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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.


Period distributions for Models 4 and 4′.Model 4 and Model 4′ differ by the existence of autocatalysis, in which Model 4′ includes an autocatalytic process on its protein modification. Each panel is obtained from 1100 consecutive cycles of a stochastic simulation when N = 10 and 100. The values μ and σ stand for the mean period and standard deviation, respectively.
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f5: Period distributions for Models 4 and 4′.Model 4 and Model 4′ differ by the existence of autocatalysis, in which Model 4′ includes an autocatalytic process on its protein modification. Each panel is obtained from 1100 consecutive cycles of a stochastic simulation when N = 10 and 100. The values μ and σ stand for the mean period and standard deviation, respectively.

Mentions: It is reported that the model becomes more robust to molecular noise in the presence of a positive feedback26. Hence we investigate the effect of a positive feedback with stochastic versions of Model 4 and Model 4′, which is distinguished by the absence or presence of autocatalytic process, respectively. Figure 5 displays histograms showing the distribution of periods obtained from 1,100 consecutive cycles of each stochastic simulation with Model 4 (top panel) and Model 4′ (bottom panel) when N = 10 and N = 100. For each volume size, the histograms are more concentrated in Model 4′, which proves that a positive feedback strengthens the robustness to molecular noise. The two distributions from Models 4 and 4′ are statistically different with p-value less than 0.0001 using Kolmogorov-Smirnov test for each volume size.


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

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

Period distributions for Models 4 and 4′.Model 4 and Model 4′ differ by the existence of autocatalysis, in which Model 4′ includes an autocatalytic process on its protein modification. Each panel is obtained from 1100 consecutive cycles of a stochastic simulation when N = 10 and 100. The values μ and σ stand for the mean period and standard deviation, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Period distributions for Models 4 and 4′.Model 4 and Model 4′ differ by the existence of autocatalysis, in which Model 4′ includes an autocatalytic process on its protein modification. Each panel is obtained from 1100 consecutive cycles of a stochastic simulation when N = 10 and 100. The values μ and σ stand for the mean period and standard deviation, respectively.
Mentions: It is reported that the model becomes more robust to molecular noise in the presence of a positive feedback26. Hence we investigate the effect of a positive feedback with stochastic versions of Model 4 and Model 4′, which is distinguished by the absence or presence of autocatalytic process, respectively. Figure 5 displays histograms showing the distribution of periods obtained from 1,100 consecutive cycles of each stochastic simulation with Model 4 (top panel) and Model 4′ (bottom panel) when N = 10 and N = 100. For each volume size, the histograms are more concentrated in Model 4′, which proves that a positive feedback strengthens the robustness to molecular noise. The two distributions from Models 4 and 4′ are statistically different with p-value less than 0.0001 using Kolmogorov-Smirnov test for each volume size.

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.