Rigid Cooperation of Per1 and Per2 proteins

Period circadian clock (Per) genes Per1 and Per2 have essential roles in circadian oscillation. In this study, we identified a new role of Per1-Per2 cooperation, and its mechanism, using our new experimental methods. Under constant light conditions, the period length of Per1 and Per2 knockout mice depended on the copy number ratio of Per1:Per2. We then established a light-emitting diode-based lighting system that can generate any pattern of light intensity. Under gradually changing light in the absence of phase shift with different periods, both Per1(−/−) and Per2(−/−) mice were entrained to a broader range of period length than wild-type mice. To analyse Per1-Per2 cooperative roles at the cell culture level, we established a Per2 knockout-rescue system, which can detect period shortening in a familial advanced sleep phase syndrome (FASPS) mutant. Upon introduction of the Per1 coding region in this system, we saw period shortening. In conclusion, short period-associated protein Per1 and long period-associated Per2 cooperated to rigidly confine the circadian period to “circa” 24-h. These results suggest that the rigid circadian rhythm maintained through the cooperation of Per1-Per2 could negatively impact modern society, in which the use of artificial lighting is ubiquitous, and result in circadian disorders, including delirium.

"Circadian" comes from the Latin circa (about) and dies (day). Many physiological functions have diurnal variation 1-3 that follows an approximately 24-h cycle and is regulated by an endogenous circadian clock 4 ; dysregulation of these functions leads to circadian disorders, including delirium 5,6 . The mechanism underlying the mammalian circadian clock is a transcriptional network that consists of a feedback loop of about 20 genes (clock genes) 7,8 . Because every cell in the body has a circadian clock, we can see circadian oscillation in fibroblasts transfected with plasmids encoding luciferase under the control of a circadian clock gene promoter and cultured in luciferin-containing medium 9 . To coordinate the clock in many cells in mammals, the suprachiasmatic nucleus (SCN) in the hypothalamus functions as a central clock 10,11 . The SCN entrains clocks of cells in individual organs (peripheral clocks) through neural and humoral mechanisms. The SCN is also important because SCN neurons have an intercellular coupling (synchronization) mechanism that makes the circadian oscillation robust and self-sustainable and maintains period length of approximately 24 h in all cells in the organ more precisely than clocks in individual cells 12 .
Period circadian clock (Per) genes Per1 and Per2 are main components of the circadian clock feedback loop and have three important roles. First, they are essential for circadian oscillation, as demonstrated by the fact that Per1/Per2 double-knockout mice become arrhythmic 13 . Second, Per genes are also important as a core component of the ruler of the circadian period 14 . Sequential phosphorylation, primarily by casein kinase 1 (CK1), at a large number of sites is important for this property and may constitute the actual posttranslational oscillator in mammalian circadian clocks 15,16 . Third, induction is a key factor of circadian entrainment. Light-induced expression of Per1 and Per2 proteins in the SCN appears to be important in entrainment 17 . However, the cooperative roles of Per1 and Per2, especially in determining circadian period length and under various light conditions, still remain to be elucidated. In this study, we found a new role, and its mechanism, of Per1-Per2 cooperation using new methods we established. Per1 and Per2 cooperatively confine the range of circadian period length to approximately 24-h. We then performed experiments using T-cycles, patterns of regular alternation of light and dark with period different than 24 h, to mimic the experience of shift workers 24,25 . Although a previous study showed that WT, Per1 (−/−) , and Per2 (−/−) genotypes have similar T-cycle properties 26 , we hypothesized that this is because of a rectangular-type light pattern, characterized by abrupt changes between light and dark, which induces strong and unnatural phase shifts. In fact, several studies showed that a gradually changing or natural pattern of light induces a different entrainment pattern than that induced by a rectangular-type light pattern [27][28][29] . We also hypothesized that we would be able to see endogenous circadian clock rigidity and flexibility in WT and Per knockout mice if we could create a system without strong phase shifts. To avoid initiating a phase shift by turning the lights on and off, we established a light-emitting diode (LED)-based lighting system that can generate any pattern of light intensity at 1-min resolution and produces 256 levels of light intensity ( The results of these three sets of experiments suggest that Per1 expression is associated with a shorter free-running period, Per2 with a longer period, and that Per1 and Per2 cooperatively confine the range of circadian period length to approximately 24 h. Cooperation between Per1 and Per2 results in a rigid 24-h rhythm that Six mice of each genotype were used in each (a and b) crossover design experiment. Animals were exposed to the indicated number of hours of light and/or dark for the indicated number of days. The light intensity was within the range of 100-300 Lux in the light phase at the centre bottom of the cage. (C) Representative actogram for each genotype. (D) Periodicity is defined as the mean amplitude (Q[p]) minus the level of significance at the determined period length within ± 1 h of the circadian