A RT I C L E S

Proof-by-synthesis of the transcriptional logic of
mammalian circadian clocks
Maki Ukai-Tadenuma1,3, Takeya Kasukawa2,3 and Hiroki R. Ueda1,2,4
Mammalian circadian clocks consist of complex regulatory loops mediated through—at least—morning, daytime and night-time
DNA elements. To prove the transcriptional logic of mammalian clocks, we developed an in cellulo mammalian cell-culture
system that allowed us to design and implement artificial transcriptional circuits. Here we show that morning activation andnight-time repression can yield the transcriptional output during the daytime, and similarly that daytime activation and morning
repression can yield night-time transcriptional output. We also observed that the diverse transcriptional outputs of other phases
can be generated through the expression of simple combinations of transcriptional activators and repressors. These results reveal
design principles not only for understanding the continuous transcriptional outputs observed in vivo but also for the logicalconstruction of artificial promoters working at novel phases. Logical synthesis of artificial circuits, with an identified structure
and observed dynamics, provides an alternative strategy applicable to the investigation of complex biological systems.
The transcriptional circuit underlying mammalian circadian clocks consists of at least three clock-controlled DNA elements (CCEs): morning(E-box/E´-box, CACGT[G/T])1–4, daytime (D-box, TTA[T/C]GTAA)4,5
and night-time (RRE, [A/T]A[A/T]NT[A/G]GGTCA)6–8, and at least
20 clock or clock-controlled genes4,7,9–28 (Fig. 1a). E-box-mediated transcription is directly or indirectly controlled by at least 11 transcription
factors9–21 and thus has a critical function as the core of mammalian
circadian clocks4,29, whereas the D-box-mediated and RRE-mediatedtranscriptions are controlled by four9,24–26 and five4,7,9,27,28 transcription
factors, respectively, and function primarily as output or stabilizing
loops4,7,9,25–27 of mammalian circadian clocks.
Although the network structure of these cis-elements and trans-regulators has been described comprehensively4, the dynamic principles governing this transcriptional circuit remain elusive. With an eye towards
gaining a system-level understanding of the transcriptional logic underlying mammalian circadian clocks, we carefully reviewed its network
structure (Fig. 1a). First, we examined the daytime expression mediatedthrough the D-box, which is bound competitively by its transcriptional
activators (Dbp, Tef and Hlf) and its transcriptional repressor (E4bp4).
Dbp, Tef and Hlf are expressed during the morning under the control of
the E-box, whereas E4bp4 is expressed during the night-time under thecontrol of the RRE4. On the basis of this circuit information, we formed
the hypothesis that one (or more) morning activator(s) and a night-time
repressor could together determine the daytime transcriptional output
mediated through the D-box. Similarly, we examined the night-time

expression mediated through the RRE, which is bound competitively
by its activators (Rorα, Rorβ and Rorγ) and its repressors (RevErbAα andRevErbAβ). Because two of the three RRE activators (Rorα and Rorβ) are
expressed during the daytime under the control of the D-box, and because
the RRE repressors (RevErbAα and RevErbAβ) seem strongly influenced
by the two morning elements (E-boxes) in their intronic promoter regions
for their morning expression, we formulated another simple hypothesis:
one or more daytime activators and one or more morning repressors can
specify the night-time transcriptional output by regulating the RRE. As an
initial investigation into the dynamic principles governing circadian transcriptional circuits, we focused on the daytime and night-time expression among three timings in mammalian circadian clocks. To test the
hypotheses derived above (from examining the natural circadian circuit)we synthesized artificial transcriptional circuits to simulate the natural
circuits physically and then observed the resulting system dynamics.
Results
In cellulo mammalian cell-culture system for physical simulationof natural transcriptional circuits
We developed an in cellulo mammalian cell-culture system consisting of mouse clock cells (NIH3T3 (ref. 30)), an artificial activator(destabilized GAL4–VP16 fusion proteins, dGAL4–VP16), an artificial repressor (destabilized GAL4 proteins, dGAL4), and an output
reporter harbouring a gene encoding destabilized luciferase (dLuc)
driven by a minimal cytomegalovirus promoter (CMVmini) fused with1
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
These authors contributed equally to this work.
4
Correspondence and requests for materials should be addressed to H.R.U. (e-mail: uedah-tky@umin.ac.jp).

Received 16 June 2008; accepted 8 August 2008; published online 21 September 2008; DOI: 10.1038/ncb1775

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

1

A RT I C L E S
a

E4BP4

DBP
TEF
HLF

BMAL2
BMAL1
CLOCK
NPAS2

E/E´box

CRY2

D-box

CRY1
RevErbAa

DEC1
RevErbAb

DEC2
RORa
PER1

RORb

PER2

RORc

RRE

PER3

b
ActivatordGAL4–VP16

SV40
SV40

CCE CCE CCE

Gal4

VP16

Repressor

PEST

dGAL4

NIH3T3 cell
SV40
SV40

CCE CCE CCE

PEST

Gal4

Bioluminescence

OutputdLuc

dGAL4–VP16

dGAL4

UAS UAS UAS UAS

CMVmini

Luc

Luciferin
+ATP

PEST

c
dGAL4–VP16–Flag
0

2

4

6

dGAL4–Flag
0

2

4

6

h M (K)r
30

AntiFlag20
Antitubulin

dGAL4–VP16–Flag
dGAL4–Flag
Relative protein level

Cycloheximide
treatment :

1.0

0.5

0

0

2

4

6

Cycloheximide treatment (h)Figure 1 Using an in cellulo mammalian cell-culture system for the physicalsimulation of natural transcriptional circuits. (a) The natural transcriptional
circuit of mammalian circadian clocks. Clock-controlled elements (CCE;
rectangles), transcriptional activators (green ovals) and repressors (magenta
ovals) are indicated. Grey lines between CCEs and transcription factors(that is, activators or repressors) indicate that the evolutionarily conserved
CCEs are located on the promoter (or enhancer) regions of the respective
transcription factor genes (grey dotted lines indicate putative CCEs determinedby bioinformatics analysis). Green lines from transcriptional activators to CCEs
indicate activation; magenta lines from transcriptional repressors to CCEs
indicate repression. (b) The artificial transcriptional system synthesized in thisstudy. A destabilized (that is, PEST-fused) GAL4–VP16 fusion protein(dGAL4–VP16) and destabilized GAL4 protein (dGAL4) were used as theactivator and repressor, respectively (top and middle). These transcription
factors are expressed under the control of three tandem repeats of clockcontrolled (DNA) elements (CCEs). Once expressed, the artificial activatorand repressor competitively bind the four tandem repeats of the galactose
UAS in the artificial promoter to regulate the output reporter gene, encoding
destabilized luciferase (dLuc, bottom). SV40, SV40 promoter; CMVmini,
minimal CMV promoter. (c) Western blot analysis by cycloheximide treatment
experiments revealed the protein half-life of dGAL4–VP16–Flag or dGAL4–Flag.
The levels of dGAL4–VP16–Flag (white arrowhead) and dGAL4–Flag (blackarrowhead) proteins were normalized by using tubulin-α protein levels as aloading control (left panel). Quantitative densitometric analysis shows thecomparable half-lives of dGAL4–VP16–Flag and dGAL4–Flag to be 3.76 h and2.96 h, respectively (right panel). The protein levels are shown relative to t = 0.

four tandem repeats of the galactose upstream activating sequence(UAS; Supplementary Text and Supplementary Fig. S1a), which arebound by the GAL4 DNA-binding domain (Fig. 1b). This system isdesigned on the basis of a previous finding31 that the hybrid protein
GAL4–VP16 can activate transcription efficiently in mammalian cells
but the GAL4 protein alone cannot. We found that the half-lives of2

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

A RT I C L E S
dGAL4–VP16 and dGAL4 were comparable in our system: 3.76 h and2.96 h, respectively (Fig. 1c). Thus, by extension, the artificial activatorand repressor can competitively regulate the output reporter throughthe UAS. Finally, the artificial activator and repressor are driven by
the SV40 basic promoter fused with three tandem repeats of CCEs
(Supplementary Text and Supplementary Fig. S1b). We control theexpression of these artificial regulators by using either the morning(E´-box), the daytime (D-box) or the night-time (RRE) elements as
the CCEs4. To observe the dynamic behaviour of this artificial circuit,
NIH3T3 host cells were transiently transfected with activator, repressor and reporter plasmids, stimulated with forskolin to synchronize
the circadian rhythmicity of the individual cellular clocks, and thenmonitored in real time for bioluminescence over several days.
We reasoned that if (and only if) the peak timing of the expression(that is, the ‘phase’) of the transcriptional activator(s) and repressor(s)is a good determinant of the phase of the downstream transcriptional
output, it should be possible to generate the natural phases in the clock
cells by using synthetic transcription factors and promoters. If so, thefinding would be remarkable because transcription factors are regulated by various post-transcriptional mechanisms32, including translation33, phosphorylation9,22,34–38, ubiquitylation9,38–40, sumoylation41 andnuclear transportation9,40,42—these post-transcriptional mechanisms arethought to contribute, at least in part, to the phases of the downstream
transcriptional outputs. In other words, a successful reconstruction of
the natural circadian phases would imply that the network structureof transcriptional circuits determines the fundamental timing of theoutputs from the circadian system. After transcription, the system
output timing can then be reinforced or modified by the various posttranscriptional mechanisms listed above.
Proof-by-synthesis of daytime and night-time transcriptional
regulations
Using the artificial circuit system (Fig. 1b), we attempted to test our
hypothesis for daytime output by examining the dynamic behaviour of
the transcriptional output generated by an artificial morning activatorand an artificial night-time repressor, which were controlled by E´-box
elements and RRE elements, respectively. We first confirmed the circadianoscillations of output dLuc messenger RNA (mRNA), as well as the timingof the binding of the activator (dGAL4–VP16) and repressor (dGAL4)
to the UAS—the peak times were at 2.0 h, 3.0 h and 16.0 h before thesecond peak of output luciferase activity, respectively (Fig. 2a, b, andSupplementary Fig. S1c). We noted that the peak time of output mRNA
abundance closely (within about 1.0 h) matched the peak time of theactivator binding in our in cellulo system. Natural circadian systems show
similar timing between the peak times of mRNA output and activatorbinding to the DNA element—at least for E-box activators (BMAL1/
CLOCK)—where the peak time of E-box-controlled mRNA expression
is at zeitgeber time (ZT) 7 (ref. 43) which is in the middle of the range ofpeak time binding of BMAL1/CLOCK to the E-box, ZT 6–8.
When monitored by luciferase activity, the phases of the activator and repressor in this experiment were detected at circadian time(CT) 4.0 ± 0.29 (s.d., n = 3), and CT 17.1 ± 0.37 (n = 3; Fig. 2c andSupplementary Fig. S2a, left). The transcriptional output driven by theseregulators showed circadian oscillation with a phase at CT 7.7 ± 0.85
(n = 4), which is close (1.0 h or less) to the corresponding natural daytime (D-box) phase, CT 8.7 ± 1.13. This result suggests that morning

activation and night-time repression are sufficient to determine thedaytime transcriptional output. High-amplitude circadian oscillation
was not detected by expressing either the morning activator or the nighttime repressor alone (Supplementary Fig. S2b). Even when we used thethymidine kinase (TK) promoter fused with 3 × CCE as a weaker driver,which generates sevenfold less expression than the SV40 promoter(1:(7.28 ± 0.70); Supplementary Fig. S2b, left), we still could not detect
high-amplitude circadian oscillations (Supplementary Fig. S2b). These
results illustrate that the competition between a morning activator andnight-time repressor is essential for generating detectable circadian oscillations during daytime, which confirms observations of natural circadiansystems, in which a morning activator (Dbp, Tef or Hlf) and a night-time
repressor (E4bp4) also competitively bind to the D-box element9,24–26.
Through this competitive binding, we speculate that the D-box element
can integrate both the morning-phase information conferred by its activator (Dbp, Tef or Hlf) and the night-time-phase information conferredby its repressor (E4bp4) to generate the daytime information.
We next tested the hypothesis for night-time output by examining
another artificial circuit, consisting of an artificial daytime activator
under D-box control and a morning repressor under E´-box control(Fig. 2d and Supplementary Fig. S2a, right). When monitored by luciferase activity, the phases of a transcriptional activator and repressor inthis experiment were at CT 8.7 and 9.1 (mean = 8.9, n = 2) and CT 3.8
and 4.0 (mean = 3.9, n = 2), respectively. The transcriptional output
driven by the regulators showed circadian oscillation with its phase at
CT 16.6 ± 1.04 (n = 3), which is also very close (1.0 h or less) to the corresponding natural night-time phase (CT 17.0 ± 0.81). As with the daytime
transcriptional output, a high-amplitude circadian oscillation could not
be generated by expressing the daytime activator or morning repressor
alone (Supplementary Fig. S2b). These results therefore also confirmedthat the competition between a daytime activator and a morning repressor is important in generating detectable circadian oscillation during
the night-time in cells. Together, our reconstruction experiments fordaytime and night-time expressions imply that the input phases of transcription factors can determine the phases of transcriptional output.
Synthesis of novel output phases in cellulo and in vivo
These findings led us to reason that various combinations of transcription
factors with CCEs for the three basic circadian phases (morning, daytime
and night-time) might generate not only the basic phases, such as daytime and night-time, but also other phases. To explore this possibility, we
examined artificial circuits with various other activator–repressor pairs. In
a circuit with an artificial night-time activator under RRE control and a
daytime repressor under D-box control, we observed high-amplitude circadian output with the phase at CT 22.2 ± 0.70 (n = 4), which is 1.8 h before
a subjective dawn (Fig. 3a and Supplementary Fig. S2c, left). We then tested
the remaining combinations of regulators: that is, a night-time activator anda morning repressor, a morning activator and a daytime repressor, and a
daytime activator and a night-time repressor. All of these artificial circuits
showed circadian transcriptional outputs, with phases at CT 20.6 ± 0.91 (s.d,n = 4; a subjective late night), CT 4.7 ± 0.40 (s.d., n = 3; 1.3 h before a subjective noon) and CT 11.0 ± 0.79 (s.d., n = 3; 1.0 h before a subjective dusk),
respectively (Fig. 3b–d and Supplementary Fig. S2c). From these results weconcluded that, through simple combinations of the transcription factorsof the three basic circadian phases, we can generate diverse transcriptional
outputs that peak close to a subjective noon, dawn, dusk or late night.

