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BISTABILITY AND SELF-OSCILLATIONS IN CELL CYCLE CONTROL

VALKO PETROV

Institute of Mechanics and Biomechanics, Acad. G. Bonchev St., bl.4, 1113 Sofia, Bulgaria

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MARTIN PEIFER

Centre for Data Analysis and Modelling, University of Freiburg, Eckerstr.1, 79104 Freiburg, Germany

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, and

JENS TIMMER

Centre for Data Analysis and Modelling, University of Freiburg, Eckerstr.1, 79104 Freiburg, Germany

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https://doi.org/10.1142/S0218127406015313Cited by:4 (Source: Crossref)

Abstract

A qualitative model of cell cycle control is presented and its transition from bistability to limit cycle oscillations and vice versa is discussed. The origin of this model is the two-dimensional system of kinetic equations introduced by Novak–Tyson which is illustrated computationally and analytically. For this purpose a qualitative model is numerically reconstructed from the steady state behavior of the dynamical variables including the bifurcation parameter. Then, the reconstructed cubic polynomial model is generalized to an appropriate canonical form and is analyzed in terms of Lyapunov values. On this basis, the relationship between bistability and self-oscillatory behavior of mitotic cell cycle is approached qualitatively.

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