period length, determined using the chi-square periodogram. Values represent mean ± standard deviation (SD) of a single experiment. P-values were calculated using one-way ANOVA and Tukey's post hoc tests. The F and P-values from the Tukey's test are shown in Supplemental Table S3. is not perturbed by the environment. On the other hand, this system is relatively inflexible with regard to adapting to environmental change, which leads to morbid deterioration (i.e., arrhythmicity or lack of entrainment to new environmental conditions) under various light conditions. Establishment of Per2 knockout-rescue system to detect period shortening in FASPS. Next, to analyse cooperative roles of Per1 and Per2 at the cell culture level, we established a Per2 knockout-rescue system. Rescue of clock gene knockouts can be used to analyse many mutant phenotypes 30 , and several systems have been described for period genes, including one involving Per2 knockout in mouse embryonic fibroblasts with adenoviral induction 31 , and another system employing stable transfection of NIH3T3 cells 32 . However, these systems failed to detect a change in period length, probably because period length is influenced by the amount of Per protein in each cell, and gene dosage is critical for Per genes [33][34][35] . The amount of Per protein in each cell should be tightly controlled at a low level (~1,000 molecules/cell) 36,37 . Therefore, we used a Per2 knockout-rescue system with Rosa26 targeting and embryonic stem (ES) cell differentiation because genes introduced into the Rosa26 locus on murine chromosome 6 are expressed in every tissue in the body 38,39 . If we insert only one copy of the rescue gene cassette at Rosa26, we can compare the period length of each mutant precisely.
First, we focused on the fact that ES cells do not have a circadian rhythm, but circadian oscillation appears with retinoic acid (RA)-induced differentiation 40 , and we can see circadian oscillation in ES cells of any genotype without generating an organism. We performed a broad-parameter search to produce sustained oscillation with high amplitude to detect precise period length. Finally, we improved the ES differentiation system 40 (Fig. 4A)  Table S4. and succeeded in detecting 10 peaks of oscillation in Per2::luciferase knockin (KI)/KI ES cells (Fig. 4B) 41 . We also used this protocol in several independent experiments and observed reproducible, precise period length, that is, most of the cell culture dishes were included within approximately 1-h, although some outliers were apparent (Fig. 4C,D).
We then introduced Per2 into the Rosa26 locus of Per2 (−/−) ES cells using TAL effector nuclease (TALEN) (Fig. 5A). Specifically, we constructed a vector containing the Per2 promoter (3.5 kb, P(Per2L)), Per2 coding region, and luciferase gene between the Rosa26 long arm (4 kb, modified from 8 kb) and short arm (4 kb) (Fig. 5B). We transiently cotransfected Per2 (−/−) ES cells with this vector and TALEN vectors 42 , which create a double-strand break in the Rosa26 region, to improve recombination efficiency. Then we selected ES cells with puromycin and picked colonies under a phase contrast microscope. We checked the structure of the Rosa26 locus by polymerase chain reaction (PCR) (targeted arm 5′ , 3′ , WT arm 5′ , 3′ ) and quantitative PCR of the puromycin resistance gene (Supplemental Figure S4). We obtained several rescued Per2 knockout ES cell lines that contained only one copy of the Per2 gene cassette correctly introduced into Rosa26. By introducing the WT Per2 gene, we were able to detect the 24-h oscillation from two independent ES clones ( Fig. 5C,D, Supplemental Figure S5A).
Next, we used a familial advanced sleep phase syndrome (FASPS) mutant to verify this system. FASPS is an autosomal dominant disease characterized by a natural tendency to go to sleep and wake up at times considered earlier than normal. This phenotype is caused by period shortening of the circadian rhythm due to Per2 point mutation 5 . This is the only known disorder caused by a Per gene mutation and can be modelled with Per2 knockout mice rescued with a bacterial artificial chromosome (BAC) clone containing the Per2 gene locus with the S659G mutation, which corresponds to the human S662G mutation 43 . We introduced the FASPS mutant into this system and detected period shorter than 24 h in two independent ES clones [WT (mean ± standard deviation [SD]): 23.4 ± 0.17 h, FASPS: 20.3 ± 0.6 h; P < 0.001] (Fig. 5C,D, Supplemental Figure S5A). To our knowledge, this is the first system to detect period shortening in a FASPS mutant at the cell culture level. Moreover, we also introduced two known mutants. The first, mut6, consists of six mutations of amino acids downstream of the FASPS mutation (S662A/S665A/S668A/S670A/S671A/T672A) that are said to be phosphorylated serially after phosphorylation of the FASPS site and thought to function in a manner similar to FASPS. In a previous study, mut7, which includes the FASPS site mutation, was used, but we omitted that mutation from this mutant 32 . The second known mutant introduced was S477A/G479A, a mutant of the β -transducin repeat-containing protein (β -TrCP) binding site 44,45 , which is the E3 ubiquitin ligase for Per proteins. Both mutants were used in a previous study, but period length was not determined. With introduction of the mut6 and β -TrCP mutants, period shortening similar to that observed with FASPS was observed for mut6 (20.3 ± 0.8 h) but period change was not observed in β -TrCP mutants (24.1 ± 0.8 h) (Supplemental Figure S6). These data demonstrate that our Per2 knockout-rescue system can produce the phenotypes of other Per2 mutations.
