Limits...
Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics.

Nienałtowski K, Włodarczyk M, Lipniacki T, Komorowski M - BMC Syst Biol (2015)

Bottom Line: The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters.As a results, a relevant insight into identifiability analysis and experimental planning can be obtained.The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design.

View Article: PubMed Central - PubMed

Affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland. k.nienaltowski@sysbiosig.org.

ABSTRACT

Background: Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.

Results: In order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF-κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF-κB dynamics reveals that the experiments jointly ensure identifiability of only 60% of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.

Conclusions: We currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.

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Related in: MedlinePlus

Identifiability study of the NF- κB system. a Clustering results together with the identifiability analysis computed based on all the major published experiments. Non-identifiable parameters are marked in red. We used δ=0.95,ζ=1 to verify the identifiability condition. Sensitivity coefficients, i.e diagonal elements of the FIM, are shown below the dendrogram. b Clustering results as in (a) but for the published experiments together with the suggested experimental protocols
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Fig4: Identifiability study of the NF- κB system. a Clustering results together with the identifiability analysis computed based on all the major published experiments. Non-identifiable parameters are marked in red. We used δ=0.95,ζ=1 to verify the identifiability condition. Sensitivity coefficients, i.e diagonal elements of the FIM, are shown below the dendrogram. b Clustering results as in (a) but for the published experiments together with the suggested experimental protocols

Mentions: Experiments examining the NF-κB dynamics jointly exhibit highly correlated parameters. It is debatable how much data is needed to ensure parameters’ identifiability in systems biology models, and whether it is realistically achievable. Here we examined collectively all experiments reported in 9 papers [18–26] that contain rich data sets on the dynamics of the NF- κB system. We asked which parameters of the NF- κB model can be estimated from the published experiments (see Table 1 in Additional file 1). We found that 18 out of 39 model parameters cannot be estimated as they fail to satisfy the δ-condition (red parameters in Fig. 4a). The huge amount of literature available data, providing a comprehensive knowledge on the dynamics of the NF- κB system, was not sufficient to ensure identifiability of all model parameters. The identifiability problem is widely reported. Here we demonstrate that it is not mitigated by a huge number of experiments performed to obtain insights other than values of kinetic rates. To draw our conclusions we have initially set δ=0.95 and ζ=1. As we used logarithmic parameterisation, i.e. log(θi) instead of θi the latter corresponds to learning a parameter more accurately than with an order of magnitude error if the remaining model parameters were known. Value δ=0.95 requires the estimate’s variance not to increase by more than approximately 10 times when the single parameter and multi-parameter scenarios are compared. Thereafter we have verified that our main findings remain robust to assumptions regarding specific values of δ and ζ (Figure 3 in Additional file 1). We have also analysed how each of the analysed papers increased the number of identifiable parameters (Figure 2 in Additional file 1). Chronologically first two papers [18, 19], rendered 13 parameters identifiable. Subsequent 7 papers provided information to estimate 8 new parameters, which gives approximately 1 parameter per paper. This indicates that making more parameters identifiable requires specifically tailored experiments different to these performed to address conventional biological questions.Fig. 4


Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics.

Nienałtowski K, Włodarczyk M, Lipniacki T, Komorowski M - BMC Syst Biol (2015)

Identifiability study of the NF- κB system. a Clustering results together with the identifiability analysis computed based on all the major published experiments. Non-identifiable parameters are marked in red. We used δ=0.95,ζ=1 to verify the identifiability condition. Sensitivity coefficients, i.e diagonal elements of the FIM, are shown below the dendrogram. b Clustering results as in (a) but for the published experiments together with the suggested experimental protocols
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4587803&req=5

Fig4: Identifiability study of the NF- κB system. a Clustering results together with the identifiability analysis computed based on all the major published experiments. Non-identifiable parameters are marked in red. We used δ=0.95,ζ=1 to verify the identifiability condition. Sensitivity coefficients, i.e diagonal elements of the FIM, are shown below the dendrogram. b Clustering results as in (a) but for the published experiments together with the suggested experimental protocols
Mentions: Experiments examining the NF-κB dynamics jointly exhibit highly correlated parameters. It is debatable how much data is needed to ensure parameters’ identifiability in systems biology models, and whether it is realistically achievable. Here we examined collectively all experiments reported in 9 papers [18–26] that contain rich data sets on the dynamics of the NF- κB system. We asked which parameters of the NF- κB model can be estimated from the published experiments (see Table 1 in Additional file 1). We found that 18 out of 39 model parameters cannot be estimated as they fail to satisfy the δ-condition (red parameters in Fig. 4a). The huge amount of literature available data, providing a comprehensive knowledge on the dynamics of the NF- κB system, was not sufficient to ensure identifiability of all model parameters. The identifiability problem is widely reported. Here we demonstrate that it is not mitigated by a huge number of experiments performed to obtain insights other than values of kinetic rates. To draw our conclusions we have initially set δ=0.95 and ζ=1. As we used logarithmic parameterisation, i.e. log(θi) instead of θi the latter corresponds to learning a parameter more accurately than with an order of magnitude error if the remaining model parameters were known. Value δ=0.95 requires the estimate’s variance not to increase by more than approximately 10 times when the single parameter and multi-parameter scenarios are compared. Thereafter we have verified that our main findings remain robust to assumptions regarding specific values of δ and ζ (Figure 3 in Additional file 1). We have also analysed how each of the analysed papers increased the number of identifiable parameters (Figure 2 in Additional file 1). Chronologically first two papers [18, 19], rendered 13 parameters identifiable. Subsequent 7 papers provided information to estimate 8 new parameters, which gives approximately 1 parameter per paper. This indicates that making more parameters identifiable requires specifically tailored experiments different to these performed to address conventional biological questions.Fig. 4

Bottom Line: The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters.As a results, a relevant insight into identifiability analysis and experimental planning can be obtained.The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design.

View Article: PubMed Central - PubMed

Affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland. k.nienaltowski@sysbiosig.org.

ABSTRACT

Background: Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.

Results: In order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF-κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF-κB dynamics reveals that the experiments jointly ensure identifiability of only 60% of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.

Conclusions: We currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.

Show MeSH
Related in: MedlinePlus