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

3

A RT I C L E S

0

12

24
Time (h)

36

48

0

Activator: E´-box

0

1

2

4

5

30

16

20

8

10

0

0

12

1

2

24
Time (h)048

36Using dGAL4–Flag
UAS ChIP product by anti-Flag
UAS ChIP product by anti-V5
LUC activity

Activator: D-box

01

Repressor: RRE

0

40

24

d

3

*

Using dGAL4–VP16–Flag
UAS ChIP product by anti-Flag
UAS ChIP product by anti-V5
LUC activity

Luc mRNA using dGAL4–VP16–Flag
Luc mRNA using dGAL4–Flag
LUC activity using dGAL4–VP16–Flag
LUC activity using dGAL4–Flag

c

*

32

2

3

4

5

Repressor: E´-box

3

4

5

0

1

2

3

4

5

Output: UAS

Output: UAS

Normalized bioluminescence

0.5

50

Bioluminescence (103 counts min–1)

1.0

100

0

b

1.5

ChIP abundance (relative to Act-5´ )*150mRNA / Gapdh (average=1)

Bioluminescence (103 counts min–1)

a

High

0

Low
0

1

2

3

4

5

0

1

2

24/0

2

bo

x

20

22

4.0
4

24/0

ox

b
E´-

Output

16.6
16
14

12

Figure 2 Proof-by-synthesis of daytime and night-time transcriptional
regulations. (a) Quantification of the output dLuc mRNA from the artificial
output reporter. The amounts of dLuc mRNA relative to constitutively
expressed Gapdh (glyceraldehyde-3-phosphate dehydrogenase) mRNA(points) are indicated along with the luciferase (LUC) activity (lines) for two
different artificial transcriptional circuits: one using dGAL4–VP16–Flag(green) and another using dGal4–Flag (magenta). The estimated peak of
output dLuc mRNA (marked with an orange asterisk) occurs 2.0 h before thesecond peak of output luciferase activity. (b) Quantification of GAL4–VP16–
Flag and GAL4–Flag bindings to the UAS in artificial transcriptional circuits.
After normalization for the amount of input DNA, the amounts of UAS
regions immunoprecipitated by anti-Flag antibody (squares) and by anti-V5
antibody (triangles) were quantified relative to a constitutively unbound actin
promoter region (Act-5´). These relative amounts of UAS ChIP products areindicated along with the luciferase activity (line) for two different artificialtranscriptional circuits using dGAL4–VP16–Flag (green) and dGAL4–Flag(magenta) (see also Supplementary Fig. S1c for other results of the negative4

Output

6

RRE
x

7.7
8

18

bo

10

3.9
4

D-

x
bo
D- -boxD

14

Repressor

E/

6

RRE
RRE

17.1
16

5

2

20

b
E´-

E'
E/

ox

Activator

E/

18
Repressor

4

–1

Day

Day

22

3

1

10
12

8
8.9
Activator

control). The estimated peak times of UAS ChIP products bound by theactivator (dGAL4–VP16, marked with a green asterisk) and the repressor(dGAL4, marked with a magenta asterisk) were 3.0 and 16.0 h before thesecond peak of output luciferase activity, respectively. (c, d) Synthesis ofdaytime or night-time expressions from two different artificial transcriptional
circuits: morning activator under E´-box control and night-time repressor
under RRE control (c), and daytime activator under D-box control andmorning repressor under E´-box control (d). Heat maps (top) indicate high(magenta) or low (green) representative promoter activities and output ofeach artificial transcriptional circuit monitored by bioluminescence from
NIH3T3 cells. The bioluminescence data were detrended in baseline andamplitude, then normalized to set their maximum, minimum and average
to 1, −1 and 0, respectively (see also Supplementary Fig. S2a for the
raw bioluminescence data). The schemes at the bottom summarize thetimings of peaks (that is, ‘phases’) of promoter activity, where an activator(green oval), repressor (magenta oval) and output reporter (orange oval) areindicated with their phases in circadian time (magenta numbers).

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

A RT I C L E SbActivator : RRE

0

1

0

2
3
4
Repressor : D-box

1

0

2
3
Output : UAS

1

2

5

4

3

0

5

4

Activator : RRE

1

0

1

0

5

2
3
4
Repressor : E´-box

2
3
Output : UAS

1

2

Day
Output3

22.2 24/0
22Output

2

20.6
20

4

ox

22

E

RRE

18

RRE

1

2
3
4
Repressor : D-box

5

0

1

0

1

2
3
Output : UAS

4

5

0

1

0

1

4

5

0

1

2

Activator

3.9
4
ox 4.7
b
´-

E

18

E/

2

12

5

4

5

2

20
Repressor

7.4
8
Repressor

10

18.4
18

ox

4

´-b
/E

E

RRE

6

16

x

14

4

bo

x

16

3
Day
24/0

5

D-

bo

D-

RRE

8

10

12

2
3
Output : UAS

22

Output6

Repressor
3.9
4

2
3
4
Repressor : RRE

Day

20

–1

Activator : D-box

0

24/0

Low

6

x
bo

d

3

2
ox

14

Repressor

Activator : E´-box

22

0

5

b
E´E/

Activator 16.9
16

8
9.0

10

12

2

1

D-

x
bo

14

c

6

D-

16.9
16

5

4

24/0

´-b
/E

Activator

4

High

Day

20
18

5

Normalized bioluminescence

a

14

8

10 9.7
Activator
12 11.0
OutputFigure 3 Synthesis of various output phases from three basic circadianphases in artificial transcriptional circuits. Promoter activities of anactivator, repressor and output reporter in four different artificialtranscriptional circuits: (a) night-time activator under RRE control anddaytime repressor under D-box control, (b) night-time activator under
RRE control and morning repressor under E´-box control, (c) morning

activator under E´-box control and daytime repressor under D-box control,and (d) daytime activator under D-box control and night-time repressor
under RRE control. Heat maps at the top indicate representative
promoter activities, and the schemes at the bottom summarize theresults, as described for Fig. 2 (see also Supplementary Fig. S2c for the
raw bioluminescence data).

Even if the phase of the activator was not changed, an advance or delayin the repressor phase led to a corresponding change in the phase of transcriptional output (Fig. 4a–c). Conversely, a change in the activator phasealso led to a corresponding alteration in the output phase (Supplementary
Fig. S3). We can deduce from these findings that mammalian circadianclocks can start from three basic circadian phases to generate finally,

through the transcriptional cascade, practically continuous phases,
which have been observed in vivo in central and peripheral clock tissues including the suprachiasmatic nucleus, heart and liver8,44–46. This
concept is reinforced by our observations that many transcription factors
are expressed rhythmically at various phases in the liver (Fig. 4d), andthat some seem to be controlled directly by the circadian clock throughnature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

5

A RT I C L E S
d

24/0

2

LD

Repressor: D-box
4
x
o
4.7
-b

20
E´

E/

18

6

RRE
Dx

14

b
22

Activator: D-box

10

12
24/0

8 7.7
Repressor: RRE

2

20

ox

4

´-b
/E

E

18

6

RRE
x
bo

D-

16.6 16
Repressor: E´-box
14

8

Transcription factor genes

bo

16

10
Repressor: RRE

12
11.0

c
Activator: RRE
20.6
Repressor: E´-box 2022.2 Repressor: D-box
24/0
22
2
ox

DD

4

Ssrp1
Nfkb1
Tgif
Nr2f6
Id3
Smad1
Sp3
Isgf3g
Nr5a2
Id2
Gabpa
Nfix
Klf9
Foxd4
Klf9
Pcaf
Ppara
Nfix
Nr1h4
Zfp36
Zbtb7a
Ets1
Foxa3
Cbfb
Esrra
Nr1i3
Onecut1
Irf4
Nr1i3
Ldb2
Hsp90ab1
Zfpn1a2
Gata2
Nr0b2
Id1

0

´-b
/E

12

24

36

E

18

6

RRE

+2.5

bo

Dx

16
14

12

0
4
8
12
16
20
24
28
32
36
40
44

22

Activator: E´-box

0
4
8
12
16
20
24
28
32
36
40
44

a

8

44 0
Time (h)

12

24

36

44

0
–2.5
Expression level

10

Figure 4 Transcriptional mechanisms to generate various output phases.
(a–c) Output phases in artificial transcriptional circuits with a morning
activator (a), daytime activator (b) or night-time activator (c). The phase ofan output reporter (green lines and numbers) is indicated in circadian time(hours) for each repressor used. In artificial transcriptional circuits
in cellulo, the output phase could be changed according to the input phaseof the repressor even if that of the activator was unchanged. (d) In vivo
periodic gene expression of various known transcription factors in mouse
liver under light/dark (LD) and constant darkness (DD) conditions. Columns
represent time points, and rows represent the probe sets for transcription
factors. The expression levels of each probe set were normalized so that theiraverage and standard deviation were set to 0 and 1, respectively.

E-boxes, D-boxes or RREs (Supplementary Table S1). Furthermore, transcriptional activator(s) and repressor(s) binding to similar DNA elements
are expressed at various phases in vivo (Supplementary Table S1), andare therefore expected, from our in cellulo findings, to generate additional output phases.

using an activator, a repressor and an output reporter. To implement
this transcriptional system numerically, we searched for the sets ofparameters that could reproduce the observed reporter output of thein cellulo mammalian cell-culture system (see Supplementary Text).
We then plotted the theoretical relationship between the output phases(the delay/advancement of output expressions) and the input phases(the phase differences between activators and repressors; Fig. 5a) andfound that the experimental data (coloured dots) matched the theoreticalplot (black line). This supported the ‘repressor-precedes-activator’ and‘activator-precedes-repressor’ mechanisms for the output phases. These
repressor-precedes-activator and activator-precedes-repressor mechanisms can delay or advance the default output phase (Fig. 5a, dashed line)
to generate new output phases, respectively (see also Fig. 5a, green circle
and square), which probably serve to create the seemingly continuous
output phases observed in vivo8,44–46.
We also plotted the theoretical relationship between the relative amplitudes of outputs and the input phases (the phase differences between
activators and repressors; Fig. 5b). We noticed that some outliers had

Transcriptional logic underlying mammalian circadian clocks
On the basis of the findings in this study, we can now examine two
predictions on the timing (‘phase’) and relative amplitude of circadian
output oscillations in our previous report4, which proposed that thephase advancement of a repressor relative to an activator causes a phasedelay of expression (‘repressor-precedes-activator’ mechanism), whereas
the phase advancement of an activator relative to a repressor causes aphase advancement of expression (‘activator-precedes-repressor’ mechanism). The previous paper also proposed that a larger phase difference
between an activator and a repressor generates a greater relative amplitude of output rhythm (‘repressor-antiphasic-to-activator’ mechanism).
To verify these predictions, we modelled the transcriptional system by
6

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

A RT I C L E SaCircadian expression of activator ( αA ,γA )dInput transcription factors
5

Morning activator/night-time repressor
Daytime activator/morning repressor
Night-time activator/daytime repressor
Morning repressor/night-time activator
Daytime repressor/morning activator
Night-time repressor/daytime activator
Activator/repressor in same phase

0
–5

–10

0.6

Relative amplitude

Output – activator (h)(protein level)

10

0.4
0.2

–10 –50
510Activator – repressor (h)

c

5.0

2.5

0

0

1

2

Day

*

3

4

5

0.4

0.2

0
0

–10 –50
510Activator – repressor (h)2468
Ratio of activator to repressor(promoter activity)

0.4

0 µg
0.1 µg0.3 µg0.6 µg0.9 µg1.2 µg1.5 µg

*

0.3
0.2
0.1
0
DBP

E4BP4

9

0.9

0 µg
0.1 µg0.3 µg0.6 µg0.9 µg1.2 µg1.5 µg6

Relative amplitude

Bioluminescence (106 counts min–1)

