Molecular-timetable methods for detection of bodytime and rhythm disorders from single-time-point
genome-wide expression profiles
Hiroki R. Ueda*†‡§, Wenbin Chen*, Yoichi Minami*, Sato Honma¶, Kenichi Honma¶, Masamitsu Iino†,
and Seiichi Hashimoto**Molecular Medicine Laboratories, Institute for Drug Discovery Research, Yamanouchi Pharmaceutical Company, Limited, 21 Miyukigaoka, Tsukuba, Ibaraki
305-8585, Japan; †Department of Pharmacology, Graduate School of Medicine, University of Tokyo, 7-3-1 Bunkyo-ku, Tokyo 113-0033, Japan; ‡Laboratory
for Systems Biology, Center for Developmental Biology, RIKEN, 2-2-3 Minatojiima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan; and §Departmentof Physiology, Hokkaido University Graduate School of Medicine, Sapporo 060-8638, Japan
Edited by Michael S. Waterman, University of Southern California, Los Angeles, CA, and approved May 27, 2004 (received for review March 17, 2004)

DNA microarray 兩 gene expression 兩 chronotherapy

D

iverse physiological and metabolic processes exhibit circadian rhythms, which are endogenous self-sustained oscillations with a period of ⬇24 hours. In mammals, several clock
genes, including Clock, Bmal1兾Mop3, Per1, Per2, Cry1, Cry2,
Cki␧, and RevErbA␣, and clock-controlled transcription factors, including Dbp, E4bp4, Dec1兾Stra13, Dec2, Per3, Npas2,
RevErbA␤, Ror␣, Ror␤, and Ror␥, regulate, at least in part, gene
expression in central and兾or peripheral clocks (1). Reflecting the
temporal changes in gene expression in central and peripheral
clocks (2–5), the potency and兾or toxicity in drug administration
depend on an individual’s body time (BT) (6–10). It has beensuggested that drug administration at the appropriate BT can
improve the outcome of pharmacotherapy by maximizing potency and minimizing the toxicity of the drug (11), whereas drug
administration at an inappropriate BT can induce severe side
effects (12). Despite the effectiveness and importance of such
BT-dependent therapy, termed ‘‘chronotherapy’’ (6–10), its
clinical use has been obstructed by the lack of clinically applicable methods for BT detection. To address these difficulties, we
attempted to create standard expression profiles, termed a‘‘molecular timetable,’’ composed of ⬎100 ‘‘time-indicating
genes’’ and their expression levels during the course of a day, andthen to apply this timetable to BT detection.
Materials and Methods
Animals. To select time-indicating genes and construct theirstandard expression profiles, we analyzed the previously obtained genome-wide expression profiles (5) from pooled livers offour Balb兾c mice (male) every 4 h over 2 d under 12-h light兾12-hdark (LD) or constant-dark (DD) conditions. We independently
sampled livers from eight individual Balb兾c mice (male) at
Zeitgeber time (ZT)12 (n ⫽ 4), ZT6 (n ⫽ 1), ZT18 (n ⫽ 1),
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0401882101

