letters

Melanopsin-dependent photo-perturbation reveals
desynchronization underlying the singularity of
mammalian circadian clocks
Hideki Ukai1,10, Tetsuya J. Kobayashi1,4,10, Mamoru Nagano5, Koh-hei Masumoto1,, Mitsugu Sujino5,
Takao Kondo6, Kazuhiro Yagita7,8, Yasufumi Shigeyoshi5 and Hiroki R. Ueda1,2,3,9Singularity behaviour in circadian clocks1,2 — the loss of robust
circadian rhythms following exposure to a stimulus such as apulse of bright light — is one of the fundamental but mysterious
properties of clocks. To quantitatively perturb and accurately
measure the dynamics of cellular clocks3,4, we synthetically
produced photo-responsiveness within mammalian cells byexogenously introducing the photoreceptor melanopsin5­–8 andcontinuously monitoring the effect of photo-perturbation on
the state of cellular clocks. Here we report that a critical lightpulse drives cellular clocks into singularity behaviour. Our
theoretical analysis consistently predicts and subsequent singlecell level observation directly proves that desynchronization ofindividual cellular clocks underlies singularity behaviour. Our
theoretical framework also explains why singularity behaviours
have been experimentally observed in various organisms, and it
suggests that desynchronization is a plausible mechanism forthe observable singularity of circadian clocks. Importantly, thesein vitro and in silico findings are further supported by in vivo
observations that desynchronization underlies the multicell-level
amplitude decrease in the rat suprachiasmatic nucleus induced
by critical light pulses.
To synthetically produce photo-responsiveness, we transiently transfected mouse melanopsin complementary DNA5–8­ into NIH3T3 mouse
fibroblast cells (ref. 4; Fig. 1a). To evaluate the effect of photo-perturbation on the state of circadian clocks, the cells were also transfectedwith a plasmid containing luciferase driven by the promoter of the PER2
clock gene (PER2-luciferase reporter) and stimulated with forskolin tosynchronize circadian rhythmicity. We then monitored multicell-level

PER2-luciferase reporter activity in real time9,10. About two days after
forskolin stimulation, cells with or without melanopsin were exposed
to a 6-h light pulse, and then evaluated for the effect on multicell-level
PER2-luciferase reporter activity about one day after the light pulse(see Fig. 1b, in which the bioluminescence data were detrended bysubtracting their baseline tendency (see Supplementary Information
for the details)). Melanopsin-positive cells exhibited a 1.8-h phaseadvance and a 2.5-fold amplitude change in PER2-luciferase reporter
activity induced by the light pulse compared with that of cells that had
not been exposed (Fig. 1b, upper panel; Fig. 1c, red bars). By contrast,
melanopsin-negative cells exhibited little phase shift or fold change in
amplitude induced by the light pulse (Fig. 1b, lower panel; Fig. 1c, bluebars). These results clearly indicate that the light pulse can perturb thestate of mammalian circadian clocks in a melanopsin-dependent manner. In addition, the administration of the intracellular calcium chelator
BAPTA-AM (1–10 μM) or PLC (phospholipase C) inhibitor U73122(0.1–3 μM) into medium 1 h before light-pulse exposure inhibited thephase advance induced by the light pulse in a dose-dependent manner(see Supplementary Information, Fig. S1), indicating that PLC-mediatedintracellular Ca2+ release is crucial for melanopsin-dependent photoperturbation of mammalian clock cells.
To systematically quantify the phase shifts induced by light pulses ofvarious timings and durations, high-throughput continuous monitoring of
PER2-luciferase reporter activity was employed9–11. Twelve sets of melanopsin-positive and -negative cells were prepared and stimulated with forskolin every 2 h over a 24-h period. About 3 days after the first forskolin
stimulation, melanopsin-positive and -negative cells were exposed to alight pulse and then evaluated for its effect on multicell-level PER2-luciferase reporter activity. These experiments were repeated using light pulses

Laboratory for Systems Biology and 2Functional Genomics Unit, Center for Developmental Biology, RIKEN, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo
650-0047, Japan. 3Department of Bioscience, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan. 4Research Fellow of Japan Society
for the Promotion of Science. 5Department of Anatomy and Neurobiology, Kinki University School of Medicine, 377-2 Ohno-Hagashi, Osaka-Sayama, Osaka 589-8511,
Japan. 6Division of Biological Science, Graduate School of Science, Nagoya University and CREST & SORST, Japan Science and Technology Corporation, Furo-cho 1,
Chikusa, Nagoya 464-8602, Japan. 7COE Unit of Circadian Systems, Division of Molecular Genetics, Department of Biological Sciences, Nagoya University Graduate
School of Science, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan. 8Department of Cell Biology and Neuroscience, Osaka University Graduate School of Medicine,
2-2 Yamadaoka, Suita, Osaka, 565-0871, Japan.
9
Correspondence should be addressed to H.R.U. (uedah-tky@umin.ac.jp)
10
These authors contributed equally to this work.
1

Received 23 July 2007; 27 September 2007; published online 21 October 2007; DOI: 10.1038/ncb1653

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Figure 1 Synthetic implementation of photo-responsiveness within
mammalian clock cells. (a) A diagram showing melanopsin-dependent
photo-responsive NIH3T3 cells, and the known Gq signalling pathway8.
Melanopsin-coupled Gq proteins stimulate phospholipase C (PLC). Active
PLC hydrolyses phosphatidylinositol 4,5-bisphosphate (PIP2) to produce
inositol triphosphate (InsP3) and diacylglycerol (DAG). These secondary
messengers then activate protein kinase C (PKC), either directly (DAG) or
indirectly through the release of internally stored calcium (InsP3).
(b) Photo-responsiveness of multicell-level PER2-luciferase reporter

activities of melanopsin-positive and -negative cells. The multicell-levelbioluminescence data from the cells with (red) and without (blue) light-pulse
exposure has been detrended (the baseline tendency has been removed) andthen normalized by the level of the last peak before the light pulse (yellow) forcomparison (see Supplementary Information for details of data processing).
The phase shift (advance) and amplitude change (increase) of melanopsinpositive cells induced by the light pulse are indicated in the upper panel.
(c) Quantification of the phase shifts and the fold changes in amplitude of themelanopsin-positive (red) and -negative (blue) cells induced by light pulse.

of different durations including 0.5, 1, 3, 6 and 12 h. To quantify the phaseshift, we extracted the oscillatory components of detrended bioluminescence data (see Supplementary Information for the details). As shown in
Fig. 2a and b, phase shifts induced by light pulses depended on the timingof light pulse. We then calculated multicell-level phase response curves(PRCs), where phase shifts are plotted against the timing of light pulses(Fig. 2c). The calculated PRCs for all tested durations show that the transition from phase advance to phase delay is around circadian time (CT)~6(subjective noon), whereas the reverse transition is around CT~17 (nearsubjective midnight). Similar phase shifts were observed in BMAL1-luciferase reporter activity (see Supplementary Information, Fig. S2), suggesting that melanopsin-dependent photo-perturbation can control the corecomponents of mammalian circadian clocks10. Notably, these multicelllevel PRCs resemble light-type PRCs observed in mammals at the organism level12,13 (see Supplementary Information for details).
In addition to inducing phase shifts, light pulses can also increase or
decrease the amplitude of PER2-luciferase reporter activity (Fig. 3a, b)(see Supplementary Information for the details). We averaged the amplitude change during the two days after the light pulse to quantify themulticell-level amplitude response curves (ARCs), where multicell-level
amplitude changes are plotted against the timing of light pulses (Fig. 3c).

All ARCs are continuous, and the maxima and minima of ARCs arelocated around CT~6 (subjective noon) and CT~17 (near subjective
midnight), respectively. Moreover, the maximum and minimum valuesof the ARCs depend on the light duration. On the basis of these results,
we conclude that the phase and amplitude of mammalian cellular clocks
can be adjustably and quantitatively controlled by melanopsin-dependent photo-perturbation.
From the ARCs, we found that a 3-h light pulse applied at CT~17
significantly decreased the amplitude of PER2–luciferase reporter activity at the multicell level. By conducting photo-perturbation of cellular
clocks with 3‑h light pulses delivered at around CT~17 at high temporal
resolution (see Supplementary Information, Fig. S3), we found a criticallight pulse capable of driving cellular clocks into singularity behaviour where robust multicell-level PER2-luciferase reporter activity wasabolished (Fig. 4a). Because the circadian oscillation is recovered by asecond light pulse applied about 3 days after the first one (Fig. 4a), we
confirmed that the clocks or cells themselves are not impaired permanently, but only stopped transiently by the critical light pulse, suggestingthat this multicell-level singularity behaviour holds the same properties
as those already observed at the multicell level in populations of unicellular organisms or multicellular organisms14.

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Figure 2 Phase shift of mammalian clocks induced by photo-perturbation.
(a) Phase advance (upper panels) and delay (lower panels) induced by lightpulses of different durations. The oscillatory components of PER2-luciferase
reporter activities of melanopsin-positive (red) and -negative (blue) cells(see Supplementary Information for details of data processing) are shownwith light pulses (yellow). The timing and duration of light pulses are as
designated in each panel. (b) High-throughput analysis of phase shifts
induced by light pulses (yellow) of various timings and durations. Magenta

and green denote high and low oscillatory components of PER2-luciferase
reporter activities. (c) Phase-response curves (PRCs) of the PER2-luciferase
reporter activities of melanopsin-positive cells against the timings of lightpulses in circadian time (CT). Simulated PRCs by using the multiple cellular
clock model are shown in red curves. Bioluminescence data of the negative
control experiment using melanopsin (-) cells as well as the superimpositionof five PRCs induced by different durations of light pulses are shown in the
Supplementary Fig. S9.

