A mathematical model of periodic processes in membranes (with application to cell cycle regulation)

Intracellular Time Keeping: Epigenetic Oscillations Reveal the Functions of an Ultradian Clock

“…The model is based on an earlier one of Chernavskii et al (1977) in which a mitotic or cell division cycle oscillator with one slow variable (h, of the order of hours) and one fast variable (TR' of the order of minutes) may be described by the following system of equations:…”

Temporal variability in a system of coupled mitotic timers

“…In two-oscillator systems, the coexistence of two limit cycles was found semianalytically (Mustafin and Volkov 1984) and numerically (Volkov and Pertsova 1987). Detailed examination of the phase diagram showed that in contrast to other oscillators used earlier, the relaxation cell cycle timer (Chernavskii et al 1977) provides birhythmicity in a wide region of parameter space if the exchange of slow variables dominates. Such an exchange may be realized with a semipermeable membrane between chemical reactors or may be caused by selective features of the medium in which diffusion occurs.…”

“…Independently, the behavior of coupled oscillators playing the role of the cell's timers was studied in the framework of the membrane model of cell cycle regulation (Chernavskii et al 1977).…”

Rhythms in Plants

“…Using an established mathematical model of the cell cycle (Mustafin and Volkov 1977;Chernavskii et al 1977), it is possible to see how quantisation arises, provided that the ultradian clock modulates the mitotic oscillator Volkov 1990, 1991). Interestingly, chaotic solutions of the model can be obtained over quite a wide range of parameter values.…”