Circadian time (CT)6 (n ⫽ 1), and CT18 (n ⫽ 1) to verify thecapability of the molecular-timetable method. ZT is used for atimescale under LD conditions, whereas CT is used for atimescale under DD conditions. ZT0 represents lights on, and
ZT12 represents lights off, whereas CT0 represents subjective
dawn, and CT12 represents subjective dusk. We use the term‘‘subjective,’’ because there are no external time cues in the DD
condition. We sampled livers from seven individual Clock兾Clockhomozygous mutant mice (male) at ZT12 (n ⫽ 4) or ZT8 (n ⫽3) and three individual Balb兾c mice (male) at ZT8 (n ⫽ 3) toverify the feasibility of expression-based diagnosis of circadianrhythm disorders. We further sampled livers from three individual C3H mice (male) at ZT12 (n ⫽ 3) to verify the feasibilityof the molecular-timetable method for individuals with heterogeneous genetic background. All these Balb兾c, C3H, and Clock兾
Clock homozygous mutant mice were adapted under LD conditions for 2 weeks from 5 weeks postpartum and then sampled.
Microarray Experiments. Total RNA was prepared by using Trizol
reagent (GIBCO兾BRL). cDNA synthesis and cRNA labelingreactions were performed as described (5). Affymetrix highdensity oligonucleotide arrays (Murine Genome Array U74A,
Version 1.0, measuring 9,977 independent transcripts) were
hybridized, stained, and washed according to the Technical
Manual (Affymetrix). Affymetrix software was used to determine the average difference (AD) between perfectly matchedprobes and single-base-pair-mismatched probes. The AD of eachprobe was then scaled globally so that the total AD of eachmicroarray was equal. The resulting AD values reflect theabundance of a given mRNA relative to the total RNA population and were used in all subsequent analyses.
Time-Indicating Genes. To select time-indicating genes whose
expression exhibits circadian rhythmicity with high amplitude,
the expression profile of each gene was analyzed through two
filters, one for circadian rhythmicity and the other for highamplitude. To extract genes with circadian rhythmicity underboth LD and DD conditions, we first calculated the correlation
over time between 12-point time courses under LD (or DD)
conditions and cosine curves of defined periods and phases. We
prepared cosine curves of 24-h periodicity with peaks from 0 to
24 h in increments of 10 min, yielding a total of 144 test cosine
curves, and calculated the correlation value of the best-fitted
cosine curve for each probe set. We selected the probe sets

This paper was submitted directly (Track II) to the PNAS office.
Abbreviations: LD, light兾dark; DD, constant dark; ZT, Zeitgeber time; CT, Circadian time; BT,body time(s).
§To whom correspondence should be addressed. E-mail: uedah-tky@umin.ac.jp.

© 2004 by The National Academy of Sciences of the USA

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Detection of individual body time (BT) via a single-time-point assay
has been a longstanding unfulfilled dream in medicine, because BT
information can be exploited to maximize potency and minimize
toxicity during drug administration and thus will enable highly
optimized medication. To achieve this dream, we created a ‘‘molecular timetable’’ composed of >100 ‘‘time-indicating genes,’’
whose gene expression levels can represent internal BT. Here we
describe a robust method called the ‘‘molecular-timetable method’’for BT detection from a single-time-point expression profile. The
power of this method is demonstrated by the sensitive andaccurate detection of BT and the sensitive diagnosis of rhythm
disorders. These results demonstrate the feasibility of BT detection
based on single-time-point sampling, suggest the potential for
expression-based diagnosis of rhythm disorders, and may translate functional genomics into chronotherapy and personalized
medicine.

whose best correlation values in LD and DD conditions wereboth above the cutoff correlation value of 0.8. To further extract
genes with high amplitude under both LD and DD conditions,
we calculated the coefficient of variation of the expression levels
under LD (or DD) conditions, which is defined as its SD divided
by the average of expression levels. We selected the probe sets
whose coefficients of variation in LD and DD conditions wereboth above the cutoff value of 0.15. Based on two successive
filtrations, 168 genes (182 probes) in the liver were identified.
Estimation of Molecular Peak Time. To estimate the peak time ofcycling genes, we tested for correlation over time between the
12-point time course of each gene and the 24-h period cosine
curves with different peak times at 10-min intervals. We estimated the peak time of each cycling gene from the peak time of
the best-fitted cosine curve and defined it as the molecular peaktime.
Molecular-Timetable Method. We first normalized an expression

