A Computational Method to Quantify Fly Circadian Activity

Summary

A method to quantify the main temporal features seen in fly circadian locomotor rhythms is presented. The quantification is achieved by fitting fly activity with a multi-parametric model waveform. The model parameters describe the shape and size of the morning and evening peaks of daily activity.

Abstract

In most animals and plants, circadian clocks orchestrate behavioral and molecular processes and synchronize them to the daily light-dark cycle. Fundamental mechanisms that underlie this temporal control are widely studied using the fruit fly Drosophila melanogaster as a model organism. In flies, the clock is typically studied by analyzing multiday locomotor recording. Such a recording shows a complex bimodal 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 effects in producing the observed patterns in behavioral data. Here we provide instructions on using a recently developed computational method that mathematically describes temporal patterns in fly activity. The method fits activity data with a model waveform that consists of four exponential terms and nine independent parameters that fully describe the shape and size of the morning and evening peaks of activity. The extracted parameters can help elucidate the kinetic mechanisms of substrates that underlie the commonly observed bimodal activity patterns in fly locomotor rhythms.

Introduction

The circadian clock is an endogenous biochemical oscillator with a period of approximately 24 hours and is almost ubiquitous in animals and plants^1,2. The clock helps synchronize an organism's internal processes and behavior to the external light dark cycle. The genetic structure of the circadian clock has been widely studied since the 1960s using the fruit fly, D. melanogaster. In this insect, the core of the circadian clock consists of four proteins: PERIOD, TIMELESS, CLOCK, and CYCLE. These core components together with other molecules form a feedback loop that produces nearly sinusoidal oscillations of clock genes^3,4. The circadian clock in flies is widely studied using multiday locomotor recordings where fly activity is detected with a single infrared beam crossing the middle of an individual tube⁵. A typical fly recording has a complex bimodal pattern with two well distinguishable peaks: Morning peak (M) that starts at the end of the night and has a maximum when lights turn on; and Evening peak (E) that starts at the end of the day and has a maximum when lights turn off⁶. Interestingly, the shape of such behavioral recording is very different from the simple sinusoidal oscillations observed at the molecular level, suggesting the action of additional mechanisms contributing to the observed temporal patterns. To better understand these hidden mechanisms, we have developed a computational tool that provides a quantitative description of the temporal patterns.

In our work, locomotor rhythms are defined in terms of a waveform that mimics fly activity pattern. Since simple sine waves cannot be used to model the observed rhythmic changes in activity, we tested various signal shapes to select the simplest one that captures all the salient features seen in the recordings. Fruit fly circadian behavior is controlled by the activity of clock neurons that often have exponential patterns of activation and deactivation⁷. The exponential dynamics and visual analysis of the data motivated us to build a model with exponential terms consisting of four exponents with nine independent parameters and closely resembling the fly activity pattern⁸. In addition to the locomotor data, we also analyze its power spectrum. Typical fly activity spectrum shows multiple peaks at harmonics T₀/2, T₀/3, etc., in addition to the expected fundamental peak at the circadian period T₀. According to the Fourier theorem, only a pure sine wave produces a single peak in power spectra, while more complex waveforms show multiple spectral peaks at harmonics of the primary period (Figure 1). Therefore, given the non-sinusoidal temporal pattern in fly activity⁸, a multi-peak power spectrum of the data is mathematically expected and does not necessarily imply the presence of multiple periods of oscillation. Importantly, the power spectrum of the proposed model waveform also shows peaks at all harmonics of the primary period, similar to the fly locomotor recordings, thus underscoring the high fidelity with which our model describes fly data both in time and in frequency.

At time resolutions of a few minutes or less, fly activity data appears noisy, making it difficult to extract parameters directly from the raw data. Binning data into longer time intervals can decrease noise level, but, can alter the data in ways that can affect the estimation of model parameters. We therefore obtain the parameters from power spectra of the recordings, using an analytical expression for the expected power spectra calculated from the Fourier transform of the model function⁸ (see Additional File 1 of reference⁸). This approach of obtaining parameters from the power spectra yields accurate parameter values without any additional manipulations, such as binning or filtering, of the raw activity data. Mathematical details of the model and applications to wild-type and mutant data are described in reference⁸. The protocol presented here focuses on the step-by-step instructions to use the computational tool.

Protocol

1. Measuring Fly Locomotion Using Drosophila Activity Monitor (DAM)

NOTE: For more details see reference⁵.

