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Hysteresis and Cell Cycle Transitions: How Crucial Is It?

Zhangang Han ^* , Ling Yang ^* , W. Robb MacLellan ^*  , James N. Weiss ^*   and Zhilin Qu ^* 

^* Cardiovascular Research Laboratory, Departments of Medicine (Cardiology) and Physiology, David Geffen School of Medicine at the University of California, Los Angeles, California 90095

Correspondence: Address reprint requests to Zhilin Qu, PhD, Dept. of Medicine (Cardiology), 47-123 CHS, 10833 Le Conte Ave., University of California, Los Angeles, CA 90095. Tel.: 310-794-6050; Fax: 310-206-9133; Email: zqu{at}mednet.ucla.edu.

Recently, experiments have shown that cyclin-dependent kinase (CDK) activity exhibits hysteresis in its response to total cyclin when cyclin is made nondegradable and controlled externally. This observation was taken to support mathematical modeling predictions regarding the underlying dynamics of the cell cycle. However, cell cycle dynamics can also be generated by other nonhysteretic mechanisms. To examine the robustness of the hysteretic response of CDK activity to total cyclin, we simulated various cell cycle signal transduction networks, and correlated the dynamics to the response function of CDK activity versus total cyclin. By randomly searching the parameter space, we assessed robustness by estimating the frequency of hysteretic versus nonhysteretic dynamical mechanisms. When the dynamical instabilities were caused by feedback loops in CDK phosphorylation and dephosphorylation or by feedback between cyclin and the CDK inhibitor, the response function of CDK activity versus total cyclin correlated well with the dynamical instabilities. However, when the dynamical instabilities originated from feedback between cyclin and APC-CDH1 or RB-E2F, the response function did not correlate with dynamical instabilities. Thus, although a hysteretic response is neither necessary nor sufficient, it is in general a much more robust mechanism for generating cell cycle dynamics than nonhysteretic mechanisms.

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