The circadian, or daily, rhythm is one of the most obvious and well-studied periodic processes in living organisms. Studies of transcriptional output in different tissues report that expression of approximately 5%–15% of all mammalian genes show a circadian oscillation [1,2]. This circadian oscillation is driven by a molecular mechanism involving a transcriptional/translational feedback loop, which generates the basic rhythm driving gene expression. In mammals, the master circadian clock is located in the hypothalamus and is constantly adjusted to the daily light cycle through photic stimuli from the retina. Analysis of gene expression in peripheral tissues indicates that relatively few genes share the same circadian expression profile in more than one tissue [3].

We have completed independent circadian studies in AKR/J mice acclimated to a 12 h light: 12 h dark cycle, harvesting sets of three to five mice at 4-h intervals (details of the experiment given in Zvonic et al. [8] ). Total RNA samples from inguinal white adipose tissue (iWAT), brown adipose tissue (BAT), and liver have been assayed by RT-PCR and Affymetrix microarrays. In initial analyses, candidate genes were selected for validation by RT-PCR of their circadian expression profile in all three tissues. In further analyses, tissue samples harvested from three mice at 4-h intervals over a single 24-h period were pooled and assayed on duplicate microarrays. The resulting individual datasets for each of three different tissues contained more than 22,000 gene expression profiles. Each profile consisted of 12 time points, representing six periods of the day sampled two times. For analysis of periodicity, we considered this data as reflecting two complete daily cycles. The data was smoothed by a third-degree polynomial procedure and converted to a frequency domain (represented by a periodogram) by Discrete Fourier Transformation (DFT).

To identify periodically expressed genes, we applied three different algorithmic approaches in our analysis of the microarray data: the Fisher's g-test of periodogram, autocorrelation, and the permutation test. The Fisher's g-test estimates nonrandomness of the dominating frequency in the periodogram from the signal-to-noise ratio. In our case, the signal is a diurnal frequency, reflected by a specific peak in the periodogram, and the noise level is estimated from the height of all other frequencies represented in the periodogram (see description in Materials and Methods). Autocorrelation is based on a different principle: if a gene expression profile is formed by a periodic process, it should have parts of the profile repeating each other. Autocorrelation analysis determines if the expression profile correlates with itself to a shift of one day, thereby identifying a diurnal periodicity. These first two approaches, Fisher's g-test and autocorrelation, have been widely used for analysis of periodic gene expression and have been recommended in recent publications [4,5]. We have developed a permutation test as a noise-resistant alternative for the analysis of periodicity in short time series. Like the Fisher's g-test, it starts with DFT, producing a periodogram. However, unlike other tests, all nondiurnal frequencies are ignored along with their associated noise. The nonrandomness of only a single diurnal peak is estimated in simulation experiments by random shuffling of the original time series (see description in Materials and Methods). Although this method would be computationally ineffective for a longer time series, analysis of microarray data with only 12–24 datapoints in each expression profile offers no computational challenge. We have further employed these analytical tools to analyze two previously reported, independent circadian datasets, each prepared from murine liver [3,6]. Our findings suggest that experimental design, dataset size, and the frequency of datapoint collection can significantly impact the experimental outcome. We conclude that analyses using Fisher's g-test and autocorrelation alone may underestimate the contribution diurnal rhythms to global gene regulation.

In the first step of our analysis, we applied standard procedures for the detection of circadian gene expression based on the widely accepted Fisher's g-test [7]. This estimation revealed only 650 genes shared in BAT, iWAT, and liver for which the p-value was less than 0.05, representing 12.8%, 14.8%, and 12% of the individual tissue oscillatory transcriptomes, respectively [8]. Within the periodic genes shared among these tissues were the circadian clock oscillator genes Npas2, Bmal1 (Arntl), Per1, Per2, Per3, and Cry1, as well as the circadian output gene Dbp. Our qRT-PCR studies [8] show these genes follow a circadian expression pattern (periodicity confirmed by cosine-fit analysis). A similar analysis of circadially expressed genes in BAT, iWAT, and liver using the permutation test developed by the authors revealed fewer (456) shared genes for which the p-value was less than 0.05 in all three tissues (Figure S1). However, among these genes there were more genes (nine) representing the circadian clock; based on mapping to the biological pathways (KEGG database), this is the largest functional category among genes periodically expressed in all three tissues (see Table S1). Functional annotation and mapping to the biological pathways of the tri-tissue overlapping list (see Table S2) suggests that most of the remaining genes with an oscillatory expression profile belong to the common “housekeeping” functional categories, indicative of basic cell physiology rather than tissue-specific functions.

