State vector description of the proliferation of mammalian cells in tissue culture. I. Exponential growth

Abstract

Proliferation of mammalian cells, even under conditions of unlimited growth, presents a complex problem because of the interaction of deterministic and stochastic processes. Division of the cell cycle into a finite number of parts establishes a multidimensional vector space. In this space an arbitrary culture can be represented by a vector called the state vector. The culture's subsequent growth is represented mathematically as a series of transformations of the state vector. The operators effecting these transformations are presented in matrix form and their relationship to the distribution of cell generation times is described. As an application of the model, the growth of an initially synchronized culture is considered and an unambiguous measure of the degree of synchrony is proposed. Results of a computer simulation of such a culture show the behavior with time of the degree of synchrony, the total cell number, and the mitotic index. In particular the importance of the magnitude of the coefficient of variation of the generation time distribution is illustrated.