1. Prepare individual fly tubes with food on one end and cotton on the other. The end with food should be sealed to prevent the food from drying out.
   1. Put 5-6 g of fly food in a 50 mL beaker. Cut the food into small pieces so that it is easier to melt it.
   2. Connect 32 individual glass tubes with a rubber band.
   3. Melt the food in the beaker by heating it in a microwave oven for 10-15 s. Stop the microwave every 5 s and carefully shake the beaker to ensure equal melting of food.
   4. While the food is still liquid, put the prepared individual tubes in the beaker with food. Move the tubes up and down so they are equally filled.
   5. Allow the food to cool down and solidify for approximately 1 h.
   6. After the food is solid, remove the tubes with the food from the beaker.
   7. Seal the end containing the food using wax. First, carefully clean a 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.
   8. Close the other end of the tube with cotton; cotton will permit air to go through while keeping a fly locked in the tube.
2. Place a single fly in each individual tube and place the tubes in the DAM.
3. Place monitors in an incubator that maintains constant temperature and humidity. Based on the experiment, set the proper light/dark conditions as follows.
   1. For light/dark experiments keep the flies in light/dark cycle for the whole experiment. Do not use the first day of measurements in the analysis.
   2. For constant darkness experiments, first keep the flies for two days in light/dark conditions for entrainment and synchronization of the clocks and then switch to constant darkness. Do not use the measurements from the first day of constant darkness in the analysis.
4. Collect at least four days of data that can be used in the analysis.
   NOTE: The DAM system will output a single file with a locomotion recording of all flies in the monitor.

2. Data Analysis

1. Split the monitor output file into multiple single fly activity files; each file should be a single column '.txt' file with an individual fly locomotion measurement.
2. Run 'ModelFitPS3.m' function in a Matlab command window with the following input parameters:
   1. For samplingrate, set the data sampling time interval in seconds. For example, if activity was measured every minute, enter 60 as the samplingrate.
   2. For bin_interval, set the time interval in minutes to which data will be binned for better visualization; the recommended bin interval is 20-30 min.
   3. For trend, enter "1" if the data show baseline trend and "0" otherwise; data with trend will be detrended first by fitting a second order polynomial and then subtracting it from the data.
3. In the popup window select a single fly activity file.
   Note: The first plot is data power spectrum, and not the familiar activity plot. From the plotted power spectrum, determine the primary period T₀: Either click with the left mouse button on the circadian peak, or with right mouse button on the second harmonic peak (around T₀/2).
4. On the opened data plot, check if the morning and evening peaks are well visualized. If not, change the bin_interval value by right clicking anywhere on the graph and inputting the new bin_interval value in the dialog box. The program will redraw the data with the new value of the interval. To accept the bin_interval value, left click anywhere on the graph.
5. The program will redraw the data again and show the first five days of activity. On this plot, click on the first M peak that will be used in the analysis (sometimes it is necessary to skip one or two days).
   NOTE: The program will redraw the graph starting from the picked morning peak. The blue and red lines will show the approximate position of the E peak and next day M peak, respectively, based on the period determined in step 2.4.
6. On the same graph, choose data for a preliminary fit of the data with the model: Click on the following points (in this order; note that the click location will be indicated with a red star on the bottom): (i) Top of M peak; (ii) End of the M peak; (iii) Start of the E peak; (iv) Top of the E peak; (v) End of the E peak; (vi) Top of the M peak of the next day.
7. Note that the program now presents the power spectrum.
   NOTE: The x axis is now given in frequency.
   1. In the opened window with the power spectrum, pick points that will be used for fitting the analytical expression for the model power spectrum. The period detected in step 2.4 is marked with a red line. To pick fitting points, first roughly determine the primary period, similar to step 2.4. Then using the slider, fine tune the primary period value so that the fitting points (shown with red circles, will appear after moving the slider) are closed to peak values.
8. After the visual peak selection, click "Accept" and the program will fit selected points with the analytical expression to calculate the model parameters.
9. Note that the parameters and spectral fit error are saved to the file "model_fit_parameters.txt"; the program will additionally save 2 figures with fits of the locomotor data and its power spectrum.

Results

The method presented here allows quantification of the main features in fly locomotion pattern. The quantification is achieved by fitting the activity data with a model that consists of four exponential terms:

Discussion

This work presents instructions for using a computational tool that provides a quantitative description of fly locomotion pattern. The tool fits locomotion data with a mathematical model consisting of four exponential terms that together describe the shape and size of the M and E peaks. The final values for the model parameters are obtained from fitting the power spectra of the data, where the use of the raw data can avoid artefactual effects that data binning or filtering can impose on parameter values. The model parame...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Drosophila Activity Monitor	TriKinetics	DAM2, DAM5	Measures fly locootion using single infrared beam
MatLab	Mathworks		Computing environment and programming language, MatLab should include Optimization and Symbolic Math toolboxes
Drosophila melanogaster		per[S], per[L], iso31(wild type)	Our analysis can be performed with fly mutants of any circadian period