The coding regions appear to be important in the difference between Per1 and Per2. Because our system proved to be versatile, we also analysed cells transfected with the construct without the Per2 coding region (Fig. 6A). Oscillation was weaker and period was shorter than in cells expressing WT Per2 (Fig. 6B,C, Supplemental Figure S5B). This suggests that cooperative roles of Per1 and Per2 are also important at the cell culture level. Next, we replaced the Per2 coding region in the construct with that of Per1 (Fig. 6D). Likewise, we utilized western blotting to examine Per1 and Per2 expression in Per1-and Per2-rescued ES cells. Both ES cell lines lacked native Per2 but expressed similar levels of native Per1. As expected, Per1::Luc was only expressed in the Per1-rescued ES cells, and Per2::Luc was only expressed in the Per2-rescued ES cells (Supplemental Fig. 7). Per1 and Per2 have different promoter structures, mRNA expression patterns, and mRNA stability controlled by the 3′ UTR 17,46,47 . Moreover, in the Per2 knockout-rescue system with adenoviral induction described in a previous report, Per1 and Per2 coding regions showed a similar effect on oscillation, although period was not determined 31 . Therefore, we expected to see similar periods with this experiment. Contrary to our expectations, we observed period shortening with Per1 expression (22.3 ± 0.4 h) compared to Per2 (25.4 ± 1.6 h) in the two independent ES clones ( Fig. 6E,F, Supplemental Figure S5C). That is, the association of Per1 expression with a shorter period and that of Per2 with a longer period is at least partly explained by differences in the Per coding regions, and not the Per promoters as previously reported 31 . We also analysed data from all ES cell experiments (Fig. 7A). The period length could be divided into three groups. WT and β -TrCP mutant lines had periods of approximately 24 h. Cells expressing constructs in which the Per2 coding region was lacking or replaced by that of Per1 had periods of approximately 22-23 h, and the FASPS and mut6 mutants had periods of approximately 20 h. Per1 has a paradoxically longer half-life than Per2. Until now, the effects of Per1 and Per2 on circadian oscillation were thought to be similar, and specific properties of the two proteins were not a focus. To analyse the mechanism underlying differences in period length associated with Per1 and Per2 expression, we calculated protein half-life. Several groups reported that FASPS mutants have shorter half-lives than WT Per2, and Per protein half-life and period length are believed to be correlated 32,48,49 . To analyse the half-lives, we transfected NIH3T3 cells with luciferase fusion proteins, treated the cells with cycloheximide, and conducted real-time monitoring of bioluminescence 14 . We chose this approach for two reasons. First, the bioluminescence system has a broad dynamic range, and it is possible to quantitate small differences in protein level with sensitivity. Second, with real-time monitoring, we can track the same cell population and compare luminescence in the same cells at different time points to calculate the half-life. Using this approach, we observed a shorter half-life of the FASPS mutant, but Per1 had a paradoxically longer half-life than Per2 (Fig. 7B, Supplemental Figure S8A). Because we wanted to show that the observed difference in half-life was not just the consequence of phase difference, we also performed the experiments under dispersed circadian phase conditions 14 and obtained clearer results (Supplemental Figure S8B). We also compared the half-lives of Per1 and Per2 by western blotting without the luciferase fusion (Supplemental Figure S8C,D) and observed that Per1 appeared to be more stable (P = 0.01). Likewise, we demonstrated that period length and protein half-life are not always correlated (Supplemental Figure S9A). These findings suggest that the mechanisms underlying period shortening in FASPS and underlying the association of Per1 expression with a short period are different.

