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Bifurcation analysis of a model of the budding yeast cell cycle

Dorjsuren Battogtokh, John J. Tyson

2004
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Chaos
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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 activity͒. 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
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... 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 states͒, we explore possible effects of extrinsic fluctuations on cell cycle progression. Most important events of the cell cycle-DNA synthesis, mitosis, and cell division-are regulated by a complex network of protein interactions that control the activities of cyclin-dependent protein kinases. The network can be modeled by a set of nonlinear differential equations, whose dynamics can be studied through numerical simu- lations. Bifurcation analysis is a mathematical tool which provides insights to numerical results. We illustrate this tool by comparing predictions from Chen's budding yeast cell cycle model to experiments carried out by Cross et al. †Mol. Biol. Cell. 13, 52 "2002... ‡, and by identifying reduced systems of equations retaining the main features of Chen's model. Bifurcation analysis also identifies a parameter region where cell cycle progression can be particularly sensitive to extrinsic fluctuations. D.; Tyson, J. J., "bifurcation analysis of a model of the budding yeast cell cycle," Chaos 14, 653 (2004); http://dx. Characteristic concentrations ͑dimensionless͒ ͓Cln3͔ max ϭ0.02 ͓Bck2͔ 0 ϭ0.0027 J d2,c1 ϭ0.05 J a,sbf ϭJ i,sbf ϭ0.01 J a,mcm ϭJ i,mcm ϭ1 J a,swi ϭJ i,swi ϭ0.1 J a,t1 ϭJ i,t1 ϭ0.05 Kinase efficiencies ͑dimensionless͒ ⑀ c1,n3 ϭ20 ⑀ c1,k2 ϭ2 ⑀ c1,b2 ϭ0.067 ⑀ c1,b5 ϭ1 ⑀ i,t1,n2 ϭ1 ⑀ i,t1,b2 ϭ1 ⑀ i,t1,b5 ϭ0.5 ⑀ sbf,n3 ϭ75 ⑀ sbf,b5 ϭ0.5 Other parameters f ϭ0.433 J n3 ϭ6 D n3 ϭ1 ϭ0.005 776

doi:10.1063/1.1780011
pmid:15446975
fatcat:kfq5hnjx7rgf3iamcqn3p7mvum