The three algorithms used for microarray data analysis (Fisher's g-test, autocorrelation, and permutation test) revealed that ~20% of all genes in each tissue alone followed a circadian expression pattern with confidence levels of at least 95% (p ≤ 0.05). The results of the analyses are summarized in Figure 1 and Table 1. Although these values were higher than previously reported in the liver [3,9,10], they may still underestimate the actual number of oscillating genes in these tissues. As in previous reports, we examined these genes one at a time, and retained only those whose individual estimated p-value was ≤0.05. However, from a biological perspective, it may be incorrect to consider expression values solely as independent variables as rhythmicity may exist in the noise; indeed, Hogenesch et al. [2] have speculated that the circadian clock may regulate as much as 10% of the genome, which includes genes responsible for the basic cell metabolism. Since these genes all are elements of a common, complex network, any change in the expression of an upstream element can cause a significant alteration in downstream elements of the same biological pathway. Previous studies have documented a role for the circadian clock in the regulation of key metabolic pathways [6]. This implies that large groups of genes could oscillate in a coordinated manner and their expression patterns should be studied in relation to one another.

We have conducted a computer simulation to model the distribution of p-values obtained using each of our three algorithms. As a test case, we modeled a system where only a limited percentage of the genes were permitted to display a circadian expression pattern. We deliberately disrupted the oscillatory pattern by randomly rearranging the time points within each series. Consecutive simulations produced datasets where all genes were reshuffled, then 0%, 5%, 15%, or 50% of randomly selected genes were left intact, while all others remained in the shuffled format. For each simulated dataset, we applied the same analysis to identify periodically expressed genes similar to the original microarray dataset. Figure 2 shows the distribution of p-values obtained either from the permutation test or the distribution of the highest positive autocorrelations with a circadian lag. In both cases the distributions were significantly different from the original data. Even with a complete disruption of true periodicity (0% line), ~1,000, or ~5%, of the total transcripts display an apparent false-positive circadian rhythm. Since the time series is relatively short, and there is the potential for biological and technical variability exists, it is expected that some profiles may appear “periodic” for purely stochastic reasons. As expected, the occurrence of genes identified as components of the basic circadian mechanism (such as Clock, Bmal1, Cry, etc.) decreases as the portion of shuffled genes increases. Indeed, none of these are found among false-positive circadian genes when all 100% are shuffled. Thus, if only ~20% of the transcriptome followed a circadian rhythm, as initially observed, the p-value distribution would be expected to resemble the corresponding simulated curve, rather than the profile depicted in Figure 2.

A variety of statistical models have been proposed for the description of periodic gene expression [5,11], and these include factors such as the true deviation in gene expression level and the stochastic component. Shuffling affects the order of time points, but does not alter the observed levels of gene expression. Our simulation preserves variation of gene expression and does not affect the probability that the circadian oscillations are observed due to a random arrangement of “noise.” The observed distribution can be explained if we assume that the number of periodically expressed genes is at least >50%, rather than the 10%–15% previously reported. This difference implies that relatively few genes can be identified as “circadian” based solely on a p-value derived from a single gene in the face of stochastic noise (signal-to-noise ratio). As the degree of stochastic noise increases due to biological variability between individual animals, technical differences introduced by the microarray methodology, and other sources of “background,” the accuracy of time series analyses of circadian expression profiles decreases.

