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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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The model reproduces the systematic entrainment observed in LD cycles. A. Simulated variation of conidiation onset with photoperiod length. As in [16], conidiation onset was identified with the time ϕFRQ at which FRQ has decreased to the approximate midpoint of its peak and trough values. Peak and trough times of frq mRNA and FRQ protein are also shown. White and grey regions denote light and dark respectively while the dotted line indicates the middle of the night. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures plotted in A for short and long days (see Additional file 1, Figure S2A for the sensitivities at intermediate photoperiods). The peak and trough times of frq mRNA are locked to either dusk (∂ϕ/∂tDUSK = 1) or dawn (∂ϕ/∂tDUSK = 0). By contrast, conidiation onset ϕFRQ varies systematically with photoperiod (∂ϕFRQ/∂tDUSK ≈ 0.5).
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Figure 4: The model reproduces the systematic entrainment observed in LD cycles. A. Simulated variation of conidiation onset with photoperiod length. As in [16], conidiation onset was identified with the time ϕFRQ at which FRQ has decreased to the approximate midpoint of its peak and trough values. Peak and trough times of frq mRNA and FRQ protein are also shown. White and grey regions denote light and dark respectively while the dotted line indicates the middle of the night. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures plotted in A for short and long days (see Additional file 1, Figure S2A for the sensitivities at intermediate photoperiods). The peak and trough times of frq mRNA are locked to either dusk (∂ϕ/∂tDUSK = 1) or dawn (∂ϕ/∂tDUSK = 0). By contrast, conidiation onset ϕFRQ varies systematically with photoperiod (∂ϕFRQ/∂tDUSK ≈ 0.5).

Mentions: Figure 4A shows how the simulated phase ϕFRQ of this molecular conidiation correlate varies with photoperiod. It can be seen that the peak of frq mRNA expression is locked to dawn, while the trough is locked to dawn in short days and dusk in all other photoperiods. Conidiation phase ϕFRQ, however, roughly tracks midnight in agreement with experimental results, even though the cost function used to fit our model to data had no terms involving conidiation time. In our simulations the FRQ-dependent phase of conidiation is thus dissociated from the frq mRNA profile which instead directly reflects the light environment, tracking dawn and dusk through its peak and trough phases.


Robustness from flexibility in the fungal circadian clock.

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

The model reproduces the systematic entrainment observed in LD cycles. A. Simulated variation of conidiation onset with photoperiod length. As in [16], conidiation onset was identified with the time ϕFRQ at which FRQ has decreased to the approximate midpoint of its peak and trough values. Peak and trough times of frq mRNA and FRQ protein are also shown. White and grey regions denote light and dark respectively while the dotted line indicates the middle of the night. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures plotted in A for short and long days (see Additional file 1, Figure S2A for the sensitivities at intermediate photoperiods). The peak and trough times of frq mRNA are locked to either dusk (∂ϕ/∂tDUSK = 1) or dawn (∂ϕ/∂tDUSK = 0). By contrast, conidiation onset ϕFRQ varies systematically with photoperiod (∂ϕFRQ/∂tDUSK ≈ 0.5).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: The model reproduces the systematic entrainment observed in LD cycles. A. Simulated variation of conidiation onset with photoperiod length. As in [16], conidiation onset was identified with the time ϕFRQ at which FRQ has decreased to the approximate midpoint of its peak and trough values. Peak and trough times of frq mRNA and FRQ protein are also shown. White and grey regions denote light and dark respectively while the dotted line indicates the middle of the night. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures plotted in A for short and long days (see Additional file 1, Figure S2A for the sensitivities at intermediate photoperiods). The peak and trough times of frq mRNA are locked to either dusk (∂ϕ/∂tDUSK = 1) or dawn (∂ϕ/∂tDUSK = 0). By contrast, conidiation onset ϕFRQ varies systematically with photoperiod (∂ϕFRQ/∂tDUSK ≈ 0.5).
Mentions: Figure 4A shows how the simulated phase ϕFRQ of this molecular conidiation correlate varies with photoperiod. It can be seen that the peak of frq mRNA expression is locked to dawn, while the trough is locked to dawn in short days and dusk in all other photoperiods. Conidiation phase ϕFRQ, however, roughly tracks midnight in agreement with experimental results, even though the cost function used to fit our model to data had no terms involving conidiation time. In our simulations the FRQ-dependent phase of conidiation is thus dissociated from the frq mRNA profile which instead directly reflects the light environment, tracking dawn and dusk through its peak and trough phases.

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