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Open Access Highly Accessed Research article

Biochemical fluctuations, optimisation and the linear noise approximation

Jürgen Pahle1*, Joseph D Challenger2, Pedro Mendes13 and Alan J McKane2

Author Affiliations

1 School of Computer Science and Manchester Centre for Integrative Systems Biology, The University of Manchester, 131 Princess Street, Manchester M1 7DN, UK

2 Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, UK

3 Virginia Bioinformatics Institute, Virginia Tech, Washington Street 0477, Blacksburg, VA 24061, USA

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BMC Systems Biology 2012, 6:86  doi:10.1186/1752-0509-6-86

Published: 17 July 2012



Stochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive.


We implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.


Our strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.

Linear noise approximation; Optimisation; Mitogen-activated kinases signalling; COPASI; Intrinsic noise; Stochastic biochemical models; Systems biology