level, X i, of the time-indicating gene i (i ⫽ 1 . . . N) using its
average ␮ i and SD ␴ i in the molecular timetable. The normalized
expression level Y i is described as follows: Y i ⫽ (X i ⫺ ␮ i)兾 ␴ i. We
created an expression profile {t i, Y i} (i ⫽ 1 . . . N) composed ofthe molecular peak time t i of gene i and its normalized expression
level Y i. To estimate the BT of an expression profile, we
calculated the correlation over genes (i ⫽ 1 . . . N) between an
expression profile {t i, Y i} and a 24-h cosine curve {t i, 公2
Cos(2␲(t i ⫺ b)兾24)} with a certain phase b (0 ⱕ b ⬍ 24). The
amplitude of the cosine curve is set to 公2, so that the SD of thenormalized expression level Y i matches the SD of a continuous2
公2).
cosine waveform (公1兾24 兰24
0 Cos (2␲(t ⫺ b)兾24) dt ⫽ 1兾We prepared 24-h cosine curves with a phase b from 0 to 24 h
in increments of 10 min. We then selected the best-fitted cosine
curve that gave the best correlation value c. We noted that thebest correlation value c is always positive, because we calculated
the maximum value of correlation between an expression profileand 144 test cosine curves. We also noted that the phase of thebest-fitted cosine curve (b c) indicates an estimated BT.
Statistical Significance in the Detection of BT. To evaluate thestatistical significance of BT estimation, we generated a random
expression profile {t i, Y r} (i ⫽ 1 . . . N), where Y r represents a
random variable following the distribution of Y i and thencalculated the correlation value c r and the phase b rc of thebest-fitted cosine curve as described above. We repeated thisprocedure 10,000 times to create the distribution of correlation
value c r and the phase b rc (e.g., Fig. 4 A and B, which is publishedas supporting information on the PNAS web site). The probability (termed P r value) that a random expression profile has abest-fitted cosine curve giving correlations equal to or greaterthan those of the real expression profiles was determined fromthe distribution of correlation value (c r) from 10,000 random
expression profiles.
Estimation of Measurement Noise. To estimate the measurement
noise of eight Bablc兾C expression profiles (see Animals above)
at ZT12 (n ⫽ 4), ZT6 (n ⫽ 1), ZT18 (n ⫽ 1), CT6 (n ⫽ 1), andCT18 (n ⫽ 1), we first calculated the difference d i between a real
and an estimated expression level of gene i (i ⫽ 1 . . . N). d i isdefined as d i ⬅ Y i ⫺ 公2 Cos(2 ␲ (t i ⫺ b c)兾24), where b c
represents estimated BT. We then calculated the SD of d i over
all time-indicating genes and defined it as the measurement
noise. Measurement noises of wild-type expression profiles
range from 86% to 108% (95 ⫾ 8% for mean ⫾ SD).
Statistical Significance in the Detection of Circadian Rhythm Disorders. To evaluate the statistical significance of circadian rhythm

disorders, we generated a control expression profile with 100%11228 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0401882101

measurement noise {t i, 公2 Cos(2 ␲ (t i兾24)) ⫹ d r)} (i ⫽ 1 . . . N),
where d r represents a random variable following the distributionof d i, and then calculated the correlation value c c and the phaseb cc of the best-fitted cosine curve, described above. We repeatedthis procedure 10,000 times to create the distribution of correlation value c c and the phase b cc (e.g., Fig. 4 A and B). The
probability (termed P c value) that a control expression profile
has a best-fitted cosine curve giving a correlation equal to or
lower than those of the observed expression profiles was determined from the distribution of the correlation value c c from10,000 control expression profiles.
Sensitivity and Specificity of Molecular-Timetable Methods. We cancalculate the sensitivity and specificity of the molecular timetable method in the presence of a certain level of measurement
noise (100% or 200% measurement noise). First, we generated
10,000 control or random expression profiles in the presence ofa certain measurement noise level and then calculated the
distribution of c c or c r from 10,000 control or random expression
profiles as described above. We determined the P c or P r value atthe certain threshold value of correlation (c) from the distribution of c c or c r, respectively. Sensitivity (S c) is defined as S c(c) ⬅
1 ⫺ P c(c), indicating the probability of true positives or the
probability of circadian rhythmicity (control expression profile),
correctly identified by the test as meeting a certain thresholdvalue of correlation. Specificity (S r) is defined as S r(c) ⬅ 1 ⫺P r(c), indicating the probability of true negatives or of circadianrhythm disorder (random expression profile), correctly identified by the test as not meeting a certain threshold value ofcorrelation. There are tradeoffs between sensitivity and specificity, because sensitivity monotonically decreases, whereas specificity monotonically increases, with the threshold correlation
value. This tradeoff relationship is plotted as the receiver
operating characteristic (ROC) curve (e.g., Fig. 4C). The ROC
curve is defined as {S r(c), S c(c)} (0 ⱕ c ⱕ 1).
Performance of Molecular-Timetable Methods with Different Numbers of Time-Indicating Genes with Simulated Expression Profiles.

