The mammalian circadian clock is a biochemical network of molecular interactions, orga- nized into a structure that includes a number feedback loops, that oscillates with a period of approximately 24 hours. Genes are expressed and proteins are modified rhythmically with all concentrations following cyclic trajectories. The circadian expression of clock-related genes is controlled by clock-related transcription factors.
The clock machinery has been modeled mathematically on different levels of detail [90, 68, 69, 29], and the models are often used to further the understanding of systematic network properties [59, 44, 94, 47, 10]. In this chapter, the most detailed current model of
the mammalian circadian clock [29] was extended in order to incorporate recent advances and findings in experimental circadian molecular biology. The aim was to create an up- to-date model, using mass-action kinetics exclusively, that reflects as much as possible the current knowledge and represents correct mutant and wild-type behavior. This model was created for further analysis using the phase sensitivity methods from Chapter 2, which is presented in Chapter 6. A summary of current knowledge in circadian molecular biology is presented next, followed by a review of the model by Forger & Peskin [29]. The extended model and its behaviors is described in Sections 4.2 through 4.2.1.
A transcriptional activator at the heart of the mammalian clock is a heterodimeric complex formed by the Clock protein CLK and the BMAL1 protein, called the Bmal1- Clock-Complex (BCC). Both BMAL1 and CLK are helix-loop-helix, PAS domain-containing transcription factors [93]. BMAL1 acts as a shuttle to facilitate the nuclear accumulation of CLK [60], and heterodimerization increases their degradation.
Although clk was the first mammalian clock gene to be identified [26], it is not as well studied as some of the others. Clk+/− mutant mice have a prolonged period, and homozy- gote mutants display an initially prolonged period that then decays into arrhythmicity in constant darkness [26]. It is expressed rhythmically in the mouse liver [65, 83] but not in the suprachiasmatic nucleus (SCN) [93], and it does not appear to control its own expres- sion level through feedback, as shown through mutant studies. Preitner et al. [83] report that Rev-Erbα participates in regulating the Clk mRNA levels in the liver. Additionally, it appears that CLK is rhythmically phosphorylated in at least 4 different forms [65, 105], which might affect its stability and nuclear trafficking [88].
The BCC is a transcriptional activator of many other clock-related genes. It binds to CACGTG E-box sequences within the promotor regions of the three per (period) homo- logues [58], two cry (cryptochrome) homologues, the ror gene and the rev-erb genes. Bmal1 is expressed under the control of two upstream promotor regions called ROREs (retinoic acid receptor-related orphan receptor response elements). Both REV-ERBα and ROR have been shown to bind to both ROREs. While REV-ERBα represses bmal1 expression [83], ROR increases it [36]. Beyond its role in its own feedback regulation through Bmal1, REV-ERBα regulates clock and cry1 expression [83]. Because cry1 expression is lowered by REV-ERBα, and CRY1 is an inhibitor of the BCC, which activates rev-erbα expression, a positive feedback loop is formed. In Figure 4-1, square arrowheads represent the negative
feedback interactions, while large, regular arrowheads indicate positive transcriptional con- trol. A deletion of Rev-Erbα causes a shortened period, but more importantly, it causes the rhythmicity to cease in the Bmal1 concentrations. The rhythmicity in the other clock genes persists [83].
The BCC is inactivated by the binding of both CRY and all three PER proteins, prob- ably through different mechanisms [2]. The CRY proteins have stronger inhibitory action than the PER proteins [58, 45]. This action closes five negative feedback loops affecting the expression of the cry and per genes. PER1 and PER2 in their different states of phospho- rylation can enter and leave the nucleus at different rates and can form stable complexes with the kinases and either CRY protein [26, 2]. The PER proteins are rate limiting for this step and necessary for the nuclear import of the complex, making them the shuttle for nuclear CRY proteins [65]. PER2 plays a second, positive role in the regulation of bmal1 expression [87, 83], thereby closing a positive feedback loop interlocked with the negative feedback through the BCC.
The BCC is also inactivated by another circadian protein family, that of DEC1 and DEC2 [45]. Both are basic helix-loop-helix transcription factors shown either to bind to BMAL1 or to compete for DNA binding, thereby influencing the transcription of per1. The DEC proteins are similarly strong transcriptional inhibitors than the CRY proteins, and are also rhythmically expressed in the SCN, and Dec1 expression was shown to respond to light pulses. The dec genes were shown to be expressed under positive control of the BCC. Much like the per and cry genes, they posess CACGTG E-boxes where the BCC binds [40, 54]. The negative autofeedback loops around the dec genes might interact with the other negative feedback loops, though details are not known.