DBP

*

0.2
0

–10
–5
0
5
10
Activator – repressor (h)

7.5

0.4

0.6

Relative amplitude

*

0.2
0

e

*

0.6

Bioluminescence (106 counts min–1)*

Relative amplitude(protein level)

0.6

×2

Circadian expression of repressor ( αR ,γR )0.8

Relative amplitude

Relative amplitude(protein level)

0.8

0.4

×1

0

–10 –50
510Activator – repressor (h)

b

×0.5

3

0

0

1

2

Day

3

4

5

0.6

0.3

0
E4BP4

Figure 5 Transcriptional logic underlying mammalian circadian clocks.
(a) Observed and simulated relationships between input transcription
factors and the phase of the output reporter. Axes represent the phasedifferences (hours) between activator and repressor (x axis) and between
output and activator (y axis). Points show the means of the measurement data
(duplicated independently)—different point colour and shape combinations
represent different transcription factor combinations. The curve shows asimulated relationship calculated from a theoretical model. The dashedline (at about +4 h) shows the default output reporter phase that occurs
when a repressor is antiphasic to an activator. (b) Observed and simulated
relationships between input transcription factors and the relative amplitudeof the output reporter. The y axis represents the relative amplitude of theoutput reporter. The curve shows a simulated relationship calculated fromour theoretical model. The points marked with an asterisk indicate outliers
that have a lower relative amplitude (by 0.2 or more) than the predictedcurve. (c) Observed relationships between the changes in expression levels
of input transcription factors and the relative amplitude of the output

reporter. The x axis represents the ratio of activator expression to repressor
expression. The outlier points marked with an asterisk indicate experiments
in which there was a large difference (more than fourfold) in the expression
levels of activator relative to repressor (the points marked with an asterisk
here are consistent with the outliers from b). (d) The predicted sensitivityof the relative amplitude when the circadian expression of an activator or arepressor is changed fourfold (proportional changes in the expression level oftranscription factor affect both amplitude α and baseline γ simultaneously).
Activator or repressor expression levels were varied fourfold (from ×0.5 to×2); the coloured curves indicate the predicted effects of these changes in
expression levels of transcription factors on relative amplitude of reporter
output. (e) Perturbation experiments of natural transcriptional circuits.
The relative amplitudes of luciferase activity are derived from the raw
bioluminescence data of a daytime output reporter (p3 × D-box-SV40-dLuc)for various amounts of activator (DBP from p3 × E´-box-SV40-Dbp) or
repressor (E4BP4 from p3 × RRE-SV40-E4bp4). Shown are the averages of
the raw bioluminescence data from two or three independent samples.

a lower relative amplitude (by 0.2 or more; Fig. 5b, asterisked) than thepredicted curve (Fig. 5b, black line), which seems to have been due to thelarger changes (fourfold or more) in the expression levels of activator or
repressor (Fig. 5c). These results are consistent with the prediction fromthe sensitivity analysis of the relative amplitude and phase for a simulation
model with representative parameter values (Supplementary Text andSupplementary Fig. S4), in which the increased circadian expression ofactivator (simultaneous increase in both amplitude αA and baseline γA)
can decrease the relative amplitude of output oscillations (Fig. 5d), while
not greatly affecting the output phase (Supplementary Fig. S4a, panels
enclosed in the frame). Aside from the outliers (which are due to thegreater expression of the activator), experimental data (Fig. 5b, coloureddots) matched the theoretical plot (Fig. 5b, black line), supporting the‘repressor-antiphasic-to-activator’ mechanism for the relative amplitude.

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

7

A RT I C L E SThis ‘repressor-antiphasic-to-activator’ mechanism is intuitive because
it probably reflects the number of hours during which the activator canactivate before the repressor begins to repress. However trivial it may
seem, this intuitive repressor-antiphasic-to-activator mechanism is nontrivial and is even critical in generating higher-amplitude promoter activity in living cells, because no detectable oscillations are generated when arepressor is expressed in phase with an activator in various combinations(Supplementary Fig. S2d) or when an activator or repressor is expressedalone (Supplementary Fig. S2b).
Perturbation experiments of the natural transcriptional circuit inmammalian circadian clocks
One of the benefits and meanings of theoretical analysis is its formulation of a prediction that, if verified, leads us to a deeper understanding of
the system in question. As discussed above, our simulation model withrepresentative parameter values (see Supplementary Text) shows thatan increase in circadian expression of an activator or repressor causes
a decrease or an increase, respectively, in the relative amplitudes of theoutputs (Fig. 5d). We reasoned that if (and only if) our simulation model
could recapitulate the natural circadian system, it should be possible toapply the predictions derived from our simulation model to the naturaltranscriptional circuit in mammalian circadian clocks. To verify our
predictions, we performed two perturbation experiments to increase thecircadian expression of a natural activator, DBP, or repressor, E4BP4, by
using p3 × E´-box-SV40-Dbp or p3 × RRE-SV40-E4bp4, respectively.
As predicted, the relative amplitude of a natural downstream output
from the D-box element, which is monitored by p3 × D-box-SV40-dLuc,is decreased (0.68-fold) or increased (1.76-fold) by the increase in circadian expression of activator or repressor, respectively (Fig. 5e). On
the basis of these results, we concluded that both our simulation modeland the derived design principles successfully recapitulated the naturaltranscriptional circuit in the mammalian circadian clocks.
Discussion
In this study we successfully reconstructed two natural phases of the circadian clock (that is, daytime and night-time expression). The probability
that any artificially generated peak will lie within 1 h of the naturally
observed output peak is 2 in 24 (or 0.083) at best. The chance that twoof two experiments would produce outputs within a 1 h difference fromthe targets is therefore 0.083 × 0.083 = 0.0069 (less than 0.05). Even if we
adopt more stringent statistical criteria (the probability that two of threebasic phases would be generated), the chance is (number of ways of selecting any 2 from 3) × 0.083 × 0.083 × (1 − 0.083) = 0.0191 (less than 0.05).
On the basis of these calculations, we conclude that our reconstruction of
two natural phases in the circadian clock is statistically significant.
In this study we focused mainly on the competitive binding between
transcription activators and repressors that control the phase and amplitude of the circadian output oscillations in mammalian circadian clocks.
However, in the natural circadian clock systems of mammals and otherorganisms, transcription factors undergo various types of post-transcriptional regulation9,22,32,34–42 such as modification and degradation, which
may also contribute to the timing of the output phase and its amplitude.
It will therefore be important in future to incorporate such post-transcriptional regulation into our in cellulo system to investigate its physicalrole in a circadian system. For example, it is already known that the VP16
polypeptide used in our in cellulo system is subject to ubiquitylation,
8

which is important in transcriptional activation47. Once the VP16-specificubiquitin ligase has been identified (it is as yet unidentified) it can beapplied to our in cellulo system to investigate the impact of the posttranscriptional regulation on the circadian output oscillations.
In theory, the design principles described here for the phase and relative amplitude in mammalian circadian clocks can also be applied to thepost-transcriptional regulation of transcription factors in mammals andother organisms, thereby allowing one to predict whether cyclic posttranscriptional regulation—depending on its phase—advances or delays
the phase of the output, and whether it increases or decreases the relative
amplitude of the output. For instance, the WC-1–WC-2 activator complex isexpressed rhythmically by post-transcriptional regulation, whereas the wc-1
and wc-2 mRNAs in the Neurospora clock system are expressed constantly.
The WC-1–WC-2 activator complex peaking at CT 17–18 and the FRQ
repressor peaking at CT 8–10 drives many clock-controlled genes, and theovert rhythm in banding peaks at about CT 22 (refs 48, 49). This is quiteconsistent with the behaviour of our artificial circuit, in which an artificialnight-time activator under RRE control (peaking at about CT 17–18) anda daytime repressor under D-box control (peaking at about CT 8) yielda high-amplitude circadian output whose phase is at CT 22.2—about
1.8 h before subjective dawn (Fig. 3a). This consistency implies a generalapplicability of the transcriptional logic that we describe in this study.
In summary, this study presents a synthetic approach to the ‘proof-bysynthesis’ of transcriptional logic. This approach provides us with a new
strategy, not only to investigate the sufficiency of identified componentsof transcriptional circuits and their interactions, but also to reveal as
yet unidentified components or interactions. For example, although we
successfully (re)generated two basic phases, daytime and night-time, as
well as additional phases near the subjective noon, dawn, dusk and latenight, from the three basic circadian phases, we have not yet been able
to regenerate one basic circadian phase, morning, which we expect to be
regulated directly or indirectly by the three basic phases, to maintain circadian oscillations. Thus, in our in cellulo study, morning transcriptional
regulation is still a ‘missing link’ in the mammalian clock system. Because
a strong repressor at evening phase seems indispensable to the reconstruction of the morning phase, a candidate transcription factor could be
CRY1, which is a transcriptional repressor expressed during the evening4.
However, the expression regulation mechanism of the Cry1 gene remains
unknown because more than one DNA element seems involved in theexpression4. Hence, the challenge of synthesizing evening and morning
expression still lies ahead as we work towards the complete reconstructionof the transcriptional circuits underlying mammalian circadian clocks.
Methods
Construction of plasmid pG4-dLuc, p3 × CCE-SV40-dGAL4–VP16 andp3 × CCE-SV40-dGal4. To construct the output reporter plasmids, the pG5Luc(containing five UAS) plasmid in the CheckMate Mammalian Two-Hybrid system(Promega) was modified to contain four tandem repeats of the galactose UASs anda gene encoding destabilized luciferase (dLuc) as follows: pG5Luc was digested
with EcoRI and NheI, blunted with T4 DNA polymerase, and ligated with itself.
The product was then digested with SphI and SalI, ligated to the SphI–SalI fragment from the SV40-dLuc plasmid, containing the PEST sequence of dLuc4, andtermed pG4-dLuc. To construct activator or repressor plasmids, we modified thepBIND and pACT (Promega) vectors as follows. We amplified the VP16 coding
sequences from pACT (Promega) by PCR with a forward primer containing an
EcoRV recognition sequence (5´-GATATCCTCGACGGCCCCCCCGACCG-3´) and a reverse primer containing a NotI recognition sequence (5´-GCGGCCGCTCTAGATGGCGATCCCGGACCCGGGGAATC-3´). The PCR product was thendigested with EcoRV and NotI, and then fused to the Gal4 gene in the pBIND vector.
nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

A RT I C L E S
A PEST fragment, amplified from the SV40-dLuc plasmid by PCR with forward(5´-ATGCGGTACCAGCCATGGCTTCCCGCCG-3´) and reverse (5´-CGTGG
GTACCCACATTGATCCTAGCAGAAGC-3´) primers containing the KpnI recognition sequence, was inserted into the VP16-fused and original pBIND vectors,
previously digested with KpnI. These products were termed pCMV-dGAL4–VP16
and pCMV-dGal4, respectively. To drive the artificial activator or repressor in threebasic circadian phases (morning, daytime or night-time), p3 × CCE-SV40-dLuc
plasmids4—which contained the Per2 E´-box (5´-gcgcgcgcggtCACGTTttccactatgtg
acagcggagg-3´), the Per3 D-box (5´-cccgcgcgTTATGTAAggtactcg-3´) or the Bmal1
RRE (5´-aggcagAAAGTAGGTCAgggacg-3´) as a CCE (CCEs are indicated with
underlines)—were digested with KpnI and HindIII, blunted by T4 DNA polymerase,and inserted into the BglII and NheI site of pCMV-dGAL4–VP16 or pCMV-dGal4.
The end products, p3 × CCE-SV40-dGAL4–VP16 and p3 × CCE-SV40-dGal4, wereused as the activator or repressor plasmids for the artificial transcription circuits.
Real-time circadian reporter assays. Real-time circadian assays were performed as
described previously4,29, with the following modifications. NIH3T3 cells (American
Type Culture Collection) were grown in DMEM medium (Invitrogen) supplemented
with 10% FBS (JRH Biosciences) and antibiotics (25 U ml−1 penicillin, 25 mg ml−1
streptomycin; Invitrogen). At 24 h before transfection, cells were plated at 105 cells
per well in 35-mm dishes. These cells were transfected with FuGene6 (Roche) in
accordance with the manufacturer’s instructions. The cells in each well were transfected with three plasmids (0.4 µg of dLuc reporter plasmid, 0.025 µg of p3 × CCESV40-dGAL4–VP16 and 0.1 µg of p3 × CCE-SV40-dGal4). As the dLuc reporter
plasmid we used p3 × CCE-SV40-dLuc4 for monitoring the promoter activity of theartificial transcription factors, or pG4-dLuc for monitoring the transcriptional output
in artificial transcriptional circuits. The amount of transfected plasmid was adjusted
to 2.0 µg with empty vector. 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; Invitrogen), 0.1 mM luciferin (Promega), antibiotics and 0.01 µM forskolin(Nacalai Tesque). Bioluminescence was measured with photomultiplier tube detector assemblies (LM2400; Hamamatsu Photonics). The modules and cultures weremaintained in a darkroom at 30 °C and interfaced with computers for continuous
data acquisition. Photons were counted for 1 min at 12-min intervals.
Rhythmicity, period length and phase analysis of real-time bioluminescencedata. The rhythmicity and period length of the promoter activity for each reporter
were determined as described previously29. Bioluminescence time-series data weredetrended by subtracting the trend curve of a 42 h timescale, calculated by thesmoothing spline method with corresponding stiffness29, and then used in the following analysis. Autocorrelation of the detrended time-series data was then calculated within the range 16–28 h to determine the circadian period of oscillation,
which was defined to provide the strongest autocorrelation. Statistical significance(with p = 0 as most significant and p = 1 as least significant) of the circadian oscillation was evaluated by comparing the strongest autocorrelation of the detrended data
within the range 16–28 h against that of white noise (p < 0.01). The periods of threedLuc reporters (two p3 × CCE-SV40-dLuc reporters for monitoring the promoter
activity of the activator or repressor, and a pG4-dLuc reporter for monitoring thepromoter activity of the output reporter) were calculated for each artificial circuit,and the mean value of the three periods was considered the ‘circuit period.’
To calculate the normalized bioluminescence data (that is, the oscillatorycomponent of the bioluminescence data) shown in Fig. 2c–d and Fig. 3a–d, themoving average of the absolute value of the detrended bioluminescence data
was calculated first. The window size of the moving average was set to half of thecircuit period calculated above. Then the oscillatory component of the detrended
data was calculated by dividing the data by the moving average of the data at eachtime point. To calculate the peak time, a cosine curve was fitted to have maximum
correlation with the normalized bioluminescence data. The peak time of the fitted
cosine curve was used as the phase of each reporter.
Calculation of natural output phases of the E´-box, the D-box and the RRE. For
comparison with the artificial output phases, the natural output phases controlled by the CCEs were determined as follows. NIH3T3 cells were transfected with
p3 × CCE-SV40-dLuc, the dLuc gene being driven by the SV40 basic promoter
fused with three tandem repeats of CCEs, and then monitored for 5 days foreach CCE (n = 25–30). The means and standard deviations of the phase for the
CCEs were 3.8 ± 0.84 (E´-box), 8.7 ± 1.13 (D-box) and 17.0 ± 0.81 (RRE) in CT,