Performance of the molecular-timetable method with N timeindicating genes (N 僆 {3, 5, 10, 20, 30, 50, 100, 182}) was
calculated with simulated expression profiles in the presence of
100% or 200% measurement noise. First, we randomly selected
N from 168 time-indicating genes. Then, we generated control{t i, 公2 Cos(2 ␲ (t i兾24)) ⫹ d r} and random expression profiles{t i, Y r} in the presence of 100% measurement noise, where d r
and Y r represent random variables following the distributions ofd i and Y i, respectively. In the presence of 200% noise, we
generated control {t i, 公2 Cos(2 ␲ (t i兾24)) ⫹ 2d r} and random
expression profiles {t i, 2Y r}. We repeated these procedures
10,000 times and then calculated the distribution of the correlation value (c c and c r) and the phase (b cc and b rc) from 10,000
control and random expression profiles and determined the P cand P r values, sensitivity S c, and specificity (S r) at a certain
threshold value of correlation, as described above (Fig. 5, which
is published as supporting information on the PNAS web site).
Performance of Molecular-Timetable Methods with Different Numbers of Time-Indicating Genes with Real Expression Data. Perfor-

mance of the molecular-timetable method with N timeindicating genes (N 僆 {10, 20, 30, 40, 50, 60, 70, 80, 90, 100,
110, 120, 130, 140, 150}) was calculated with real expression
profiles. To select N time-indicating genes from 168 timeindicating genes in the order of high-amplitude circadian rhythmicity, we first calculated the sum of correlation in LD, correlation in DD, coefficient of variation in LD, and coefficient ofvariation in DD for each gene. We then selected the top N
time-indicating genes in the order of this sum.
To determine a cutoff correlation value in the detection of
Ueda et al.

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Fig. 1. Time-indicating genes in the mouse liver. (A) Temporal expression data of 168 time-indicating genes (182 probes) in the mouse liver. The colors, inascending order from green to red to blue, represent the molecular peak time of time-indicating genes (the color code is represented above the diagrams). An
expression level of each time-indicating gene is subtracted by its average and divided by its SD over 12-point time courses. The blocked horizontal bars below
the diagrams correspond to the LD schedule. White blocks indicate periods of exposure to light, whereas black blocks correspond to periods of darkness, andgray blocks indicate the period of subjective light under constant darkness. (B) Distribution of the average of molecular peak time between LD and DD conditions.
Average molecular peak times are distributed from 0 to 24 h. (C) Distribution of differences of molecular peak times between LD and DD conditions. Molecularpeak times in LD and DD conditions are similar to each other. (D) Expression profiles of 168 time-indicating genes in the mouse liver at different ZT under LD
conditions or CT under DD conditions. The best-fitted cosine curve is represented, and its peak indicates the estimated BT.

