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- A proposal for robust temperature compensation of circadian rhythms

In summary, we found that Ruoff's equation is not robust to mutation if it requires delicate balancing of many rate constants in a limit cycle model for the circadian rhythm mechanism. We propose that temperature compensation and other indicators of the robustness of circadian period to genetic variation are more likely the results of a molecular mechanism for which only a few control parameters significantly affect the period of oscillation, and we suggest a resetting hypothesis as a candidate mechanism. Resetting works by moving an effective rate constant back and forth across a SNIC bifurcation. SNIC bifurcations are common features of regulatory networks with both positive and negative feedback loops, of which the circadian machinery is richly endowed. In general, many different rate constants in the mechanism can serve the resetting role.

Our modeling presumes that circadian rhythm properties such as robust 24-h period and temperature compensation are determined at the level of single pacesetting cells. We have not considered any role for intercellular communication in determining the period or the temperature-independence of circadian rhythms. That circadian period mutants commonly leave temperature compensation intact (Table 1) may reflect a difference in levels of organization for these properties. For example, oscillator period may be temperature-compensated at the cellular level exactly as proposed by Ruoff and colleagues, but the overt period of the rhythm in a multicellular organism may be determined, in addition, by intercellular couplings that are insensitive to temperature changes. If that were the case, then mutations affecting intracellular interactions might change the period without upsetting temperature compensation. Although this alternative explanation may apply to Drosophila, it is unlikely for Neurospora.

The oscillatory period of a cell-autonomous, limit-cycle model, based on detailed biochemical interactions among circadian genes and proteins, is a complicated function of all of the rate constants in the mechanism. Because reaction rate constants increase rapidly with temperature, the period-lengthening and period-shortening effects of the parameters must be delicately balanced to achieve temperature compensation. Consequently, temperature-independence of circadian period (in this paradigm) should be fragile with respect to mutation. By contrast, our resetting hypothesis concentrates all of the period-determining effects on just two parameters (μ and σ), which makes temperature compensation easier to achieve. Although the temporal dynamics of the underlying reactions are still strongly temperature dependent (within the resetting paradigm), the control system switches back and forth between the domain of attraction of a stable steady state and the domain of attraction of a stable limit cycle. As temperature changes, any alterations in the relative timing of events in the limit-cycle region are made up for by compensatory changes in the time spent under attraction of the stable steady state. The 24-h period is determined solely by the rules for switching between the two domains.

On the other hand, the resetting hypothesis may appear to be too robust: only mutations that alter μ and σ impinge significantly on period and temperature compensation. We are not proposing that the circadian rhythm mechanism is such a simple process that only two parameters dictate the period of the system. We suppose that, in reality, μ and σ are functions of other molecular processes (phosphorylation, ubiquitination, complex formation, etc.) and that mutations that disrupt any of these processes may interfere with temperature compensation.

The resetting hypothesis makes a number of testable predictions.

Prediction 1.

For many reasons independent of our theory, it seems reasonable to do a thorough screen for genetic mutations that disrupt temperature compensation. Are such mutations common and broadly distributed across the circadian rhythm regulatory network, as the limit cycle hypothesis would suggest, or are they rare and concentrated among a few components of the network, as the resetting hypothesis would suggest?

Prediction 2.

Resetting requires a dynamic system with both positive and negative feedback loops that operates in a region of parameter space exhibiting both multiple steady states (bistability) and limit cycle oscillations (see Fig. 1). Hysteresis in our model relies on the autocatalytic increase of PER based on its homodimerization and stabilization. One could test this assumption directly by measuring the half-lives of monomeric PER (by disrupting the PAS-binding domain) compared with PER–PER complexes. One could also test for hysteresis directly, along the same lines that proved successful in demonstrating bistability in the mitotic control of frog eggs (38, 39), in a per-null mutant with the wild-type per gene under the control of an inducible promoter (e.g., the Tet On/Off system). When PER synthesis is ramped up from low rates, there should be an abrupt increase in the PER expression level at a certain threshold synthesis rate. Once the system is in the PER-high state, it will stay there as the PER synthesis rate is ramped back down, until it falls below a lower threshold synthesis rate for turning the bistable switch off.

Prediction 3.

If bistability can be demonstrated in the circadian rhythm control system, then it is likely on theoretical grounds that if the positive feedback loop is genetically severed, then oscillations continue with shorter period and smaller amplitude. This effect has been observed experimentally in the analogous case for M-phase promoting factor in frog egg extracts (40).



This research was initiated at the Collegium Budapest, Hungary, with financial support from the Santa Fe Institute, the Volkswagen Stiftung, and the Defense Advanced Research Project Agency (AFRL 30602-02-0572).



  • §To whom correspondence should be addressed. E-mail: [email protected]
  • Author contributions: C.I.H. and E.D.C. contributed equally to this work; J.J.T. designed research; C.I.H. and E.D.C. performed research; and C.I.H., E.D.C., and J.J.T. wrote the paper.

  • In test B, a small percentage of perturbations of some key parameters (Pcrit and Jp) of the RS model lead to complex rhythmic oscillations that are not exactly periodic but still “circadian,” i.e., the oscillations are almost periodic, with a repeat interval of ≈24 h, and with peaks and troughs varying up to ≈5%. These cases were considered to be arrhythmic, to avoid any bias for the resetting model over limit cycle models, neither of which is capable of such complex behavior.

  • The authors declare no conflict of interest.

  • This article is a PNAS direct submission.

  • This article contains supporting information online at

  • The authors declare no conflict of interest.

  • Abbreviation:
    coefficient of variation.
  • Freely available online through the PNAS open access option.

  • © 2007 by The National Academy of Sciences of the USA

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