The observed distribution of p-values is clearly different from the simulated data, where an identified fraction of nonperiodic genes have been introduced. This conclusion is substantiated by the gene expression heatmap, presented in Figure 1. Within each phase-group (based on the relative circadian time of peak expression), expression profiles are sorted by their p-values in ascending order, and illustrate that there is no obvious point at which we can differentiate between periodic and constitutively expressed genes, thus recapitulating the fact that only a small fraction of all genes examined do not follow an oscillatory expression pattern. Alternatively, there may be enough circadian genes mixed in to trick the eye. Nevertheless, we postulate that the fraction of expressed genes with a constant steady state mRNA level (unaffected by circadian oscillation) does not exceed 50% of all genes (Table 1). The introduction of alternative analytical tools to more detailed circadian datasets is likely to reveal additional genes as circadially regulated. The concept of “steady state mRNA levels” may become a temporally dependent term.

To further prove the conclusion that the majority of the expressed genes oscillate with a circadian rhythm we have reanalyzed two additional independent datasets. The first independent dataset, provided courtesy of Dr. Storch [3], was collected from murine liver and heart. Each dataset consisted of 12 time points collected at even intervals of 4 h over a period of 48 h. The experimental design was similar to our own based on number of time points and the period of observation. The summary of analysis for the liver dataset is presented in Table 1 and Figure S2. In our analysis of their data, both the Fisher's g-test and the autocorrelation approach have yielded fewer circadian genes (3.2% and 2.2%, respectively) than their reports. However, the permutation test revealed circadian pattern in 17.4% of all genes, which is more than originally reported by the authors (4.6% of all genes in the liver dataset). As in the previous analyses, a visual inspection of the heatmap of phase-grouped expression profiles showed no clear landmark demarcating that fraction of genes with a non-oscillating profile, i.e., a flat line. Indeed, it would appear that the expression profile of the majority of genes shows an oscillatory pattern.

The second dataset was provided courtesy of Dr. Hogenesch [6] and contains microarray expression profiles of nearly 10,000 genes in murine liver, measured at 4-h intervals over a 48-h period with two replicates for each time point. Although similar to the microarray used in our analysis of the murine liver, this dataset represents fewer genes, has twice as many datapoints, and differs in the methods of sample collection and processing. Nevertheless, use of the same computational analyses of periodicities led to similar results. The Fisher's g-test revealed 511 circadian expressed genes with p ≤ 0.05, or ~5% of all genes examined (Table 1). The autocorrelation method identified 1278 or ~13% of all genes as circadially expressed. In contrast to the first two methods, our permutation test reported an oscillatory profile in ~43% of all genes. The heatmap, generated after assigning a phase to each expression profile, suggested that this latter method is likely to be a correct, although still conservative, estimation of the true number of circadially expressed genes (Figure S3). We conclude that the increased number and frequency of datapoints collected in this dataset permits a more accurate assignment of circadian rhythmicity to individual genes using the permutation test.

