Efficient Estimation of the Robustness Region of Biological Models with Oscillatory Behavior (Robustness of Periodic Systems)
Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the LaubLoomis model, a nonlinear model for... Full description
Journal Title:  PLoS ONE 2010, Vol.5(4), p.e9865 
Main Author:  Apri, Mochamad 
Other Authors:  Molenaar, Jaap , de Gee, Maarten , van Voorn, George 
Format:  Electronic Article 
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English 
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ID:  EISSN: 19326203 ; DOI: 10.1371/journal.pone.0009865 
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recordid:  plos10.1371/journal.pone.0009865 
title:  Efficient Estimation of the Robustness Region of Biological Models with Oscillatory Behavior (Robustness of Periodic Systems) 
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ispartof:  PLoS ONE, 2010, Vol.5(4), p.e9865 
description:  Robustness is an essential feature of biological systems, and any mathematical model that describes such a system should reflect this feature. Especially, persistence of oscillatory behavior is an important issue. A benchmark model for this phenomenon is the LaubLoomis model, a nonlinear model for cAMP oscillations in Dictyostelium discoideum. This model captures the most important features of biomolecular networks oscillating at constant frequencies. Nevertheless, the robustness of its oscillatory behavior is not yet fully understood. Given a system that exhibits oscillating behavior for some set of parameters, the central question of robustness is how far the parameters may be changed, such that the qualitative behavior does not change. The determination of such a “robustness region” in parameter space is an intricate task. If the number of parameters is high, it may be also time consuming. In the literature, several methods are proposed that partially tackle this problem. For example, some methods only detect particular bifurcations, or only find a relatively small boxshaped estimate for an irregularly shaped robustness region. Here, we present an approach that is much more general, and is especially designed to be efficient for systems with a large number of parameters. As an illustration, we apply the method first to a well understood lowdimensional system, the RosenzweigMacArthur model. This is a predatorprey model featuring satiation of the predator. It has only two parameters and its bifurcation diagram is available in the literature. We find a good agreement with the existing knowledge about this model. When we apply the new method to the high dimensional LaubLoomis model, we obtain a much larger robustness region than reported earlier in the literature. This clearly demonstrates the power of our method. From the results, we conclude that the biological system underlying is much more robust than was realized until now. 
language:  eng 
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identifier:  EISSN: 19326203 ; DOI: 10.1371/journal.pone.0009865 
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