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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 driven entrainment observed in photic T-cycles. A. Simulated variation of conidiation onset with photic T-cycle length. As in Figure 4, conidiation onset was identified with the FRQ falling phase ϕFRQ. Also plotted are the peak and trough times of frq mRNA and FRQ protein. White and grey regions denote light and dark respectively. The dotted line indicates a fixed period of time following dusk. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures shown in A for T = 21 (see Additional file 1, Figure S3 for the sensitivities over the full range of T-cycle lengths). ∂ϕFRQ/∂tDUSK is close to 1: conidiation onset therefore tracks dusk.
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Figure 5: The model reproduces the driven entrainment observed in photic T-cycles. A. Simulated variation of conidiation onset with photic T-cycle length. As in Figure 4, conidiation onset was identified with the FRQ falling phase ϕFRQ. Also plotted are the peak and trough times of frq mRNA and FRQ protein. White and grey regions denote light and dark respectively. The dotted line indicates a fixed period of time following dusk. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures shown in A for T = 21 (see Additional file 1, Figure S3 for the sensitivities over the full range of T-cycle lengths). ∂ϕFRQ/∂tDUSK is close to 1: conidiation onset therefore tracks dusk.

Mentions: Interestingly, our model also reproduces the driven entrainment observed experimentally in symmetric T-cycles. Figure 5A shows that for T in the range 18 ≤ T ≤ 24, FRQ-dependent conidiation onset occurs roughly the same number of hours following dusk irrespective of cycle length; that is, ϕFRQ tracks dusk. Again, like the variation of ϕFRQ with photoperiod in 24 hr LD cycles, this is a correctly simulated system-level property that was not a direct target of the cost function. The good fits to phase data can thus be viewed as a validation of our model. For both the T-cycle and photoperiod simulations, we numerically quantified these phase variations by considering the sensitivities of frq mRNA and conidiation onset with respect to dawn and dusk, as described below.


Robustness from flexibility in the fungal circadian clock.

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

The model reproduces the driven entrainment observed in photic T-cycles. A. Simulated variation of conidiation onset with photic T-cycle length. As in Figure 4, conidiation onset was identified with the FRQ falling phase ϕFRQ. Also plotted are the peak and trough times of frq mRNA and FRQ protein. White and grey regions denote light and dark respectively. The dotted line indicates a fixed period of time following dusk. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures shown in A for T = 21 (see Additional file 1, Figure S3 for the sensitivities over the full range of T-cycle lengths). ∂ϕFRQ/∂tDUSK is close to 1: conidiation onset therefore tracks dusk.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: The model reproduces the driven entrainment observed in photic T-cycles. A. Simulated variation of conidiation onset with photic T-cycle length. As in Figure 4, conidiation onset was identified with the FRQ falling phase ϕFRQ. Also plotted are the peak and trough times of frq mRNA and FRQ protein. White and grey regions denote light and dark respectively. The dotted line indicates a fixed period of time following dusk. B. Dusk sensitivities ∂ϕ/∂tDUSK of the phase measures shown in A for T = 21 (see Additional file 1, Figure S3 for the sensitivities over the full range of T-cycle lengths). ∂ϕFRQ/∂tDUSK is close to 1: conidiation onset therefore tracks dusk.
Mentions: Interestingly, our model also reproduces the driven entrainment observed experimentally in symmetric T-cycles. Figure 5A shows that for T in the range 18 ≤ T ≤ 24, FRQ-dependent conidiation onset occurs roughly the same number of hours following dusk irrespective of cycle length; that is, ϕFRQ tracks dusk. Again, like the variation of ϕFRQ with photoperiod in 24 hr LD cycles, this is a correctly simulated system-level property that was not a direct target of the cost function. The good fits to phase data can thus be viewed as a validation of our model. For both the T-cycle and photoperiod simulations, we numerically quantified these phase variations by considering the sensitivities of frq mRNA and conidiation onset with respect to dawn and dusk, as described below.

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