Two alternative single-cell-level mechanisms have been proposed
for this multicell-level singularity behaviour. The first is arrhythmicity or suppression of amplitude of individual clocks (Fig. 4b,
upper panel) and the second is desynchronization of individual
rhythmically oscillating clocks (Fig. 4b, lower panel)1,2. Althoughboth mechanisms are based on the limit-cycle model for circadianclocks1,2, where circadian oscillation is represented as an attractive
closed orbirt, there is a fundamental difference between the dynamic
scenarios of these mechanisms (see Supplementary Information forthe details). The former mechanism relies on a simple limit-cycle
model in which an unstable fixed point, called the ‘singularity point’,
exists within the single limit-cycle orbit. Limit-cycle oscillation will
be stopped once it is brought to this point by an external perturbation at the appropriate timing and strength. In this dynamic scenario,
singularity behaviour observed at the multicell level is predicted tobe caused by arrhythmicity of all individual cellular clocks1,2. With
the increasing number of reports on singularity behaviours in various organisms, this hypothesis has come to predominate to the pointthat the observed behaviour is named after the singularity point of
the limit cycle.

By contrast, the second mechanism predicts that the singularity behaviour observed at the multicell level is due to the desynchronization ofindividual cellular clocks induced by critical perturbation1,2. This scenario
can also be explained by a limit-cycle model, especially in the presence of
substantial fluctuations among individual cellular clocks. If such fluctuations exist, most of the circadian oscillators brought to the unstable fixed
point cannot stay at this point for a long time, and therefore quickly returnto the original orbit. The phases of the oscillators after recovery can vary
greatly because small differences in the phases will be amplified by passing near the unstable fixed point, where all possible phases are defined
theoretically. Thus, when stimuli are applied to a set of cellular circadianclocks at the appropriate timing and strength, the clocks can become
desynchronized as the result of amplification of internal fluctuations inthe state of cells or external fluctuations in the applied stimulus, leading toapparent arrhythmicity or suppression of amplitude in the averaged behaviour of the clocks at the multicell level. Arthur T. Winfree supported thesecond mechanism (desynchronization) on the basis of his experimental
data1, whereas the first scenario has gained wide acceptance as the main
explanation for observed singularity behaviours although the underlying
mechanism has not been directly verified at the single-cell level.

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Figure 3 Amplitude changes of mammalian clocks induced by photoperturbation. (a) Amplitude increase (upper panels) and decrease (lower
panels) of PER2-luciferase reporter activities induced by light pulses (yellow)
of different durations. The bioluminescence data from melanopsin-positive(red) and -negative (blue) cells were detrended (the baseline tendency has
been removed) and normalized as in Fig. 1b. (b) High-throughput analysis
of fold changes in amplitude induced by light pulses (yellow) of various

timings and durations. Magenta and green denote high and low normalized
amplitudes of PER2-luciferase reporter activities. The fold-change in
amplitude is obtained by data processing of the original bioluminescencedata (see Supplementary Information for details of data processing).
(c) Amplitude response curves (ARCs) of the PER2-luciferase reporter
activities of melanopsin-positive cells against the timings of light pulses in CT.
Simulated PRCs by the multiple cellular clock model are shown in red curves.

To directly verify these predictions at a single-cell level, we measured
PER2-luciferase reporter activity in individual cells11,15. As reported previously15,16 and also shown in Fig. 4c, d, left panels, the phases of melanopsin-negative cells gradually diverge over time independently of thestimulus (Fig. 4c, d, left panels and see Supplementary Information,
Movie 1), which is consistent with a multicell-level decrease in amplitude.
By contrast, when melanopsin-positive cells are exposed to a critical lightpulse capable of inducing the singularity behaviour, the phases of cells areabruptly diversified by the pulse (Fig. 4c, d right panels, Supplementary
Information, Fig. S5, and Supplementary Information, Movie 2), suggesting that desynchronization was induced by the light pulse. To exclude
the possibility that this diversification of phase might be due to arrhythmic behaviour of individual cells, we tried to verify that the oscillation isregularly sustained after the light pulse by rearranging the order of cells
in Fig. 4d according to the timing of the third peaks of individual cells(Fig. 4e). We observed that the single-cell-level oscillations of melanopsin-positive cells were sustained after the light pulse, and that the onsetof those single-cell-level oscillations was within one day of the light pulse

for most of the individual cells, indicating that the observed singularity
behaviour cannot be attributed to the arrhythmicity of individual cells.
In addition, we verified that the critical light pulse induced no significant
changes in single-cell-level amplitude (see Supplementary Information,
Figs S4, S5), which excludes the possibility that the multicell-level amplitude decrease could be simply attributed to the single-cell-level amplitudedecrease. Given these findings, we conclude that desynchronization ofcellular clocks underlies the multicell-level singularity behaviour.
Although we have experimentally verified desynchronization ofcells near the phase divergence (CT~17) points of the PRC, it remained
unknown whether this single-cell-level mechanism can consistently
explain the multicell-level phase shifts and amplitude changes observed
for light pulses of various timing and duration. To address this question, we firstly verified that synchronization of cells can be induced by alight pulse near the convergence point of the PRC (CT~6), demonstrating that a multicell-level amplitude increase can be caused by synchronization of cell phases (see Supplementary Information, Fig. S5b, c).
In addition, we constructed a mathematical model for multiple

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Time (h)Figure 4 Desynchronization underlying the singularity behaviourof mammalian clocks. (a) Singularity behaviour of mammalian
circadian clocks. Robust circadian rhythmicity of mammalian clocks
is abolished after the first light pulse, and recovered by the second
light pulse. The detrended (the baseline tendency has been removed)
and normalized PER2-luciferase reporter activities of melanopsinpositive (red) and -negative (blue) cells are displayed with light pulses(yellow). (b) Schematic diagrams of two alternative single-cell-levelmechanisms for the multicell-level singularity behaviour; arrhythmicity(upper panel) and desynchronization (lower panel) of individual

cellular clocks. (c) The normalized PER2-luciferase reporter activities
from individual cells with their averages (black thick lines) (seeSupplementary Information for details of data processing). The timingof the light pulse (yellow) is designated in each panel. PER2-luciferase
reporter activities from randomly selected representative cells wereshown in Supplementary Fig. S4. (d, e) The detrended and normalized
PER2-luciferase reporter activities from individual cells (seeSupplementary Information for details of data processing). Magenta
and green denote high and low bioluminescence. The data are sortedby the timing of the second peaks (d) and that of the third peaks (e).

cellular clocks (see Supplementary Information for details) to evaluate multicell-level PRCs and ARCs on the basis of single-cell level
dynamics. As shown in Figs 2c and 3c, the model qualitatively reproduced the topology of PRCs and the maximum and minimum values of the ARCs as well as their detailed shapes observed in theexperimental data. Moreover, the identified parameter value of phasevariation (σ=0.24) was consistent with the values of phase variation(σ=0.22~0.26) estimated from the single-cell-level measurement.
Given these findings, we concluded that the proposed single-celllevel mechanism of the singularity behaviour is capable of consistently explaining the multicell-level light response of mammalian
circadian clocks.

To further extend our in vitro and in silico findings, we next investigated their in vivo relevance to examine whether desynchronization
underlies the multicell-level amplitude decrease in mammalian central
clocks (suprachiasmatic nucleus; SCN) induced by critical light pulses.
To quantify expression of clock genes in the rat SCN after the critical light pulses, rats were entrained under light–dark conditions (LD)for 2 weeks followed by 1 day in constant darkness (DD), exposed tothe critical light pulses (two sequential 12-h light pulses started from
CT16) and then kept in the DD condition. Rats were exposed to multiple
light pulses, on the basis that a similar experiment produced singularity behaviours in humans17, where multiple sequential light pulses wereapplied to induce strong (type 0) phase shifts and, hence, singularity

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(a) Spatio-temporal expression of Per1 and Per2 genes in the rat SCN
examined by in situ hybridization using a digoxigenin-labelled Per1 and Per2cRNA probes. Upper and lower panels indicate the expression of Per1 (upper)
and Per2 (lower) genes in the SCN with (light) or without (control) the criticallight pulses. The left side of each figure is the medial side of the SCN. Dashedlines indicate the SCN boundaries. The bar indicates 100 µm. (b) Numberof positive cells in the entire SCN (red), dorsomedial (DM) region (green)and ventrolateral (VL) region (blue). Each point corresponds to data from one
SCN sample, and the curves are the linear interpolations of the averages of
two independent samples. (c) Time series of the locomotor activities of two
independent rats who showed substantial decrease in amplitude of locomotor
activity one day after the critical light pulses. To extract long-term trend of
locomotor activity, we applied moving average with 4-h window size threetimes to the original locomotor activity data collected every 5 min.

behaviours. In humans17 and rats (this study), a single light pulse could
induce only weak (type 1) phase shifts. Expression of Per1 and Per2 genes
in the SCN in rats detected by in situ hybridization exhibit a remarkablemulticell-level amplitude decrease after the critical light pulses (Fig. 5a,b, red lines). Importantly, this multicell-level amplitude decrease in the
SCN is correlated with the spatially desynchronized expression pattern of Per1 and Per2 within the SCN observed between dorsomedial(DM) and ventrolateral (VL) regions (Fig. 5b, green and blue lines). The
observed spatial desynchronization was also verified more locally byusing a computer program that can automatically analyse the intensities of sequential SCN slice images at the pixel level (see Supplementary
Information, Fig. S6 and Supplementary Information for details).
Under the same experimental condition, we also confirmed thatthe critical light pulses can induce the temporal amplitude decreaseof locomotor activity in a substantial portion of rats (30%) about

1 day after the second light pulse (Fig. 5c). This percentage of observed
temporal amplitude decrease is comparable to, or even higher than,the previous observations in other mammalian organisms (~20% bothin chipmunk18 and human17). As in the case of other organisms, thetemporal amplitude decrease of locomotor activity is strongly dependent on the timing of light pulses, because the reductions in amplitude
were induced only by light pulses applied near CT16 (data not shown).
These results suggest that the critical light pulse used in this experimentcan also predispose an organism to the temporal amplitude decrease of
locomotor activity in vivo.
There are differences between our in vitro system and in vivo organisms. First, our melanopsin-positive NIH3T3 cells seem to lack cell–cell
coupling, whereas the SCN has cell­–cell communication. Second, light
directly hastens desynchrony in our in vitro system, whereas it is presumed to initiate transient desynchrony in vivo indirectly through retinal

