In most animals, circadian clocks orchestrate behavioral and molecular processes and synchronize them to daily light-dark cycle. In fruit flies, the clock is typically studied using locomotor recordings. Here is an example of average wild type locomotion measured in 12-hour light, 12-hour dark cycle, the light-dark cycle shown with yellow-black bar on top.

A typical fly recording shows a complex, biomodal pattern with two peaks of activity, a morning peak that happens around dawn and an evening peak that happens around dusk. These two peaks together form a waveform that is very different from sinusoidal oscillations observed in clock genes, suggesting that mechanisms, in addition to the clock, have profound effect in producing the observed pattern in behavioral data. Here we present the first method that mathematically describes temporal pattens in fly activity.

We fit activity data with a model waveform that mimics fly locomotion. Our model consists of four exponential terms, two terms from the morning peak and two terms from the evening peak. Together with circadian period, our model has nine independent parameters.

B parameters define the rate of morning rise, morning decay, evening rise, and evening decay. TM and TE define widths of the morning and evening peaks, and HM and HE define heights of the peaks. Together these parameters fully describe size and shape of the morning and evening peaks in the activity pattern.

Our method can be applied to elucidate the mechanisms and substrate that underlie the commonly observed bimodal activity pattern in fly locomotor readings. For the locomotion experiment, prepare individual tubes with food on one end and cotton on the other. For that, first, put five to six grams of fly food in a 50-milliliter beaker.

Cut food into small pieces, so it will be easier to melt it in the microwave. Single activity monitor fits 32 individual tubes. Therefore, take 32 tubes and connect them together using a rubber band.

Melt the food in the beaker in a microwave. Heat the food for approximately 10 to 15 seconds. Stop microwave every five seconds, and shake the beaker with food a little bit to ensure equal melting of the food.

Make sure that all food is melted and there are no solid pieces of food left in the beaker. While food is still liquid, insert tubes in the beaker with food. Move tubes up and down a little bit, so they are equally filled.

Let the food cool down and solidify for approximately one hour. After food is solid, remove tubes from the beaker using rotational motion so that food won't stuck to the bottom of the beaker. Then remove the rubber band.

Seal the end with food using wax. For that, first, carefully wipe the tube using a paper towel. Then press the tube against the wax.

Visually check the quality of the seal, and, if necessary, repeat the sealing again. Using this technique, seal all the tubes for the experiment. The other end of the tubes close with the cotton.

The cotton will let the air to go through while keep the flies locked inside the tubes. It is also easy to remove and put back in, which will be useful when we will load the tubes with the flies for the experiment. Now, after tubes are ready, load them with flies for the experiment.

For that, unload flies on the pad with CO2. Then, using brush, carefully put single fly in each individual tube. Put the tube with the fly in the monitor.

In the same order as in the monitor, fly locomotion will be recorded in the output file by the monitor system. Connect monitor to the computer, and place it in an incubator that maintains constant temperature and humidity. Based on the experiment, set the proper light/dark conditions.

For light/dark experiment, keep flies in light-dark cycle for the whole experiment. Do not use the first day of measurements in the analysis. For constant darkness experiment, first, keep flies for two days in light/dark conditions for entrainment and synchronization of the clocks, and then switch to constant darkness.

Do not use measurements from the first day of constant darkness in the analysis. Before moving to the next section, we recommend reading the protocol. The monitor system will output a single file that contains activity of all flies in the monitor.

Last 32 columns of the output file contains activity of individual flies. Our program works with single fly activities. Therefore, split the output file into multiple single fly activity files.

Each file should be a single-column TXT file. Now, after we prepare the activity files, we can run our analysis. Run the ModelFitPS3 function in MATLAB Command Window with the following input parameters.

Sampling rate, put data sample time interval in seconds. For example, our data was taken with 20-second sampling rate. Therefore, we put 20 here.

As bin interval, put time interval in minutes, to which data will be binned for better visualization. We recommend binning to 20 or 30 minutes, but, for now, I will put 10 here, just to show you later how it can be easily changed. For trend, put one if data shown baseline trend and zero otherwise.

Our data doesn't have any baseline trend. Therefore, I put zero here. Press Enter to run the function.

In popup window, select single fly activity file, and press Open. The program will calculate and plot data power spectrum. In this window, determine the primary period in the data.

For that, either click with left mouse button on peak at circadian period or with right mouse button on peak at second harmonic, replicated approximately at circadian period divided by two. In our case, peak at second harmonic is much bigger and sharper than peak at circadian period. Therefore, we use second option.

Then, program will plot data binned to the selected bin interval. As you can see, at 10-minute bin interval, morning and evening peak are not very well-visualized. Therefore, we want to change this value.

To do that, simply right-click anywhere on the graph. In the new dialog box, type the new value for the bin interval. We recommend binning to 20 minutes time interval.

Therefore, we put 20 here. Press OK.The program immediately redraws the data with the new value of the bin interval. To accept this value, simply left-click anywhere on the graph.

The program now will redraw the data and show only five days of measurement. This window, select the first morning peak that will be used in the analysis. Sometimes it's necessary to skip first one or two days, which takes for fly to adapt to the light-dark cycle.

To select the morning peak, simply click on the preferred peak. Program will redraw the data, and now show only three days of measurements starting from the selected morning peak. The blue and red vertical lines show the first evening peak and second morning peak based on the period selected in the first window.

In this window, select the point the tube used for preliminary fit of the data with the model function. For that, click on the following points in this particular order. First, click on the top of the first morning peak.

The click is indicated with the red star on the bottom, showing the location of the click. Then click on the end of the morning peak, then on the start of the evening peak, then on the top of the evening peak, then on the end of the evening peak, and last on the top of the morning peak of the next day. The program will plot the power spectrum again since the final parameters are obtained from spectral fit.

The spectrum now is plotted as frequency on the x-axis, and circadian peak is located on the left side of the plot. The period determined in first step is shown with red vertical line. To select fitting points, first, roughly determine the primary period.

For that, either left-click on peak at circadian period, or right-click on peak at second harmonic. We will again use second option. After that, a slider will appear on the bottom to select the points for the spectral fit.

The points will be shown with red circles and will appear after moving the slider. Move slider left and right, and place the points as close as possible to the tops of the spectral peaks. After the best picture is achieved, press the Accept button, and the program will fit the selected points with the analytical expression for model power spectrum.

After fitting, the program will output two more graphs. First is a power spectrum of the model constructed with the extracted parameters. Second is data fitted with the model.

Data is shown with black line, and the model is shown with red line. It can be seen that function closely resembles the data, especially the last three days of activity. The extracted parameters are saved to the model fit parameters TXT file.

After the name of the file, the parameters are saved in the following order, first b of morning decay, then b of morning rise, b of evening rise, b of evening decay, circadian period, then width of morning peak divided by the circadian period, width of evening peak divided by the circadian period, height of morning peak, height of evening peak, and the fitting error of the spectral fit. In addition to the model fit parameters file, the program will also output two more files. First, is the data fit with the model function, and second is a spectral fit.

Perform this analysis with other activity files. All extracted parameters are saved to the model fit parameters TXT file and can be further used to connect behavioral output to underlying mechanisms that regulate fly daily behavior controlled by model activity pattern.