The dynamics of zeroth-order ultrasensitivity: A critical phenomenon in cell biology

Pages: 1457 - 1464, Volume 4, Issue 6, December 2011

doi:10.3934/dcdss.2011.4.1457       Abstract        References        Full Text (374.8K)       Related Articles

Qingdao Huang - College of Mathematics, Jilin University, Changchun 130012, China (email)
Hong Qian - Department of Applied Mathematics, University of Washington, Seattle, WA 98195, United States (email)

Abstract: It is well known since the pioneering work of Goldbeter and Koshland [Proc. Natl. Acad. Sci. USA, vol. 78, pp. 6840-6844 (1981)] that cellular phosphorylation- dephosphorylation cycle (PdPC), catalyzed by kinase and phosphatase under saturated condition with zeroth order enzyme kinetics, exhibits ultrasensitivity, sharp transition. We analyse the dynamics aspects of the zeroth order PdPC kinetics and show a critical slowdown akin to the phase transition in condensed matter physics. We demonstrate that an extremely simple, though somewhat mathematically "singular" model is a faithful representation of the ultrasentivity phenomenon. The simplified mathematical model will be valuable, as a component, in developing complex cellular signaling netowrk theory as well as having a pedagogic value.

Keywords:  Ultrasensitivity; PdPC; critical phenomenon; cooperative processes.
Mathematics Subject Classification:  92C40.

Received: March 2009;      Revised: September 2009;      Published: December 2010.

 References