Discussion
In this study, we have shown that Per1 expression is associated with a short period and Per2 expression with a long period, and this is explained, at least in part, by differences in the properties of the two proteins, and not the Per promoters as previously reported. Per1 and Per2 cooperatively confine the circadian period to 24 h, and prevent the period length from oscillating far from 24 h. However, this system is relatively inflexible and deteriorates readily, i.e., does not become entrained to the environmental cycle or becomes arrhythmic under various light conditions (Fig. 7C). With regard to methodology, we established new experimental methods to analyse the cooperativity of Per1 and Per2. First, we established an LED-based lighting system that can generate any pattern of light intensity to measure oscillation period at the organismal level. Next, we established an ES cell differentiation system to precisely measure period length at the cell culture level. Finally, we established a Per2 knockout-rescue system that is the first to recapitulate the period shortening seen in FASPS at the cell culture level. Using these new methods, we have clearly shown the importance of Per1-Per2 cooperativity at the organismal and cell culture levels.   We have shown that cooperation between Per1 and Per2 results in rigid circadian oscillation and confines the circadian period to approximately 24 h. Until relatively recently in evolutionary history, most mammals lived in the same general area on the earth; there was little artificial light, and they had to adjust their circadian clocks only to the 24-h environmental cycles. Thus, a rigid circadian rhythm maintained through Per1-Per2 cooperativity would be beneficial for survival, to predict the day-night transition unperturbed by environmental noise 50 . However, in modern society, artificial lighting is nearly ubiquitous, producing conditions of constant light similar to those used in the experiments described in Figs 1 and 2. Long airline flights and systems employing shift workers are also features of modern life, and generate conditions such as cycles of different period length observed with gradually changing light in the experiments described in Fig. 3.
Recent reports have suggested that delirium is one of the most common 51,52 circadian disorders of the hypothalamus [53][54][55] . Delirium is characterized by the onset of sudden and severe confusion and occurs in more than 30% of aged or dementia inpatients. Although delirium is defined as a transient and reversible disturbance of attention and cognition, one of the most common symptoms of delirium is sleep-wake cycle disorder, or day-night reversal, or arrhythmicity 6,53-55 . One study 6 showed that 97% of delirium patients suffered from sleep-awake cycle disturbance and attention disturbance. Further, delirium is a serious concern in the geriatric field because it causes many in-hospital accidents, including falls and fractures 56 . However, the results of a randomized controlled trial have shown that delirium is treatable with chronobiological therapies 57,58 , including ramelteon, a melatonin receptor agonist 57 . Hence, circadian disorders are a core symptom and perhaps one of the primary causes of delirium.
We have attempted to mimic the conditions of circadian disorders, including delirium, using constant and gradually changing light in our experiments. One of the major causes of delirium in patients in intensive care units is the constant light, as in the experiments described in Figs 1 and 2. WT mice in these experiments may have experienced a condition similar to delirium. Under these conditions, a rigid circadian rhythm maintained  Per1 knockout) is longer than the period length observed at a greater concentration of Per1 (e.g. Per2 knockout) because the degradation rate of Per2 is higher and its rate of accumulation is slower than Per1. The study by Gerard et al. 82 that modelled the negative autoregulation of gene expression showed that the period increases with an increased degradation rate when degradation is described by a Michaelis-Menten function. This was in accord with the results of the current study that indicated a difference in the period length and half-lives of Per1 and Per2.
Scientific RepoRts | 6:32769 | DOI: 10.1038/srep32769 through Per1-Per2 cooperation would negatively affect humans and result in morbid deterioration, similar to that observed in mice in the experiments described in Figs 2 and 3. As shown in Fig. 3, Per knockout mice were not likely to develop day-night reversal; thus, we think that the independent regulation of Per1 and Per2 expression is a potential drug target for the treatment of circadian disorders. Nonetheless, we cannot mimic the symptoms of delirium, because there are no experimental systems using mice to model the other characteristic symptoms of delirium, including disorientation or illusion and delusion, which are related to consciousness.
The question of whether Per knockout mice are resistant to "day-night reversal" in "non-gradually changing light" or a "rectangular-type light pattern" has been addressed in three previous studies. Although one prior study showed that WT, Per1 (−/−) , and Per2 (−/−) mice have similar T-cycle entrainment patterns 26 , a smaller proportion of WT mice were entrained at the T21 T-cycle compared to Per2 (−/−) mice, which was similar to our observations (Fig. 3). Next, there is the extreme case of Per1 (−/−) Per2 (−/−) double-knockout mice that never progress to the state of day-night reversal, not even when exposed to the 12 h LD cycle or any period cycle, which is called masking 59 . Third, our findings that Per1 (−/−) and Per2 (−/−) mice could be adapted to a broader range of periods under various T-cycles was in accord with previous findings in which Per2/Cry2 and Per1/Cry1 double knockout mice entrained to the 16-32 h LD cycle 60 . However, our findings varied slightly because the T-cycle entrainment patterns of Per1 and Per2 knockout mice were different under gradually changing light.
