How the active process of temperature compensation is achieved by organisms is an area of intense research interest to both chronobiologists and mathematical modelers. Hastings and Sweeney almost 60 years ago proposed that temperature compensation could be achieved if two temperature-dependent reactions oppose each other, although at the time there was no inkling of what those reactions might be (9). This conceptual model was extended by Ruoff with the notion that positive and negative feedback loops of the oscillators might act as the opposing reactions and lead to temperature compensation in any kinetic oscillator model (15). As specific molecular members of the clock were identified, Hong et al. first proposed that PER protein dimerization might regulate temperature compensation (16). Ten years later, as the complexity of the clock mechanism became clearer, many of the newly described regulatory steps have been tested in mathematical models of the clock to assess their potential contribution to temperature compensation. For example, Hong et al. suggested that switch-like mechanisms acting on sensitive parameters such as phosphorylation, ubiquitination, or complex formation controlling PER protein might regulate temperature compensation (17). Others have suggested using modeling that the concentration of a rate-limiting enzyme involved in processes like phosphorylation can determine temperature compensation (18).

In Neurospora, the core clock gene frequency (frq) undergoes alternative splicing that is temperature sensitive. The resulting two isoforms have opposing effects on clock speed and was once proposed to underlie temperature compensation (19–21). More recently, casein kinase 2 in Neurospora was implicated in temperature compensation. Decreased CK2 activity, or mutation of a specific CK2 phosphorylation site, leads to altered temperature compensation, probably due to an altered balance of phosphorylation at distinct sites. Interestingly, CK2 itself had a normal Q10, i.e., its activity changed twofold with a 10°C increase in temperature (22). In this system, casein kinase 1 (CK1) was important for clock speed but not temperature compensation. Although these studies have provided some insights for understanding the mechanisms of temperature compensation, either they lack good experimental evidence to support their mathematical model or these models are not tested in mammalian system.

Many of the mathematical models suggested that temperature compensation could be due to two opposing reactions acting on a rate-limiting step of the circadian clock machinery (9, 18). The reversible multisite phosphorylation of PER2 is a potential target in this regard due to its rate-limiting role in regulating clock speed (Figure 1) (23, 24). The importance of phosphorylation in the control of circadian rhythms was demonstrated first by the finding of short- and long-period mutations in Drosophila that both mapped to the Dbt kinase gene, the ortholog of mammalian CK1δ and CK1ε (25, 26). CK1 is a family of serine/threonine kinases with seven different isoforms in mammals that are encoded by distinct genes (α, β, γ1, γ2, γ3, δ, and ε), which are involved in diverse biological functions including circadian rhythms, Wnt signaling, membrane trafficking, cytoskeleton maintenance, DNA replication, DNA damage response, RNA metabolism, and parasitic infections (23, 27–30). The first circadian clock phenotype in mammals was found in tau hamsters with 20-h short period (31). Later, it was identified that a missense mutation in hamster CK1ε^tau(Arg178Cys) is to underlie the short-period phenotype of the tau hamster (32). Subsequently, point mutation of a CK1δ/ε-regulated motif in human PER2 [S662G, familial advanced sleep phase (FASP) site] (33) and a point mutation of CK1δ were found in families with FASP syndrome (34). A body of evidence suggests that CK1δ is the major driver of clock timing, but that CK1ε plays an important role as well.

The mechanism by which CK1 regulates phosphorylation of PER2 is complex and is slowly being teased apart. Phosphorylation of PER2 by CK1ε leads to recruitment of the ubiquitin ligase, β-TrCP, and proteasomal-mediated degradation of PER2 (35). But the impact of CK1ε activity on the clock speed has been puzzling, due to opposing observations that reduced CK1 activity shorten (32, 34) and lengthen the circadian period (35). To solve this puzzle, mathematical modeling was applied and then experimentally confirmed the non-intuitive prediction that the short-period tau mutation of CK1ε is in fact functionally a gain of function, not a loss of function mutation. It was further reported that the CK1ε^tau is a highly specific gain of function for its substrate PER2, which gets phosphorylated and degraded much faster, resulting in a faster clock and shorter circadian period (36). These studies emphasized the value of combining experimental studies with predictive mathematical models to advance our understanding of the clock and how changes in kinase activity can alter the clock.

We and others have shown that there are two phosphorylation sites, the FASP and the β-TrCP site, regulating stability of mammalian PER2 (Figure 1) (35, 37). The FASP site is a missense mutation at S662G (S659 in mouse) associated with FASPS, which prevents priming phosphorylation by an unknown priming kinase. Priming phosphorylation of S659 (FASP site) is required for the phosphorylation of four immediate downstream serines of PER2 (659-SVVSLTSQCSYSS-671) by CK1ε/δ (33, 37). The second functional phosphorylation site is β-TrCP site that is also a CK1ε-dependent phosphorylation site (S478 in mPER2), but that seems to be independent of priming phosphorylation (35). It has been identified that surprisingly PER2 undergoes three distinct stages of degradation upon addition of the protein synthesis inhibitor cycloheximide during the PER2 accumulation phase (CT 14–26) of the circadian cycle. Mathematical modeling predicts that a phosphoswitch generates the three-stage degradation of PER2 (38). Accordingly, the first rapid decay phase is β-TrCP site phosphorylation dependent, the second slow plateau phase is dependent on FASP site phosphorylation, and in the third and falling phase, PER2 protein is degraded in a CK1δ/ε-independent manner that is not well understood. Importantly, the model was experimentally confirmed (38). Further experiments showed that CK1ε^tau has decreased activity on the FASP site, leading to an increased activity on the β-TrCP (S478) site. This explains how CK1ε^tau is a gain of function on phosphorylation at S478 and further supports the phosphoswitch between the two sites (the FASP and the β-TrCP site) (38).

