Mathematical identification of critical reactions in the interlocked feedback model.

Dynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a part...

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Main Authors: Hiroyuki Kurata, Takayuki Tanaka, Fumitaka Ohnishi
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2007-01-01
Series:PLoS ONE
Online Access:http://europepmc.org/articles/PMC2040204?pdf=render
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spelling doaj-59971b25216944cebb34f068599e891b2020-11-25T01:47:00ZengPublic Library of Science (PLoS)PLoS ONE1932-62032007-01-01210e110310.1371/journal.pone.0001103Mathematical identification of critical reactions in the interlocked feedback model.Hiroyuki KurataTakayuki TanakaFumitaka OhnishiDynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a particular choice of plausible parameter values, because it is hard to know the exact parameter values in vivo. Global and firm results are needed that do not depend on particular parameter values. We propose mathematical analysis for robustness (MAR) that consists of the novel evolutionary search that explores all possible solution vectors of kinetic parameters satisfying the target dynamics and robustness analysis. New criteria, parameter spectrum width and the variability of solution vectors for parameters, are introduced to determine whether the search is exhaustive. In robustness analysis, in addition to single parameter sensitivity analysis, robustness to multiple parameter perturbation is defined. Combining the sensitivity analysis and the robustness analysis to multiple parameter perturbation enables identifying critical reactions. Use of MAR clearly identified the critical reactions responsible for determining the circadian cycle in the Drosophila interlocked circadian clock model. In highly robust models, while the parameter vectors are greatly varied, the critical reactions with a high sensitivity are uniquely determined. Interestingly, not only the per-tim loop but also the dclk-cyc loop strongly affect the period of PER, although the dclk-cyc loop hardly changes its amplitude and it is not potentially influential. In conclusion, MAR is a powerful method to explore wide parameter space without human-biases and to link a robust property to network architectures without knowing the exact parameter values. MAR identifies the reactions critically responsible for determining the period and amplitude in the interlocked feedback model and suggests that the circadian clock intensively evolves or designs the kinetic parameters so that it creates a highly robust cycle.http://europepmc.org/articles/PMC2040204?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Hiroyuki Kurata
Takayuki Tanaka
Fumitaka Ohnishi
spellingShingle Hiroyuki Kurata
Takayuki Tanaka
Fumitaka Ohnishi
Mathematical identification of critical reactions in the interlocked feedback model.
PLoS ONE
author_facet Hiroyuki Kurata
Takayuki Tanaka
Fumitaka Ohnishi
author_sort Hiroyuki Kurata
title Mathematical identification of critical reactions in the interlocked feedback model.
title_short Mathematical identification of critical reactions in the interlocked feedback model.
title_full Mathematical identification of critical reactions in the interlocked feedback model.
title_fullStr Mathematical identification of critical reactions in the interlocked feedback model.
title_full_unstemmed Mathematical identification of critical reactions in the interlocked feedback model.
title_sort mathematical identification of critical reactions in the interlocked feedback model.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2007-01-01
description Dynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a particular choice of plausible parameter values, because it is hard to know the exact parameter values in vivo. Global and firm results are needed that do not depend on particular parameter values. We propose mathematical analysis for robustness (MAR) that consists of the novel evolutionary search that explores all possible solution vectors of kinetic parameters satisfying the target dynamics and robustness analysis. New criteria, parameter spectrum width and the variability of solution vectors for parameters, are introduced to determine whether the search is exhaustive. In robustness analysis, in addition to single parameter sensitivity analysis, robustness to multiple parameter perturbation is defined. Combining the sensitivity analysis and the robustness analysis to multiple parameter perturbation enables identifying critical reactions. Use of MAR clearly identified the critical reactions responsible for determining the circadian cycle in the Drosophila interlocked circadian clock model. In highly robust models, while the parameter vectors are greatly varied, the critical reactions with a high sensitivity are uniquely determined. Interestingly, not only the per-tim loop but also the dclk-cyc loop strongly affect the period of PER, although the dclk-cyc loop hardly changes its amplitude and it is not potentially influential. In conclusion, MAR is a powerful method to explore wide parameter space without human-biases and to link a robust property to network architectures without knowing the exact parameter values. MAR identifies the reactions critically responsible for determining the period and amplitude in the interlocked feedback model and suggests that the circadian clock intensively evolves or designs the kinetic parameters so that it creates a highly robust cycle.
url http://europepmc.org/articles/PMC2040204?pdf=render
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AT takayukitanaka mathematicalidentificationofcriticalreactionsintheinterlockedfeedbackmodel
AT fumitakaohnishi mathematicalidentificationofcriticalreactionsintheinterlockedfeedbackmodel
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