Peripheral tissues were dissected from D. melanogaster adults as described in Krishnan et al . The per-luc (BG-luc) and tim-luc transgenic strains were originally described elsewhere [20, 21]. Automated monitorings of luciferase (LUC) activity were the same previously described [20, 23]. All of the data from light-dark cycles (LD 12:12) and from constant darkness (DD) were from the LUC monitorings reported in Krishnan et al , although most of the pertinent data were not separated as to per-luc versus tim-luc expressions, and many of the results were included as supplementary material. Additional cry
+ specimens in Table 1, which did not appear in the earlier report, have been included here, substantially to augment the appreciation of normal clock-gene cycling in isolated tissues. We also include data from additional experiments collected under constant high temperature (27°C) . These data were collected after the submission of the earlier report.
In these new experiments flies were reared in DD and in temperature cycles (12-hr 27°C: 12-hr 18°C). One-to-three day-old ether-anesthetized males were collected and housed for 2 days in these same conditions before the antennal pairs were dissected. The antennal pairs were placed immediately in luciferin-containing medium in 96-well plates and transferred to the luminometer (as described in ), where they were exposed to 2 additional days of the temperature-cycle in DD before being maintained at a constant temperature of 27°C for the duration of the LUC-monitoring runs.
The basic flow-chart for handling data from a given specimen and from an ensemble of like ones was as follows: Each record was evaluated for an adequate level of expression above 'no-specimen' background to insure that the tissue had survived and was producing valid data [cf. ]. If expression levels were adequate, the specimen was assessed for rhythmicity. Temporally varying LUC activity was detrended and normalized as described in Figure 1. Next, autocorrelation analysis  was performed to look for a rhythmic pattern of activity. The correlogram is a plot that reports correlation-coefficient values on the vertical axis versus time-lags plotted on the horizontal axis. Zero lag always provides a value of 1, because the correlation is perfect between the activity record and a copy of itself at each point. However, as one copy of the activity record is shifted along the time axis (in either direction) by one point (in other words, a lag of 1 hour), the correlation falls off. This process is repeated, and a correlation coefficient is calculated for the activity record against itself for each lag shown in the correlogram (see bottom row of Figure 1 for an example). If the correlation coefficients fall and rise in a periodic fashion, resembling a sinusoidal curve, the record of LUC activity is "rhythmic." As to whether such periodicity is significant, a 95% confidence interval is calculated based on the number of observations in the experiment. Rhythmic activity is statistically significant if the peaks and troughs of the autocorrelation function cross the boundary set by the confidence interval centered at 0 on the correlogram (for further detail see  and references therein). As noted above in Results text, we do not require statistical significance to score a record as rhythmic. The appearance of rhythmicity in the correlogram is applied as a qualitative criterion so that we do not treat weakly rhythmic data as arrhythmic data. The justification for this strategy is given in Levine et al . In addition, we keep track of the number of specimens that generated statistically significant rhythms as indicated in Table 1 and Table 2.
We quantify the strength of a rhythm with the aforementioned Rhythmicity Index. RI is the height of the third peak of the correlogram [27, 31]. Whereas the confidence interval for the correlogram is based solely on the number of observations, the RI value is based on the robustness of any regular fluctuations in the data. For example, we record LUC activity every hour. If we increased the sampling frequency from once every 60 minutes to once every 30 or 15 minutes, the confidence interval would become smaller while the shape and amplitude of the correlogram would presumably remain unchanged from the curve obtained by 60 minute sampling. The RI value, however, would not vary, while the estimates of statistical significance would vary according to the sampling frequency.
It is nevertheless informative to monitor the statistical significance of periodicities; for this we devised a ratio that allows us to track whether or not a specimen is significantly rhythmic, the so-called Rhythmicity Statistic (RS). An RS value is a ratio of the RI value to the absolute value of the 95% confidence line. If RI is equal to or greater than the numerical height of the confidence line, then the rhythm is significant (by definition, the height of the peak is ≥ the height of the confidence interval used to determine statistical significance). Alternatively, if RI is less than the confidence line, the rhythm is not statistically significant. Thus, RS provides a numerical accounting of significance for an individual specimen or an average signal.
We define the amplitude of a rhythmic LUC time-course as the (plotted) distance (in arbitrary units) from the mean peak or mean trough of the normalized activity record to 1 (the latter is always the mean value of detrended and normalized data, as exemplified in Figure 1). The complete range of the rhythm is twice the amplitude.
Most of the analyses applied in the current study were described in detail in the companion paper . We augmented such treatments of the data by developing two additional parameters, the Rhythmicity Statistic (RS) and a metric that allows specification of cycling amplitude. Analyses leading to the rhythmic parameters were applied to individual samples; their averages appear in Tables 1 and 2. In addition, averages of the LUC data computed across all records within a given group (which varied as to body part, luc reporter type, and cry allele) were obtained; and such averaged time-courses were formally analyzed, as shown in Figures 3,4 and Figures 5,6. Consequently, there are differences between the Tables and Figures in values of parameters such as the Rhythmicity Index (RI, see below), because the tables specify the means determined from individual-specimen analyses, while the figures provide parameters determined after computing the average time-courses.
Maximum Entropy Spectral Analysis (MESA) was employed to estimate the period of a rhythm, i.e., for a given time-course previously determined to be significantly periodic by correlogram. This method is presented in detail elsewhere [37, 27].
We have discussed the analysis of phase using circular statistics in the companion paper . Briefly, an average estimate of peak phase, obtained for each specimen, is plotted as a point on a unit circle. A mean vector, extending from the center of the unit circle towards the diameter is calculated for each group of points; the direction of the vector indicates mean peak phase for the group and the length of the vector represents the variability or dispersion between the points (phase estimates for each specimen). The Watson-Williams-Stevens test returns an F-statistic for the comparison of vectors between two groups to determine whether they represent significantly different estimates of phase (see Figures 5,6 and [27, 32] for further detail).
One disadvantage of this phase analysis is the loss of information about the variability of phase across cycles for each specimen. Therefore, we have also introduced another approach using bivariate statistics to represent the molecular cycles more completely . In this approach, the record of each specimen is represented as the tip of a vector whose direction indicates the mean phase estimate (as above) and whose distance from the origin in the x-y plane represents intraspecimen variability (see Figures 7,8). Each group appears as a distribution of points. A mean vector extending from the origin to the center of the distribution is calculated to describe the overall mean peak phase and variability of the group of points (see Figures 7,8, for example). Finally, the two groups are compared using Hotelling's two-sample test to determine whether the respective vectors are different. If a significant difference between vectors is obtained, this method does not specify whether the difference is due to the variability, the peak phase estimate or some combination of the two.
All of the analyses described above as well as the subsequent output (the figures) come from programs written for the current study and the just-previous one  using Matlab6 (Mathworks). This software is available on request.