Although jet-lag experiments are often used to mimic patterns experienced by shift workers 61 , we used T-cycles 24,25 , which can also reproduce some features of the shift worker environment. The two types of shift worker rotations are forward and backward 24 . The forward shift is associated with a regularly delayed phase of the sleep-wake cycle (e.g. the morning shift, then the afternoon shift, then the night shift) that resembles a greater than 24-h entrainment cycle, whereas the backward shift is the reverse. Forward shifts are often used because a shift will generate rhythms that coincide with most rhythms of the human free-run cycles 25,62 .
With regard to the intrinsic period of Per1 (−/−) and Per2 (−/−) cells, a detailed predictive modelling study 63 showed that Per1 (−/−) knockout cells have a longer period whereas Per2 (−/−) knockout cells have a shortened period, which was compatible with the majority of our findings, including our protein stability results. However, a number of studies have reported diverse results 12,64-66 , which could be due to the fact that bioluminescence experiment results are difficult to interpret, and are substantially dependent on long culture conditions, reporter differences, and period calculation methods. The results from organ culture might also reflect the complicated aftereffects 67,68 and the period modification apparent following intercellular signal transduction in heterogeneous cells 69 , which could be greater in 3D organ culture than in 2D cultured cells. Complicated aftereffects and the interaction of heterogeneous cells might also cause tissue-specific differences 64,66 . Thus, organ culture might not accurately reflect the period length of the intracellular molecular machinery.
Although a former study demonstrated that Per2 (−/−) cultured cells are arrhythmic 12 , we found that Per2 (−/−) cells had a shorter period similar to Per1::Luc-rescued ES cells [Figs 6Cb and 7A Luc (no coding)]. However, the oscillation of the Per2 (−/−) cells was weak and unstable, and we could only detect the oscillation in cell culture under optimal conditions, which was consistent with the prior results. The former study 12 also showed that Per1 (−/−) Per2::Luc cultured cells are arrhythmic, which could indicate that the period length of Per1 (−/−) cells was too long to detect periodicity, although we have to be cautious considering that the luciferase fusion appears to diminish the function of Per2 to some extent (Fig. 4). Nonetheless, our data and the results of former studies indicate that Per1 (−/−) cells have a longer intrinsic period and Per2 (−/−) cells have a shorter period, although both are unstable in the absence of intercellular synchronization.
Under constant dark conditions, Per1 or Per2 knockout mice had a free-running period of approximately 24 h, but the circadian period was dramatically different under the LL condition, in that Per1 (−/−) mice displayed a long period, whereas Per2 (−/−) mice exhibited a short period 22 (Fig. 1). Hence, we confirmed the prior results, although the results were slightly different, most likely due to the construct difference between the Brd and the ldc mice.
Previous studies have likewise shown that the ratio of the phase advance portion to the phase delay portion of the phase response curve (PRC) accurately predicts the lengthening of the activity rhythm period in LL 26 in Per1 (−/−) and Per2 (−/−) mice. However, the molecular mechanisms involved have not yet been elucidated. In our studies, we examined Per1 (+/−) mice and Per2 (+/−) mice and found that the ratio of the Per1:Per2 copy number was important to the period length in the LL condition. A possible explanation is that the light-dependent induction of Per proteins enlarged the difference in the accumulation rate between Per1 and Per2 proteins 17,70 .
Another possible hypothesis is the occurrence of intercellular uncoupling in LL. Many studies involving clock gene mutant mice have shown that although there are some exceptions, the period length in animals is closer to 24 hours than the period length observed at the cell culture or organ level 12,30,49,71,72 , most likely due to the synchronization mechanism of coupling. As previously discussed, we believe that Per1 (−/−) cells have a longer intrinsic period and Per2 (−/−) cells have a shorter period; however, the period length in animals could be close to 24 hours due to SCN coupling in the DD condition. Further, conditions of constant light might induce the uncoupling of SCN neurons, allowing the endogenous cellular period length to surface 18,19 . Finally, this uncoupling hypothesis does not necessarily exclude the phase response curve hypothesis, but these might be two aspects of the same phenomenon.