The roles of the two cry homologues appear similar and perhaps redundant, in that neither of them is indispensable for rhythmicity. This is not so for the per homologs [112]; the deletion of per3 unlike per1 and per2 hardly affects rhythmicity, and per3 is hypothesized to play a role only as a potential output [8]. In humans, a single mutation in per2 causes FASPS [97], and its loss causes arrhythmicity in mice [113, 8]. The phenotype of per1 null mutant mice shows continued oscillations with unchanged period for 10–14 days but then loses rhythmicity in one study [8]. In another study, it was found that the absence of per1 caused short periods but otherwise undisturbed rhythmicity [113]. On the molecular level, it was found that the loss of per1 lowers the peak levels of certain clock proteins, but does
not affect mRNA levels in both studies. Disruption of per2 expression results in reduced transcription levels of other clock genes and their protein levels. It was concluded that PER1 appears to participate predominantly in regulation at the posttranscriptional level [8, 113].
The PER proteins are phosphorylated by several isoforms of casein kinase 1 (CK1ǫ, CK1δ, and possibly others) in a complex manner that regulates their degradation and nuclear trafficking [103]. In particular, the phosphorylation pattern of PER2 was studied in detail, showing that its phosphorylation sites can be classified in 2 groups that yield opposite period phenotypes. One class of phosphorylation sites leads to an increase in degradation and a slight increase of nuclear import. A distinct phosphorylation site at Ser659 in mice (Ser662 in humans) significantly increases both the rate of nuclear import of phosphorylated PER2 as well as its stability [103]. This phosphorylation site is that of a known mutation in humans that leads to familial advanced sleep phase syndrome (FASPS) [97]. An alternate view of the importance of PER phosphorylation is given by Forger and coworkers [31], who showed that the tau mutation in CK1ǫ is not as previously thought a loss-of-function mutation, but instead a gain-of-function mutation specifically for the substrates PER1 and PER2 in vivo. Hyperphosphorylation is shown to lead to increased degradation rates; however different phosphorylation sites are not tracked individually, and the effects of their phosphorylation cannot distinguished in this study. On the other hand, Vanselow et al. [103] have identified 21 phosphorylation sites, only one of which — the FASPS site — was shown to increase stability; all others were shown to increase PER2 degradation. An increase in PER degradation might account for the shortened period phenotype found in hamsters with the tau mutation as well as humans with the FASPS mutation.
With the recent discovery of clock mechanisms based solely on posttranslational chains of events [75], namely, based on phosphorylation–dephorphorylation reactions, the question has been posed if there could possibly exist such a ‘phoscillator’ in mammals as well [73]. It is known that phosphorylation plays an integral role in the mammalian circadian clock, as discussed above. Furthermore, it was recently shown that the dephosphorylation of casein kinase 1 ǫ by protein phosphatase 5 (PP5) regulates its activity, and that the CRY proteins in turn regulate the activity of PP5 [80]. Furthermore, it was shown that protein phosphatase 1 (PP1) regulates the stability of PER2 by removing the phosphate groups that tag PER2 for ubiquitin-mediated degradation [32]. This new evidence might support
the existence of additional, non-transcriptional feedback loops in the mammalian circadian clock.
One of the most important features of the mammalian circadian clock is its ability to process input signals in the form of light, temperature, food or other stimuli, and entrain to a stable 24-hour oscillation that is in the correct phase with the entraining stimulus. In other words, the molecular network, even though it has a free running period (FRP) of slightly longer than 24 hours [20, 52], can be forced to oscillate at exactly 24 hours. Moreover, molecular events adapt in phase to match the entraining signal, so that, e.g., the molecular events signaling ‘morning’ will adjust to occur with the onset of light. It is not well understood how entraining signals are transmitted into the molecular clock, though it is known that the clock’s ability to process input signals depends on the time of subjective day, due to a phenomenon called ‘gating’ [26]. It is known that Per1 mRNA increases very quickly after a light stimulus is applied during both early night (i.e., shortly after sunset) and late night [88]. On the other hand, Per2 mRNA levels rise slower [26], and only following signals introduced during early night [88]. The mRNA levels of Per3 and either Cry are not affected by light [26].