Data Analysis

The data analysis is described in Subheadings 3.6.1. through 3.6.4., and will focus on using the "standard" luc rhythm analysis package (2,16). Another software package has been developed for analyzing luc rhythms that runs in MatLab (19). We have not used this software package to analyze luc data, and thus will not be discussing this package further. Our description of luc data analysis includes raw data import by I&A software, raw data modification, FFT-NLLS analysis, and graphic analysis of output (Fig. 1). It is advisable to analyze the data on a separate Windows PC rather than in the TopCount Windows NT to accommodate the next run.

3.6.1. Raw Data Import

I&A software is an interface between Microsoft Excel and the raw data time series collected by the TopCount. I&A can import luminescence output from the TopCount into an Excel spreadsheet format, thus enabling the use of Excel analysis functions such as graphic and statistical analysis. I&A is also designed to interface with the FFT-NLLS software that is used to analyze rhythmic time series data. Readers should refer to the website of Steve Kay's laboratory (www.scripps.edu/cb/kay/ianda/) for details on the use of I&A software. The order on the I&A data sheet can be tracked from the "Sample Map" that was defined when setting up the TopCount monitoring program (e.g., in a given plate, data in well No. 1 are from the sample UNK001; see Note 5).

3.6.2. Raw Data Modification

1. Discard data from any unhealthy flies. Unhealthy flies are defined as those having less than 1000 cps for tim-luc or less than 200 cps for per-luc on day 6 of the run.

2. Discard the data from the first partial LD cycle (i.e., the first 13 to 24 h of data, assuming sample loading was performed in the light) to allow for the inactivation of not recently synthesized luciferase (16).

After these steps, the modified raw data time series is now ready for analysis.

3.6.3. FFT-NLLS Analysis

FFT-NLLS is employed to extract rhythms from the modified raw data. Modified raw time series data are initially detrended via linear regression to produce data with a slope of zero and a mean of zero, which are then subjected to FFT. An FFT power spectrum is calculated, and the period and phase values of the most powerful spectral peak are used as a starting point for a sequential nonlinear least squares multicomponent cosine analysis (2).

1. Export data from I&A (Version 99.8.31) to the FFT-NLLS program. Only one plate can be exported and analyzed at a time. Designate the data to be analyzed by selecting the start and end time-points, and then export these data to the folder containing the FFT-NLLS program. Enter a unique file name for the exported data. After export, a file will be generated for each sample on the plate, and a ".in" file will be generated for the entire plate. All of the files generated in this step can be found in the FFT-NLLS folder.

2. Run FFT-NLLS analysis.

a. The FFT-NLLS software is run in DOS. To change the working environment to DOS, go to the "Start" menu and select "All Programs," on the list of choices select "Accessories," then on the next list of choices select "Command Prompt." Once you have a command prompt, change directory into the FFT-NLLS directory.

b. To perform FFT analysis, enter "\four-anl < filename.in". This analysis will generate a ".sum" file in the FFT-NLLS folder.

c. To generate theoretical curves for each sample, the bestplot.exe program is run by entering "\fls-plot filename.sum filename.out 0 1". This analysis produces ".the" files for each sample and a ".out" file for the entire plate in the FFT-NLLS folder.

d. To condense the data in the ".out" file into an easily readable form, run the condense program by entering "\condense". The program will show the prompt "FLS-PLOT output file to condense," which should be responded to by entering "filename.out". The next prompt to appear is "Name of condensed file to produce," which should be responded to by entering "filename.cnd". The next prompt to appear is "Choose lower, upper period to keep," which is typically set to a range of between 10 and 50 h by entering "10,50". After performing these steps, a ".cnd" file is generated in the FFT-NLLS folder.

3. To read the data analyzed by FFT-NLLS, they must be imported into the I&A program. To import the data, go to "Import" under the I&A menu and select "Condensed files." In the dialog window that appears, choose a destination folder to place the ".cnd" files. Each ".cnd" file appears as a sheet within an Excel file that contains the relative amplitude (Rel-Amp), period, and phase values generated by FFT-NLLS for each fly. The theoretical curves for each sample can be imported via the same procedure as the condensed files. In this case, "THE files" are selected in "Import" under the I&A menu. In the dialog window that appears, choose a destination folder to place the ".the" files. Each ".the" file appears as a sheet within an Excel file that contains theoretical time series values generated by FFT-NLLS for each fly.

Rel-Amp is an indicator of rhythmicity. Theoretically, the range of Rel-Amp value is from 0.0 to 1.0. A value of 0.0 means a rhythm is infinitely precise and 1.0 means a rhythm is not statistically significant. By testing luciferase activity of hsp-luc flies, Stanewsky et al. determined that a Rel-Amp value below 0.7 can be considered rhythmic with 95% confidence (16).

3.6.4. Graphic Output

The following steps describe how graphic output is generated for individual flies and groups of flies (Fig. 1).

