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Robustness from flexibility in the fungal circadian clock.

Akman OE, Rand DA, Brown PE, Millar AJ - BMC Syst Biol (2010)

Bottom Line: Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator.More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Systems Biology at Edinburgh, The University of Edinburgh, Edinburgh, UK.

ABSTRACT

Background: Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.

Results: The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.

Conclusions: Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

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Robustness from flexibility in the Neurospora clock. A. Variations in the relative flexibility and robustness of FRQ-dependent conidiation phase with wc-1 loop coupling strength a7. Both measures decreases monotonically as the wc-1 loop is progressively decoupled from the negative frq loop. B. Relative flexibility and phase robustness are positively correlated, suggesting that one of the benefits of the increased flexibility conferred by the wc-1 loop is greater phase robustness against photoperiod changes. C. Dependence on a7 of the evaluation function  used to compute the relative robustness measure  plotted in A.  measures the extent to which entrained phase varies locally with photoperiod P : driven and systematic entrainment are quantified by  values of 0 and 1 respectively. In long days, decreases to 0 as a7 is reduced, causing the observed decrease in .
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Figure 7: Robustness from flexibility in the Neurospora clock. A. Variations in the relative flexibility and robustness of FRQ-dependent conidiation phase with wc-1 loop coupling strength a7. Both measures decreases monotonically as the wc-1 loop is progressively decoupled from the negative frq loop. B. Relative flexibility and phase robustness are positively correlated, suggesting that one of the benefits of the increased flexibility conferred by the wc-1 loop is greater phase robustness against photoperiod changes. C. Dependence on a7 of the evaluation function used to compute the relative robustness measure plotted in A. measures the extent to which entrained phase varies locally with photoperiod P : driven and systematic entrainment are quantified by values of 0 and 1 respectively. In long days, decreases to 0 as a7 is reduced, causing the observed decrease in .

Mentions: The robustness index defined in (1) can be used to quantify the effect of decoupling the positive wc-1 loop from the negative frq loop. The ratio of the value for a system with modified coupling to that of the WT yields a measure of relative robustness: a score greater than 1 implies a clock that is more robust than the WT; a score less than 1 a less robust network (see Additional file 1, section 4 for details). Figure 7A shows that decoupling the wc-1 loop reduces the relative robustness of the modified system, as quantified by a significant decrease in the measure from 1. The corresponding changes to the evaluation function are plotted in Figure 7C. It can be seen that while the function remains close to 1 in short days, its value in long days decreases to 0 as positive feedback is removed, reflecting the transition from systematic to dusk-driven entrainment plotted in Figure 6. In this case, therefore, the overall reduction in robustness is largely attributable to the small values of the evaluation function observed for longer photoperiods.


Robustness from flexibility in the fungal circadian clock.

Akman OE, Rand DA, Brown PE, Millar AJ - BMC Syst Biol (2010)

Robustness from flexibility in the Neurospora clock. A. Variations in the relative flexibility and robustness of FRQ-dependent conidiation phase with wc-1 loop coupling strength a7. Both measures decreases monotonically as the wc-1 loop is progressively decoupled from the negative frq loop. B. Relative flexibility and phase robustness are positively correlated, suggesting that one of the benefits of the increased flexibility conferred by the wc-1 loop is greater phase robustness against photoperiod changes. C. Dependence on a7 of the evaluation function  used to compute the relative robustness measure  plotted in A.  measures the extent to which entrained phase varies locally with photoperiod P : driven and systematic entrainment are quantified by  values of 0 and 1 respectively. In long days, decreases to 0 as a7 is reduced, causing the observed decrease in .
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2913929&req=5

Figure 7: Robustness from flexibility in the Neurospora clock. A. Variations in the relative flexibility and robustness of FRQ-dependent conidiation phase with wc-1 loop coupling strength a7. Both measures decreases monotonically as the wc-1 loop is progressively decoupled from the negative frq loop. B. Relative flexibility and phase robustness are positively correlated, suggesting that one of the benefits of the increased flexibility conferred by the wc-1 loop is greater phase robustness against photoperiod changes. C. Dependence on a7 of the evaluation function used to compute the relative robustness measure plotted in A. measures the extent to which entrained phase varies locally with photoperiod P : driven and systematic entrainment are quantified by values of 0 and 1 respectively. In long days, decreases to 0 as a7 is reduced, causing the observed decrease in .
Mentions: The robustness index defined in (1) can be used to quantify the effect of decoupling the positive wc-1 loop from the negative frq loop. The ratio of the value for a system with modified coupling to that of the WT yields a measure of relative robustness: a score greater than 1 implies a clock that is more robust than the WT; a score less than 1 a less robust network (see Additional file 1, section 4 for details). Figure 7A shows that decoupling the wc-1 loop reduces the relative robustness of the modified system, as quantified by a significant decrease in the measure from 1. The corresponding changes to the evaluation function are plotted in Figure 7C. It can be seen that while the function remains close to 1 in short days, its value in long days decreases to 0 as positive feedback is removed, reflecting the transition from systematic to dusk-driven entrainment plotted in Figure 6. In this case, therefore, the overall reduction in robustness is largely attributable to the small values of the evaluation function observed for longer photoperiods.

Bottom Line: Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator.More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

View Article: PubMed Central - HTML - PubMed

Affiliation: Centre for Systems Biology at Edinburgh, The University of Edinburgh, Edinburgh, UK.

ABSTRACT

Background: Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.

Results: The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.

Conclusions: Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

Show MeSH
Related in: MedlinePlus