where we define CT 0 as the time of forskolin stimulation. These mean values
were regarded as the natural output phases for the morning (E´-box), daytime(D-box) and night-time (RRE) elements in the experiments.
GeneChip expression data. The previously published genome-wide expression
data for the liver8 were re-analysed and re-annotated in this study, as describedin detail in Supplementary Methods.
Theoretical model of the circadian circuit. Our theoretical model is based on the formula in our previous report4 and has been extended to introduce basal transcription,
degradation of mRNAs, and the translation and degradation of proteins to express theamount of the output proteins. The model comprises five formulas: the protein levelsof the activator and repressor, the transcriptional activity of the output reporter, themRNA level of the output reporter, and the protein level of the output reporter.
The protein levels of the activator and repressor are modelled as the sum ofan oscillating component and a constant component. A formula for the protein
level of an activator at time t is

A(t) ≡ αA 1 + cos 2π

t −α

+γA

24

where αA, a and γA are the amplitude, phase and constant component of the activator, respectively. A formula for the protein level of a repressor at time t isR(t) ≡ αR 1 + cos 2π

t−b

+γR

24

where αR, b and γR are the amplitude, phase and constant component of the repressor, respectively.
The transcriptional activity of an output reporter at time t is formulated as
A(t)KA

T (t) ≡ V1

n

n

1+

A(t)
KA

n

+

+β

R(t)
KR

where 1/KA and 1/KR are the strengths of the binding affinities of the activator andrepressor, respectively. The constants KA and KR are inversely proportional to thestrengths of the binding affinities (the larger the values of KA and KR, the weaker
the binding), n is the Hill coefficient, β is the basal transcriptional activity andV1 is the efficiency of transcription.
The mRNA and protein levels of an output reporter, M(t) and P(t), are modelled using differential equations, and formulated asdM(t) = T(t) −
dt

log 2
T1

d
P(t) = V2M (t) −
dt

M(t)

log 2
T2

P(t)

where V2 is the efficiency of translation, and T1 and T2 are the half-life of themRNA and protein, respectively.
Detailed information of the other experimental and computational methods
is described in Supplementary Methods.
Note: Supplementary Information is available on the Nature Cell Biology website.
Acknowledgements
This research was supported by an intramural Grant-in-Aid from CDB (H.R.U.), theUehara Memorial Foundation (H.R.U.) and 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.). We thank Hideki Ukai for
critical discussion, Rikuhiro G. Yamada and Tetsuya J. Kobayashi for programming thereal-time bioluminescence data analysis, Yuichi Kumaki for the Promoter Database, andErik A. Kuld, Douglas Sipp and Michael Royle for critical reading of the manuscript.

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

9

A RT I C L E S
Author contributions
H.R.U. developed the concept of the proof-by-synthesis of the transcriptional logic
underlying mammalian circadian clocks. M.U. constructed all materials used in thiswork and performed the real-time luminescence assays. T.K. developed the data
analysis methods for the in cellulo and in silico data, and conducted these analyses.
All the authors discussed the results and commented on the manuscript text.
Competing financial interests
The authors declare no competing financial interests.
Published online at http://www.nature.com/naturecellbiology/
Reprints and permissions information is available online at http://npg.nature.com/
reprintsandpermissions/
1. Hogenesch, J. B. et al. Characterization of a subset of the basic-helix–loop–helix-PAS
superfamily that interacts with components of the dioxin signaling pathway. J. Biol.
Chem. 272, 8581–8593 (1997).
2. Gekakis, N. Role of the CLOCK protein in the mammalian circadian mechanism.
Science 280, 1564–1569 (1998).
3. Yoo, S. H. et al. A noncanonical E-box enhancer drives mouse Period2 circadian oscillations in vivo. Proc. Natl Acad. Sci. USA 102, 2608–2613 (2005).
4. Ueda, H. R. et al. System-level identification of transcriptional circuits underlying
mammalian circadian clocks. Nature Genet. 37, 187–192 (2005).
5. Falvey, E., Marcacci, L. & Schibler, U. DNA-binding specificity of PAR and C/EBP
leucine zipper proteins: a single amino acid substitution in the C/EBP DNA-binding
domain confers PAR-like specificity to C/EBP. Biol. Chem. 377, 797–809 (1996).
6. Harding, H. P. & Lazar, M. A. The orphan receptor Rev-ErbAα activates transcription
via a novel response element. Mol. Cell. Biol. 13, 3113–3121 (1993).
7. Preitner, N. The orphan nuclear receptor REV-ERBα controls circadian transcription
within the positive limb of the mammalian circadian oscillator. Cell 110, 251–260(2002).
8. Ueda, H. R. et al. A transcription factor response element for gene expression during
circadian night. Nature 418, 534–539 (2002).
9. Reppert, S. M. & Weaver, D. R. Coordination of circadian timing in mammals. Nature
418, 935–941 (2002).
10. Bunger, M. K. Mop3 is an essential component of the master circadian pacemaker inmammals. Cell 103, 1009–1017 (2000).
11. King, D. P. Positional cloning of the mouse circadian clock gene. Cell 89, 641–653(1997).
12. Reick, M., Garcia, J. A., Dudley, C. & McKnight, S. L. NPAS2: an analog of clock
operative in the mammalian forebrain. Science 293, 506–509 (2001).
13. Okano, T., Sasaki, M. & Fukada, Y. Cloning of mouse BMAL2 and its daily expression
profile in the suprachiasmatic nucleus: a remarkable acceleration of Bmal2 sequence
divergence after Bmal gene duplication. Neurosci. Lett. 300, 111–114 (2001).
14. Zheng, B. et al. The mPer2 gene encodes a functional component of the mammalian
circadian clock. Nature 400, 169–173 (1999).
15. Shearman, L. P., Jin, X., Lee, C., Reppert, S. M. & Weaver, D. R. Targeted disruptionof the mPer3 gene: subtle effects on circadian clock function. Mol. Cell. Biol. 20,
6269–6275 (2000).
16. Zheng, B. Nonredundant roles of the mPer1 and mPer2 genes in the mammalian
circadian clock. Cell 105, 683–694 (2001).
17. Cermakian, N., Monaco, L., Pando, M. P., Dierich, A. & Sassone-Corsi, P. Alteredbehavioral rhythms and clock gene expression in mice with a targeted mutation in the
Period1 gene. EMBO J. 20, 3967–3974 (2001).
18. Bae, K. Differential functions of mPer1, mPer2, and mPer3 in the SCN circadian clock.
Neuron 30, 525–536 (2001).
19. van der Horst, G. T. Mammalian Cry1 and Cry2 are essential for maintenance of circadian rhythms. Nature 398, 627–630 (1999).
20. Vitaterna, M. H. et al. Differential regulation of mammalian period genes and circadianrhythmicity by cryptochromes 1 and 2. Proc. Natl Acad. Sci. USA 96, 12114–12119(1999).
21. Honma, S. Dec1 and Dec2 are regulators of the mammalian molecular clock. Nature
419, 841–844 (2002).
22. Lowrey, P. L. Positional syntenic cloning and functional characterization of the mammalian circadian mutation tau. Science 288, 483–491 (2000).

10

23. Xu, Y. et al. Functional consequences of a CKIδ mutation causing familial advanced
sleep phase syndrome. Nature 434, 640–644 (2005).
24. Lavery, D. J. et al. Circadian expression of the steroid 15 α-hydroxylase (Cyp2a4) andcoumarin 7-hydroxylase (Cyp2a5) genes in mouse liver is regulated by the PAR leucine
zipper transcription factor DBP. Mol. Cell. Biol. 19, 6488–6499 (1999).
25. Gachon, F. et al. The loss of circadian PAR bZip transcription factors results in epilepsy.
Genes Dev. 18, 1397–1412 (2004).
26. Mitsui, S., Yamaguchi, S., Matsuo, T., Ishida, Y. & Okamura, H. Antagonistic role of
E4BP4 and PAR proteins in the circadian oscillatory mechanism. Genes Dev. 15,
995–1006 (2001).
27. Sato, T. K. A functional genomics strategy reveals Rora as a component of the mammalian circadian clock. Neuron 43, 527–537 (2004).
28. André, E. et al. Disruption of retinoid-related orphan receptor β changes circadianbehavior, causes retinal degeneration and leads to vacillans phenotype in mice. EMBO
J. 17, 3867–3877 (1998).
29. Sato, T. K. et al. Feedback repression is required for mammalian circadian clock function. Nature Genet. 38, 312–319 (2006).
30. Akashi, M. & Takumi, T. The orphan nuclear receptor RORα regulates circadian transcription of the mammalian core-clock Bmal1. Nature Struct. Mol. Biol. 12, 441–448(2005).
31. Sadowski, I., Ma, J., Triezenberg, S. & Ptashne, M. GAL4–VP16 is an unusually potent
transcriptional activator. Nature 335, 563–564 (1988).
32. Gallego, M. & Virshup, D. M. Post-translational modifications regulate the ticking of
the circadian clock. Nature Rev. Mol. Cell Biol. 8, 139–148 (2007).
33. Kojima, S., Hirose, M., Tokunaga, K., Sakaki, Y. & Tei, H. Structural and functional
analysis of 3´ untranslated region of mouse Period1 mRNA. Biochem. Biophys. Res.
Commun. 301, 1–7 (2003).
34. Lee, C., Etchegaray, J., Cagampang, F. R., Loudon, A. S. & Reppert, S. M.
Posttranslational mechanisms regulate the mammalian circadian clock. Cell 107,
855–867 (2001).
35. Eide, E. J., Vielhaber, E. L., Hinz, W. A. & Virshup, D. M. The circadian regulatory
proteins BMAL1 and cryptochromes are substrates of casein kinase Iepsilon. J. Biol.
Chem. 277, 17248–17254 (2002).
36. Sanada, K., Okano, T. & Fukada, Y. Mitogen-activated protein kinase phosphorylates
and negatively regulates basic helix–loop–helix-PAS transcription factor BMAL1. J.
Biol. Chem. 277, 267–271 (2002).
37. Toh, K. L. et al. An hPer2 phosphorylation site mutation in familial advanced sleep
phase syndrome. Science 291, 1040–1043 (2001).
38. Yin, L., Wang, J., Klein, P. S. & Lazar, M. A. Nuclear receptor Rev-erbα is a critical lithium-sensitive component of the circadian clock. Science 311, 1002–1005(2006).
39. Akashi, M., Tsuchiya, Y., Yoshino, T. & Nishida, E. Control of intracellular dynamics ofmammalian period proteins by casein kinase I ε (CKIε) and CKIδ in cultured cells. Mol.
Cell. Biol. 22, 1693–1703 (2002).
40. Yagita, K. et al. Nucleocytoplasmic shuttling and mCRY-dependent inhibition of ubiquitylation of the mPER2 clock protein. EMBO J. 21, 1301–1314 (2002).
41. Cardone, L. et al. Circadian clock control by SUMOylation of BMAL1. Science 309,
1390–1394 (2005).
42. Vielhaber, E. L., Duricka, D., Ullman, K. S. & Virshup, D. M. Nuclear export of mammalian PERIOD proteins. J. Biol. Chem. 276, 45921–45927 (2001).
43. Ripperger, J. A. & Schibler, U. Rhythmic CLOCK-BMAL1 binding to multiple E-box
motifs drives circadian Dbp transcription and chromatin transitions. Nature Genet.
38, 369–374 (2006).
44. Akhtar, R. A. et al. Circadian cycling of the mouse liver transcriptome, as revealed by cDNA
microarray, is driven by the suprachiasmatic nucleus. Curr. Biol. 12, 540–550 (2002).
45. Panda, S. et al. Coordinated transcription of key pathways in the mouse by the circadianclock. Cell 109, 307–320 (2002).
46. Storch, K. F. et al. Extensive and divergent circadian gene expression in liver and heart.
Nature 417, 78–83 (2002).
47. Salghetti, S. E., Caudy, A. A., Chenoweth, J. G. & Tansey, W. P. Regulation of transcriptional activation domain function by ubiquitin. Science 293, 1651–1653 (2001).
48. Lee, K., Loros, J. J. & Dunlap, J. C. Interconnected feedback loops in the Neurospora
circadian system. Science 289, 107–110 (2000).
49. Dunlap, J. C. et al. A circadian clock in Neurospora: how genes and proteins cooperate
to produce a sustained, entrainable, and compensated biological oscillator with a period
of about a day. Cold Spring Harb. Symp. Quant. Biol. 72, 57–68 (2007).

