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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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Phase and amplitude sensitivities of the entrained system. A. Phase and relative amplitude changes resulting from perturbations of the entrained clock in its maximally flexible direction. Solid and open symbols denote WT and 1% wc-1 loop coupling respectively. Perturbed solutions were computed for proportional parameter increases of 2%. Note that the reduction in wc-1 loop coupling strength causes the variation in FRQ protein phase to decrease significantly. B. Comparisons of the FRQ phase changes sFRQ for WT and 1% loop coupling with the corresponding changes ΔϕFRQ in FRQ-dependent conidiation phase. sFRQ and ΔϕFRQ are similar, indicating that the reduced FRQ phase sensitivity also results in reduced conidiation phase sensitivity.
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Figure 8: Phase and amplitude sensitivities of the entrained system. A. Phase and relative amplitude changes resulting from perturbations of the entrained clock in its maximally flexible direction. Solid and open symbols denote WT and 1% wc-1 loop coupling respectively. Perturbed solutions were computed for proportional parameter increases of 2%. Note that the reduction in wc-1 loop coupling strength causes the variation in FRQ protein phase to decrease significantly. B. Comparisons of the FRQ phase changes sFRQ for WT and 1% loop coupling with the corresponding changes ΔϕFRQ in FRQ-dependent conidiation phase. sFRQ and ΔϕFRQ are similar, indicating that the reduced FRQ phase sensitivity also results in reduced conidiation phase sensitivity.

Mentions: Figure 8A plots the changes in phase and relative amplitude resulting from a perturbation of the WT solution along its first principal component u1, obtained through a parameter variation in the direction of the corresponding right singular vector v1. Clearly, FRQ protein undergoes a significantly greater change in phase than frq and wc-1 mRNA. Also, as can be seen in Figure 8B, the large variation in FRQ phase results in a correspondingly large shift of conidiation phase ϕFRQ. The analysis also implies a non-uniform shift in amplitude, with wc-1 mRNA exhibiting a greater change compared to frq mRNA and FRQ protein (see Figure 8A). These phase/amplitude sensitivity calculations are confirmed by Additional file 1, Figure S5 which plots the corresponding changes to the mRNA and protein time series.


Robustness from flexibility in the fungal circadian clock.

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

Phase and amplitude sensitivities of the entrained system. A. Phase and relative amplitude changes resulting from perturbations of the entrained clock in its maximally flexible direction. Solid and open symbols denote WT and 1% wc-1 loop coupling respectively. Perturbed solutions were computed for proportional parameter increases of 2%. Note that the reduction in wc-1 loop coupling strength causes the variation in FRQ protein phase to decrease significantly. B. Comparisons of the FRQ phase changes sFRQ for WT and 1% loop coupling with the corresponding changes ΔϕFRQ in FRQ-dependent conidiation phase. sFRQ and ΔϕFRQ are similar, indicating that the reduced FRQ phase sensitivity also results in reduced conidiation phase sensitivity.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Phase and amplitude sensitivities of the entrained system. A. Phase and relative amplitude changes resulting from perturbations of the entrained clock in its maximally flexible direction. Solid and open symbols denote WT and 1% wc-1 loop coupling respectively. Perturbed solutions were computed for proportional parameter increases of 2%. Note that the reduction in wc-1 loop coupling strength causes the variation in FRQ protein phase to decrease significantly. B. Comparisons of the FRQ phase changes sFRQ for WT and 1% loop coupling with the corresponding changes ΔϕFRQ in FRQ-dependent conidiation phase. sFRQ and ΔϕFRQ are similar, indicating that the reduced FRQ phase sensitivity also results in reduced conidiation phase sensitivity.
Mentions: Figure 8A plots the changes in phase and relative amplitude resulting from a perturbation of the WT solution along its first principal component u1, obtained through a parameter variation in the direction of the corresponding right singular vector v1. Clearly, FRQ protein undergoes a significantly greater change in phase than frq and wc-1 mRNA. Also, as can be seen in Figure 8B, the large variation in FRQ phase results in a correspondingly large shift of conidiation phase ϕFRQ. The analysis also implies a non-uniform shift in amplitude, with wc-1 mRNA exhibiting a greater change compared to frq mRNA and FRQ protein (see Figure 8A). These phase/amplitude sensitivity calculations are confirmed by Additional file 1, Figure S5 which plots the corresponding changes to the mRNA and protein time series.

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