[Effect of delay on auto-oscillations in cell populations]

Abstract

A model of homogenous cell population is analysed, the mitotic activity of which is controled by an inhibitor produced by the cells themselves. While deducing the model it is assumed that the inhibitor concentration is proportional to the population density at some preceding time moment. The density change in time is described by a delay differential equation: dx/dt=alpha x/(1+x(v)(t--0))--x. According to this equation oscillation of cell number may be observed in the population with an increase of the critical value of delay in the mechanism of mitotic activity inhibition. The oscillation period determined analytically in linear approximation equals the quadruplicated time of delay. Numerical integration of the model has shown that the period observed is close to the calculated one.