Send to

Choose Destination
PLoS One. 2012;7(5):e36321. doi: 10.1371/journal.pone.0036321. Epub 2012 May 14.

A linear framework for time-scale separation in nonlinear biochemical systems.

Author information

Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America.

Erratum in

  • PLoS One. 2013;8(12). doi:10.1371/annotation/6830fba7-6e52-48f9-9f55-75ee37c75b5a.
  • PLoS One. 2013;8(6). doi:10.1371/annotation/fa4c5f9f-4071-4b32-864f-b82c2e4e973b.


Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for Public Library of Science Icon for PubMed Central
Loading ...
Support Center