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Biochemical fluctuations, optimisation and the linear noise approximation.

Pahle J, Challenger JD, Mendes P, McKane AJ - BMC Syst Biol (2012)

Bottom Line: Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species?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.We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.

View Article: PubMed Central - HTML - PubMed

Affiliation: School of Computer Science and Manchester Centre for Integrative Systems Biology, The University of Manchester, 131 Princess Street, Manchester, UK. juergen.pahle@manchester.ac.uk

ABSTRACT

Background: 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.

Results: 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.

Conclusions: 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.

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Related in: MedlinePlus

Screen shot of the LNA implementation in COPASI. Screen shot of the COPASI graphical user interface and the linear noise approximation task. Shown is the resulting covariance matrix of species' particle numbers in the p38 MAPK model by Hendriks et al. [24]. The matrix is colour coded, positive values have a green background and negative values a red one with intensities corresponding to the absolute values.
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Figure 1: Screen shot of the LNA implementation in COPASI. Screen shot of the COPASI graphical user interface and the linear noise approximation task. Shown is the resulting covariance matrix of species' particle numbers in the p38 MAPK model by Hendriks et al. [24]. The matrix is colour coded, positive values have a green background and negative values a red one with intensities corresponding to the absolute values.

Mentions: The software COPASI [21,22] gives all interested researchers easy access to modelling and simulation for biochemical networks, because it is freely available under the Artistic license version 2.0 at [22] and supports the Systems Biology Markup Language (SBML) standard [25] for the exchange of model files with other software. An implementation of the method described here was integrated in COPASI, comprising a new LNA task that, using the linear noise approximation (see Methods), generates as output a matrix of covariance estimates between all the species' particle numbers in a given biochemical model (see Figure 1). Prior to this, the method can also automatically calculate a steady state for the model which is important if parameters, and thus the system's steady state, have been changed. The covariances estimated by the LNA task can then be subsequently used by other tasks in COPASI, in particular optimisation, parameter scanning or sampling in a closed-loop fashion. This combination results in a practical method for the investigation of fluctuations in models even when some or many of the model parameters have not yet been fully characterised.


Biochemical fluctuations, optimisation and the linear noise approximation.

Pahle J, Challenger JD, Mendes P, McKane AJ - BMC Syst Biol (2012)

Screen shot of the LNA implementation in COPASI. Screen shot of the COPASI graphical user interface and the linear noise approximation task. Shown is the resulting covariance matrix of species' particle numbers in the p38 MAPK model by Hendriks et al. [24]. The matrix is colour coded, positive values have a green background and negative values a red one with intensities corresponding to the absolute values.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3814289&req=5

Figure 1: Screen shot of the LNA implementation in COPASI. Screen shot of the COPASI graphical user interface and the linear noise approximation task. Shown is the resulting covariance matrix of species' particle numbers in the p38 MAPK model by Hendriks et al. [24]. The matrix is colour coded, positive values have a green background and negative values a red one with intensities corresponding to the absolute values.
Mentions: The software COPASI [21,22] gives all interested researchers easy access to modelling and simulation for biochemical networks, because it is freely available under the Artistic license version 2.0 at [22] and supports the Systems Biology Markup Language (SBML) standard [25] for the exchange of model files with other software. An implementation of the method described here was integrated in COPASI, comprising a new LNA task that, using the linear noise approximation (see Methods), generates as output a matrix of covariance estimates between all the species' particle numbers in a given biochemical model (see Figure 1). Prior to this, the method can also automatically calculate a steady state for the model which is important if parameters, and thus the system's steady state, have been changed. The covariances estimated by the LNA task can then be subsequently used by other tasks in COPASI, in particular optimisation, parameter scanning or sampling in a closed-loop fashion. This combination results in a practical method for the investigation of fluctuations in models even when some or many of the model parameters have not yet been fully characterised.

Bottom Line: Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species?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.We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model.

View Article: PubMed Central - HTML - PubMed

Affiliation: School of Computer Science and Manchester Centre for Integrative Systems Biology, The University of Manchester, 131 Princess Street, Manchester, UK. juergen.pahle@manchester.ac.uk

ABSTRACT

Background: 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.

Results: 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.

Conclusions: 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.

Show MeSH
Related in: MedlinePlus