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THE ROLE OF TIME-DELAYS, SLOW PROCESSES AND CHAOS IN MODULATING THE CELL-CYCLE CLOCK

By E. V. Presnov A and Z. Agur B

Abstract

The regulation of the cell-cycle clock is examined using a theoretical model for the embryonic cell-cycle, where the clock is described as a single limit cycle [1]. By taking the coefficient of the autocatalytic reaction as proportional to the deviation of the system from its equilibrium state we show how such clocks can be adjusted to function on several time scales. This feedback control, causing a periodic change in the sign of the autocatalytic reaction, may be interpreted as a periodic change in the ratio of cdc25/wee1 activity. Its introduction results in the appearance of a double limit cycle, signifying the acquisition of the G2-phase and the G1-phase, during embryonic development. Following the loss of stability of the double cycle, through a period doubling bifurcation, another limit set- a strange attractor- is born. The complicated geometry of this strange attractor can be viewed as an unlimited reservoir of periods in the phase space

Topics: cyclin, morphogenesis, Hopf bifurcation, limit cycle, autocatalysis. 1
Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.9809
Provided by: CiteSeerX
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