Before CK1ε was even identified as a clock component, its role in temperature compensation was suggested by the observation that retinas from tau mutant hamsters have significantly impaired temperature compensation (14). Isojima et al. subsequently reported that unlike virtually all other kinases, CK1ε/δ are temperature insensitive (39). Therefore, they proposed that CK1ε/δ-dependent phosphorylation process might play a central role in temperature compensation of the circadian clock (39). Indeed, in further study, the CK1ε/δ phosphorylation of a β-TrCP peptide was temperature insensitive (39). The mathematical model of Kim and Forger, building on the pioneering work of Forger and Peskin in understanding the mammalian clock system using mathematical tools (40–42), predicted a potential role for the phosphoswitch mechanism in temperature compensation. A key feature of the model requires that there are two sites involved in the phosphoswitch, the FASP and the β-TrCP sites (Figure 1) (38). Since CK1 is relatively temperature insensitive (39), the model assume that priming of the FASP site has normal temperature sensitivity, i.e., its activity increases with increasing temperature, while CK1ε/δ phosphorylation of the β-TrCP site is temperature insensitive, i.e., the rate of phosphorylation is constant regardless of temperature. Incorporating this differential kinase temperature sensitivity into the mathematical model indeed predicted that this could underlie temperature compensation. This model was then experimentally tested in immortalized Per2^Luc mouse embryonic fibroblasts (MEFs). It was found that at higher temperatures, increased FASP site phosphorylation by the priming kinase leads to slow second-phase degradation and more accumulation of PER2, eventually lengthening and compensating period length. Similarly, Per2^Luc MEFs at 30°C showed a marked decrease in second-phase degradation, whereas first-stage degradation remained intact. These findings underscore the importance of the relative rates of phosphorylation of the two phosphoswitch sites in temperature compensation (38). Additional experiments indirectly tested if an intact phosphoswitch mechanism is necessary for temperature overcompensation. An abnormal temperature compensation was observed in CK1ε^tau; Per2^Luc MEFs, and also in Per2^Luc MEFs treated with a CK1ε/δ inhibitor, further supporting a role for CK1ε/δ and an intact phosphoswitch mechanism as a prerequisite for temperature compensation. The studies also support the value of a robust mathematical model that makes testable predictions about complex systems when biological intuition has reached its limits (38).

Recently, it has been reported that cells with knockouts of specific circadian clock components retain temperature compensation (43). The authors concluded that temperature compensation is likely determined by a rate-limiting process(es) that are temperature sensitive, consistent with the phosphoswitch mechanism (43). Another mathematical model for temperature compensation has recently proposed a temperature insulation mechanism where oscillation period is determined by very few temperature-independent or only slightly temperature-dependent parameters, but where other parameters remain strongly temperature dependent (44). This model is analogous to the proposed phosphoswitch mechanism in which the CK1ε/δ is temperature independent or slightly dependent, whereas the priming kinase is temperature dependent (38).

There are a number of unresolved issues. The priming kinase has not been identified yet. It also remains unclear what happens to PER2 phosphorylation over the full 24-h day, in part because the methods to study this in mammalian systems are not suitably sensitive. This is relevant to another unsolved question: how PER2 is degraded in the third phase of three phase decay, when neither CK1 nor proteasome inhibitors impact PER2 loss? Moreover, further study is necessary to understand whether fluctuations in body temperature, which can entrain the clock, do so in part via the phosphoswitch mechanism in addition to the proposed heat shock factor 1 (HSF1) mechanism (7, 45). Finally, it is also important to address whether the mechanisms regulating temperature compensation in peripheral cells and the central pacemaker (SCN) cells are the same and whether temperature-induced changes in peripheral clocks can feed back to the central clock.

It is remarkable that the complex yet robust phenomenon of temperature compensation is regulated by subtle differences in phosphorylation of the same protein at different sites. Notably, this finding is in general agreement with predictions of earlier mathematical models that suggested that opposing outputs with switch-like mechanisms might control temperature compensation (9, 17). In the future, it will be important to identify the priming kinase that plays a central role in the phosphoswitch model. This phosphoswitch mechanism of temperature compensation may be a core feature of clocks in many species, as a similar interaction of phosphorylation sites is operative in Drosophila and Neurospora as well (46–48).

RN and DV were involved in conceptualizing, researching and writing this review.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.