nature cell biology advance online publication© 2008 Macmillan Publishers Limited. All rights reserved.

s u p p l e m e n ta r y i n f o r m at i o n

2

3

4

5

Repressor

6000000020000023451200000

2xUAS

150000RRE

11000004000000

50000
0CT17.71 ± 0.19
0

1

2

3

Day

4

5

Bioluminescence (counts/min)

00600000Relative Amplitude

Relative Amplitude

0.6

0200000100000

0.2
0

Day

4

5

1

2

3

4

5

0

2

3

2

3

4

5

3xRRE

800000

-1

40

24

30

CT2.6 ± 0.09

16

20

0

1

2

3

4

5

8

10

2xRRE

0

0

12

24

36

48

0

Time (h)1000000
5000004000000CT16.8 ± 0.08
0

1

2

3

4

0

5

2400002000001200001000000CT8.4 ± 0.14
01

CT16.7 ± 0.02
0300000

UAS

2

3

4

0

5

1

2

5

5xUAS

4

5

CT9.5 ± 0.21
0

1

2

3

Day

Relative Amplitude
2xCCE

0.4

3xCCE

0.3

4

32

40

24

30

16

20

8

10

0
0

12

24

36

48

Time (h)05Using dGAL4-VP16-Flag
Tbp-5’ ChIP product by anti-Flag
Tbp-5’ ChIP product by anti-V5
LUC activity
Using dGAL4-Flag
Tbp-5’ ChIP product by anti-Flag
Tbp-5’ ChIP product by anti-V5
LUC activity

0.2
0.1
0

1500000

3

UAS

Day

CT8.58 ± 0.171401500000

0.5

0

32

3

1

4xUAS

2000000
30360000CT9.09 ± 0.06
02500000
2

5

CT2.3 ± 0.09

300000

3xUAS
5xUAS

4

200000

2xUAS
4xUAS

0.4

3

400000400000

1xUAS

2

3xUAS

5000000.8

1Output2000000

3000006000000

Bioluminescence (10 counts min )1

1200000

Relative Amplitude

00

2xE’-box

600000-1

CT3.45 ± 0.08

Repressor

0

3xE’-box

1800000

3

40000

900000

Bioluminescence (10 counts min )2000000

1xUAS
Activator

80000

c
2400000

ChIP abundance (relative to Act-5’ )Bioluminescence (counts/min)E’-box

4000000b

Output

120000ChIP abundance (relative to Act-5’ )Activator

6000000

Bioluminescence (counts/min)

a

2

3

Day

4

5

1000000
5000000CT8.53 ± 0.23
0

1

2

3

4

5

Day

Supplementary Figure S1

Figure S1 Evaluating our in cellulo mammalian cell culture system. a,
Determination of number of UASs in the artificial promoter to regulate theoutput reporter gene. We first constructed reporter vectors, varying the number
of UAS (from 1 through 5) on the promoter driving a reporter gene (dLuc).
We transfected them with a morning activator and a night-time repressor into
NIH3T3 cells and then monitored the bioluminescence from the cells. The raw
bioluminescence data from two independent samples are shown. The relative
amplitudes of each output signal from two independent samples are also
shown (lower left panel). b, Determination of number of CCEs in the artificial
promoter to regulate the activator and repressor genes. We first constructed
two sets of vectors with two and three copies of the clock-controlled elements(CCE; E’-box from the Per2 gene, or RRE from the Bmal1 gene) on promotersdriving a reporter gene (dLuc), an artificial activator gene (dGal4-VP16) or an
artificial repressor gene (dGal4). We then monitored their promoter activities(either 2× or 3× E’-box, and either 2× or 3× RRE) as well as the output

Ukai-Tadenuma et al.

(UAS) from artificial transcriptional circuits with a morning activator and anight-time repressor. The raw bioluminescence data from two independent
samples are shown. The relative amplitudes of each output signal from two
independent samples are also shown (lower left panel). c, Negative controls
for quantification of GAL4-VP16-FLAG and GAL4-FLAG bindings to the UAS
in the artificial transcriptional circuits. After normalization for the amount of
input DNA, the amount of Tbp promoter (Tbp-5’) region immunoprecipitatedby anti-FLAG antibody (squares) and by anti-V5 antibody (triangles) were
quantified relative to a constitutively unbound region (Act-5’). These relative
amounts of Tbp-5’ ChIP products are indicated along with the LUC activity(line) for two different artificial transcriptional circuits using dGAL4-VP16FLAG (green) and dGAL4-FLAG (magenta). ChIP assays were performed withthe artificial transcriptional circuit (morning activator and night-time repressor)
in NIH3T3 cells at 4-h intervals for 24 h with anti-FLAG antibody and anti-V5
antibody as negative control.

www.nature.com/naturecellbiology

1© 2008 Macmillan Publishers Limited. All rights reserved.

s u p p l e m e n ta r y i n f o r m at i o n

b

2

3

4

5

Output

1

2

3

4

5

1800000

9000001200000

600000300000600000

RRE
0

1

2

3

4

5

0
900000200000600000100000
0

1

2

3

4

SV40
0

1

2

3

4

5

75000
50000
25000
0

5

TK
0

1

2

3

4

5

Day

300000100000

UAS
0

1

2

3

4

5

0

3000000

2400000

Output200000E’-box03000000D-box
02400000

1200000

00

morning (E’ -box)

1

day-time (D-box)

E’-box01000000

UAS
0

1

2

Day

3

4

5

SV40

180000500000120000250000

60000

0

0

1

30000

16000

20000

8000

10000
0

1

2

3

4

0

5

0

1

2

3

4

5

30000

1000000
0

1

2

3

4

1800000

0

5

1

2

3

4

5

0

1

2

3

4

5

0

1

2

3

4

5

16000
10000

0

1

2

3

4

0

5

24000045000

160000

30000

80000

15000

8000
0

1

2

3

4

5

0

32000
24000
16000

1200000
600000
0

0

24000

20000

60000
0

0
32000

120000

0

1

2

3

4

0

5

0

1

2

Day

3

4

0

5

8000
0

1

2

3

4

5

0

Day

Day

Day

2000000

2400000

6000006000001500000

1800000

4000004000001000000

1200000

200000
0

0

1

2

3

4

500000200000

RRE
5

0

RRE
0

1

2

3

4

5

0

1800000

7500004500000

1200000

5000003000000

6000002500001500000

600000E’-box
0

1

2

3

4

5

0

Activator
Repressor

800000

D-box
0

1

2

3

4

5

320000240000160000

0

D-box
0

1

2

3

4

5

0

E’-box
0

1

2

3

4

5

300000

0

1

2

3

4

5

0

3000000

15000000

4500000

2000000

10000000

3000000

1000000

5000000

0E’-box
0

1

2

3

0

1

2

3

4

5

4

0

5

1500000

D-box
0

1

2

3

4

5

0

3000000

2400000

2400000

2000000

1600000

1600000

1000000

800000

RRE
0

UAS
0

1

2

3

4

5

0

0

RRE
0

1

2

3

0

1

2

3

4

5

800000

UAS
1

2

3

4

5

0

UAS

Day

Day

24000012000020000045Day160000

80000

100000100000

50000
0

80000

D-box

1600002000001500000

Bioluminescence (counts/min)

800000

OutputActivator

0

5

24000

d
Bioluminescence (counts/min)

Repressor

4

TK

32000

40000

180000Day

250000

Output

3

SV40

50000

240000

c

UAS
0

1

2

3

Day

4

5

0

80000

40000

UAS
0

1

2

Day

3

4

5

0

UAS
0

1

2

3

4

5

0

UAS
0

1

Day

Figure S2 Raw bioluminescence data from artificial transcriptional circuitswith various combinations of activators and repressors. a, Synthesis of daytime and night-time expressions in two different artificial transcriptional
circuits. Promoter activities of an activator, repressor, and output reporterin two different artificial transcriptional circuits: (left) morning activator
under E’-box control and night-time repressor under RRE control, and(right) day-time activator under D-box control and morning repressor
under E’-box control. b, High-amplitude transcriptional oscillation cannot
be generated by an activator or a repressor alone. (left) The activities of
the SV40 promoter and thymidine kinase (TK) promoter. The promoter
activities were monitored by bioluminescence from NIH3T3 cells, whichwere transfected SV40-dLuc and TK-dLuc. The transcriptional activityof TK promoter indicates lower expression than SV40 promoter (1:7.28± 0.70). (right) Promoter activities of the output reporter in six different
artificial transcriptional circuits. The promoters used to regulate theactivator and repressor genes were SV40 promoter (SV40, left panels) and
TK promoter (TK, right panels): morning activator or repressor alone (upper2

2

Repressor only
TK

2400007500002000000

Output02000000

300000

OutputBioluminescence (counts/min)

1000000

Bioluminescence (counts/min)

6000000

2000000

Bioluminescence (counts/min)

Activator

3000000

1500000

Repressor

40000010000000

4000000

Activator only

night-time (RRE)

a

2

Day

3

4

5

Supplementary Figure 2

Ukai-Tadenuma et al.

panels), day-time activator or repressor alone (middle panels) and nighttime activator or repressor alone (lower panels). c, Synthesis of various
phases from three basic circadian phases in artificial transcriptional
circuits. Promoter activities of an activator, a repressor, and an output
reporter in four different artificial transcriptional circuits: (left) nighttime activator under RRE control and day-time repressor under D-box
control, (middle left) night-time activator under RRE control and morning
repressor under E’-box control: (middle right) morning activator underE’-box control and day-time repressor under D-box control: and (right)
day-time activator under D-box control and night-time repressor under
RRE control. d, Promoter activity in artificial transcriptional circuits witha repressor in phase with an activator. Promoter activities of an activator,
repressor, and output reporter in three different artificial transcriptional
circuits: (left) morning activator and repressor both under E’-box control:(middle) day-time activator and repressor both under D-box control: and(right) night-time activator and repressor both under RRE control. The raw
bioluminescence data from two independent samples are shown.

www.nature.com/naturecellbiology© 2008 Macmillan Publishers Limited. All rights reserved.

s u p p l e m e n ta r y i n f o r m at i o nabRepressor : E’-box

Activator : RRE

20.6

22

22.2

24/0

20

RRE

20

4.7
18

10

16
14

4
6

RRE

x

12

x

'bo

E
E/

Activator : E’-box

8

2

bo

14

24/0

D-

10

16

x

12

4
6

bo

x

14

8

x

D-

bo

16

Activator : D-box

22

'bo

E
E/

18

Repressor : RRE

2

20

4
6

RRE

24/0

D-

16.6

x

'bo

E
E/

18

Activator : RRE 222c

Repressor : D-box

12

10

8

7.7

Activator : E’-box

11.0

Activator : D-box

Supplementary Figure 3

Figure S3 Transcriptional mechanisms to generate novel phases. Output
phases in artificial transcriptional circuits with a morning repressor(a), day-time repressor (b), or night-time repressor (c). The phase of an
output reporter (magenta lines and numbers) is indicated in circadianUkai-Tadenuma et al.

time (h) with the activator used (bold black). In artificial transcriptional
circuits in cellulo, the output phase could be changed according to
the input phase of the activator, even if that of the repressor was
unchanged.

www.nature.com/naturecellbiology

3© 2008 Macmillan Publishers Limited. All rights reserved.