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projections to the in vivo SCN. Thus, the interpretation that desynchronization seen in our in vitro system is relevant to that of the in vivo SCN
depends on the assumptions that (1) substantial fluctuations exist in thestates of SCN clock cells19,20, and that (2) the phase shifts in our in vitro
system induced directly by light is basically the same as those in SCN
evoked indirectly by light (Fig. 2), those of which seem valid at least in
mammals (see Supplementary Information for details).
In other organisms, we expect that the desynchronization of individual circadian oscillators will underlie the singularity behaviour. The
simple limit-cycle model predicts that the singularity behaviour can be
induced merely by the infinitesimal range of perturbation strength andtiming, which stands in sharp contrast to the reproducible observationsof singularity behaviours in various organisms. By contrast, our multiple
cellular clock model predicts that the multicell-level singularity behaviour will be robustly induced by the experimentally achievable rangeof perturbation strength and timing (green regions in Supplementary
Information, Fig. S7) if there are substantial fluctuations in the state ofindividual cellular clocks. Because recent single-cell level measurementof individual cellular clocks in the SCN revealed substantial fluctuationsin the states of central clocks19,20, our model predicts that desynchronization of cellular clocks in the SCN can be stably induced by the criticallight pulses, which is quite consistent with our robust observations thatthe desynchronization actually underlies the multicell-level amplitudedecrease in the SCN after the critical light pulses that can also probabilistically induce temporal amplitude decrease of locomotor activity.
Although we suggest desynchronization as a plausible and generalmechanism for singularity behaviours not only in mammalian and otherorganisms, we cannot completely exclude the possibility that arrhythmicity of individual clocks might underlie singularity behaviours in otherorganisms because various extended models of singularity behaviour
have been proposed21–23. In the investigation of singularity behaviours
in such systems, the direct verification by single-cell level measurement
and quantitative perturbation will play a crucial part in determining theunderlying mechanism as demonstrated in this report.
Methods

Plasmid construction. Plasmid construction protocols are provided in the
Supplementary Information.
Cloning of full-length mouse melanopsin (Opn4) cDNA. We prepared total
RNA from C57BL/6 mouse eyes using TRIzol reagent (Invitrogen, Carslbad, CA).
A cDNA library was synthesized from total RNA using pd(T)12-18 (GE Healthcare,
Chalfont, UK) and SuperScriptII Reverse Transcriptase (Invitrogen) according
to the standard protocol. The full-length coding sequence of melanopsin was
amplified from the cDNA library by polymerase chain reaction with a forward
primer containing the I-SceI recognition sequence and a reverse primer containing the PI-PspI recognition sequence. PCR product was digested with I-SceI and
PI-PspI, cloned into the pMU2-P(GAPDH)-control vector, and termed pMU2P(GAPDH)-melanopsin. melanopsin-forward:5ʹ-ATTACCCTGTTATCCCTAATGACTCTCCTTCAGGACCAAG-3ʹ. melanopsin-reverse:5ʹ-ACCCATAATACCCATAATAGCTGTTTGCCACAGATGTCTGAGAGTCACATC-3ʹ.
High-throughput real-time PER2- and BMAL1-luciferase-reporter assays. Highthroughput real-time PER2- and BMAL1-luciferase reporter assays were performed
as described previously11 with the following modifications. NIH3T3 cells (American
Type Culture collection, Manassas, VA) were grown in Dulbecco’s modified Eagle’s
minimal essential medium (DMEM) supplemented with 10% fetal bovine serum(FBS; JRH Biosciences, Lenexa, KS) and antibiotics (25 units ml–1 penicillin, 25
μg ml–1 streptomycin; GIBCO, Carlsbad, CA). Cells were plated at 2×105 cells per
35-mm dish 24 h before transfection. Transfection was carried out with FuGene6(Roche Applied Science, Indianapolis, IN) according to the manufacturer’s instructions, and cells in each dish were transfected with 5 μg of plasmid (1 μg of PER2- or
BMAL1-luciferase reporter plasmids and 4 μg of pMU2-P(GAPDH)-control or melanopsin). After 72 h, the medium in each well was replaced with 2 ml of culture
medium (DMEM, 10% FBS) supplemented with 10 mM HEPES (pH 7.2), 0.1 mM
luciferin (Promega, Madison, WI), antibiotics, and 0.01 μM forskolin (Nacalai
Tesque, Kyoto, Japan). Cells were maintained in complete darkness except for brief
exposure to weak red light. Bioluminescence was measured using a photomultiplier tube (PMT) detector assemblies (Hamamatsu Photonics, Shizuoka, Japan).
The modules and cultures were maintained in a darkroom at 30 °C and interfacedwith computers for continuous data acquisition. Light pulses were generated bya 100-W tungsten source, filtered with far-infrared cut filter, and calibrated by aradiometer (LI-250A Light Meter; LI-COR Biosciences, Lincoln, NE). The intensityof light pulse was set to 3.0 μM s–1 m–2 before individual experiments. Photons werecounted for 2 min at 24-min intervals. The protocols for pharmacological assays andthe methods for bioluminescence data analysis are provided in the Supplementary
Information. In this protocol, we started with the forskolin stimulation followedby the quantitative melanopsin-mediated stimulation. Although melanopsin cells
can be directly entrained by sequential light-dark cycle (H. U., T.J.K. and H.R.U,
unpublished data), the phase shift induced by melanopsin-mediated stimulation
seems weaker than that of forskolin-mediated stimulation in our cellular system.
A single forskolin-stimulation can generate quantitatively reproducible circadianoscillations in our system despite presumable experimental fluctuations in preculture, and enables us to define the good reference time point (circadian time 0)
as the timing of folskolin stimulation. Thus, we combined these two stimulations
in order to maximize the reproducibility and quantitativeness in our experiments.
The detailed information on the number of cultures and repeated experiments isshown in Supplementary Information, Table S1.
Real-time single-cell bioluminescence imaging. Samples were prepared as
described previously in high-throughput real-time reporter assay except for theuse of pGL4-PER2-Luc reporter plasmid11. 35-mm culture dishes were sealedwith cover slips, placed on the stage of a luminescence microscope (Luminoview,
LV100, Olympus, Tokyo, Japam), and kept at 30 °C in a heated chamber (Olympus).
Bioluminescence was imaged using a 10× objective (LUCPlanFLN 10, Olympus,
NA 0.3) and transmitted to a cooled CCD camera (ORCA-II ER, Hamamatsu
Photonics) mounted on the bottom port of the microscope. Readout noise was
reduced by using 4×4 binning of the 336×256 pixel array. Time-lapse images werecollected at 30-min intervals with 25-min exposures by a computer using image
analysis software (Metamorph, Universal Imaging Corp., Ontario, Canada). The
light pulse was applied by opening the shutter for bright-field illumination with
the intensity of 3.0 μM s–1 m–2. The light pulse was filtered with far-infrared cut
filter and calibrated by a radiometer. During the light-pulse exposure, the image
collection was stopped, and then restarted following light-pulse exposure.
Image processing for real-time single-cell bioluminescence imaging. Images
were corrected for bias and dark current by subtracting a background image using
Matlab (MathWorks, Natick, MA). Hot pixels and cosmic rays were removed byapplying the spatial and temporal local median filters, respectively. The positionsof the hot pixels were detected by measuring the dark image. The cosmic rays weredetected by comparing the intensities of pixels for the temporally adjacent images.
Supplementary movies were then created with Metamorph (Ontario, Canada).
The bioluminescence of each cell was estimated from the average of the top ten
maximum pixels within the region of interest manually defined for each cell by acustom-made software program developed with Matlab. Before the estimation,
the spatial Gaussian filter was applied to avoid counting noise pixels. Remaining
data processing of the obtained single-cell bioluminescence data was conductedwith Mathematica (Wolfram Research, Champaign, IL). The methods for singlecell bioluminescence data analysis are provided in Supplementary Information.
Animals and housing. Adult male Wistar rats (JAPS, Osaka, Japan) were purchased 5 weeks after birth. Rats were housed on a 12-h light (400 lux): 12-h dark
(LD12: 12) cycle (light on at Zeitgeber time 0 (ZT0), and light off at ZT12), andwere given food and water ad libitum. Rats were maintained under these lighting
conditions for at least 2 weeks. On Day 0, animals were transferred to constantdarkness (DD) for one day, and on the first day (Day1) and the second day (Day2) they were exposed to a 12-h fluorescent light (400 lux) from circadian timenature cell biology volume 9 | number 11 | NOVEMBER 2007
© 2007 Nature Publishing Group

