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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.


Averaged Half-life of autocorrelations of five models.For each model, the half-life of autocorrelation is measured in each species and then is averaged over species within the model. N is varied with 10, 100, and 500.
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f4: Averaged Half-life of autocorrelations of five models.For each model, the half-life of autocorrelation is measured in each species and then is averaged over species within the model. N is varied with 10, 100, and 500.

Mentions: As known, the half-life of the autocorrelation, the time interval corresponding to 50% decrease from the start, is a useful tool to measure the robustness of periodic systems in the presence of molecular noise2324. In Fig. 4, the half-life of autocorrelations is averaged over all species within each model and is compared between five models as N varies. Note that the half-life of autocorrelation functions can vary in different species within the model. In the presence of strong noise, corresponding to N = 10, the half-life of five models ranks them in the order of insensitivity as Model 1, Model 4, Model 5, Model 2, and Model 3. However, as N increases, which reduces the noise strength in the system, the ranking of robust models is switched around. For example, when N = 500, the half-life of five models is classified into two groups, more robust (Model 5, Model 1, and Model 2 in order of insensitivity) and less robust (Model 4 and Model 3 in order of insensitivity) models. As we can see, the half-life of Model 5 increases drastically with an increasing volume size, indicating that Model 5 is relatively more robust than other models as the fluctuations in the number of molecules decreases. In contrast, Model 4 becomes less robust as the strength of noise decreases. Interestingly, Model 3 maintains the low half-life steadily, resulting in the most sensitive model to molecular noise. Recall that Model 3 is also the least robust model when the random variations of parameter values were taken into account, see Fig. 3. Model 1 with random parameter perturbations was also classified into a less robust group; however, its stochastic model becomes more robust in the presence of molecular noise.


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

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

Averaged Half-life of autocorrelations of five models.For each model, the half-life of autocorrelation is measured in each species and then is averaged over species within the model. N is varied with 10, 100, and 500.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Averaged Half-life of autocorrelations of five models.For each model, the half-life of autocorrelation is measured in each species and then is averaged over species within the model. N is varied with 10, 100, and 500.
Mentions: As known, the half-life of the autocorrelation, the time interval corresponding to 50% decrease from the start, is a useful tool to measure the robustness of periodic systems in the presence of molecular noise2324. In Fig. 4, the half-life of autocorrelations is averaged over all species within each model and is compared between five models as N varies. Note that the half-life of autocorrelation functions can vary in different species within the model. In the presence of strong noise, corresponding to N = 10, the half-life of five models ranks them in the order of insensitivity as Model 1, Model 4, Model 5, Model 2, and Model 3. However, as N increases, which reduces the noise strength in the system, the ranking of robust models is switched around. For example, when N = 500, the half-life of five models is classified into two groups, more robust (Model 5, Model 1, and Model 2 in order of insensitivity) and less robust (Model 4 and Model 3 in order of insensitivity) models. As we can see, the half-life of Model 5 increases drastically with an increasing volume size, indicating that Model 5 is relatively more robust than other models as the fluctuations in the number of molecules decreases. In contrast, Model 4 becomes less robust as the strength of noise decreases. Interestingly, Model 3 maintains the low half-life steadily, resulting in the most sensitive model to molecular noise. Recall that Model 3 is also the least robust model when the random variations of parameter values were taken into account, see Fig. 3. Model 1 with random parameter perturbations was also classified into a less robust group; however, its stochastic model becomes more robust in the presence of molecular noise.

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.