Bifurcation analysis of a model of the budding yeast cell cycle

• DOI: 10.1063/1.1780011
• Publication Date: 2004-08-31T22:13:02Z
• Authors: Dorjsuren Battogtokh; John J. Tyson
• Keywords: 0303 health sciences; Models, Statistical; Saccharomyces cerevisiae Proteins; Time Factors; Molecular Networks (q-bio.MN); Cell Cycle; Mitosis; DNA; Cyclin B; Models, Biological; 03 medical and health sciences; Nonlinear Dynamics; FOS: Biological sciences; Saccharomycetales; Quantitative Biology - Molecular Networks; Cell Division; Transcription Factors

We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression.