Skip Navigation



Mathematical Medicine and Biology Advance Access published online on July 6, 2009
Mathematical Medicine and Biology, doi:10.1093/imammb/dqp016
This Article
Right arrow Full Text (PDF)
Right arrow Supplementary Data
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Lavi, O.
Right arrow Articles by Louzoun, Y.
PubMed
Right arrow PubMed Citation
Right arrow Articles by Lavi, O.
Right arrow Articles by Louzoun, Y.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

What cycles the cell? –Robust autonomous cell cycle models

Orit Lavi

Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel

Yoram Louzoun{dagger}

Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat Gan 52900, Israel

{dagger} Email: louzouy{at}math.biu.ac.il

Received on October 29, 2008. Revised on June 1, 2009. Accepted on June 7, 2009.

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


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.