An automaton model for the cell cycle

Abstract

We consider an automaton model that progresses spontaneously through the four successive phases of the cell cycle: G1, S (DNA replication), G2 and M (mitosis). Each phase is characterized by a mean duration t and a variability V. As soon as the prescribed duration of a given phase has passed, the transition to the next phase of the cell cycle occurs. The time at which the transition takes place varies in a random manner according to a distribution of durations of the cell cycle phases. Upon completion of the M phase, the cell divides into two cells, which immediately enter a new cycle in G1. The duration of each phase is reinitialized for the two newborn cells. At each time step in any phase of the cycle, the cell has a certain probability to be marked for exiting the cycle and dying at the nearest G1/S or G2/M transition. To allow for homeostasis, which corresponds to maintenance of the total cell number, we assume that cell death counterbalances cell replication at mitosis. In studying the dynamics of this automaton model, we examine the effect of factors such as the mean durations of the cell cycle phases and their variability, the type of distribution of the durations, the number of cells, the regulation of the cell population size and the independence of steady-state proportions of cells in each phase with respect to initial conditions. We apply the stochastic automaton model for the cell cycle to the progressive desynchronization of cell populations and to their entrainment by the circadian clock. A simple deterministic model leads to the same steady-state proportions of cells in the four phases of the cell cycle.

Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle

“…Likewise, phase locking of the cell cycle of budding yeast using periodic forcing of the G1 cyclin CLN2 has been demonstrated (9). Moreover, 1:1 phase locking has been shown for mechanistically detailed mathematical and automaton models of the mammalian systems (8,10,11).…”

Selecting a Differential Equation Cell Cycle Model for Simulating Leukemia Treatment

“…Therefore, the amplitude of the oscillations depends partly on the variability in G phase, which was also observed in cell automata models 33 and experimentally. 34 To summarize, the amplitude of the oscillations is controlled by phase durations at earlier times and by a balance of phase durations and phase variability at later times.…”

Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

“…Cellular automata enable to describe individual cancer cell evolution within a population of cells. Thus Altinok et al developed a cellular automaton for the cell cycle [3,4,5,6]. This automaton does not take into account molecular events but phenomenologically describes cell cycle progression.…”