In this study, we have shown that the Per1/Per2 ratio is important for period length, but we have not assessed the effect of total Per protein level. Previous studies have suggested that both total Per protein level and Per1/Per2 ratio are important in endogenous period determination 33,35,71 . Our hypothesis regarding the determination of endogenous period length is shown in Fig. 7D. A previous immunohistochemical analysis revealed that Per1 (−/−) mice have lower Per2 protein levels than WT mice, and Per2 (−/−) mice have lower Per1 protein levels in the SCN than WT mice, which might be the result of a mechanism that balances the ratio of Per1:Per2 13 . Future studies involving western blotting of the SCN could lead to a more refined conclusion; however, at least 10 animals of each genotype 73 would be necessary for each SCN western blotting assay, and additional animals would be required for the clock proteins. Utilizing western blotting to examine Per1 and Per2 expression in Per1-and Per2-rescued ES cells, we have shown that both ES cell lines lacked native Per2 but expressed similar levels of native Per1, that Per1::Luc was only expressed in the Per1-rescued ES cells, and that Per2::Luc was only expressed in the Per2-rescued ES cells. However, we could not determine the ratio of Per1 and Per2 because the Per1 and Per2 antibodies are different, and the transfer efficiency of the native protein and the luciferase-fusion protein from the acrylamide gel to the membrane varied due to a 60 kD difference in the molecular weights of the proteins. One might assume that measuring the total amount of the native (e.g. Per1) and the luciferase-fusion protein (e.g. Per1::Luc) is possible using the standard purified form of each protein. However, in the current study, we had to determine the absolute concentration of each standard protein using Coomassie Brilliant Blue (CBB) stain. Because each protein stain has a preference for specific amino acids (e.g. basic amino acids in the case of CBB), the native and luciferase-fusion proteins were not comparable 74 . Thus, it appears impossible to compare the ratio of Per1 and Per2 by western blotting using a mixture of the native protein (e.g. Per1) and the luciferase-fusion protein (e.g. Per1::Luc). Future studies involving mass spectrometry and the use of common peptides from the native and luciferase-fusion proteins as standards could enable the measurement of the Per1:Per2 ratio in these ES cells 75 .
Half-life analysis showed that Per1 has a paradoxically longer half-life than Per2. This difference in half-life may have important consequences for the mechanism(s) underlying the association of Per1 expression with a short period and of Per2 with a long period, which is independent of FASPS period shortening. Our hypothesis is shown in Supplemental Figure S9B. Degradation of Period proteins is thought to occur at the fully phosphorylated state. In the case of the FASPS mutant, these proteins are thought to quickly become fully phosphorylated 76,77 and overall half-lives would become shorter [77][78][79] . Because Per1 and Per2 have similar phosphorylation sites, including the FASPS site, we think the difference would come, not from the rate of serial phosphorylation, but from the rate of protein degradation itself. In the case of Per1, degradation is slower and accumulation is quicker; then, early negative feedback occurs, leading to shorter circadian period length. In the case of Per2, degradation is faster and it accumulates for a longer time. This hypothesis is consistent with previous simulation analyses 80,81 . Another theoretical study of the negative autoregulation of circadian gene expression also showed that the period increases with an increased degradation rate when degradation is described by the Michaelis-Menten function 82 . Thus, an enzyme sequestration mechanism might be important for aligning the Per1 and Per2 cycling rates 16 . The results of a detailed predictive modelling study of the Per1 and Per2 proteins were likewise consistent with our findings and our model ( Fig. 7C and Supplemental Figure S9B) 63 . This detailed predictive modelling study showed that Per1 (−/−) knockout cells have a longer period and Per2 (−/−) knockout cells have a shortened period. In addition, this model indicated that Per2 is degraded more quickly than Per1. Moreover, the peak phase of the Per1 protein was earlier than the Per2 peak phase, which is consistent with the notion that Per1 accumulates more rapidly, as indicated by our results. However, these models represent only one possible explanation of our results; thus, future studies that focus on the mechanisms underlying the differences between Per1 and Per2 are required.
In this study, we used clock protein-luciferase fusion proteins, which are widely used and reflect endogenous degradation 14,83 . Moreover, the behaviour and function of these fusion proteins are generally consistent with endogenous proteins 84 . Although we assumed that Per2 and Per2::Luc would have slightly different functions, we believed the comparison between Per1::Luc and Per2::Luc would be valid. Because the C-terminal end is longer in Per1 than Per2 17 , the possibility exists that the differences in the half-lives of Per1 and Per2 could simply be due to different effects of the luciferase on the stability of the Per1 and Per2 proteins. However, this possibility is not likely because a prior study ( Fig. S5B; Isojima et al. 14 ) showed that Luc::Per1 is more stable than Luc::Per2 in HEK 293 cells. Interestingly, the differences in the half-lives were apparent when the CK1ε vector was cotransfected. Therefore, CK1ε might play a role in the difference in the half-lives of Per1 and Per2.