circadian rhythmicity and circadian rhythm disorders, we first
calculated the receiver operating characteristic (ROC) curve of
the molecular-timetable method with N time-indicating genes in
the presence of 100% measurement noise, as described above.
We then determined a cutoff correlation value c (0 ⱕ c ⱕ 1) as
the value yielding equal sensitivity and specificity in the ROC
curve [S r(c) ⫽ S c(c)]. We noted that c is a monotonicallydecreasing function of N.
To calculate sensitivity, specificity, and accuracy with real
expression data, we examined 11 wild-type Balb兾c expression
profiles at ZT12 (n ⫽ 4), ZT6 (n ⫽ 1), ZT18 (n ⫽ 1), CT6 (n ⫽1), CT18 (n ⫽ 1), and ZT8 (n ⫽ 3), and 7 Clock兾Clock mutant
expression profiles at ZT12 (n ⫽ 4) and ZT8 (n ⫽ 3). We
calculated sensitivity, which is defined as the percent of wild-type
Balb兾c expression profiles (n ⫽ 11), with a correlation value
higher than a cutoff. We also calculated specificity, which isdefined as the percent of Clock兾Clock mutant expression profiles(n ⫽ 7), with a correlation value lower than a cutoff. To evaluate
the accuracy of molecular-timetable methods, we calculated
mean estimation error in BT detection, which is defined as theaverage of absolute differences between sampling times andestimated BT of wild-type Balb兾c expression profiles (n ⫽ 11).
Calculated sensitivity, specificity, and mean errors are plottedalong with N time-indicating genes (Fig. 6, which is published as
supporting information on the PNAS web site).
Ueda et al.

Results and Discussion
Recently, we, along with others, performed genome-wide gene
expression analyses using high-density DNA microarrays toidentify clock-controlled genes in the mouse central [suprachiasmatic nucleus (SCN)] and peripheral (liver) clocks (2–5). We
analyzed the previously obtained genome-wide expression profiles from four pooled livers every 4 h over 2 d under LD or DD
conditions and found 168 time-indicating genes (Fig. 1 and Table
1, which is published as supporting information on the PNAS
web site) whose expression exhibits high circadian rhythmicity
and whose peak time, termed molecular peak time, can therefore
indicate the time of day (see Materials and Methods). Importantly, the molecular peak times of time-indicating genes were
distributed over 24 h (Fig. 1B). Moreover, each time-indicating
gene exhibited similar expression patterns under LD and DD
conditions (Fig. 1 A), and the molecular peak times of each gene
under LD and DD conditions were similar to each other (Fig.
1C), suggesting that expression profiles of time-indicating genes
can indicate BT, the endogenous state of the circadian clock.
To verify this possibility, we attempted to extract the BT
information from the expression profiles of 168 time-indicating
genes (see Materials and Methods). As expected, BT information
can be extracted from the expression profiles of 168 timeindicating genes with high accuracy and estimation errors from
0.0 to 1.3 h (0.4 ⫾ 0.3 h for mean ⫾ SD, Fig. 1D). For instance,
at ZT0 (the beginning of day) or CT0 (the beginning of a
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0subjective day), dawn-indicating genes (green), whose molecularpeak times are approximately ZT0 or CT0, are highly expressed,
whereas dusk-indicating genes (red), whose molecular peaktimes are approximately ZT12 or CT12, are expressed at a low
level (Fig. 1D). At ZT12 or CT12, on the other hand, dawnindicating genes are expressed at a low level, whereas duskindicating genes are highly expressed (Fig. 1D). In both cases, thenormalized expression levels of day-indicating genes (yellowgreen to orange) or night-indicating genes (purple to blue)
gradually change from higher to lower expression levels or fromlower to higher levels along their molecular peak times. Such
gradual and cyclic changes in expression along the molecularpeak time line allow us to extract the BT from the expression
profiles via cosine curve fitting (Fig. 1D). The peak of thebest-fitted cosine curve to an expression profile of 168 timeindicating genes indicates the estimated BT. For example, the BT
extracted from expression profiles at ZT0 on the first day under
LD or at CT0 on the first day under DD are BT0.2 and BT1.3,
respectively. We termed this the molecular-timetable method(see Materials and Methods).
To demonstrate the capability of this molecular-timetable
method, we attempted to infer BT from independent samples.
We obtained fresh liver samples from four individual mice at
ZT12, which was thought to be one of the noisiest time points,
because lights out at that time resets the phase of circadian clocks
in species, such as mice, with a free running period shorter than
24 h. We then measured the expression profiles of 168 timeindicating genes (Fig. 2 A). Using the molecular-timetable
method, we significantly detected the circadian rhythmicity in all
expression profiles of these samples (P ⬍ 0.0001, Fig. 2 A), andthe estimated BT indicated BT12.8, BT10.2, BT11.2, and BT11.7,
respectively (Fig. 2 A). These results suggest that BT can be
accurately inferred from individual expression profiles withestimation errors from 0.3 to 1.8 h (1.0 ⫾ 0.6 h for mean ⫾ SD,
Fig. 2 A). To further demonstrate the capability of the moleculartimetable method, we obtained new liver samples from individual mice at ZT6, ZT18, CT6, and CT18, all times that weredifferent from the time points used to construct the molecular
timetable, and measured the expression profiles of 168 timeindicating genes (Fig. 2B). We significantly detected the circadian rhythmicity in all expression profiles of ZT6, ZT18, CT6,and CT18 samples (P ⬍ 0.0001, Fig. 2B) and found that theestimated BT indicated BT6.7, BT19.3, BT5.7, and BT20.0,
respectively (Fig. 2B). These results suggest that BT can be
accurately inferred from expression profiles at time points thatwere not used to construct the molecular timetable, with estimation errors from 0.3 to 2.0 h (1.1 ⫾ 0.7 h for mean ⫾ SD,
Fig. 2B).
The molecular-timetable method can be applied for the
diagnosis of circadian rhythm disorders (see Materials andMethods). To demonstrate the feasibility of expression-based
diagnosis of circadian rhythm disorders, we sampled livers at
ZT12 from four individual Clock兾Clock homozygous mutant
mice, which were known to have altered circadian behavioral
rhythms (13, 14), and then measured the expression profiles of
168 time-indicating genes (Fig. 3A). We significantly detected
the rhythm disorders in all expression profiles of Clock兾Clockhomozygous mutant samples at ZT12 (P ⬍ 0.0001, Fig. 3A). To
further demonstrate the feasibility of the expression-based diagnosis of circadian rhythm disorders, we simultaneously sampled livers from three individuals of wild-type (⫹兾⫹) mice andClock兾Clock mutant mice at ZT8 and measured the expression
profiles for 168 time-indicating genes (Fig. 7, which is publishedas supporting information on the PNAS web site). We significantly detected the circadian rhythmicity in all expression profiles of wild-type (⫹兾⫹) samples (P ⬍ 0.0001, Fig. 7) and foundthat the estimated BT indicated BT7.3, BT6.7, and BT9.5 (Fig.
7), which were around sampling time ZT8. On the other hand,
11230 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0401882101