Recent reports have connected the basic circadian mechanisms to nutrient homeostasis [12]. Specifically, at least two components of the basic circadian pacemaker, Bmal1 and Clock, were found to regulate glucose levels, and thus play a significant role in the energy balance [12]. This finding is consistent with the accepted view that circadian clocks are important in driving the activity and feeding behavior in mammals. Our analysis of a large collection of time series expression profiles in peripheral tissues leads to the conclusion that a high percentage, possibly a majority, of all genes has an oscillatory expression pattern. Direct application of the standard methods for identification of circadian expressed genes to our data already revealed a larger percentage of oscillating genes relative to previous reports, ranging from 7%–21% of all, in contrast to previously reported fraction of 5%–15 % of “actively expressed” genes. To allow for a direct comparison, we have calculated the percentage of expressed genes based on the total number of gene expression profiles available in each particular dataset. The results are presented in Table 1. In part, the increase in the numbers of oscillating genes could be explained by the improvement in the microarray technology over recent years, permitting more transcripts to be identified. Yet, our simulation studies have shown that, if there were fewer oscillating genes, we would continue to detect them, even with the present degree of stochastic noncircadian variation. We believe the discrepancy may result from the traditional 0.05 cutoff for p-values as well as the assumption that each gene's expression profile should be tested independently. The data presented in Figure 3 illustrate the latter point. In cases such as Per2, where the microarray contained multiple probe sets for an individual gene, the p-values were not identical, and fell both above and below the 0.05 cutoff points. This observation may also account for the low percentage of overlap between the lists of circadian-expressed genes identified in different tissues [3,8]. The lists of genes in all three tissues coexpressed in a circadian manner with p ≤ 0.05 were dominated by those involved in basic cell metabolic activities as well as the elements of the circadian molecular oscillator themselves [3,8]. Additional qRT-PCR analysis was performed using primers for a randomly selected subset of genes included on the Affymetrix microarray that were not directly associated with the core circadian oscillator (Figures 4,5). The specific genes were: glycogen synthase 2 (GYS), lipoprotein lipase (LPL), peroxisome proliferator activated receptor γ coactivators 1 α and β (PGC1a, PGC1b), 6-phosphofructo-2 kinase/fructose 2,6 biphosphatase 3 (PFKFB3), and pyruvate dehydrogenase kinase isozyme 4 (PDK4). These genes had been identified as oscillating based on the permutation analysis uniquely in our liver dataset but not by the Fisher's g test in the liver datasets previously published [3,6]. All genes in the subset play an important role in energy metabolism and showed a pattern of peaks consistent with two complete diurnal periods. All qRT-PCR expression profiles displayed the same phase of oscillation as their microarray-derived counterparts. It is of interest to note that previously published studies have reported a diurnal or circadian oscillation of lipoprotein lipase serum enzyme levels in mice, rats, and humans, consistent with the current observations [13–16].

Permutation analysis of the liver data collected with the most comprehensive experimental design (based on the number of independent datapoints) [6], identified circadian expression in ~43% of the total number of genes (Table 1). The application of global transcriptomic approaches and statistical analytical tools permits a greater appreciation of the potential contribution of circadian biology to metabolism in peripheral tissues [3,4,6,9,10]. Our analyses lead us to conclude that circadian rhythms influence the expression of the majority of genes in metabolic tissues. Previous analyses using alternative statistical tools may have underestimated the full extent of the circadian contribution to gene regulation. The main reason for this underestimation might be that the null hypothesis is formulated on an equivocal assumption. It is commonly assumed that the default state for a gene expression over time is constant, only obscured by stochastic noise. Most currently applied methods test the data for the presence of oscillation based on signal-to-noise ratio. Applied on a gene-by-gene basis, these methods have limited resolution ability, curbed by the number of replicated periods in time series. Applying different methods, we observed continuous improvement but no obvious limit to the number of genes expressed in circadian oscillation pattern. This observation makes us question the basic assumption of the default non-oscillating expression. The alternative assumption would be that all genes in a living tissue are expressed in an oscillating pattern, only obscured by stochastic deviations. For a relatively small number of genes, a constant level of expression may be imposed by their function. In this case, expression profiles should be statistically tested for the absence of a circadian pattern. Our thesis of default assumption of oscillation for the timeline expression profiles is corroborated by the analysis of phase distribution in different datasets, presented in Figure 1 and in Figures S2 and S3. Each gene is assigned a proper phase by maximum correlation to an ideal sinusoidal profile.

Our conclusions have significant implications for investigators examining metabolic pathways related to diabetes, obesity, and their associated co-morbidities. First of all, the assumption of oscillation means that synchronization of time at which gene expression is measured for different experimental conditions is important for the majority of genes, not only for a fraction of circadian genes. Phase, along with fold change or amplitude, becomes an important factor in understanding gene expression. The biological importance of oscillation cannot be estimated by simply measuring amplitude and should be considered within a specific functional, spatial, and temporal context. Relatively small diurnal variations of upstream regulators may have a large impact on the downstream functions. Also, even without an absolute change in peak expression level, a phase shift can be equivalent to a downregulation at a defined time point. Hence, gene interaction within biological pathways should also be perceived and modeled in the context of the phase of a dynamic diurnal oscillation, similar to an alternating electrical current circuit, rather than by assuming it to be a static or unchanging process, similar to a direct electrical current circuit.