Two non-covalent (weak) bonds existed between Per proteins and the peroxidase used for western blotting due to the use of primary and secondary antibodies. In contrast, only covalent (strong) bonds existed between the Per proteins and luciferase in the fusion protein assay. In addition, western blots involve lysed and dead cells, whereas living cells are continuously used in luminescence assays. Thus, we felt that the fusion protein assay was the more direct and powerful approach for assessing protein concentration.
In conclusion, we have shown that short period-associated Per1 and long period-associated Per2 proteins cooperatively confine circadian period to "circa" 24 h, which is rigid and relatively inflexible.

Materials and Methods
Extended details of the materials and methods are described in the Supplemental Methods, including the recombinant plasmid production, the animals and the behavioural analysis, the LED-based lighting system, genotyping, the ES cells and cell culture conditions, methods for gene targeting and colony picking, the PCR screening, the Arm PCR, the quantitative PCR for confirmation of copy number, the ES cell differentiation system used to detect the precise circadian period length, the measurement of Per1 and Per2 half-life, western blotting, and other statistical analyses. Below is an abbreviated description of the major experimental procedures.

Recombinant Plasmid Production.
With the Per2 promoter, we refer to the distal (3518 bps) promoter as the Per2 long promoter (P(Per2L)). Luc(c) refers to the luciferase gene inserted into the PI-Psp1 site and positioned to fuse with the coding region for the C-terminal end of the gene of interest.
The animal behaviour analyses were performed using a behavioural analysis rack (Nihon-Ika) as previously described 87 . These racks are a special order product based on Clean Rack (Nihon-Ika, CR-1600S) and are made specifically for exposing mice to light-dark conditions.
The periodicity shown in Fig. 2 is defined as the mean amplitude (Q[p]) minus the level of significance at the determined period length within ± 1 h of the circadian period length, determined using the chi-square periodogram. We calculated the periodicity for weeks 3 and 4 after initiation of constant light conditions. LED-based lighting system. An LED-based lighting system containing 12 lights was developed. This system uses the proportionate relationship between light strength and electric current. Linear lighting power (256 levels) was produced using a combination of eight resistance units. In this system, 12 mice can be exposed to any pattern of light intensity, with 256 levels at 1-min resolution to 12 mice, e.g., 6 mice exposed to two patterns each. The lighting program was used with the following formula: I = 128 + [0.5 + A sin2π(x min /(T h *60))], where I represents light intensity level (integer from 0-255); A represents amplitude of light intensity level (we used 127); T h represents period of environmental light cycles (we performed the experiment using periods of 22-27 h, in increments of 1 h, (but not in that order) for 2 weeks each); and x min represents the number of minutes after the start of the experiment. For the chi-square periodogram, more than 10 days are desired to avoid short-term random variations 88 . However, the transient or aftereffects were quite large in the first week because we could not connect the phase of each environmental cycle in these experiments. Hence, we performed both chi-square periodograms for a duration of 2 weeks and one with a final week for each environmental period.
Light intensity levels of 0-255 on the floor of the rack just below the LED were monitored using a CL-200A Chroma Meter (Konica Minolta) and changed almost linearly. Resistance of the main unit can be increased to 10× and 100× , i.e., 1/10 and 1/100 of electric current and lighting strength, respectively. So as not to make mice sense conditions of constant light 27 , we chose 256 levels from approximately 0.01 to 5.4 lux.
Gene targeting and colony picking. On day 0, Per2 (−/−) ES cells (5 × 10 5 ) were plated in 2.0 mL ES medium 2i(+ )LIF(+ ) on 35-mm culture dishes (Falcon) that had been coated with 0.2% gelatine. Five hours after plating, cells were transfected with 1 μ g targeting vector, 2 μ g pCAGGS-ROSA-TALEN-N153C63-R, and 2 μ g pCAGGS-ROSA-TALEN-N153C63-L using Xfect Stem mESC reagent (Clontech) according to the manufacturer's protocol with the modifications described in the Supplemental Methods. On day 3, cells were harvested and seeded at 1 × 10 6 on 0.2% gelatine-coated 60-mm dishes. Selection with 1.2 μ g/mL puromycin (Sigma) was carried out for 24 h on days 4 and 6. ES clones were picked on or after day 8 as described in the Supplemental Methods. Cells were plated in ES medium 2i(+ )LIF(+ ) on 0.2% gelatine-coated 24-well plates (Techno Plastic Products). Approximately one third of the cells were lysed and used in PCR screening. PCR Screening. Pellets of picked ES cell colonies were treated with proteinase K (Roche). After centrifugation, supernatant was used in PCR to amplify the 3′ arm of the targeted allele (4.0 kb). Primer sequences and PCR conditions are described in the Supplemental Methods.