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letters
16 (CT16) to CT4. After the light exposure, rats were transferred to DD conditions. Brain samples were collected during the DD cycle on Day 0 or during thefirst entire DD cycle after the light exposure (Day 4) every 2 h. This study was
performed in compliance with the Rules and Regulations of the Animal Care and
Use Committee, Kinki University School of Medicine, and in strict compliancewith the Guide for the Care and Use of Laboratory Animals, Kinki University
School of Medicine. The detailed information on the sampling timing for in situ
hybridization is shown in Supplementary Information, Fig. S8.
In situ hybridization using digoxigenin-labelled probes. Rats were deeply anesthetized with ether and intracardially perfused with 50 ml saline and 100 ml of a
fixative containing 4% paraformaldehyde in 0.1 M phosphate buffer (PB), pH 7.4.
Rat brain samples were postfixed in the same fixative for 24 h at 4 °C, soaked in PB
containing 20% sucrose for 48 h and finally stored frozen at –70 °C. To examine
the fine localization of messenger-RNA-expressing cells, cRNA fragments of rat
Per1 (nucleotides 736–1720) and Per2 (nucleotides 1390–2915) were labelled withdigoxigenin-UTP (Roche, Mannheim, Germany) by in vitro transcription with
T7 RNA polymerase. Digoxigenin-labelled cRNA probes were synthesized using
digoxigenin-UTP through the standard protocol for cRNA synthesis (Roche). The
in situ hybridization method using digoxigenin-labelled probes was performed
as described previously24.
Stored tissues were cut to a thickness of 30 µm on the coronal plane using a cryostat and processed using the free-floating in situ hybridization method as described
previously25. Briefly, tissue sections were processed with 1 µg ml–1 proteinase K (0.1
M Tris-HCl, pH 8.0, 50 mM EDTA) for 10 min at 37 °C, and 4% paraformaldehyde
in 0.1 M PB for 10 min. Then sections were treated with 0.25% acetic anhydride in
0.1 M triethanolamine for 10 min and 2×SSC for 10 min. The sections were thenincubated in hybridization buffer (60% formamide, 10% dextran sulphate, 10 mM
Tris–HCl, pH 8.0, 1 mM EDTA, pH 8.0, 0.6 M NaCl, 0.2% N-laurylsarcosine, 0.2
mg ml–1 transfer RNA, 1×Denhardt’s, 0.25% sodium dodecyl sulphate and 10 mM
dithiothreitol) containing Per1 or Per2 cRNA probe (20 ng per 100 ml) for 12 h
at 60 °C. After two rinses in 2×SSC and 50% formamide at 60 °C, sections weretreated with a solution containing 20 µg ml–1 RNase A (10 mM Tris-HCl, pH 8.0,
1 mM EDTA, and 0.5 M NaCl) for 30 min at 37 °C. The sections were further
washed in 2×SSC and 50% formamide and then in 0.4×SSC at 60 °C (30 min foreach wash). They were then transferred into buffer 1 (100 mM Tris-HCl, pH 7.5
and 150 mM NaCl, room temperature, 5 min) and buffer 2 (1.5% blocking reagent added to buffer 1) for 1 h. They were further incubated overnight at 4 °C
with alkaline-phosphatase-conjugated digoxigenin antibodies (Roche), diluted 1:1000 in buffer 1. On the following day, the sections were washed twice in buffer
1 (5-min each) and incubated in buffer 3 (100 mM Tris–HCl buffer, pH 9.5, containing 100 mM NaCl and 50 mM MgCl2) for 3 min. Finally, they were incubatedin a solution containing nitroblue tetrazolium salt (0.34 mg ml–1) and 5-bromo4-chloro-3-indolyl phosphate toluidinium salt (0.18 mg ml–1) (Roche) for 16 h.
The colouring reaction was stopped by immersing the sections in buffer 4 (10 mM
Tris–HCl containing 1 mM EDTA, pH 8.0). The sections were analysed under abright-field microscope. The methods for data processing of in situ hybridization
images are provided in the Supplementary Information.
Behaviour analysis. To assess locomotor activity, rats were housed individually
under the same experimental condition as in the in situ hybridization assays. The
locomotor activity of an individual rat was recorded every 5 min by an area sensor(FA-05 F5B; Omron, Tokyo, Japan). To filter out noise and extract the long-term
trend of locomotor activity, the moving average with 4-h window size was applied
three times to the original locomotor activity data.
Note: Supplementary Information is available on the Nature Cell Biology website.
Acknowledgements
This research was supported by intramural Grant-in-Aid from the Center for
Developmental Biology (CDB), Director’s Fund from CDB (H.R.U.), KAKENHI(Grant-in-Aid for Scientific Research) on Priority Areas ‘Systems Genomics’
from the Ministry of Education, Culture, Sports, Science and Technology of Japan(H.R.U. and H.U.), Grant-in-Aid for Scientific Research on ‘Development of BasicTechnology to Control Biological Systems Using Chemical Compounds’ from the
New Energy and Industrial Technology Development Organization (NEDO) of
Japan (H.R.U.) and Research Fellowships of the Japan Society for the Promotion of
Science for Young Scientists 17-4169 (T.J.K). We thank for Wataru Kishimoto fortechnical supports on high-throughput monitoring system, Rikuhiro G. Yamada

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for support for data analysis, Maki Ukai-Tadenuma for technical support, Yoichi
Minami for discussion for in vivo experiments, and Douglas Sipp Michael Royle,
Danny Forger for critical comments on the manuscript. We also thank John J.
Tyson for his suggestion regarding Winfree’s original idea of desynchronization.
Author contributions
K.Y. and H.R.U. developed the concept of synthetic implementation of photoresponsiveness within NIH3T3 cells by using melanopsin. T.K. designed a highthroughput monitoring device. H.U. constructed all materials used in this workand performed high-throughput real-time luciferase reporter assays, single-cellreal-time bioluminescence imaging and pharmacological assays. T.J.K. developed
the theory, data-analysis methods, and the image-analysis software used in thiswork, analysed high-throughput, single-cell real-time bioluminescence, in situ
hybridization, and locomotor activity data, and performed single-cell real-time
bioluminescence imaging. M.N. and M.S. performed behaviour analysis of rats.
M.N., K.M. and Y.S. performed in situ hybridization and analysed the data. H.U.,
T.J.K. and H.R.U wrote the manuscript. All authors discussed the results andcommented on the manuscript text.
Published online at http://www.nature.com/naturecellbiology/
Reprints and permissions information is available online at http://npg.nature.com/
reprintsandpermissions/
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administration of intracellular calcium chelator BAPTA-AM (1-10 µM) or PLC
inhibitor U73122 (0.1-3 µM) into medium 1 h before light-pulse exposure
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Error bars represent the standard deviations of the phase shifts. The doses
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PER2-luciferase reporter activities. The intervals of light pulses are 20 min (a)and 10 min (b), respectively. (c and d) PRC (c) and ARC (d) for 3-hour lightpulse near CT~17 of the second day (blue) or third day (cyan) at high temporal
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The light-pulse has been applied about between 2nd and 3rd peaks. Bluebars represent the amplitude of melanopsin negative cells. Red and green
bars represent the amplitude of melanopsin positive cells after the lightpulses inducing desynchronization (red) and synchronization (green),
respectively. The average amplitudes were normalized by those of the 2nd
peak for comparison. The first peak right after the forskolin stimulation
was omitted here because it might be affected by forskolin stimulation. (b)The normalized PER2-luciferase reporter activities from individual cells(left panel) with their averages (black thick lines) and the detrended andnormalized PER2-luciferase reporter activities from individual cells (middle
and right panels) The timing of the light pulse (yellow) is designated in eachpanel. The data is sorted by the timing of the second peaks (middle panel)and that of the third peaks (right panel). (c) The cumulative plot of phasefor the first (red), second (green), third (blue), and fourth (purple) peaks(see Supplementary Data for details of data processing). The phases of cells
are normalized so that their median value is zero. In this plot, the slopeof each curve describes the variation of the phase. For example, a small
slope represents that the phases of cells aggregate at their median phase,indicating synchronization of cellular clocks. On the other hand, a large slope
represents that the phases of cells are broadly distributed, indicating thedesynchronization of cellular clocks. Therefore, the gradual diversification ofphases of the melanopsin-negative cells was represented in the cumulativeplot of phase as the gradual increase in the slopes of the curves for the first,
second, third, and fourth peaks (left panel). The abrupt divergence of phaseof the melanopsin-positive cells after light pulse was described by the sharp
increase in the slopes for the third peak (middle panel). The synchronizationof phase was indicated by the no change in slopes for the second and third
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30
CT at light pulse

Figure S7 Simulated fold-changes in multi-cell-level amplitude as afunction of the timing of light pulse and the intensity of single-cell-level
phase shift. Each heatmap corresponds to the result for different phasevariation before light pulse. Magenta and green denote increase anddecrease of multi-cell-level amplitude.

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5© 2007 Nature Publishing GroupS U P P L E M E N TA R Y I N F O R M AT I O N

ZT 0

ZT 2

ZT 4

ZT 6

ZT 8

ZT 10

ZT 12

ZT 14

ZT 16

ZT 18

ZT 20

ZT 22

CT 0

CT 2

CT 4

CT 6

CT 8

CT 10

CT 12

CT 14

CT 16

CT 18

CT 20

CT 22

2 weeks

Day 0
Day 1

12 hr light pulse (from 23:00 to 11:00)

Day 2

12 hr light pulse (from 23:00 to 11:00)

Day 3
Day 4
7:00

9:00

11:00

13:00

15:00

17:00

Figure S8 Sampling timings of rats for in situ hybridization. Rats
maintained on the light/dark cycle [lights on at ZT0 (7 A.M.) and lights off
at ZT 12 (7 P.M.)] for 2 weeks. On day 0, rats were transferred to constantdarkness. On day 1 and day 2, rats were exposed to a 12 hr fluorescent light,aMelanopsin(-)

19:00

21:00

23:00

1:00

3:00

5:00

from CT16 (11 P.M.) to CT4 (11 A.M.). After the light exposure, rats weretransferred to constant darkness. The brain samples were collected during
the Day0 or during the Day4 every 2h. Arrowheads indicate the sampling
points of rats. ZT, Zeitgeber time; CT, Circadian time.

b

Superposition of
all PRCs
12

20
6

16
12

0

8

6

12

18

24

4
-6

0/24
24 48 72 96 120

Figure S9 Effect of photo-perturbation on phase shift of melanopsin (-) cells.
(a) High-throughput analysis of phase shifts of melanopsin (-) cells inducedby 3h light pulses (yellow) of various timings. Magenta and green denotehigh and low normalized PER2-luciferase reporter activities.

-12(b) Superposition of all phase response curves (PRCs) of the PER2-luciferase
reporter activities shown Fig.2. The phase shifts of melanopsin-positive cells
are plotted against the timings of light pulses in circadian time (CT).

6

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a
Y

Y

Y

X

12

12

6

6

6

12

24

18

30

36

Phase Shift

Phase Shift

b

Time

6

X

12

18

24

30

36

-6

-6

-12

-12

Circadian Time (h)Circadian Time (h)

c
Y

Y

Y

Time

X

X

d
Y

Y

X

Time

Figure S10 Schematic diagrams of the theoretical models for circadianclocks. (a) The simple clock model; its stable orbit and trajectory (a blackline) shown in 2-dimensional phase space (left panel) and in 1-dimensionaltime course (middle panel). Possible perturbations to the simple clock
oscillator are shown in yellow arrows (right panel). (b) Typical type 1 (leftpanel) and type 0 (right panel) phase response curves. (c) The simple limitcycle model; its stable orbit (a black line) and trajectories after perturbations
from the stable orbit (blue and red dashed lines) shown in 2-dimensional

phase space (left panel) and in 1-dimensional time course (middle panel).
Possible perturbations to the limit-cycle oscillator are shown in yellow
arrows (right panel). (d) The clockshop model; the common stable orbit (ablack line) and individual states of multiple circadian oscillators (colored
circles) shown in 2-dimensional phase space (left panel), and individual
trajectories of multiple circadian oscillators (colored dashed lines) and theirsuperposition (a black line), which is defined as the average of individual
trajectories, shown in 1-dimensional time course (right panel).

