# Data Analysis

1. Plot the activity data as a vertical stack of 24-h traces. This is called an actogram or actograph (see Fig. 1). Alternatevely, produce double- or triple-plotted actographs (Fig. 1) by stacking the data in overlapping 48- or 72-h traces.

2. Analyze the actogram by visual inspection in order to estimate the following parameters:

• Amplitude: The difference between peak and trough of activity.

• Circadian time (CT): Subjective time of the organism in which one circadian period is divided into 24 equal parts (circadian hour). By convention CT 0 corresponds to subjective dawn and CT 12 corresponds to subjective dusk.

• Activity onset and offset: The times of day when the animal starts and ends its activity, respectively (Fig. 2; see Note 6). Calculation of these parameters can be easily obtained by eye-fitting connecting with a line the start or the end

Mouse 43789 5/25/98

Mouse 43789 5/25/98

Time (hrs)

Fig. 1. Double plotted actogram of locomotor activity over a 60-d period. Changes in the light-dark cycle are shown on the right. Note the effect of a light pulse (LP) on the circadian rhythms (courtesy of Actimetrics and Dr. J. S. Takahashi, Northwestern University).

Time (hrs)

Fig. 1. Double plotted actogram of locomotor activity over a 60-d period. Changes in the light-dark cycle are shown on the right. Note the effect of a light pulse (LP) on the circadian rhythms (courtesy of Actimetrics and Dr. J. S. Takahashi, Northwestern University).

of locomotor activity (represented by the dots on the left and right side of Fig. 2, respectively) for each subsequent day.

• Alpha (a): The portion of the daily rest-activity cycle corresponding to the activity period (Fig. 2). Alpha can be easily calculated by measuring the interval (in units of time) between activity onset and offset.

• Rho (p): The portion of the daily rest-activity cycle corresponding to the rest period (Fig. 2). Rho corresponds to the interval (in units of time) between activity offset and onset.

• Free-running period (FRP) or tau (t): The periodicity of the rhythm in the absence of any external cue. It can be estimated by calculating the linear regression of the activity onset.

• Total activity: the total number of running-wheel turns (or movements) recorded during 24 h.

• Phase shift: The shift in locomotor activity with respect to a reference (typically the pattern of activity under light-dark conditions) after a disturbance of the circadian clock (Fig. 3). It is determined by measuring magnitude and direction (i.e., advance or delay) of the difference in the onset of activity before and after the phase shifting stimulus was presented (see Note 7).

N6F20515 Percentiles 10 15 0 50 0 710 810

N6F20515 Percentiles 10 15 0 50 0 710 810

Fig. 2. Calculation of a and p using the ClockLab data analysis kit. The dots on the left and right sides indicate the onsets and offset of the daily activity, respectively. The interval between the left and right lines represents a, wheras p is represented by the opposite. Usually, as shown by this example, the activity onset show a more consistent pattern than the activity offset (courtesy of Actimetrics and Dr. J. S. Takahashi, Northwestern University).

Fig. 2. Calculation of a and p using the ClockLab data analysis kit. The dots on the left and right sides indicate the onsets and offset of the daily activity, respectively. The interval between the left and right lines represents a, wheras p is represented by the opposite. Usually, as shown by this example, the activity onset show a more consistent pattern than the activity offset (courtesy of Actimetrics and Dr. J. S. Takahashi, Northwestern University).

• Transients: the variability in the onset of locomotor activity observed in the 2 to 3 d that follow a phase shift (see Note 7).

• Splitting: this term is used to describe when the FRP separates into two different components.

Although the visual inspection of actograms can provide useful information about the periodicity of the rhythm, it cannot provide an accurate estimate of the FRP. The most commonly used statistical method to estimate the FRP is the periodogram analysis developed by Enright (4) and then refined by Sokolove and Bushnell (5). This method utilizes the chi-square (x2) distribution to determine the statistical significance of the calculated FRP. The x2 periodogram analysis presents the best combination of accuracy, tolerance to waveform irregularity, and tolerance to noise. However, it is important to note that the x2 periodogram analysis cannot be applied to time-series data that have been collected at irregular intervals or with many missing points. Other methods currently used to calculate the FRP of locomotor activity include Fourier analysis (6), autocorrelation (7), and linear regression of the onset (8).

N6FZ051S Peiceutiles i 0 16 0 50 0 71 0 82 0

N6FZ051S Peiceutiles i 0 16 0 50 0 71 0 82 0

Fig. 3. Phase shift of locomotor activity calculated with ClockLab data analysis kit. Note the instability of the activity onset immediately after the phase shift (courtesy of Actimetrics and Dr. J. S. Takahashi, Northwestern University).

Several companies have now developed software packages that allow automated analysis of circadian parameters. The following list provides a brief description (and the company website, where more detailed information is available) of the most commonly used programs:

• Actiview. This software has been developed by Minimitter (www.minimitter. com) and allows the analysis of most circadian parameters.

• ClockLab. This program has been developed by Actimetrics (www. actimetrics.com) and allows the calculation of all circadian parameters previously mentioned.

• The Chronolobiology Kit. This software (www.query.com) includes the capability to produces actogram, periodogram, and rhythm profiles.

4. Notes

1. Because working in complete darkness is very difficult, many laboratories are now using red dim light (<1 lux) instead of complete darkness.

2. The monitoring of locomotor activity by running wheel is relatively inexpensive, as running wheels can be easily built in the laboratory. It is also very reliable and convenient, as it can be used for several different species (i.e., rat, mouse, and hamster).

3. Because the transmitter needs a battery, the major limitation of this method is that the transmitter must be replaced every 2 to 3 mo, making it unsuitable for long-term studies. However, it must be mentioned that a new technology (transponder) that does not require batteries has been recently developed.

4. The major advantage of telemetry is that the same transmitter can monitor other parameters, such as body temperature and heart rate, in addition to locomotor activity. However, telemetry monitoring can be expensive and the need for surgery to implant the transmitter can be seen as a further complication.

5. As for the running-wheel method, the infrared sensor system is relatively inexpensive and can be easily assembled in the laboratory.

6. The FRP varies slightly among individuals and different animals may be at different circadian times at the same local time on the same day. Therefore, establishing the activity onset is very important to calculate the subsequent CT when the experiment requires the sampling of fluids or tissues of free-running animals at different CTs.

7. Because the onset of activity may show some variability for 2 to 3 d immediately after the phase shift, it is preferable to measure the phase after this interval and when the FRP has reached the steady state (see Fig. 3).