TY - JOUR

T1 - Modeling the cell cycle

T2 - Why do certain circuits oscillate?

AU - Ferrell, James E.

AU - Tsai, Tony Yu Chen

AU - Yang, Qiong

N1 - Funding Information:
We thank Markus Covert for the idea of starting this tutorial with a Boolean analysis instead of plunging right into ODEs and David Dill for helpful discussions. This work was supported by NIH GM077544.

PY - 2011/3/18

Y1 - 2011/3/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79952637804&partnerID=8YFLogxK

U2 - 10.1016/j.cell.2011.03.006

DO - 10.1016/j.cell.2011.03.006

M3 - Review article

C2 - 21414480

AN - SCOPUS:79952637804

VL - 144

SP - 874

EP - 885

JO - Cell

JF - Cell

SN - 0092-8674

IS - 6

ER -