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7© 2007 Nature Publishing GroupS U P P L E M E N TA R Y I N F O R M AT I O NaDivergence
point

Phase shift

Convergence
point

b

CT at light pulse

Desynchronization

Frequencies of cells

Synchronization

Phase of cells

Figure S11 Schematic illustration of the recovery mechanism of amplitudeinduced by the second light pulse. (a and b) Schematic representation of
single-cell-level PRC(a) and change in phase distribution induced by thesecond light pulse(b). Blue curve represents the flat distribution of phaseof cells induced by the first critical light-pulse. Red curve illustrates the

distribution of phase after the second light-pulse. By the second light pulse,
the phase of cells near convergence point get synchronized, and those near
divergence point desynchronized, resulting in the increase and decreases infrequencies of cell in the distribution around convergence and divergencepoint, respectively.

8

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Number of figures
1
S1
2, 3, S2

S3
4

Number ofcultures
n=6
n=6
n=2
n=2
n=2
n=2
n=2
n=2
n=2
n=1
n=1
n=1

Number of experiments

Remarks

2
4
1
1
3
2
2
1
3
3
3
1

0.5h light pulse
1.0h light pulse
3h light pulse
6h light pulse
12h light pulse
Light pulse at second day
Light pulse at third day
Melanopsin-negative cell
Melanopsin-positive cell (Light pulse at timing of desynchronization)
Melanopsin-positive cell (Light pulse at timing of synchronization)

Table S1 The number of cultures used for a plot in each experiment, and the number of each experiment. “Number of cultures” represents the numberof cultures used for a plot per an experiment. “Number of experiments” represents the number of each experiment that was independently performed. The
corresponding experiment is indicated in the “Remarks”.

Movie Legends
Supplementary Movie 1 Single-cell bioluminescence imaging of melanopsin- negative cells exposed to a critical light pulse.
Time-lapse image of melanopsin-negative cells exposed to a critical light pulse (yellow). Bioluminescence from cells is pseudo-colored.
Supplementary Movie 2 Single-cell bioluminescence imaging of melanopsin-positive cells exposed to a critical light pulse.
Time-lapse image of melanopsin-positive cells exposed to a critical light pulse (yellow) capable of inducing multi-cell-level singularity behavior.
Bioluminescence from cells is pseudo-colored.
Supplementary Movie 3. Single-cell bioluminescence imaging of melanopsin-positive cells exposed to a light pulse capable of increasing the averaged
amplitude.
Time-lapse image of melanopsin-positive cells exposed to a light pulse (yellow) capable of increasing the averaged amplitude of the cellular clocks.
Bioluminescence from cells is pseudo-colored.

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9© 2007 Nature Publishing GroupSupplementary Datafor
Melanopsin-dependent photo-perturbation reveals desynchronization underlying
the singularity of mammalian circadian clocks

Hideki Ukai1*, Tetsuya J. Kobayashi1,4*, Mamoru Nagano5, Koh-hei Masumoto1,,
Mitsugu Sujino5, Takao Kondo6, Kazuhiro Yagita7,8, Yasufumi Shigeyoshi5 and Hiroki
R. Ueda1,2,3

1

Laboratory for Systems Biology and 2Functional Genomics Unit, Center for

Developmental Biology, RIKEN, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe,
Hyogo 650-0047, Japan.

3

Department of Bioscience, Graduate School of Science, Osaka University, Toyonaka,

Osaka 560-0043, Japan.

4

Research Fellow of Japan Society for the Promotion of Science.

5

Department of Anatomy and Neurobiology, Kinki University School of Medicine, 377-2

Ohno-Hagashi, Osaka-Sayama, Osaka 589-8511, Japan© 2007 Nature Publishing Group6

Division of Biological Science, Graduate School of Science, Nagoya University andCREST & SORST, Japan Science and Technology Corporation, Furo-cho 1, Chikusa,
Nagoya 464-8602, Japan.
7

COE Unit of Circadian Systems, Division of Molecular Genetics, Department of

Biological Sciences, Nagoya University Graduate School of Science, Furo-cho,
Chikusa-ku, Nagoya, 464-8602, Japan.

8Department of Cell Biology and Neuroscience, Osaka University Graduate School of

Medicine, 2-2 Yamadaoka, Suita, Osaka, 565-0871, Japan*These authors contributed equally to this work.

Correspondence and requests for materials should be addressed to H.R.U. (e-mail:uedah-tky@umin.ac.jp).

2© 2007 Nature Publishing GroupSUPPLEMENTARY METHODS

Plasmid construction.
The pCMVTnT vector (Promega) was modified using the following method: Annealed
complementaryoligonucleotides(EcoRI-S.D./Kozak-Met-FLAG-I-SceI-XbaI)(Hokkaido System Science) containing EcoRI recognition sequence - Shine-Dalgarno
sequence - Kozak sequence – Met codon – FLAG - I-SceI recognition sequence - XbaI
recognition sequence were digested with EcoRI and XbaI and subcloned into EcoRI –XbaI site of pCMVTnT (hereafter referred to as plasmid A).

Another annealed

complementary

containing

oligonucleotide(XbaI-PI-PspI-stop-stop-NotI)

XbaI

recognition sequence - PI-PspI recognition sequence – tandem stop codon - NotI
recognition sequence was next digested with XbaI and NotI and inserted into XbaI –NotI digested plasmid A (hereafter referred to as plasmid B). The region from the PstI
recognition sequence to the NotI recognition sequence of plasmid B was amplified
using PCR with forward primers (PstI-ICeuI-forward) containing the PstI and ICeuI
recognition sequence and reverse primers (SalI-PI-SceI-reverse) containing the SalI and
PI-SceI recognition sequence. PCR products were digested with PstI and SalI, andcloned into the PstI - SalI site of pCMVTnT (hereafter referred to as plasmid C).

3© 2007 Nature Publishing Group

Plasmid C was found to have a hairpin structure on the EcoRI recognition
sequence in close proximity to the Kozak sequence, and this structure reduced
transcription efficiency. In order to improve transcription efficiency, plasmid C wasdigested with EcoRI, blunt-ended with T4 DNA polymerase, and self-ligated. As aresult, the hairpin structure was removed (hereafter referred to as plasmid D).
pBC-KS(+) (Stratagene) plasmid was partially digested with PvuII, and a 2.9 kbp
fragment containing replication origin and the Chloramphenicol Acetyltransferase gene
was purified. Plasmid D was completely digested with BglII and BamHI, and a 1.5 kbp
fragment containing promoter-ORF cloning site was purified. The 1.5 kbp fragmentfrom plasmid D were ligated into a 2.9 kbp fragment derived from pBC-KS(+). This
resulted in the antibiotic resistance gene being converted from β-Lactamase to
Chloramphenicol Acetyltransferase. The end product was named pMU2, and the useful
ORF-cloning cassette in this vector was termed HU2 cassette.
The PCR product containing multiple cloning sites derived from pGL3-Basic(Promega) was amplified with primers (PvuI-MCS-forward and PstI-MCS-reverse), anddigested by PvuI and PstI. The PvuI-PstI region of pMU2 containing the
CMV-promoter was then replaced with the PCR product. The resulting vector wasnamed pMU2-MCS. To drive the expression of melanopsin by the GAPDH-promoter, a4© 2007 Nature Publishing GroupPCR

product

GAPDH

containing

promoterwas

amplifiedwithprimers(P(GAPDH)-MluI-forward and P(GAPDH)-BglII-reverse), digested by MluI and BglII,
and then cloned into the MluI-BglII region of pMU2-MCS. The resulting vector wasnamed pMU2-P(GAPDH)-control.

Primers:
EcoRI-S.D./Kozak-Met-FLAG-I-SceI-XbaI:
5´-GAATTCGAAGGAGAGGCCACCATGGACTACAAGGATGACGATGACAAGAATTACCCTGTTATCCCTAATTCTAGA-3´

XbaI-PI-PspI-stop-stop-NotI:
5´-TCTAGATGGCAAACAGCTATTATGGGTATTATGGGTTAATGAGCGGCCGC-3´

PstI-ICeuI-forward:
5´-CTGCAGTAACTATAACGGTCCTAAGGTAGCGAAAGTTGGTCGTGAGGCAC
TG-3´

SalI-PISceI-reverse:

5© 2007 Nature Publishing Group5´-GTCGACTGCCATTTCATTACCTCTTTCTCCGCACCCGACATAGATTCATTAACCCATAATACCCATAATAGC-3´

PvuI-MCS-forward:
5´-CGATCGGGTACCGAGCTCTTACGCG-3´

PstI-MCS-reverse:
5´-CTGCAGAAGCTTACTTAGATCGCAG-3´P(GAPDH)-MluI-forward:
5´-ACGCGTAATGAGGCGGGTCCAAAGAG-3´P(GAPDH)-BglII-reverse:
5´-AGATCTGCTTGCACACTTCGCACCAG-3´

Pharmacological assays.
Drugs used in the inhibition experiments were applied 1 hr before light pulse. U-73122

6© 2007 Nature Publishing Groupand BAPTA-AM were obtained from Sigma Aldrich and Dojindo, respectively.

Preprocessing of bioluminescence data. The bioluminescence from each sample wasmeasured with multiple detectors. The data from individual detectors were normalized
by the averaged intensity over time. The normalized data were then averaged overdifferent detectors for the same sample at each time point to obtain the bioluminescencedata for the sample. Data from impaired detectors were removed before averaging.
Baseline trends were detrended by the smoothing spline method as described
previously1. The same parameters1 were used, except that in this case all time points
were used for the detrending.

Quantification of multi-cell-level phase shift and amplitude change induced bylight pulse.
To evaluate the phase and amplitude change purely induced by the light pulse, we
selected four independent samples by removing two samples whose phases wereinsufficiently reset by the forskolin stimulation from the six samples prepared for eachcondition . The detrended data from each sample was normalized by the amplitude of
the second peak. In Figure 1b, the average and standard deviation over four independent

7© 2007 Nature Publishing Groupsamples were calculated at each time point. In order to calculate the phase shift andamplitude change shown in Figures 1c and Supplementary Figure S1, peaks from thenormalized data were estimated by fitting the cubic polynomial to five neighboring time
points, to obtain the timing and amplitude of the fourth peak, T4 and A4, and the timingof the second peak, T2. The interval between the fourth and second peaks, T4 -T2, wereused to calibrate the slight fluctuations of samples before the light pulse. The phase shift
and amplitude change were obtained by comparing T4 -T2 and A4 between samples withor without light-pulse exposure.

