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Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Caicedo-Casso A, Kang HW, Lim S, Hong CI - Sci Rep (2015)

Bottom Line: Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology.In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type.We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA [2] Departamento de Matemáticas, Universidad del Valle, Cali, Valle, COL.

ABSTRACT
Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

No MeSH data available.


Histograms of period distribution obtained by parameter random perturbations.Top panel displays more robust models corresponding to (A) a mixed model of a Goodwin oscillator combined with Model 1, (B) a Goodwin oscillator, and (C) a negative-positive feedback loop with autocatalysis. Bottom panel displays less robust models corresponding to (D) a substrate-depletion oscillator with a reversible reaction, and (E) a negative-positive feedback loop with inhibitory degradation.
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f3: Histograms of period distribution obtained by parameter random perturbations.Top panel displays more robust models corresponding to (A) a mixed model of a Goodwin oscillator combined with Model 1, (B) a Goodwin oscillator, and (C) a negative-positive feedback loop with autocatalysis. Bottom panel displays less robust models corresponding to (D) a substrate-depletion oscillator with a reversible reaction, and (E) a negative-positive feedback loop with inhibitory degradation.

Mentions: Period distributions obtained from random perturbations of each model are illustrated by histograms in Fig. 3. This shows two classes, more robust (top panel) and less robust (bottom panel) models. Three models in the top panel, 5, 4, and 2 in order of insensitivity, are highly robust in the sense that most periods corresponding approximately to 83.5%, 79.7% and 78.5% of all random perturbations lie within 22 ± 1 hours, while the period with default values is ~22 hours in each model. However, Models 1 and 3 show that periods are distributed with a large range and only 47.1% and 27.4% of all perturbations remain within 22 ± 1 hours, respectively.


Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Caicedo-Casso A, Kang HW, Lim S, Hong CI - Sci Rep (2015)

Histograms of period distribution obtained by parameter random perturbations.Top panel displays more robust models corresponding to (A) a mixed model of a Goodwin oscillator combined with Model 1, (B) a Goodwin oscillator, and (C) a negative-positive feedback loop with autocatalysis. Bottom panel displays less robust models corresponding to (D) a substrate-depletion oscillator with a reversible reaction, and (E) a negative-positive feedback loop with inhibitory degradation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4542697&req=5

f3: Histograms of period distribution obtained by parameter random perturbations.Top panel displays more robust models corresponding to (A) a mixed model of a Goodwin oscillator combined with Model 1, (B) a Goodwin oscillator, and (C) a negative-positive feedback loop with autocatalysis. Bottom panel displays less robust models corresponding to (D) a substrate-depletion oscillator with a reversible reaction, and (E) a negative-positive feedback loop with inhibitory degradation.
Mentions: Period distributions obtained from random perturbations of each model are illustrated by histograms in Fig. 3. This shows two classes, more robust (top panel) and less robust (bottom panel) models. Three models in the top panel, 5, 4, and 2 in order of insensitivity, are highly robust in the sense that most periods corresponding approximately to 83.5%, 79.7% and 78.5% of all random perturbations lie within 22 ± 1 hours, while the period with default values is ~22 hours in each model. However, Models 1 and 3 show that periods are distributed with a large range and only 47.1% and 27.4% of all perturbations remain within 22 ± 1 hours, respectively.

Bottom Line: Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology.In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type.We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

View Article: PubMed Central - PubMed

Affiliation: 1] Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA [2] Departamento de Matemáticas, Universidad del Valle, Cali, Valle, COL.

ABSTRACT
Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

No MeSH data available.