s u p p l e m e n ta r y i n f o r m at i o n

Phase of repressor b
10

5

5

0

0

-5

-5

-10

Mean=1.01h-0.5 (h)-10Mean=0.55h

0

-5

-5

-5

-10

Mean=2.40h

Mean=2.86h-10Efficiency of transcription V1

Efficiency of transclation V2

Binding affinity of repressor 1/K R
10

10

10

10

5

5

5

5

5

5

0

0

0

0

0

0

-5

-5

-5

-5

-5

-5

Mean=2.80h-10

Mean=0.09h

10

5

5

0

0

Mean=2.24h-10

Mean=2.06h

Circadian expression of Repressor (R , R )

10

10

5

5

0

0

-5

-5

Phase of activator a-10

Mean=0h

Mean=0h

-10

-10
-5
0
5
10
Activator - Repressor (h)Phase of activator a
Phase of repressor b
Amplitude of activator α A
Amplitude of repressor α R
Baseline constant of activator γ A
Baseline constant of repressor γ R
Circadian expression of activator (α A,γ A )Circadian expression of repressor (α R, γ R)
Binding affinity of activator 1/ KA
Binding affinity of repressor 1/KR
Basal transcription β
Efficiency of transcription V1
Efficiency of transclation V2
Half-life of mRNA T1
Half-life of protein T2

0.5

1
1.5
Sensitivity (h)

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

Mean=0.10h

Phase of repressor b

Amplitude of activator A-0.5 (h)×0.5

Amplitude of repressor R

0.8

0.7
0.6

0.8

0.6

0.5
0.4

0.6

0.4

0.4

0.3
0.2

Baseline constant of activator A

0.2

0.2

0.1

0

+0.5 (h)

-10
-5
0
5
10
Activator - Repressor (h)

×2

-10
-5
0
5
10
Activator - Repressor (h)Binding affinity of repressor 1/K R

0

0

0
-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)Basal transcription 

Efficiency of transcription V1

Efficiency of transclation V2

Baseline constant of repressor R

Binding affinity of activator 1/K A

0.6

0.7

0.7

0.6

0.6

0.6

0.6

0.6

0.5

0.5

0.5

0.5

0.5

0.4

0.4

0.4

0.4

0.4

0.3

0.3

0.3

0.3

0.3

0.2

0.2

0.2

0.2

0.2

0.1
0

0.4
0.3
0.2
0.1

0.1

0.1

0.1

0

0

0

0

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)Half-life of protein T2

Half-life of mRNA T1
0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0

0
-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)Supplementary Figure 4

-10
-5
0
5
10
Activator - Repressor (h)

d

0.1

0.1

2

-10
-5
0
5
10
Activator - Repressor (h)

0.6

0.5

Mean=0h

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)0-10Mean=0.09h

-10
-5
0
5
10
Activator - Repressor (h)

0

b

-10
-5
0
5
10
Activator - Repressor (h)Circadian expression of Activator (A , A)-10

Mean=0.10h-5-5Basal transcription 

-10
-5
0
5
10
Activator - Repressor (h)Half-life of protein T2

10

-10

-10

-10
-5
0
5
10
Activator - Repressor (h)Mean=2.38h

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)Relative amplitude

Output - Activator (h)0Binding affinity of activator 1/K A

-10
-5
0
5
10
Activator - Repressor (h)Output - Activator (h)

5

0

10

-10

Relative amplitude

5

10

Half-life of mRNA T1

0.1
0
-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)

10
5
0
-5
-10
Activator - Repressor (h)Phase of activator a
Phase of repressor b
Amplitude of activator α A
Amplitude of repressor α R
Baseline constant of activator γ A
Baseline constant of repressor γ R
Circadian expression of activator (α A,γ A )Circadian expression of repressor (α R, γ R)
Binding affinity of activator 1/ KA
Binding affinity of repressor 1/KR
Basal transcription β
Efficiency of transcription V1
Efficiency of transclation V2
Half-life of mRNA T1
Half-life of protein T2

Ukai-Tadenuma et al.

Figure S4 Sensitivity of the output phase and the relative amplitude to eachparameter. a, The sensitivity of the output phase over -12 < a-b < 12 isshown when each parameter value was changed by 1 hour (a and b) or 4-fold(the others). X-axis represents the advance of a repressor compared to an
activator (h) (phase difference between an activator and repressor), while
Y-axis represents the delay of an output reporter compared to an activator(h) (phase difference between an output reporter and activator). The effectsof simultaneous increases in both absolute amplitude and base-line levelsof an input activator (αA and γA) or repressor (αR and γR) are also shown inthe boxed-panel (inbox). The black curve shows a simulation model withrepresentative parameter values of one hundred fitted parameter sets; theother curves show changed values for sensitive analysis. b, The simulatedsensitivity of the output phase to the parameter describing each process.
Each bar shows the average phase difference obtained by changing its
original parameter value by 1 hour (parameter a and b) or 4-fold (other

4

10

5

-10

×2

Baseline constant of activator A

10

-10
-5
0
5
10
Activator - Repressor (h)

-10
-5
0
5
10
Activator - Repressor (h)Relative amplitude+0.5 (h)Amplitude of repressor R

10

Baseline constant of repressor R-10

Relative amplitude

×0.5

Parameters

Output - Activator (h)

-10
-5
0
5
10
Activator - Repressor (h)cAmplitude of activator A

Output - Activator (h)Phase of activator a
10

Parameters

Output - Activator (h)

a

0

0.05

0.1
0.15
0.2
0.25
Sensitivity (Relative Amplitude)

0.3

parameters). Each error bar represents standard error. These values were
calculated from 100 simulations with trimming of the 5% outliers. c, Thesensitivity of the relative amplitude over -12 < a-b < 12 is shown when eachparameter value was changed by 1 hour (a and b) or 4-fold (the others).
X-axis represents the advance of a repressor compared to an activator(h) (phase difference between an activator and repressor), while Y-axis
represents the relative amplitude of oscillation of output protein (dLUC)
activity. The black curve shows a simulation model with representative
parameter values of one hundred fitted parameter sets; the other curves
show changed values for sensitive analysis. d, The simulated sensitivityof the relative amplitude to the parameter describing each process. Eachbar shows the average relative amplitude difference obtained by changing
its original parameter value by 1 hour (parameter a and b) or 4-fold (otherparameters). Each error bar represents standard error. These values were
calculated from 100 simulations with trimming of the 5% outliers.

www.nature.com/naturecellbiology© 2008 Macmillan Publishers Limited. All rights reserved.

Supplementary Text

Determination of number of the galactose upstream activating sequences.
The number of the galactose upstream activating sequences (UASs) was determined by
the following experiments.

We constructed reporter vectors with varying numbers of

UAS (from 1 through 5) on the promoter driving dLuc output, reporter, transfected thevector into NIH3T3 cells and then monitored bioluminescence from the transfected cells(Supplementary Fig. 1a).

We observed that reporter vectors with 1 or 2×UAS did notexhibit high-amplitude oscillations, while those with 3, 4, and 5×UAS produced
high-amplitude oscillations in comparable phases.

In this manuscript, we adopt

4×UAS because outputs with 4×UAS results in the relative amplitudes with the smallest
variation (Supplementary Fig. 1a lower left).

Determination of number of the clock-controlled elements.
To determine the number of clock-controlled elements (CCE) that we should use todrive activator/repressor expression, we constructed two sets of vectors containing
either two or three copies of the CCEs on promoters driving dLuc reporter or artificial
activators/repressors, and monitored their promoter activities and transcriptional output(Supplementary Fig. 1b).

Via bioluminescence, we observed that promoter activities

and outputs for both 2 and 3×CCE exhibited comparable phases and relative amplitudes(Supplementary Fig. 1b lower left).

Although we could have used 2xCCE, we opted

to use 3×CCE in our system, because it has been the construct used since our preceding
works1.

© 2008 Macmillan Publishers Limited. All rights reserved.

Comparison of the previous predictions and the numerical experimental data
The predictions of repressor-antiphasic-to-activator and repressor-precedes-activatormechanisms in the previous report1 is well matched with our numerical experimental
data although we should give attention to the difference of the transcription activity thatwas evaluated in the previous model and the output protein activities that were
measured in our experiment.

Due to transcription and translation of an output reporter,

the simulation model with representative parameter values (black line in Fig. 5a) in ourcurrent manuscript has an approximately 4-hour delay from the previous model. Thisdelay is comparable to the delay estimated from our experiment in Fig. 2a and b, where
the peak-time of dGAL4-VP16 binding to UAS and peak-time of Luciferase mRNA are
about 3.0-hour and 2.0-hour before that of output Luciferase activity, respectively, andthus the delay between transcription activity and output protein was estimated as about
2.0–3.0 hours.

Sensitivity analysis of the phase and relative amplitude of the output oscillations
We calculated the sensitivity of the phase and the relative amplitude of the output
oscillation to each parameter by changing the parameter's value by 4-fold (from 1/2- to
2-times the original parameter value) (Supplementary Fig. 4a, c), except for the input
phase of the transcriptional factors, which we changed by 1 h (from a 0.5-h delay to
0.5-h in advance of the original phase).

By repeating this procedure for 100 fitted

parameter sets, we also evaluated the average contribution of each process(Supplementary Fig. 4b, d).

2© 2008 Macmillan Publishers Limited. All rights reserved.

As expected from our in cellulo mammalian cell culture system results (Figs.
4a-c), the phase difference of input transcription factors can contribute to the output
phase in silico (Supplementary Fig. 4b).

For example, a 1-h alteration in the phase ofan activator or a repressor led to ~1 h changes in the output phase (0.98 h for a and 0.62
h for b).

In addition, the absolute amplitude and base-line level of the input

transcription factor phases contributed to the output phase: a 4-fold parameter change in
the absolute amplitude (αA and αR) or the absolute base-line level (γA and γR) of anactivator or repressor could alter the output phase by 1 ~ 2 h (0.95 h for αA, 1.77 h for αR,
0.70 h for γA and 1.03 h for γR).

However, the effects of absolute amplitudes andbase-line levels on output phase seemed to cancel out when they were both increased
simultaneously. This was because the effects of simultaneous increases of both absolute
amplitude and base-line levels of the inputs are smaller than independent increases inabsolute amplitude or base-line levels (0.33 h for αA and γA, and 0.80 h for αR and γR and
see also Supplementary Fig. 4a inbox).

We noted that binding affinities of the input

activator or repressor onto the promoters (1/KA, or 1/KR) are theoretically equivalent tothe simultaneous increase of αA and γA, or αR and γR, respectively (0.33 h for 1/KA and
0.80 h for 1/KR).

We also noted that the half-life of the mRNA or protein of a reporter(1.07 h for T1 and 2.14 h for T2) contributed more to the output phase than the reporter'stranscription or translation processes (<0.01 h for β, V1 and V2), which implies that thedegradation process can cause output phases to be fairly continuous, as is observed invivo2-5.
As for the contribution of input transcription factors to the relative amplitude of
the output oscillations (Supplementary Fig. 4d), we find that the absolute amplitudes
and base-line levels of the inputs have larger effects than the phases of the inputs (0.15
for αA, 0.12 for αR, 0.12 for γA and 0.08 for γR, 0.03 for a, 0.03 h for b). Interestingly,
these effects of absolute amplitudes and base-line levels of the inputs do not seem to3© 2008 Macmillan Publishers Limited. All rights reserved.

cancel out much when both are increased simultaneously since the effects ofsimultaneous increase of both absolute amplitude and base-line levels of the inputs are
similar to, or greater than, those of either absolute amplitude or base-line levels of the
inputs (0.16 for αA and γA, and 0.14 for αR and γR and see also Fig. 5d).

Hence, weobserve a marked contrast to the output phase, implying that absolute circadian
expression levels of the inputs seem to play a key role in controlling the relative
amplitudes of outputs.
To recap, we noted: 1) that binding affinity of the input activator or repressor
onto the promoters (1/KA, or 1/KR) are theoretically equivalent to the simultaneous
increase of αA and γA, or αR and γR, respectively (0.16 for 1/KA and 0.14 for 1/KR), and;2) that the half-life of the mRNA or protein of a reporter (0.08 for T1 and 0.28 h for T2)
also contributed to the relative amplitude of the output

Interestingly, however, basaltranscription is more important for the relative amplitude of the output than theefficiencies of transcription and translation (0.15 for β, <0.001 for V1 and V2).

4

© 2008 Macmillan Publishers Limited. All rights reserved.

Supplementary Methods

Construction of pCMV-dGal4-VP16-Flag and pCMV-dGal4-Flag.

To construct

Flag-tagged activator and repressor plasmids regulated by CMV promoter, theFlag-PEST coding DNA fragment, amplified from the pCMV-dGal4 plasmid (SeeMethods in main text) by PCR with forward(5'-GGCCGCAGGTACCGACTACAAGGATGACGATGACAAGAGCCATGGCTTCCC
GCCGGCGGTG-3') and reverse(5'-TTATTCAGGTACCCACATTGATCCTAGCAGAAGC-3') primers containing the
KpnI recognition sequence (under line) and Flag coding sequence (italics), was inserted
into the VP16-fused and original pBIND vectors (Promega, See Methods in main text),
previously digested with KpnI. These products were termed pCMV-dGal4-VP16-Flagand pCMV-dGal4-Flag, respectively, and used for Western Blot analysis.