Fig. 2. Significant and quantitative detection of BT from individual expression profiles at ZT12 (A) or ZT6, ZT18, CT6, and CT18 (B). The colors, inascending order from green to red to blue, represent the molecular peak timeof time-indicating genes (the color code is represented below the diagrams).
An expression level of each time-indicating gene is subtracted by its averageand divided by its SD in the molecular timetable. The best-fitted cosine curveis represented, and its peak indicates the estimated BT, BT12.8 (A Upper Left),
BT10.2 (A Lower Left), BT11.2 (A Upper Right), and BT11.7 (A Lower Right),
and BT6.7 (B Upper Left), BT19.3 (B Lower Left), BT5.7 (B Upper Right), andBT20.0 (B Lower Right).

we significantly detected rhythm disorders in all expression
profiles of Clock兾Clock homozygous mutant samples at ZT8(P ⬍ 0.0001, Fig. 7). These results suggest that the moleculartimetable method can be applied not only for BT detection but
also for the detection of circadian rhythm disorders.
In clinical situations, methods for BT detection should beapplicable for populations with heterogeneous genetic backgrounds. To demonstrate the capability of the moleculartimetable method for individuals with heterogeneous genetic
backgrounds, we attempted to apply the molecular-timetable
method for other inbred strains with different genetic backgrounds from the original strain used for the construction of themolecular timetable. We sampled livers at ZT12 from three
individual C3H mice, which were different from the original
Balb兾c strains used to construct the molecular timetable, andmeasured expression profiles for 168 time-indicating genes (Fig.
3B). We significantly detected the circadian rhythmicity in all
expression profiles of C3H samples (P ⬍ 0.0001, Fig. 3B) andfound that the estimated BT indicated BT12.3, BT11.3, andBT11.3, respectively (Fig. 3B). These results suggest that BT canbe accurately inferred from the expression profiles of individuals
Ueda et al.