3.6.4.1. Individual Plotting

1. Generating raw data plots. You can generate graphs of raw data time series (Fig. 2A) for individual flies in either an I&A data sheet or in Excel. This is done by using the "Chart Wizard" to make a line graph from the selected samples.

2. Butterworth filtered data plotting. Both linear and nonlinear trends are common in time series data from luciferase assays. These trends are thought to be caused by the depletion of substrate from the medium over time. A Butterworth filter is employed to remove linear and nonlinear trends, and to filter out high-frequency (<3 h) and low-frequency (>72 h) noise (19). This filter takes a time series x(t) and transforms it into another time series y(t) by calculating the mean of present and past luc activity values (i.e., Xt, Xt-1, •••Xt-n) to generate a moving average. This transformation produces a phase shift in the data that is removed by running the filter twice, once in the forward direction and once in the reverse direction.

a. 3-h forward and reverse filtering. The value of each time point in the modified time series is transformed to the mean of three points: a given time point and the two time points preceding that time point, i.e., Yt = (Xt-2 + Xt-1 + Xt)/3. With this manipulation, a 3-h forward-filtered time series is generated. The value of each time point in the 3-h forward-filtered time series is then reverse-

Fig. 2. Effects of filtering and normalization on bioluminescence time series data. Plots of a single yw;tim-luc fly monitored during light-dark (LD) and constant darkness (DD) conditions. Bioluminescence was measured in counts per second (cps). The x-axis indicates hours from the second LD cycle (data from the first partial LD cycle was discarded). Data from 0 to 72 h were collected during LD cycles, and data from 72 to 144 h were collected during DD. Open bars indicate lights on, hatched bars represent

Fig. 2. Effects of filtering and normalization on bioluminescence time series data. Plots of a single yw;tim-luc fly monitored during light-dark (LD) and constant darkness (DD) conditions. Bioluminescence was measured in counts per second (cps). The x-axis indicates hours from the second LD cycle (data from the first partial LD cycle was discarded). Data from 0 to 72 h were collected during LD cycles, and data from 72 to 144 h were collected during DD. Open bars indicate lights on, hatched bars represent

Firefly Luciferase Activity Assays Q 180000

Fig 2. (continued) subjective lights on, and closed bars indicate either lights off (in LD cycles) or subjective lights off (in DD). (A) Raw time series bioluminescence data. (B) Data from panel A that has undergone 3-h or 72-h filtering. (C) Detrended time series data from panel A. (D) Normalized time series data from panel A.

filtered by transforming them to the mean of three points: a given time point and the two time points following that time point. The resulting 3-h filtered time series removes periodicities less than 3 h from the raw data time series (Fig. 2B).

72-h forward and reverse filtering. The value of each time-point in the modified raw data time series is transformed to the mean of 72 points: a given time point and the 71 time points preceding that time point, i.e., Yt = (Xt.71— + Xt-1 + Xt)/72, to generate a 72-h forward-filtered time series. Then the value of each time point in the 72-h forward-filtered time series is transformed to the mean of 72 points: a given time point and the 71 time points following that time point to generate a 72-h filtered time series. This 72-h filtered time series serves as a trend line (Fig. 2B).

Detrending the time series. For each time point, subtract the value of the 72-h filtered time series from the value of the 3-h filtered time series. This manipulation removes the trend from the time series (Fig. 2C).

Normalizing the time series. For each time point, divide the value of the 3-h filtered time series by the value of the 72-h filtered time series. This manipulation normalizes the time series, whereby the mean is adjusted to 1 (Fig. 2D). Normalizing the time series removes the units of measurement (cps) and emphasizes the relative rather than absolute value. This manipulation makes it easier to observe percent changes in values that are fluctuating above and below the trend line. In an Excel sheet, you can generate the following:

a. A trend curve for a given fly from the 72-h filtered time series that reflects linear and nonlinear trends (Fig. 2B).

b. The smoother-appearing time-course graph from the 3-h filtered time series (Fig. 2B).

c. The detrended time-course graph from the detrended time series that removes linear and nonlinear trends from the original time series (Fig. 2C).

d. The normalized time-course graph that increases the viewable amplitude of oscillations in the later cycles (Fig. 2D).

3. FFT-NLLS-derived theoretical curve. Using the imported ".the" files, an FFT-NLLS-derived theoretical curve can be generated for individual flies. This is useful to make comparisons to the filtered data from steps 1 and 2 above, but is not required for analyzing luc rhythms per se.

3.6.4.2. Group Average Plotting

After individual plotting is finished, the group average can be plotted for raw data time series, 3-h filtered time series, and detrended and normalized time series. Alternatively, you can generate group average time series from the raw data and then carry out the detrending and normalization using the group average time series. By plotting the group average, the overall expression level, oscillation amplitude and waveform, and the phase can be evaluated for different genotypes.

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