Robustness analysis of biochemical network models

Kim, Jongrae; Bates, Declan G.; Postlethwaite, Ian; Ma, Lan; Iglesias, Pablo A.

doi:10.1049/ip-syb:20050024

Cited by 86 publications

(80 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is also revealed by some studies of other oscillation networks. An example is the study of cyclic monophosphate (cAMP) oscillations, which shows that a small but significant portion of uncertain parameters can seriously affect the sustained oscillations [42].…”

Section: Impacts Of Sensitive Parameters On Oscillation Behaviormentioning

confidence: 99%

Sensitivity analysis and robust experimental design of a signal transduction pathway system

Yue

Brown

et al. 2008

Int J of Chemical Kinetics

View full text Add to dashboard Cite

Experimental design for cellular networks based on sensitivity analysis is studied in this work. Both optimal and robust experimental design strategies are developed for the IκB-NF-κB signal transduction model. Based on local sensitivity analysis, the initial IKK intensity is calculated using an optimal experimental design process, and several scalarization measures of the Fisher information matrix are compared. Global sensitivity analysis and robust experimental design techniques are then developed to consider parametric uncertainties in the model. The modified Morris method is employed in global sensitivity analysis, and a semidefinite programming method is exploited to implement the robust experimental design for the problem of measurement set selection. The parametric impacts on the oscillatory behavior of NF-κB in the nucleus are also discussed.

show abstract

Section: Impacts Of Sensitive Parameters On Oscillation Behaviormentioning

confidence: 99%

Sensitivity analysis and robust experimental design of a signal transduction pathway system

Yue

Brown

et al. 2008

Int J of Chemical Kinetics

View full text Add to dashboard Cite

show abstract

“…Yet, major difficulties are that the bifurcation surface can usually not be computed explicitly in a high-dimensional parameter space, and that continuation methods may miss parts of the bifurcation surface, even if only one or two parameters are uncertain. To deal with multiparametric uncertainty, it was suggested to use the structured singular value as analysis tool [14,10,19]. However, a significant problem with the approaches based on the structured singular value is that the uncertainty in the location of the steady state due to parameter variations usually cannot be taken into account directly.…”

Section: Introductionmentioning

confidence: 99%

Robust stability and instability of biochemical networks with parametric uncertainty

Waldherr

Allgöwer

2011

Automatica

View full text Add to dashboard Cite

Parameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model's behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we develop a new method for robustness analysis of the dynamical behaviour. As a first step, we provide a characterization of non-robust perturbations as a system of polynomial equalities and inequalities. In the second step, we apply the Positivstellensatz and Handelman representation of polynomials to check for the non-existence of solutions to this system, which can be relaxed to solving a linear program. Thereby, a solution to the linear program yields a robustness certificate for the considered dynamical behaviour. With these robustness certificates, we propose an algorithm to compute a lower robustness bound corresponding to a level of parametric uncertainty up to which no local bifurcations can occur. The applicability of the proposed method to biochemical network models is illustrated by analysing the robustness of oscillations in a model of the NF-κB signalling pathway. The results may be used to define a level of confidence in the observed model behaviour under parametric uncertainty, making them valuable for evaluating dynamical models of biological networks. AbstractParameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model's behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we develop a new method for robustness analysis of the dynamical behaviour. As a first step, we provide a characterization of non-robust perturbations as a system of polynomial equalities and inequalities. In the second step, we apply the Positivstellensatz and Handelman representation of polynomials to check for the non-existence of solutions to this system, which can be relaxed to solving a linear program. Thereby, a solution to the linear program yields a robustness certificate for the considered dynamical behaviour. With these robustness certificates, we propose an algorithm to compute a lower robustness bound corresponding to a level of parametric uncertainty up to which no local bifurcations can occur. The applicability of the proposed method to biochemical network models is illustrated by analysing the robustness of oscillations in a model of the NF-κB signalling pathway. The results may be used to define a level of confidence in the observed model behaviour under parametric uncertainty, making them valuable for evaluating dynamical models of biological networks.

show abstract

“…As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters [8][9][10]. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes [11][12][13][14][15][16][17][18]. Chemical network theory and monotone systems approaches can characterize dynamics of biochemical networks based only on their structure, independently of a particular choice of parameters [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Bistability and oscillations in the Huang-Ferrell model of MAPK signaling

Li¹,

Nachbar²,

Kevrekidis³

et al. 2005

PLoS Comput Biol

View full text Add to dashboard Cite

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics.

show abstract

Robustness analysis of biochemical network models

Abstract: Background: Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed.

Cited by 86 publications

References 4 publications

Sensitivity analysis and robust experimental design of a signal transduction pathway system

Sensitivity analysis and robust experimental design of a signal transduction pathway system

Robust stability and instability of biochemical networks with parametric uncertainty

Bistability and oscillations in the Huang-Ferrell model of MAPK signaling

Contact Info

Product

Resources

About