Modeling the cell cycle: Why do certain circuits oscillate?

James E. Ferrell, Tony Yu Chen Tsai, Qiong Yang

Research output: Contribution to journalReview articlepeer-review

227 Scopus citations

Abstract

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations.

Original languageEnglish
Pages (from-to)874-885
Number of pages12
JournalCell
Volume144
Issue number6
DOIs
StatePublished - Mar 18 2011

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