Biophysical Journal 8: 1353-1398 (1968)
© 1968 the Biophysical Society

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The Stochastic Theory of Cell Proliferation

ABSTRACT

A stochastic theory of cell kinetics has been developed based on a realistic model of cell proliferation. A characteristic transit time, _i, has been assigned to each of the four states (G₁, S, G₂, M) of the cell cycle. The actual transit time, t_i, for any cell is represented by a distribution around _i with a variance _i². Analytic and computer formulations have been used to describe the time development of such characteristics as age distribution, labeling experiments, and response to perturbations of the system by, for example, irradiation and temperature. The decay of synchrony is analyzed in detail and is shown to proceed as a damped wave. From the first few peaks of the synchrony decay one can obtain the distribution function for the cell cycle time. The later peaks decay exponentially with a characteristic decay constant, , which depends only on the average cell-cycle time, , and the associated variance. It is shown that the system, upon any sudden disturbance, approaches new "equilibrium" proliferation characteristics via damped periodic transients, the damping being characterized by . Thus, the response time of the system, /, is as basic a parameter of the system as the cell-cycle time.