Data processing of high-throughput real-time reporter assays.
For the data in Figures 2, 3 and Supplementary Figures S2, S3, the averageluciferase-reporter activities of different detectors for individual samples were
calculated and then detrended as described above. To evaluate the phase and amplitudechange purely induced by the light pulse, we removed samples whose phase wasinsufficiently reset by the forskolin stimulation from further data analysis.

Quantification of multi-cell-level phase shifts induced by light pulse inhigh-throughput real-time reporter assays.

8© 2007 Nature Publishing GroupFirst, the moving average of the absolute value of the detrended data was calculated.
The window size of the moving average was set to half of the period of the oscillation s
estimated by autocorrelation from the detrended data, as described previously1. The
oscillatory component of the detrended data shown in Figures 2a, b and Supplementary
Figures S2 and S3 a,b was calculated by dividing the data by the moving average data at
each time point.
To obtain the phase shifts shown in Figure 2c and Supplementary Figure S3c, we
calculated the differences between the peak timings of melanopsin-positive and-negative cells for individual peaks following light pulses. The average and standard
deviation of phase shifts were calculated over individual peaks. The timings of lightpulses and the phase shifts were then converted to circadian time (CT) by dividing themby the period of the corresponding melanopsin-negative cells. The time of the forskolin
stimulation was set to CT0.
Notably, these multi-cell-level PRCs resemble light-type PRCs observed in
mammals at the organism-level 2,3 although there are some differences between phaseshifts induced in cells and organism. First, phase shifts at the organism-level exhibit adead zone, while phases shifts of cells exhibits no dead zone. Second, the averaged
magnitude of cellular phase shifts is relatively larger than that of organismal phase shifts.

9© 2007 Nature Publishing GroupThese properties observed at the organism-level might be attributed to a gating and/or
coupling mechanism of multiple individual clock cells, both of which are known to exitin the organism. Thus, our cellular system will provide a synthetic-biological platform
to test a hypothesis whether these organismal-level properties of phase shifts can beconferred by a gating and/or coupling mechanism.

Quantification of multi-cell-level amplitude changes induced by light pulse inhigh-throughput real-time reporter assays.
To extract the amplitude trends shown in Figure 3b, we first calculated the moving
averages of the detrended data of melanopsin-positive and -negative cells as describedabove. The moving average data of the melanopsin-negative cells was fitted by an
exponential function. The moving average data of the melanopsin-positive cells wasthen divided by the exponential function of the corresponding melanopsin-negative cells.
Finally, the data was fitted by a cubic spline function to obtain the long-term trend in
the amplitude change shown in Figure 3b. Each amplitude response in Figure 3c andSupplementary Figure S3d was calculated by averaging the amplitude change over twodays after the light pulse. The timings of light pulse were converted to CT as describedabove.

10© 2007 Nature Publishing GroupData processing for real-time single-cell bioluminescence imaging.
Supplementary Fig. S4 shows nine representative single-cell-level bioluminescence of
melanopsin negative and positive cells to which temporal moving average with 1-hour
window size was applied to the data for 10 iterations to remove local peaks attributable
to measurement noise and anomalous behavior of individual cells. To obtain the data in
Figure 4c and Supplementary Figure S5b, the bioluminescence data of each cell was
normalized so that its maximum and minimum intensities respectively became one andzero. The data used in Figure 4d, e and Supplementary Figure S5b was obtained byapplying the detrended baseline and subsequent normalization to each cell’s originaldata. The processed bioluminescence data were then sorted by their peak timings.
Before determining the peak timing, temporal moving average with 1-hour window size
was applied to the data for 10 iterations. The peak timings were then determined byfitting cubic polynomial to the five neighboring time points as described above. To sortthe data of individual cells by their peak timings, we first calculated the first four peaksof the average bioluminescence of all cells. This was then followed by collecting theclosest peak of each cell to the corresponding peak of the averaged data.

11© 2007 Nature Publishing GroupTo quantify the single-cell-level amplitude, we calculated average andstandard deviation of amplitude of 2nd, 3rd, 4th, and 5th peaks of the single-cell-levelbioluminescence data (Supplementary Fig. S5 a). The figure demonstrates that thecritical light pulse induces no significant change in the average amplitude, indicatingthat the amplitude decrease or increase in multi-cell-level can be attributed todesynchronization and synchronization of cells.
To quantify the desynchronization and synchronization observed in Figure 4c-d
and Supplementary Figure S5b, we calculated cumulative plots of phase where thesorted phases of individual cells are cumulatively plotted against the percentage of cells(Supplementary Figure S5c). The phases of cells are normalized so that their medianvalue is zero.

Data processing of in situ hybridization images.
In order to quantify the spatio-temporal expression pattern shown in Figure 5a, thenumber of Per1 and Per2 mRNA-positive cells was counted twice, separately indorsomedial (DM) and ventrolateral (VL) regions of the rat SCN, in slices with clear
separation of these two sub-regions (three sections per animal). A blinded observer
made two separate counts of the number of positive cells within DM region, VL region12© 2007 Nature Publishing Groupand the entire SCN4. Cells were counted only when the cytoplasm was clearly labelledagainst the background. As a result, there was good agreement in the numbers between
the two rounds of counting. The average numbers of positive cells per single
suprachiasmatic nucleus at each time point were plotted. The DM region was
distinguished from the VL region by using morphological criteria described previously5.
While the manual counting of positive cells is a generally adopted procedure
to quantify the spatio-temporal expression from in situ hybridization images, it isdifficult to obtain the information on more local expression patterns within the entire
SCN by manual counting. To complement manual counting, we developed a computer
program that can automatically analyze the in situ hybridization image of SCN slices(Supplementary Figure S6).

We first converted the original in situ hybridization

images to grayscale by averaging red, green and blue intensities of each pixel. To
reduce the local noise in images, we applied spatial moving average filter whose
window size was 20 × 20 pixels, and then converted the image from 700 × 700 to 220 ×
220 pixels. Each grayscale image was normalized so that the average intensity of right
top corner (Per1) or right and bottom sides (Per2) of the image was 1000. These areas
were used as reference because the positive cells were rarely observed in these areas.
The time series of each pixel was approximated by interpolating them with a cubic

13© 2007 Nature Publishing Groupspline curve. Since we obtained three slices for each SCN sample and we conducted insitu hybridization of two independent samples for each time point, we used six intensity
data for each time point to obtain the cubic spline fitting curve. The spline fitting curves
were then normalized so that the maximum and minimum intensities of all spline curves
become 0 and 1, respectively (Since the pixels of positive cells, i.e. dark pixels, havelower intensity in the in situ hybridization images, the pixels of positive cells areconverted to higher value by this normalization). To obtain Supplementary Figure S6,
we finally sorted the time series by their mean values so that time series of a pixel witha higher mean value has a lower index. As is shown in Supplementary Figure S6, theexpression timings of clock genes in the control experiment were synchronized aroundCT4~8 for Per1 and CT8~12 for Per2 within the entire SCN (Supplementary Figure S6,
upper panels) whereas the expression timings of both clock genes become spatiallydesynchronized after the critical light pulses (Supplementary Figure S6, lower panels).
Similar diversification of expression timings are also evident for Per1 (Supplementary
Figure S6, left panels), indicating that the states of circadian clocks were spatiallydesynchronized in the entire SCN after the critical light pulses. This spatial
desynchronization in the SCN was reproducibly detected in our repeated experiments,

14© 2007 Nature Publishing Groupindicating that the critical light pulses can robustly induce desynchronization of the
SCN.

15

© 2007 Nature Publishing GroupSUPPLEMENTARY RESULTS and DISCUSSION
The development of clock models.

Various theoretical models of circadian clocks have been developed in the last half
century, from fairly simple ones to more sophisticated models to accommodate
newly-discovered dynamical properties of circadian clocks.
The simplest of these is the “simple clock” model. The possible states of asimple clock model are located on a circle in a state space (Supplementary Fig. S10a
online, left panel), implying that its amplitude is constant (Supplementary Fig. S10a
online, middle panel) and that its dynamics are characterized only by its phase. Since its
state is restricted to the circle, external perturbation imposed to the clock simply shifts
its phase either forward, backward or unchanged (Supplementary Fig. S10a online, rightpanel). Mathematical analysis of the simple clock model easily demonstrates that thesimple clock model only shows weak (type 1) phase response (Supplementary Fig. S10b
online, left panel) to any external perturbations, and can exhibit neither the strong (type0) phase response (Supplementary Fig. S10b online, right panel) nor the singularity
behavior observed in organisms. Since most organisms exhibit both weak (type 1) andstrong (type 0) phase response as well as singularity behaviors, the simple clock model
has been excluded as a plausible explanatory model for circadian clocks.