Measurement of protein half-lives of dGAL4-VP16-FLAG and dGAL4-FLAG.
NIH3T3 cells (American Type Culture Collection) were grown in DMEM (Invitrogen)supplemented with 10% FBS (JRH Biosciences) and antibiotics (25 U/ml penicillin, 25
mg/ml streptomycin; Invitrogen).

Cells were plated at 1×106 cells per dish in 90-mm

dishes 24 h before transfection.

These cells were transfected with FuGene6 (Roche)

according to the manufacturer's instructions. The cells in each well were transfectedwith 12 µg of pCMV-dGal4-VP16-Flag or pCMV-dGal4-Flag.
in each well were harvested and plated in 6 35-mm dishes.

After 24 h, the cells

After 48 h, the cells weretreated with cycloheximide (CHX, SIGMA) at a final concentration of 100 µg/ml until
their harvest. The treated cells were harvested at 0, 2, 4 and 6 h and used for Western
Blot Analysis.

5© 2008 Macmillan Publishers Limited. All rights reserved.

For Western Blot Analysis, each nuclear and cytoplasmic fraction was
extracted from the harvested cells with NE-PER Nuclear and Cytoplasmic Extraction
Reagents (PIERCE). Each cell lysate was applied to a lane of polyacrylamide gels.
For immunoblot analysis, proteins were transferred to PVDF membranes.

Anti-FLAG

M2 monoclonal Antibody-Peroxidase Conjugate (SIGMA) was diluted 2000-fold andused for detection of dGAL4-VP16-FLAG and dGAL4-FLAG protein.

Anti-Tubulinα

monoclonal antibody (clone DM1A, LAB VISION) was diluted 330-fold, and used for
detection of Tubulinα protein as internal control. For visualization, ECL Plus Western
Blotting Detection System (GE Healthcare) and LAS-1000 (FUJIFILM) were usedaccording to the manufacturer's instructions.

Construction of plasmid pG1-dLuc, pG2-dLuc, pG3-dLuc and pG5-dLuc.

To

construct the output reporter plasmids, the pG5Luc (containing five UAS) plasmid in
the CheckMate Mammalian Two-Hybrid system (Promega) was modified to containone, two or three tandem repeats of the galactose upstream activating sequences (UAS)
and a gene encoding destabilized luciferase (dLuc) as follows.

pG5Luc was digested

with XbaI (partial digestion) and EcoRI (for remaining one UAS), XhoI and NheI (forremaining two UAS), or XhoI and EcoRI (for remaining three UAS). These digested
vectors were blunted by T4 DNA Polymerase, and ligated with itself.

The products

and pG5Luc (Promega) were then digested with SphI and SalI, ligated to the SphI-SalI
fragment from the SV40-dLuc plasmid, which contains the PEST sequence of the dLuc1
and termed pG1-dLuc (containing one UAS), pG2-dLuc (containing two UAS),
pG3-dLuc (containing three UAS), and pG5- dLuc (containing five UAS). These
constructs were used as the reporter plasmids for the artificial transcription circuits.

6© 2008 Macmillan Publishers Limited. All rights reserved.

Real-time circadian reporter assays using reporter vectors with UAS (1-5×).
Real-time circadian assays were performed as previously described1,6 with the following
modifications.

NIH3T3 cells (American Type Culture Collection) were grown in

DMEM (Invitrogen) supplemented with 10% FBS (JRH Biosciences) and antibiotics(25 U/ml penicillin, 25 mg/ml streptomycin; Invitrogen).

Cells were plated at 1×105

cells per well in 35-mm dishes 24 h before transfection.

These cells were transfectedwith FuGene6 (Roche) according to the manufacturer's instructions.

The cells in eachwell were transfected with three plasmids (0.4 µg of dLuc reporter plasmid, 0.025 µg of
p3×E'-box-SV40-dGal4-VP16, and 0.1 µg of p3×RRE-SV40-dGal4).

As the dLuc

reporter plasmid, we used p3×E'-box-SV40-dLuc and p3×RRE-SV40-dLuc1 formonitoring the promoter activity of the artificial transcription factors, or pG1-dLuc,
pG2-dLuc, pG3-dLuc, pG4-dLuc , and pG5-dLuc for monitoring the transcriptional
output in the artificial transcriptional circuits. The amount of transfected plasmid was
adjusted to 2.0 µg with empty vector.

After 72 h, the media in each well was replacedwith 2 ml of culture medium (DMEM/10% FBS) supplemented with 10 mM HEPES(pH 7.2, Invitrogen), 0.1 mM luciferin (Promega), antibiotics, and 0.01 µM forskolin(Nacalai Tesque).

Bioluminescence was measured with photomultiplier tube (PMT)

detector assemblies (LM2400, Hamamatsu Photonics).

The modules and cultures

were maintained in a darkroom at 30°C and interfaced with computers for continuous
data acquisition.

Photons were counted for 1 min at 12-min intervals.

Construction of plasmid p2×CCE-SV40-dLuc, p2×CCE-SV40-dGal4-VP16 andp2×CCE-SV40-dGal4.

To construct activator or repressor plasmids regulated by twotandem repeated clock-controlled element (CCE), we modified the pCMV-dGal4-VP16
or pCMV-dGal4 vectors as follows. The oligonucleotides containing two tandem
repeat sequences of CCEs were annealed, and inserted into MluI/BglII site of the7© 2008 Macmillan Publishers Limited. All rights reserved.

SV40-dLuc vectors1. These products (p2×CCE-SV40-dLuc plasmids) were digested
with KpnI and HindIII, blunted by T4 DNA polymerase, and inserted into the BglII and
NheI site of pCMV-dGal4-VP16 or pCMV-dGal4. The end products,
p2×CCE-SV40-dGal4-VP16 or p2×CCE-SV40-dGal4, and the intermediate productp2×CCE-SV40-dLuc were used as the activator or repressor plasmids for the artificialtranscription circuits, and as the reporter plasmid for promoter activity, respectively.

The oligonucleotide sequence for two tandem repeated clock-controlled element.
2× Per2 E'-box-forward:
5'-CGCGGCGCGCGCGGTCACGTTTTCCACTATGTGACAGCGGAGGGCGCGCG
CGGTCACGTTTTCCACTATGTGACAGCGGAGG-3'
2× Per2 E'-box-reverse:
5'-GATCCCTCCGCTGTCACATAGTGGAAAACGTGACCGCGCGCGCCCTCCGCTGTCACATAGTGGAAAACGTGACCGCGCGCGC-3'
2× Bmal1 RRE-forward:
5'-CGCGAGGCAGAAAGTAGGTCAGGGACGAGGCAGAAAGTAGGTCAGGGA
CG-3'
2× Bmal1 RRE-reverse:
5'-GATCCGTCCCTGACCTACTTTCTGCCTCGTCCCTGACCTACTTTCTGCCT-3'

Real-time circadian reporter assays using artificial activator and repressor derived
by 2×CCE-SV40 promoters.

Real-time circadian assays were performed aspreviously described1,6 and as mentioned above with the following modifications.

8© 2008 Macmillan Publishers Limited. All rights reserved.

NIH3T3 cells were plated at 1×105 cells per well in 35-mm dishes 24 h before
transfection, and were transfected with FuGene6. The cells in each well weretransfected with three plasmids (0.4 µg of dLuc reporter plasmid, 0.025 µg of
p2×E'-box-SV40-dGal4-VP16, and 0.1 µg of p2×RRE-SV40-dGal4).

As the dLuc

reporter plasmid, we used p2×E'-box-SV40-dLuc and p3×RRE-SV40-dLuc1 formonitoring the promoter activity of the artificial transcription factors, and pG4-dLuc formonitoring the transcriptional output in artificial transcriptional circuits.
of transfected plasmid was adjusted to 2.0 µg with empty vector.

The amount

After 72 h, the media

in each well was replaced with 2 ml of culture medium including 0.01 µM forskolin.
Bioluminescence was measured with photomultiplier tube (PMT) detector assemblies(LM2400) in a darkroom at 30°C.

Construction of p3×E'-box-SV40-dGal4-VP16-Flag andp3×RRE-SV40-dGal4-Flag.

To construct Flag-tagged activator and repressor

plasmids regulated by E'-box and RRE, the Flag-PEST coding DNA fragment,
amplified from the pCMV-dGal4 plasmid (See Methods in main text) by PCR withforward(5'-GGCCGCAGGTACCGACTACAAGGATGACGATGACAAGAGCCATGGCTTCCC
GCCGGCGGTG-3') and reverse(5'-TTATTCAGGTACCCACATTGATCCTAGCAGAAGC-3') primers containing the
KpnI recognition sequence (under line) and Flag sequence (italics), was inserted into
the KpnI sites of p3×E'-box-SV40-dGal4-VP16 and p3×RRE-SV40-dGal4 vectors (SeeMethods in main text), that were previously digested with KpnI. These products weretermed p3×E'-box-SV40-dGal4-VP16-Flag and p3×RRE-SV40-dGal4-Flag, and used
for Chromatin Immunoprecipitation assay.

9© 2008 Macmillan Publishers Limited. All rights reserved.

Chromatin Immunoprecipitation (ChIP) assay and Quantitative PCR of ChIP
pruduct.

NIH3T3 cells (American Type Culture Collection) were grown in DMEM

(Invitrogen) supplemented with 10% FBS (JRH Biosciences) and antibiotics (25 U/ml
penicillin, 25 mg/ml streptomycin; Invitrogen). Cells were plated at 1×106 cells perdish in 14 90-mm dishes 24 h before transfection. These cells were transfected with
FuGene6 (Roche) according to the manufacturer's instructions.

The cells in each dishwere transfected with three plasmids ({8 µg of pG4-dLuc, 4.8 µg of
p3×E'-box-SV40-dGal4-VP16-Flag and 19.2 µg of p3×RRE-SV40-dGal4} and {8 µgof pG4-dLuc, 4.8 µg of p3×E'-box-SV40-dGal4-VP16 and 19.2 µg of
p3×RRE-SV40-dGal4-Flag}).

After 24 h, the cells in each well were harvested andplated in 14 90-mm dishes and two 35-mm dishes. After 48 h, the media in each dishwas replaced with 10 ml of culture medium (DMEM/10% FBS) supplemented with 10
mM HEPES (pH 7.2, Invitrogen), antibiotics, and 0.01 µM forskolin (Nacalai Tesque),and cultured at 30°C.

After 12, 16, 20, 24, 28, 32, 36 h from the stimulation, thetreated cells were fixed with 1% paraformaldehyde by a set of two dishes and used for
Chromatin Immunoprecipitation.

In the same time, bioluminescence was measured

with photomultiplier tube (PMT) detector assemblies (LM2400, Hamamatsu Photonics)
with the cells in 35-mm dishes, which was replaced with 2 ml of culture medium(DMEM/10% FBS) supplemented with 10 mM HEPES (pH 7.2, Invitrogen), 0.1 mM
luciferin (Promega), antibiotics, and 0.01 µM forskolin (Nacalai Tesque). The
modules and cultures were maintained in a darkroom at 30°C and interfaced withcomputers for continuous data acquisition.

Photons were counted for 1 min at 12-minintervals.
Chromatin Immunoprecipitation assays with these NIH3T3 cells were
performed as previously described7 with the following modifications. In this report,

10© 2008 Macmillan Publishers Limited. All rights reserved.

we used Chromatin Immunoprecipitation Assay Kits (Upstate Biotechnology),
anti-FLAG M2 antibody (Sigma) and anti-V5 antibody (Sigma).

Protein G-Sepharose(GE Healthcare) was used for precipitation of antibody/protein immune complexes.
The resulting precipitated DNA was quantified by quantitative PCR.

Quantitative

PCR was performed using ABI Prism 7700 and Power SYBR Green Reagents (Applied
Biosystems).Samples contained 1×Power SYBR Green Master Mix (Applied
Biosystems), 0.5 µM primers and 1/25 ChIP product DNA in a 10 µl volume. The
PCR conditions were as follows: 10 min at 95ºC, then 45 cycles of 15 s at 94ºC, 30 s at
59ºC and 1 min at 72ºC.

Absolute DNA abundance was calculated using the standard

curve obtained from NIH3T3 cell's genomic DNA and pG4-dLuc plasmid. The Act
promoter (Act-5') and Tbp promoter (Tbp-5') regions were used as the internal control.

Primer sequence for Quantitative PCR of ChIP product.
UAS-forward: 5'-TAGGCTGTCCCCAGTGCAAG-3'
UAS-reverse: 5'-CGATAGAGAAATGTTCTGGCAC-3'
Act-5'-forward: 5'-CCAAGAGGCTCCCTCCACA-3'
Act-5'-reverse: 5'-GTGCAAGGGAGAAAGATGCC-3'
Tbp-5'-forward: 5'-GAGAGCATTGGACTCCCCAG-3'
Tbp-5'-reverse: 5'-AGCACCCACATGGCTACTCAC-3'

Quantitative PCR of dLuc mRNA.

