Journal Article

What cycles the cell? –Robust autonomous cell cycle models

Orit Lavi and Yoram Louzoun

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 4, pages 337-359
Published in print December 2009 | ISSN: 1477-8599
Published online July 2009 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqp016
What cycles the cell? –Robust autonomous cell cycle models

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The cell cycle is one of the best studied cellular mechanisms at the experimental and theoretical levels. Although most of the important biochemical components and reactions of the cell cycle are probably known, the precise way the cell cycle dynamics are driven is still under debate. This phenomenon is not atypical to many other biological systems where the knowledge of the molecular building blocks and the interactions between them does not lead to a coherent picture of the appropriate dynamics. We here propose a methodology to develop plausible models for the driving mechanisms of embryonic and cancerous cell cycles. We first define a key property of the system (a cyclic behaviour in the case of the embryonic cell cycle) and set mathematical constraints on the types of two variable simplified systems robustly reproducing such a cyclic behaviour. We then expand these robust systems to three variables and reiterate the procedure. At each step, we further limit the type of expanded systems to fit the known microbiology until a detailed description of the system is obtained. This methodology produces mathematical descriptions of the required biological systems that are more robust to changes in the precise function and rate constants. This methodology can be extended to practically any type of subcellular mechanism.

Keywords: cell cycle; feedback loops; robust; stability; bifurcation theory; Lyapunov

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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