Complexity reduction preserving dynamical behavior of biochemical networks

Apri, Mochamad; Gee, Maarten de; Molenaar, Jaap

doi:10.1016/j.jtbi.2012.03.019

Cited by 46 publications

(51 citation statements)

References 34 publications

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“…The idea that a sloppy model is insensitive to parameter changes along sloppy directions, but highly sensitive along stiff combinations of parameters, has been exploited to propose reduced order modelling techniques [42,3,9]. The aim is to obtain a non-sloppy model that captures the relevant dynamics of the original model, but with a reduced number of states and parameters.…”

Section: Model Reductionmentioning

confidence: 99%

On the relationship between sloppiness and identifiability

Chis

Villaverde

Banga

et al. 2016

Mathematical Biosciences

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Dynamic models of biochemical networks are often formulated as sets of non-linear ordinary differential equations, whose states are the concentrations or abundances of the network components. They typically have a large number of kinetic parameters, which must be determined by calibrating the model with experimental data. In recent years it has been suggested that dynamic systems biology models are universally sloppy, meaning that the values of some parameters can be perturbed by several orders of magnitude without causing significant changes in the model output. This observation has prompted calls for focusing on model predictions rather than on parameters. In this work we examine the concept of sloppiness, investigating its links with the long-established notions of structural and practical identifiability. By analysing a set of case studies we show that sloppiness is not equivalent to lack of identifiability, and that sloppy models can be identifiable. Thus, using sloppiness to draw conclusions about the possibility of estimating parameter values can be misleading. Instead, structural and practical identifiability analyses are better tools for assessing the confidence in parameter estimates. Furthermore, we show that, when designing new experiments to decrease parametric uncertainty, designs that optimize practical identifiability criteria are more informative than those that minimize sloppiness.

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Section: Model Reductionmentioning

confidence: 99%

On the relationship between sloppiness and identifiability

Chis

Villaverde

Banga

et al. 2016

Mathematical Biosciences

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show abstract

“…In [16], an implicit multiparametric variability analysis (MPVA) method is used to search the entire parameter space in order to determine the set of parameters that can be eliminated. In [17], the authors go one step further by identifying a region in the parameter space where some of the parameters are zero-valued, others have readjusted values and where nevertheless the outputs of the original model match those of the reduced model within a certain tolerance. They further show that parameter sensitivity analysis approach for model reduction may not be always successful.…”

Section: Introductionmentioning

confidence: 99%

A model reduction method for biochemical reaction networks

et al. 2014

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BackgroundIn this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.ResultsWe apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.ConclusionsThe method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

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“…It is important to underline what is original in the presented method. In Apri et al [25], the authors propose a simplification method very similar in principle to the present one. More particularly, their concept of the admissible region is close to our definition of the b-condition.…”

Section: Comparison With Other Simplification and Reduction Methodsmentioning

confidence: 99%

“…Consider for instance a situation where the model outputs X have to match some experimental data within some given tolerance. That specific part of the outputs can be classified as behaviour, a concept coined by [24] or as an admissible region as defined in [25]. In our case, there exists a condition that we will call the b-condition, which delimits a part V b , V a that matches the purposes of the modeller ( figure 1).…”

Section: On the Use Of Regression Treesmentioning

confidence: 99%

Towards a simplification of models using regression trees

Eynaud

Nérini

Baklouti

et al. 2013

J. R. Soc. Interface.

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Over-parametrization in modelling is a well-known issue that makes it hard to identify which part of a model is responsible for a given behaviour. In line with that ascertainment, this work presents the outline of an empirical method to simplify models by decreasing the number of parameters. By using regression trees to classify outputs according to related input parameters, the method provides the modeller with an objective tool to reduce the range of the used parameters and, under certain conditions, to establish relations between them. Thereby, the complexity of the model is reduced on the basis of mathematical arguments. As an example, a dynamic energy budget-based model of a mesopelagic bacterial ecosystem is simplified using the presented method. The main benefits of such a method are thus highlighted: (i) more robust parameter estimations; (ii) less complex formulations; and (iii) fewer modelling assumptions. To conclude, the difficulties encountered are discussed, and several solutions are proposed to deal with them.

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Complexity reduction preserving dynamical behavior of biochemical networks

Cited by 46 publications

References 34 publications

On the relationship between sloppiness and identifiability

On the relationship between sloppiness and identifiability

A model reduction method for biochemical reaction networks

Towards a simplification of models using regression trees

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