16© 2007 Nature Publishing GroupThe simple limit-cycle model was previously proposed to explain the strong(type 0) phase response and singularity behaviors. The simple limit-cycle model has astrongly attractive circular orbit and a unstable fixed point in a state space. Because of
an attractive circular orbit, the simple limit-cycle model behaves like a simple clock
model without external perturbation (Supplementary Fig. S10c online). In contrast to
the restricted state within the orbit in the simple clock model, external perturbation cantransiently bring the state of circadian oscillator outside the orbit in the simple
limit-cycle model (Supplementary Fig. S10c online, right panel), and hence change theamplitude of circadian oscillation (Supplementary Fig. S10c online, middle panel)although it restabilizes quickly to the original attractive orbit (Supplementary Fig. S10c
online, left panel). Based on the existence of this attractive orbit, the simple limit-cycle
model is proved to accompany an unstable fixed point within its attractive orbit. Bothstrong (type 0) and weak (type 1) phase response, as well as singularity behavior, can be
explained in the simple limit-cycle model based on the existence of this unstable fixed
point. For example, singularity behavior of circadian clocks is explained in the simple
limit-cycle model as the stopping of circadian oscillator at the unstable fixed point.
Despite its ability to explain weak (type 1) and strong (type 0) phase responses
and singularity behaviors, however, the plausibility of the simple limit-cycle model was

17© 2007 Nature Publishing Groupquestioned by Arthur T. Winfree in 1970s. In order to investigate how fast a circadianoscillator was recovered to its attractive orbit after various perturbations, Arthur T.
Winfree and others conducted extensive two-pulse experiments6,7 and unexpectedly
found the “unclocklike” behavior of circadian clocks where a circadian clock seemed tooscillate stably at a original frequency with a lower amplitude for a long time afterparticular perturbations, which apparently argued against the simple limit-cycle model.
To accommodate this “unclocklike” behavior of circadian clocks, he proposed the“clockshop” hypothesis that an organism-level circadian clock consists of multiple
circadian oscillators with substantial fluctuations (Supplementary Fig. S10d online, left
panel), and that superposition of multiple circadian oscillators defines the output of theorganism-level circadian clock (Supplementary Fig. S10d online, right panel). He also
predicted that desynchronization of multiple circadian oscillators would underlie theobserved “unclocklike” behavior (multi-cell-level amplitude decrease) of circadianclocks, although direct experimental verification of this prediction was impossible atthat time due to the lack of technology to observe circadian rhythmicity at thesingle-cell-level.

18© 2007 Nature Publishing Group

Prediction of the underlying mechanism for the multi-cell-level singularity
behavior from multi-cell-level data.

The underlying mechanism of the multi-cell-level singularity behavior in our system
can be predictedfrom the multi-cell-level dynamical properties of cellular clocks

represented in the obtained PRCs and ARCs (Fig. 2c and 3c). We first noticed that thetiming of the minima in ARCs (or timing of singularity behaviors) closely match withthose of delay-to-advance transition in PRCs (CT~17, near subjective midnight), andthen discovered that this strong correlation between ARCs and PRCs can beconsistently explained by the second mechanism (desynchronization of individual
clocks). Suppose that the phases of multiple cellular clocks are distributed around
CT~17, and that the single-cell-level PRC is close to the experimentally observed
multi-cell-level PRC. In this scenario, delayed cells with a phase less than CT~17
receive a light pulse to delay their phase and as a result are driven further from CT~17,
while the advanced cells with a phase of more than CT~17 receive the light pulse that
advances their phase, moving them further from CT~17 as well. This suggests that alight pulse applied around CT~17 diversifies the phase of cellular clocks to decrease theaveraged amplitude of cellular clocks, and hence can drive cellular clocks into themulti-cell-level singularity behavior in severe cases.

19© 2007 Nature Publishing GroupIn addition, we also noticed that the timings of the maxima in ARCs closely
match those of advance-to-delay transition in PRCs (CT~6, subjective noon), andrealized that this correlation can be also explained by the same mechanism. Supposethat phases of multiple cellular clocks are distributed around CT~6, the delayed cellswith a phase less than CT~6 receive a light pulse to advance their phase and then returnto CT~6, while the advanced cells with a phase of more than CT~6 receive the lightpulse to delay their phase and also come back to CT~6. This suggests that a light pulse
around CT~6 converges the phase of cellular clocks to increase the averaged amplitude
of cellular clocks. Since the increase of the averaged amplitude cannot be explained by
the arrhythmicity of individual clocks without additional assumptions, we can predictthat the desynchronization of individual clocks underlies the singularity behavior.

The desynchronization of individual clocks predicted above can also explain therecovery of multi-cell-level oscillation by the second light pulse observed in Figure 4a.
As already mentioned, the first critical light pulse desynchronizes the phase of cellularoscillators, resulting in the uniform distribution of the phase schematically describedwith blue line in Supplementary Figure S11. When the second pulse is applied to cells,
cells whose phase are close to the “phase convergence” point of PRC become
synchronized, while cells whose phase are close to the “phase divergence” point20© 2007 Nature Publishing Groupbecome desynchronized. Because of these synchronization and desynchronization
processes, the population at the “phase convergence” point becomes increased while thepopulation at “phase divergence” point becomes decreased. As a result, the distributionof the phase will change from uniform distribution (blue line) to ununiform distribution
peaked around “phase convergent” point (red line). This ununiform distribution resultsin the recovery of multi-cell-level oscillations as observed in our experiment.

While this prediction is not always necessary in this study due to directverification by single-cell-level measurement, the analysis described here is still worth
noting because we can apply this to inspect underlying mechanism of singularity
behaviour in other organism from their multi-cell-level data.

Synchronization underlying multi-cell-level amplitude increase.
To verify not only desynchronization underlying singularity behavior but alsosynchronization underlying amplitude increase predicted above, melanopsin-positive
cells were exposed to a light pulse capable of increasing the averaged amplitude of thecellular clocks (Supplementary Figure S5b, Supplementary Figure S5c right panel, andSupplementary Movie 3 online). As expected, we observed that the slopes of the third21© 2007 Nature Publishing Groupand second peaks were almost identical in melanopsin-positive cells (Supplementary
Figure S5c right panel) while the slope of third peak is larger than that of the second
peak in melanopsin-negative cells. This result indicates that the light pulse applied tomelanopsin-positive cells induces synchronization of phases, which negates thediversification of phases over time. We also verified that the light pulse did not induce
detectable increase in single-cell-level amplitude (Supplementary Figure S5a online).
Thus, the same single-cell-level mechanism (synchrony control of cellular clocks bylight pulse) can consistently explain the multi-cell-level amplitude increase induced by alight pulse around CT~6.

Theoretical model for the multi-cell-level phase shift and amplitude change.
In an attempt to quantitatively reproduce the multi-cell-level phase shift and amplitudechange, we constructed a mathematical model of multiple cellular clocks. To model
single-cell behavior, we adopted the simple limit cycle model that features a strongly
attractive stationary orbit 7. The strong attractive stationary orbit of our circadianoscillator in a single cell is supported by the no substantial difference between the
average amplitudes of the oscillators before and after the light pulse (Supplementary Fig.
S5a). While this assumption is not generally valid, in our system it is experimentally22© 2007 Nature Publishing Groupverified as we experimentally observed that most of cells quickly recovered theiroscillation within one cycle after the light pulse. Given this assumption, the oscillationof individual cells can be characterized by its phase, θ , defined on a unit circle. As weuse approximately 1 x 106 cells to measure the multi-cell-level response for eachexperimental condition, we can also assume that the number of cells in a population islarge enough so that the percentage of cells whose phase is θ at time t can be
represented by a probability density function, P (t ,θ ) . For simplicity of analysis,

P(t ,θ ) is assumed to satisfy P(t ,θ ) = P(t + ∆t ,θ + ω∆t ) without external perturbation.
This assumption means that the distribution of the phase moves with period 1 / ωwithout changing shape, and that the change of the distribution is induced only by theexternal perturbation. This modeling was approximately varied for analyzing our data,
since the phase shift and amplitude change induced by other perturbation or intracellularnoise than light pulse were computationally removed by comparing melanopsin-positiveand -negative cells in our experimental data. A more detailed model to ensure thissimplification will be described elsewhere (T.J.K. et al in preparation).
After the application of the light pulse at time t1 , individual cells are assumed
to change their phases according to a single-cell-level phase response curve (PRC). As

23© 2007 Nature Publishing Groupwe have so far been unable to obtain the single-cell-level PRC experimentally, we
assume that the PRC can be described as
PRC (θ , α ) = arg(exp[2πιθ ] + ια ) / 2π − θ ,(S1)where ι represents the imaginary unit 7,8. The parameter α describes the intensity ofthe phase shift (i.e. a larger α represents the longer or stronger perturbation of cellular
clocks). With this single-cell-level PRC, the single-cell-level phase transition curve(PTC) can be defined as PTC (θ , α ) = θ + PRC (θ , α ) . The parameter α abstractly
represents the intensity of the perturbation, and the perturbation with higher strength or
longer duration is therefore assumed to be represented with higher α in our model.
The PRC has qualitatively different properties depending on the value of α . When aperturbation is weak, specifically α < 1 , then PRC displays relatively small phase shifts
and has a continuous transition from delays to advances at the phase divergence point.
The phase divergence point in eqn. S1 is θ = 3 / 4 , which corresponds to circadian time(CT) 18 (subjective midnight), when we define CT0 as θ = 0 . In contrast, when aperturbation is strong, specifically α > 1 , then PRC displays large phase shifts and has
a discontinuous transition from delays to advances at the phase divergence point. The
former and the latter are called type-1 and type-0 PRCs, respectively, as the averageslopes of the corresponding PTCs are respectively 1 and 0. The simple limit cycle

24© 2007 Nature Publishing Groupmodel predicts that the perturbation with the strength α = 1 applied at the phase
divergence point is the critical perturbation that can induce the singularity behavior of alimit cycle as (α , θ ) = (1, 3 / 4) is the only point at which PRC (θ , α ) cannot be
defined.
We assume that P (t ,θ ) is the probability density function of the phase of
oscillators after the light pulse. As the oscillators typically show transient dynamics
after the light pulse, the actual P (t ,θ ) depends on the detail of dynamics of theindividual oscillator. Rather than model such complex transient dynamics, we define
P (t ,θ ) as the extrapolation of the phase distribution of oscillators after the transient
dynamics. The validity of this definition is experimentally supported by our observationthat the oscillations of individual cells were recovered within one cycle after the lightpulse. Furthermore, in our data analysis, the multi-cell-level phase shift and amplitudechange were calculated as the averages of several cycles after the light pulse, which willattenuate the effect of transient dynamics. We also assume P (t , θ ) = P (t + ∆t ,θ + ω∆t ) .
With these definitions of the PTC and P (t ,θ ) , we have the relationship between the
distributions before and after the light pulse as follows:
P (t 1 , θ )dθ = P(t1 ,θ )dθ , θ = PTC (θ ) ,where θ represents the phase after the light pulse.