with heterogeneous genetic backgrounds, with estimation errors
from 0.3 to 0.7 h (0.6 ⫾ 0.2 h for mean ⫾ SD, Fig. 3B).
In this study, we used mouse livers to construct the molecular
timetable and demonstrated the feasibility of the moleculartimetable method based on single-time-point sampling for detection of BT and diagnosis of circadian rhythm disorders. Other
tissues besides the liver can be used to construct molecular
timetables, because there are circadian oscillators scatteredthroughout the body in various tissues and organs, including themouse suprachiasmatic nucleus (SCN), liver, skeletal muscle,lung, cornea, kidney, heart, aorta, skin, oral mucosa, and whiteblood cells (2–5, 15–19). Genome-wide expression analyses insome of these tissues have been performed and have demonstrated that between 2% and 10% of the analyzed genes exhibit
circadian oscillations in RNA expression levels (2–5). In fact, weanalyzed the previous genome-wide expression data for themouse SCN (5) and found that BT can be represented in theexpression profiles of SCN time-indicating genes (Table 2, which
is published as supporting information on the PNAS web site),with low estimation errors from 0.3 to 1.8 h (1.0 ⫾ 0.4 h formean ⫾ SD, Fig. 8, which is published as supporting informationon the PNAS web site).
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Fig. 3. Significant detection of BT and rhythm disorders from expression
profiles of Clock兾Clock mutant mice at ZT12 (A) and C3H mouse at ZT12 (B).
The colors, in ascending order from green to red to blue, represent themolecular peak time of time-indicating genes (the color code is represented
below the diagrams). An expression level of each time-indicating gene issubtracted by its average and divided by its SD in the molecular timetable. The
best-fitted cosine curve is represented, and its peak indicates the estimated BT,
BT12.3 (B Upper Left), BT11.3 (B Lower Left), and BT11.3 (B Lower Right).

