Limits...
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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Coefficient of variation of nuclear phospho-p38 vs. stimulation strength in the MAPK model. Coefficient of variation of nuclear phospho-p38 vs. concentration of LPS [ng/ml].
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Figure 6: Coefficient of variation of nuclear phospho-p38 vs. stimulation strength in the MAPK model. Coefficient of variation of nuclear phospho-p38 vs. concentration of LPS [ng/ml].

Mentions: However, looking at the coefficient of variation (CV) both nuclear phospho-p38 and cytosolic phospho-Hsp27 show a decrease of variation with increasing stimulation due to increasing steady state particle numbers (Figure 6 shows the CV of nuclear phospho-p38 against the concentration of LPS). This means that, in both cases, the relative amplitude of fluctuations decreases with increasing signal strength -- the higher the stimulus, the less ambiguous it becomes.


Biochemical fluctuations, optimisation and the linear noise approximation.

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

Coefficient of variation of nuclear phospho-p38 vs. stimulation strength in the MAPK model. Coefficient of variation of nuclear phospho-p38 vs. concentration of LPS [ng/ml].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Coefficient of variation of nuclear phospho-p38 vs. stimulation strength in the MAPK model. Coefficient of variation of nuclear phospho-p38 vs. concentration of LPS [ng/ml].
Mentions: However, looking at the coefficient of variation (CV) both nuclear phospho-p38 and cytosolic phospho-Hsp27 show a decrease of variation with increasing stimulation due to increasing steady state particle numbers (Figure 6 shows the CV of nuclear phospho-p38 against the concentration of LPS). This means that, in both cases, the relative amplitude of fluctuations decreases with increasing signal strength -- the higher the stimulus, the less ambiguous it becomes.

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