Phase-space description of the cell cycle: application to noncycling, senescent, and transformed cells

The behavior of a cellular biochemical reaction system can be portrayed by its trajectory in phase space. Phase-plane trajectories are proposed which depict the concentration of a characteristic chemical species in normally reproducing diploid cells, and in their noncycling, transformed, and senescent counterparts. It is assumed that the biochemical reaction system which determines the concentration of the characteristic species is nonlinear and nonconservative; the trajectories are therefore analyzed with the help of established qualitative mathematical techniques which are applicable to such systems. Mitotic cycles are presented as stable limit cycles; noncycling and senescent states are represented as isolated stable singular points. The concentration trajectory traversed in the transformed cell cycle surrounds the trajectory traversed in the normal cell cycle, which itself surrounds the singular point corresponding to the noncycling or senescent state. Transitions between the normal cycle and the noncycling state are associated with changes in the concentration of the characteristic species which exceed cyclically varying rate-dependent threshold values. Transitions from the normal cycle to the transformed cycle or to the senescent state are described by the coalescence and disappearance of the normal stable limit cycle with one of two adjacent unstable limit cycles.