population density below which cell proliferation will not occur, (b) cell proliferation can be stimulated by supplying substance A to the medium and there is a critical initial concentration in the medium for initiating proliferation when the cell population density is subcritical, and (c) a well-defined induction period prior to exponential growth may exist whose length depends on the system parameters and initial conditions.