Arm PCR. The integrity of the genome of targeted ES cells was confirmed by Arm PCR instead of southern blotting. To confirm homologous recombination of the targeting vector to the correct region of the genome, three PCRs were carried out: target 5′ (9.0 kb), WT 5′ (8.5 kb), and WT 3′ (4.5 kb). Primer sequences and PCR conditions are described in the Supplemental Methods.
Quantitative PCR for copy number confirmation. Copy number of the inserted cassette and random integration were confirmed by quantitative PCR. The puromycin resistance gene was quantified and normalized to the level of TATA box-binding protein (TBP). The primer sequences and PCR conditions are described in the Scientific RepoRts | 6:32769 | DOI: 10.1038/srep32769 Supplemental Methods. The absolute levels of the PCR products were quantified using a standard curve. We analysed at least two lines of targeted clones that had only a single cassette inserted in the Rosa26 locus. ES cell differentiation system to detect precise circadian period length. Cells were cultured from day 0 to day 8 in differentiation medium: Dulbecco's Modified Eagle Medium (DMEM, high glucose, pyruvate, Gibco) containing 20% FBS, 0.1 mM MEM Non-Essential Amino Acids (Gibco), 100 U/mL penicillin and 100 μ g/mL streptomycin (Gibco), 2 mM L-glutamine (Gibco), 100 μ M β -mercaptoethanol (β -ME), and 1 μ M RA (Sigma-Aldrich). On day 0, 3-9 × 10 5 ES cells were plated in 10 mL differentiation medium on 0.2% gelatine-coated 100-mm dishes and cultured at 37 °C in a humidified atmosphere of 5% CO 2 . On day 5, cells were washed with DPBS without calcium and magnesium, incubated with 0.05% trypsin/0.48 mM EDTA (Gibco), and pipetted up and down in FBS. Cells were then sequentially applied to a 100-μ m Cell Strainer (BD Falcon) and 35-μ m Cell Strainer (BD Falcon). DMEM containing 10% FBS and 1× penicillin/streptomycin (Gibco) was added, followed by centrifugation. Supernatant was removed and cells were resuspended. 3-10 × 10 5 cells were plated in 2 mL differentiation medium on 0.2% gelatine-coated 35-mm dishes (Falcon). On day 8, medium was changed to detection medium (DMEM without phenol red, without pyruvate, with 25 mM HEPES; Gibco) supplemented with 10% FBS, 1× penicillin/streptomycin (Gibco), and 1 μ M RA. The medium was changed every other day. On day 20, the medium was changed to detection medium containing 1 μ M RA, 10 μ M forskolin, and 100 μ M luciferin. Plates were sealed with silicone grease (Toray), and circadian oscillation was measured in a low-level light-detection unit (Hamamatsu photonics) at 30 °C in air.
The autocorrelation analysis of the circadian period was carried out using Mathematica 9.0 (Wolfram) as previously described 89 , with slight modifications as described in the Supplemental Methods.
The primary antibodies used in this study included anti-Mouse PER2 (Rabbit; PER21-A, Alpha Diagnostic International), anti-Per1 (Mouse), pAb (Guinea pig, PM091, MBL), monoclonal ANTI-FLAG M2 antibody produced in mice (Sigma F1804-50UG)), monoclonal anti-β -actin antibody produced in the mouse clone AC-15, ascites fluid (Sigma A5441). All of the antibodies were diluted in Tris-buffered saline solution/0.1%Tween (TBST) containing 5% skim milk at 4 °C. Each primary antibody was used at a 1000× dilution except for β -actin, which was used at a 5000× dilution. The secondary antibodies used in this study included rabbit anti-guinea pig IgG (H+ L) secondary antibody, HRP-conjugate (Invitrogen 61-4620), ECL ™ anti-mouse IgG, HRP-linked species-specific whole antibody from sheep (GE, NA931), and anti-rabbit IgG, HRP-linked whole antibody from donkey (GE, NA934V). All secondary antibodies were used at a 2000× dilution in 5% skim milk except for anti-mouse HRP antibody, which was used at a 5000× dilution with the anti β -actin primary antibody. Detailed western blotting conditions are described in the Supplemental Methods.
Other statistical analysis. Comparisons of the mean circadian period, periodicity, and half-life of two groups of samples were carried out using Student's t-test (bilateral, unequal variances). Error bars represent SD. Analysis of variance (ANOVA) and Tukey's post hoc tests was used for the comparison of three or more groups using SPSS 26 (IBM).