25© 2007 Nature Publishing GroupIn our experiment, the multi-cell-level phase shift and amplitude change were
calculated from total luciferase reporter acvitivies from the population of cells. To
model single-cell-level luciferase reporter activity, we assume that the activity of theindividual cell is represented as F (t ) = F (θ (t )) where F (θ ) is a periodic function on
the unit circle. For simplicity of analysis, we use F (θ ) = sin( 2πθ ) . In this case themulti-cell-level activity of the population before the light pulse, A(t ) , can be describedasA(t ) = ∫ F (θ ) P (t , θ ) dθ = ∫ sin( 2πθ ) P (t , θ ) dθ .

(S2)Similarly, the average activity after light pulse, A (t ) , can be described as

A (t ) = ∫ F (θ ) P (t ,θ )dθ(S3)

To calculate A(t ) and A (t ) , we require detailed information on P(t ,θ ) . For
modeling P (t ,θ ) , we used a Gaussian distribution defined on a unit circle:
P (t , θ ) = ∑k∈Z⎛ − (θ − ωt − θ 0 + k ) 2 ⎞
⎟,
exp⎜⎜
⎟
2σ 2
2πσ 2
⎝
⎠
1

where θ 0 and σ describe the average phase of cells at t = 0 and the variation ofphases, respectively.

Simulation of the multi-cell-level phase shift and amplitude change.

26© 2007 Nature Publishing GroupTo obtain the multi-cell-level phase shift and amplitude change, we numericallycalculated A(t ) and A (t ) with eqns. S2 and S3 for various σ , α , and θ 0 , with ωwas set to 1 without losing generality. The multi-cell-level phases shift and amplitudechange were calculated from the peaks of A(t ) and A (t ) . We then obtained themulti-cell-level PRCs and ARCs for each parameter set of σ and α by plotting thephase shifts and amplitude changes against θ 0 . The timings of light pulses in all PRCs
and ARCs shown in Figure 2c and 3c are converted from the unit circle to CT.
The best fitted simulation data in Figures 2c and 3c were searched bymeasuring difference between the experimental data and simulated data for various
parameter sets of σ and α . We found that the simulated data whose σ = 0.24 canreproduce the experimental data qualitatively. This value was consistent with theestimated value of the phase distribution from the single-cell measurement. Thisestimation was conducted by comparing the standard deviation of the timings of thesecond peak collected from the single-cell experimental data and that of the Gaussian
distribution with fixed σ defined on a unit circle. The parameter values of α were0.35, 0.4, 0.65, 0.7, and 0.95 for 0.5, 1, 3, 6, and 12-hour light duration data,
respectively. The identified α values for different light pulses are consistent with thedurations of light pulses. As shown in Figures 2c and 3c, the types of the PRCs, and the27© 2007 Nature Publishing Groupmaximum and minimum values of ARCs as well as their shapes were qualitatively
reproduced by the simulation. This remarkable agreement between simulation andexperiment suggests that possible intercellular variations of melanopsin expression due
to transient transfection make a minor contribution, if any, to the multi-cell-level
phenotype, since intercellular variations of melanopsin expression are not included inour simulation model. In addition, we also observed more than 2-fold amplitude change
due to the synchronization of cellular clocks, which would hardly be observed if thevariation of melanopsin was the dominant source of intracellular noise inducing thedesynchronization. The simulation furthermore suggests that the multi-cell-levelsingularity behavior and the transition of the types of PRC from 1 to 0 occurs
simultaneously similarly to the simple limit cycle model, as described above. This result
indicates that the multi-cell-level singularity behavior is barely induced if perturbations
such as drug administration and temperature change are too strong to always induce
multi-cell-level type-0 phase response, or are too weak to always induce multi-cell-level
type-1 phase response.

28© 2007 Nature Publishing GroupTheory demonstrates that desynchronization is a plausible mechanism ofobservability of singularity behavior.

The simple limit-cycle model predicts that the singularity behavior can be induced
merely by the infinitesimal range of perturbation strength and timing, which is hard to
realize by experiment, standing in sharp contrast with the reproducible and prevalent
observations of singularity behaviors in various organisms. To test how theobservability of singularity can be explained by our model, we calculated the amplitudechange as a function of timing and strength of light pulse for various values of σ . As
shown in Supplementary Figure S7, the parameter range in which substantial amplitudedecrease can be observed (green regions in Supplementary Figure S7) expand as thephase variation of a population of cells before light pulse increases. Hence, if there aresubstantial fluctuations in the state of individual cellular clocks, then the multi-cell-levelsingularity behavior will be stably and robustly induced by the experimentallyachievable range of perturbation strength and timing, which has been shown in our invitro system (Fig. 4). Since recent single-cell-level measurement of individual cellular
clocks in the SCN revealed substantial fluctuations in the states of central clocks9,10, ourmodel predicts that desynchronization of cellular clocks in the SCN can be stably
induced by the critical light pulses. This prediction is quite consistent with our robust

29© 2007 Nature Publishing Groupobservations that the desynchronization actually underlies the multi-cell-level amplitudedecrease in the SCN after the critical light pulses that can also probabilistically induce
temporal amplitude decrease of locomotor activity. Furthermore, recent single-cell-levelmeasurement have revealed substantial fluctuations in the state of cellular clocks in the
peripheral or in other organism11-13, and it is reasonable to suppose that substantial
fluctuations exists in cellular clocks in general, probably due to the intracellular noise
ubiquitous in living systems14-16. Given the substantial fluctuations in cellular clocks ,our model can further explain why multi-cell-level singularity behaviors have been
experimentally observed in various organisms. On the basis of these results andconsiderations, we propose desynchronization as a plausible mechanism underlying theobservable singularity behaviors of circadian clocks.

As pointed out in the body, however, we cannot completely exclude the simple
limit cycle model because the ability of stopping the individual oscillators depends on
the amplitude of the stable limit cycle, the magnitude of the basin of attraction bounding
the phase-less set and so on. For example, extentions of the simple limit-cycle modelsuch as the limit-cycle model with stable fixed point17,18 or two-step mechanism19 havebeen proposed to explain the prevalent singularity behaviors. While the extended model
can explan the prevalent experimental observation of singularity behaviors, further

30© 2007 Nature Publishing Groupmodifications is required to accommodate the observed “unclocklike” behavior of
circadian clock.
Since a model can be extended to incorporate unexplained observations,validation of the generality of the proposed desynchronization mechanism will require
the direct verification of underlying mechanism of singularity behaviors in othercircadian systems such as Neurospora clock cells, where singularity behaviors havebeen beautifully observed in vivo19, and zebrafish clock cells, which can respond to alight pulse and can be measured in vitro at the single-cell level13,20. In any case, thedirect verification by single-cell measurement plays critical role for the validation.

Limitations of the theoretical model.

While our model qualitatively reproduces the experimental data, it has some limitations
due to its simplicity. First, as α is an abstract parameter representing the intensity ofthe perturbation, α is generally a complicated nonlinear function of the light strengthand duration. We cannot therefore discuss the quantitative relationship between thevalues of α in our simulation and the corresponding durations of light pulses. From atheoretical viewpoint, however, α is expected to monotonously depend on the31© 2007 Nature Publishing Groupstrength or duration of light pulse. This qualitative relationship between α and light
duration was reproduced in our results (Figure 2c and 3c).
Second, in our simulation the positions of the minima of the ARCs were notquantitatively reproduced. This deviation can be attributed to the simplification of ourmodel, with one possibility being, for example, that the real single-cell PRC has its
divergence point at CT~16 or CT~17 while the divergence point in our model locates at
CT18. This deviation can be corrected by using a more complicated equation for
describing the single-cell-level PRC.
Third, our model does not include intercellular interactions, which play a
crucial role in circadian oscillation of some organisms. The influence of incorporationof intercellular interactions strongly depends on the intrinsic dynamical property of
individual circadian oscillator and type of coupling. When phase shift induced by lightpulse is weakly influenced by the coupling, our model can be naturally extended tointeracting cells as the phase shifts and amplitude changes are determined in our model
depending on the mean phase and phase variation of a population of cells at the momentof the light pulse. Incorporation of the intercellular interaction to our model will thenexplain additional dynamics of cells before and after the light pulse. For example, it isexpected that the incorporation will be able to explain the recovery of multi-cell-level32© 2007 Nature Publishing Grouposcillation by the re-establishment of the synchronized state from the desynchronizedstate induced by the critical light pulse. The delay until recovery and the multi-cell-level
phase after the recovery can also be explained by the extended model (T.J.K. et al in
preparation). If the mutual interaction of coupling and light-induced perturbation is not
weak, then we need to use more detailed model which can reproduce the dynamics of acircadian oscillator in a single cell observed experimentally. However, we lackexperimentally observed quantitative data sufficient to model such detailed dynamics.
Further advance in experimental measurement in vivo and synthetic implementation of
circadian oscillation will enable us to construct the model that can handle these
problems, and other properties of circadian oscillator such as the desynchronization of
SCN neurons induced by constant light condition21,22.
Finally, the existence of peripheral clocks and nonlinear amplification of input
and ouput of core clocks may complicate the light response of the locomotor
rhythmicity such as the probabilistic observation of temporal amplitude decrease inlocomotor activity shown in Figure 5c. Since several brain regions express clock genes
and these peripheral clock tissues can sustain oscillations for a couple of days without
any signal from SCN23-26, the multi-cell-level amplitude decrease in the SCN might betransiently compensated by output peripheral clock region(s) more directly controlling33© 2007 Nature Publishing Grouplocomotor activities. Alternatively, the decreased multi-cell-level amplitude in the SCN
might be amplified by nonlinear signal transduction(s). We also cannot completely
exclude other possibilities, such as that the SCN region responsible and sufficient for
locomotor activity control is restricted, with the small portion of SCN that is less thanthe experimentally detectable size in our pixel-level (several cells at most) image
analysis. In either of the cases listed here, further modifications of our model will be
required, for example, by introducing an intercellular network structure between central
and peripheral clocks or signal transduction pathways downstream of SCN. To collectsufficient information for these modifications, further technological development
enabling real-time quantitative perturbation and single-cell-level measurement
simultaneously in living organisms will be needed.
While some of quantitative and qualitative deviations from the experimental
data may be explicitly described using a more complicated and tangled mathematicalmodel, we adopted the simplest model to avoid obscuring the conceptual essence by
unnecessary complexity. Because of this simplicity, our model,can be used toinvestigate desynchronization underlying various multi-cell biological oscillators suchas cardiac and respiratory oscillation27.

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