TEMPORAL VARIABILITY GENERATED BY COUPLING OF MITOTIC TIMERS

Cell proliferation is considered as a periodic process which is governed by a two-variable relaxation timer. The collective behavior of a system composed of three identical relaxation oscillators is numerically studied under the condition that diffusion of the slow mode (inhibitor) dominates. The phase diagrams for cyclic and linear configurations show unexpectable diversity of stable periodic regimes, some of them are only observable under intermediate but reasonable values of coupling and stiffness. For cyclic configuration we demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and unsymmetrical stable steady state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors and (4) the emergence of special kind of rotating wave which is manifested as two-loop limit cycle. The natural asymmetry of linear configuration leads to the appearance of many periodic attractors. The most of them are characterized by the large period oscillations of the middle element which has the step-like dependence of period versus coupling. The qualitative reasons for such a diversity and its possible role in the generation of cell cycle variability are discussed.