The molecular-timetable method can be also applied to organisms other than the mouse because a wide range of organisms, including human, rat, Drosophila, Arabidopsis, Neurospora,and cyanobacteria, are known to have circadian clocks (20), andgenome-wide expression analyses in some of these organisms
have shown that a substantial portion of the analyzed genes
exhibit circadian oscillations in RNA expression levels (21–27).
Actually, we analyzed the previously obtained genome-wide
expression data of Drosophila heads (24) and found that BT canbe represented in the expression profiles of 113 time-indicating
genes of Drosophila (Table 3, which is published as supporting
information on the PNAS web site) with low estimation errors
from 0 to 1.5 h (0.4 ⫾ 0.4 h for mean ⫾ SD, Fig. 9, which is
published as supporting information on the PNAS web site). We
applied this molecular timetable for the detection of BT and the
diagnosis of circadian rhythm disorders in Drosophila. We simultaneously sampled heads from wild-type (⫹兾⫹) and Drosophila Clock homozygous mutant (28) (dClock兾dClock) flies at
ZT13 and obtained expression profiles for 113 time-indicating
genes (Fig. 10, which is published as supporting information on
the PNAS web site). We significantly detected the circadianrhythmicity in all expression profiles of wild-type samples (⫹兾⫹)at ZT13 (P ⬍ 0.0001, Fig. 10) and found that the estimated BT
indicated BT13.7 and BT14.5, respectively (Fig. 10). On theother hand, rhythm disorders were significantly detected fromdClock兾dClock expression profiles (P ⬍ 0.0001, Fig. 10). These
results suggest that the molecular-timetable method can beapplied for the detection of BT and circadian rhythm disorders
in organisms other than mouse.
Performance of the molecular-timetable method is characterized by three measures specificity, sensitivity, and estimation
error (Fig. 4 and see Materials and Methods). The first measure,sensitivity, is defined as the percent of control expression profiles(blue) higher than threshold of correlation in cosine curve fitting(Fig. 4A). The second measure, specificity, is defined as thepercent of random expression profiles (red) lower than thresholdof correlation (Fig. 4A). There is a tradeoff between sensitivity
and specificity, because changing the threshold of correlationinfluences these measures in opposite directions, and thus
performance of molecular-timetable method depends on segregation between control and random expression profiles (Fig.
4C). The third measure, estimation error, is defined as thedifference between estimated BT and true BT (blue, Fig. 4B).
These results show that the molecular-timetable method with
168 time-indicating genes in mouse liver is a remarkably specific,
sensitive, and accurate method.
In this study, we devised a method for BT detection utilizing
single-time-point data for multiple molecules. To elucidate theimportance of the use of many time-indicating genes, we assessed
the specificity, sensitivity, and estimation error of the moleculartimetable method with different numbers of time-indicating
genes in the presence of measurement noise, which is inevitablein clinical situations (see Materials and Methods). In the presenceof 100% measurement noise, the application of the moleculartimetable method with 100 (or 150) time-indicating genes had
the capability of detecting the BT with ⬎99.99% (99.99%)
sensitivity and 99.99% (99.99%) specificity and with low estimation errors 0.30 ⫾ 0.24 h for mean ⫾ SD (0.25 ⫾ 0.21 h formean ⫾ SD, Fig. 5). Even in the presence of 200% measurement
noise, use of the molecular-timetable methods with 100 (or 150)
time-indicating genes still had the capability of detecting BT with
98.58% (99.72%) sensitivity and 98.58% (99.72%) specificity
and with low estimation errors 0.62 ⫾ 0.48 h for mean ⫾ SD
(0.50 ⫾ 0.39 h for mean ⫾ SD, Fig. 5). On the other hand, themolecular-timetable method with three (or five) time-indicating
genes failed to specifically, sensitively, or accurately detect BT or
rhythm disorders, suggesting the importance of the use of manytime-indicating genes (Fig. 5). The use of ⬎100 time-indicating

Clock兾Clock homozygous mutant mice. These results demonstrate the feasibility of BT detection based on single-time-point
sampling, suggest the capacity for the expression-based diagnosisof circadian rhythm disorders, and may lead to the developmentof chronotherapy and personalized medicine.

genes can confer with high sensitivity, specificity, and accuracy,
to the molecular timetable, even in the presence of high measurement noise. Interestingly, we noted that the moleculartimetable method, with as few as 60 time-indicating genes, if
selected appropriately can sensitively and accurately detect BT
and sensitively diagnose rhythm disorders in real expression
profiles (Fig. 6).
Collectively, we constructed a molecular timetable and devised a specific, sensitive and accurate method for detection of
BT and rhythm disorders from a single-time-point expression
profile using this molecular timetable. The power of the molecular-timetable method can be demonstrated by the quantitative
and accurate detection of BT from individual expression profiles
and the accurate detection of circadian rhythm disorders in

We thank Akira Matsumoto, Teiichi Tanimura, Miho Kawamura, Hisanori Wakamatsu, Yasufumi Shigeyoshi, Mamoru Nagano, Ken-ichi
Nakahama, and Akihito Adachi for fly and mouse GENECHIP analysis. We
also thank Tomoko Kojima, Toshie Katakura, and Hiromi Urata fortechnical assistance and John B. Hogenesch, Shigehiro Ohdo, Hideyuki
Terazono, and Hideo Iwasaki for stimulating discussions. This work was
performed as a part of a research and development project of theIndustrial Science and Technology Program supported by the New
Energy and Industrial Technology Development Organization (NEDO).

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