NIH3T3 cells were transfected on the same

condition as ChIP assay (as described above), and harvested at same timing of ChIP
assay.

Total RNAs were purified from the harvested cells using TRIzol reagent(Invitrogen), and treated with DNaseI with RNeasy kit (QIAGEN) and RNase-free

11© 2008 Macmillan Publishers Limited. All rights reserved.

DNase set (QIAGEN) according to the standard protocol.

The cDNA was synthesizedfrom 0.25 µg of total RNA with random 6mer (Promega) and Superscript II Reverse
Transcriptase (Invitrogen) according to the standard protocol.

Quantitative PCR was

performed using ABI Prism 7700 and Power SYBR Green Reagents (Applied
Biosystems).

Samples contained 1×Power SYBR Green Master Mix (Applied

Biosystems), 0.5 µM primers and 1/20 synthesized cDNA in a 10 µl volume. The
PCR conditions were as follows: 10 min at 95ºC, then 45 cycles of 15 s at 94ºC, 30 s at
59ºC and 1 min at 72ºC.

Absolute cDNA abundance was calculated using the standard

curve obtained from NIH3T3 cell's genomic DNA and pG4-dLuc plasmid.

GapdhmRNA expression levels were quantified and used as the internal control.

Primer sequence for Quantitative PCR of mRNA.
Luciferase-forward: 5'-CTTACTGGGACGAAGACGAACAC-3'
Luciferase-reverse: 5'-GAGACTTCAGGCGGTCAACG -3'
Gapdh-forward: 5'-CAAGGAGTAAGAAACCCTGGACC-3'
Gapdh-reverse: 5'-CGAGTTGGGATAGGGCCTCT-3'

Peak-time estimation of transcription factors' binding and Luciferase mRNA.
First, we chose the largest points in the latter 4 time points (24 h - 36 h) for thedGAL4-VP16-FLAG ChIP and the Luciferase mRNA experiments, and the largest
point in the former 4 time points (12 h - 24 h) for the dGAL4-FLAG ChIP experiment.
Next, we fitted a quadratic function to 3 time points around the largest point for eachexperiment, and identified the top of the function as a peak-time of the experiment.
The peak-times were converted into circadian time by using periods of simultaneously

12© 2008 Macmillan Publishers Limited. All rights reserved.

measured Luciferase activities (21.66 for the Luciferase mRNA experiments, and 20.92
for the ChIP experiments), by the function: (the raw peak-time / the period of theLuciferase activity) * 24.

Construction of plasmid p3×CCE-TK-dGal4-VP16 and p3×CCE-TK-dGal4. To
construct activator or repressor plasmids regulated by thymidine kinase (TK) promoter,
we modified the pCMV-dGal4-VP16 or pCMV-dGal4 vectors as follows.

We

amplified the TK promoter sequences from pMU2-P(TK) (unpublished, the origin of
TK promoter was phRL-TK (Promega)) by PCR with a forward primer containing an
BglII recognition sequence (5'-ATATATAGATCTCTAGCCCGGGCTCGAGATC-3')
and a reverse primer containing a NheI recognition sequence(5'-GTAGTAGCTAGCCCGTTATAGTTACTGCAGAAGC-3').

The PCR productwas then digested with BglII and NheI, and inserted in the pCMV-dGal4-VP16 or
pCMV-dGal4 vectors, that were previously digested with BglII and NheI. To drive theartificial activator or repressor by CCE, the oligonucleotides containing three tandem
repeat sequences of CCEs were annealed, and inserted into BglII site of thepTK-dGal4-VP16 or pTK-dGal4 vectors.

The end products,

p3×CCE-TK-dGal4-VP16 and p3×CCE-TK-dGal4 plasmids, were used as the activatoror repressor plasmids for the artificial transcription circuits.

The oligonucleotide sequence for three tandem repeated clock-controlled element.
3× Per2 E'-box-forward:
5'-GATCGCGCGCGCGGTCACGTTTTCCACTATGTGACAGCGGAGGGCGCGCG

13© 2008 Macmillan Publishers Limited. All rights reserved.

CGGTCACGTTTTCCACTATGTGACAGCGGAGGGCGCGCGCGGTCACGTTTTCCACTATGTGACAGCGGAG-3'
3× Per2 E'-box-reverse:
5'-GATCCTCCGCTGTCACATAGTGGAAAACGTGACCGCGCGCGCCCTCCGCTGTCACATAGTGGAAAACGTGACCGCGCGCGCCCTCCGCTGTCACATAGTGG
AAAACGTGACCGCGCGCGC-3'
3× Per3 D-box-forward:
5'-GATCCCCGCGCGTTATGTAAGGTACTCGCCCGCGCGTTATGTAAGGTACTCGCCCGCGCGTTATGTAAGGTACTCG-3'
3× Per3 D-box-reverse:
5'-GATCCGAGTACCTTACATAACGCGCGGGCGAGTACCTTACATAACGCGCG
GGCGAGTACCTTACATAACGCGCGGG-3'
3× Bmal1 RRE-forward:
5'-GATCAGGCAGAAAGTAGGTCAGGGACGAGGCAGAAAGTAGGTCAGGGACGAGGCAGAAAGTAGGTCAGGGACG-3'
3× Bmal1 RRE-reverse:
5'-GATCCGTCCCTGACCTACTTTCTGCCTCGTCCCTGACCTACTTTCTGCCTCGTCCCTGACCTACTTTCTGCCT-3'

Re-annotation of clock-controlled genes.

The previously published genome-wide

expression data for the liver 2 were re-analyzed and re-annotated to find transcription
factors that showed circadian expression.

Each probe set that was identified as aclock-controlled gene in the previous report 2, was annotated by using link information

14© 2008 Macmillan Publishers Limited. All rights reserved.

in the Entrez Gene database (gene name, gene symbol, and Entrez Gene ID), link
information in the TRANSFAC database (FACTOR, MATRIX, consensus binding sites,
CLASS ID, and upstream transcription factors), the Affymetrix annotation file (InterProID), and information in the mammalian promoter/enhancer database (clock-controlledelements, E-box, D-box, and RRE) (Kumaki et al., submitted). The annotation table isshown in Supplementary Table 1 online.

Parameter search.

First, the initial parameter set in the formulas of our theoreticalmodel was randomly chosen except for KA, KR (=1/2), a (=0), b and n (=1).

As

multiplying by KA, KR is equivalent to dividing by both αA, αR and γA, γR , in the formula
T(t), KA and KR were fixed to a constant (1/2) to eliminate ambiguity. If the minimum
amplitude of an output with a specific initial parameter set (obtained by changing thephase of the repressor) was too low or too high (<1/100 or >100-fold of a mean
amplitude of an activator and a repressor), the initial parameter set was discarded and a
new parameter set was randomly searched again.
Second, one parameter other than KA, KR, a, b, n was chosen, and then ten
different values of the parameter were generated within 30-fold of its original value.
For each value of the parameter, graphs like that in Fig. 5a and b were drawn bychanging the value of b. The first graph (Fig. 5a) shows relationships between phasedifferences of the activator and the repressor (activator phase – repressor phase) andphase differences of the activator and the output protein (output protein phase –activator phase).

The second graph (Fig. 5b) shows relationships between phasedifference of the activator and the repressor and the relative amplitude of the output
protein.

The points in these graphs represent observed outputs of various

combinations of activators and repressors.

The parameter value that had the lowest

15© 2008 Macmillan Publishers Limited. All rights reserved.

least squares distance to the measured experimental points was chosen as the new valueof the parameter.

We did not use *-marked points because these outlier points havelarger (>4-fold amounts of the activator than the repressor) differences between
amounts of the activator and the repressor (Fig. 5c), and also seem to have lower
relative amplitudes.

This second fitting procedure was repeated until no more

improvements were observed, and the final parameter set was recorded as a fitted
parameter set.

By repeating these procedures, we found 100 fitted parameter sets.

Sensitivity analysis.

All parameters except for n were analyzed for the degree towhich the output phase and the relative amplitude was sensitive to them.

To calculate

the sensitivity of the output phase to a certain parameter, the value of the parameter waschanged within 1 hour (0.5-hour advance and 0.5-h delay) for a or b, or changed within
a 4-fold (one-half and double the original parameter value) if it was one of the otherparameters.

For each parameter change, the maximum changes in phase difference

between the activator and the output were calculated for each b within -12 < b < 12, andthe average value of the maximum phase change (or the change of the relative
amplitude) was calculated over -12 < b < 12 and defined as the "phase change" (or"relative amplitude change") due to the parameter change.

This procedure was

performed for each parameter set in 100 fitted parameter sets.

The average and SEMof the phase change due to the parameter change were then calculated over the 100
fitted parameter sets with trimming of the 5% outliers, and defined as the measures ofsensitivity of the corresponding parameter change.

Construction of p3×E'-box-SV40-Dbp and p3×RRE-SV40-E4bp4.

To construct

Dbp and E4bp4 gene expression vectors regulated by E'-box and RRE, the Dbp and

16© 2008 Macmillan Publishers Limited. All rights reserved.

E4bp4 coding sequence were amplified from the pMU2-Dbp and pMU2-E4bp4
plasmids (Kumaki et al., submitted) by PCR with forward(5'-CTCGAAGGAGAGGCCACCATGGAC-3') and reverse(5'-GCACCCGACATAGATTCATTAACCC-3') primers, and phosphorylated byMighty Cloning kit <Blunt End> (TaKaRa). The vectors for insertion of these PCR
fragment were amplified from the p3×E'-box-SV40-dGal4 and p3×RRE-SV40-dGal4
plasmids (See Methods in main text) by invert PCR with forward(5'-GGTACCTGAATAACTAAGGCCGCTTCC-3') and reverse(5'-CAGGAGGCTTGCTTCAAGCTGGC-3') primers, and blunted by T4 DNA
Polymerase, and then dephosphorylated by Bacterial Alkaline Phosphatase.

The

dGal4 coding region was deleted by this treatment. The Dbp and p3×E'-box-SV40
PCR fragments, and E4bp4 and p3×RRE-SV40 PCR fragments were ligated,
respectively.

These products were termed p3×E'-box-SV40-Dbp and p3×RRE-

SV40-E4bp4, and used for perturbation experiment.

Perturbation experiments of natural transcriptional circuits to verify thepredictions.

Real-time circadian assays were performed as previously described1,6

with the following modifications.

NIH3T3 cells (American Type Culture Collection)

were grown in DMEM (Invitrogen) supplemented with 10% FBS (JRH Biosciences)
and antibiotics (25 U/ml penicillin, 25 mg/ml streptomycin; Invitrogen).

Cells wereplated at 1×105 cells per well in 35-mm dishes 24 h before transfection.

These cells

were transfected with FuGene6 (Roche) according to the manufacturer's instructions.
The cells in each well were transfected with two plasmids (0.5 µg of
p3×D-box-SV40-dLuc1 reporter plasmid, 0, 0.1, 0.3, 0.6, 0.9, 1.2, 1.5 µg of
p3×E'-box-SV40-Dbp or p3×RRE-SV40-E4bp4). The amount of transfected plasmid
was adjusted to 2.0 µg with empty vector.

After 72 h, the media in each well was

17© 2008 Macmillan Publishers Limited. All rights reserved.

replaced with 2 ml of culture medium (DMEM/10% FBS) supplemented with 10 mM
HEPES (pH 7.2, Invitrogen), 0.1 mM luciferin (Promega), antibiotics, and 0.01 µM
forskolin (Nacalai Tesque).

Bioluminescence was measured with photomultiplier tube

(PMT) detector assemblies (LM2400, Hamamatsu Photonics).

The modules andcultures were maintained in a darkroom at 30°C and interfaced with computers forcontinuous data acquisition.

Photons were counted for 1 min at 12-min intervals.

18© 2008 Macmillan Publishers Limited. All rights reserved.

References1.

Ueda, H.R. et al. System-level identification of transcriptional circuits

underlying mammalian circadian clocks. Nat Genet 37, 187-192 (2005).
2.

Ueda, H.R. et al. A transcription factor response element for gene expression

during circadian night. Nature 418, 534-539 (2002).
3.

Akhtar, R.A. et al. Circadian cycling of the mouse liver transcriptome, as

revealed by cDNA microarray, is driven by the suprachiasmatic nucleus. Curr Biol 12,
540-50 (2002).
4.

Panda, S. et al. Coordinated transcription of key pathways in the mouse by thecircadian clock. Cell 109, 307-20 (2002).
5.

Storch, K.F. et al. Extensive and divergent circadian gene expression in liverand heart. Nature 417, 78-83 (2002).
6.

Sato, T.K. et al. Feedback repression is required for mammalian circadianclock function. Nat Genet 38, 312-319 (2006).
7.

Yamashita, M. et al. Identification of a Conserved GATA3 Response Element

Upstream Proximal from the Interleukin-13 Gene Locus. J. Biol. Chem. 277,
42399-42408 (2002).

19© 2008 Macmillan Publishers Limited. All rights reserved.