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A mathematical model provides mechanistic links to temporal patterns in Drosophila daily activity.

Lazopulo A, Syed S - BMC Neurosci (2016)

Bottom Line: In the time domain, we find the timescales of the exponentials in our model to be ~1.5 h(-1) on average.Our results indicate that multiple spectral peaks from fly locomotion are simply harmonics of the circadian period rather than independent ultradian oscillators as previously reported.From timescales of the exponentials we hypothesize that model rates reflect activity of the neuropeptides that likely transduce signals of the circadian clock and the sleep-wake homeostat to shape behavioral outputs.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Miami, 1320 Campo Sano Avenue, Coral Gables, FL, 33146, USA.

ABSTRACT

Background: Circadian clocks are endogenous biochemical oscillators that control daily behavioral rhythms in all living organisms. In fruit fly, the circadian rhythms are typically studied using power spectra of multiday behavioral recordings. Despite decades of study, a quantitative understanding of the temporal shape of Drosophila locomotor rhythms is missing. Locomotor recordings have been used mostly to extract the period of the circadian clock, leaving these data-rich time series largely underutilized. The power spectra of Drosophila and mouse locomotion often show multiple peaks in addition to the expected at T ~ 24 h. Several theoretical and experimental studies have previously used these data to examine interactions between the circadian and other endogenous rhythms, in some cases, attributing peaks in the T < 24 h regime to ultradian oscillators. However, the analysis of fly locomotion was typically performed without considering the shape of time series, while the shape of the signal plays important role in its power spectrum. To account for locomotion patterns in circadian studies we construct a mathematical model of fly activity. Our model allows careful analysis of the temporal shape of behavioral recordings and can provide important information about biochemical mechanisms that control fly activity.

Results: Here we propose a mathematical model with four exponential terms and a single period of oscillation that closely reproduces the shape of the locomotor data in both time and frequency domains. Using our model, we reexamine interactions between the circadian and other endogenous rhythms and show that the proposed single-period waveform is sufficient to explain the position and height of >88 % of spectral peaks in the locomotion of wild-type and circadian mutants of Drosophila. In the time domain, we find the timescales of the exponentials in our model to be ~1.5 h(-1) on average.

Conclusions: Our results indicate that multiple spectral peaks from fly locomotion are simply harmonics of the circadian period rather than independent ultradian oscillators as previously reported. From timescales of the exponentials we hypothesize that model rates reflect activity of the neuropeptides that likely transduce signals of the circadian clock and the sleep-wake homeostat to shape behavioral outputs.

No MeSH data available.


Related in: MedlinePlus

Power spectrum of fly locomotor activity shows multiple peaks. a Schematic representation of fly activity measurement. Each time the enclosed fly crosses an IR beam, the computer receives a “1”. b Activity of a single wild type fruit fly measured in constant darkness. Subjective day/night time is shown in white/grey bars. c Power spectrum of the fly activity. Spectrum from 0 to 30 h is shown on top, dashed rectangle is enlarged in the lower panel. Power spectra calculated with Lomb–Scargle (LS, black) and maximum entropy spectral analysis (MESA, red) methods show the expected ~24 h circadian peak and additionally show a series of statistically significant peaks at lower . Dashed horizontal line represents statistical significance of 0.005 for the Lomb–Scarge spectrum. Peak positions detected by LS and MESA agree to within 2 %
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Fig1: Power spectrum of fly locomotor activity shows multiple peaks. a Schematic representation of fly activity measurement. Each time the enclosed fly crosses an IR beam, the computer receives a “1”. b Activity of a single wild type fruit fly measured in constant darkness. Subjective day/night time is shown in white/grey bars. c Power spectrum of the fly activity. Spectrum from 0 to 30 h is shown on top, dashed rectangle is enlarged in the lower panel. Power spectra calculated with Lomb–Scargle (LS, black) and maximum entropy spectral analysis (MESA, red) methods show the expected ~24 h circadian peak and additionally show a series of statistically significant peaks at lower . Dashed horizontal line represents statistical significance of 0.005 for the Lomb–Scarge spectrum. Peak positions detected by LS and MESA agree to within 2 %

Mentions: Fruit fly activity was measured using the standard Drosophila Activity Monitor (DAM). Each fly is placed in an individual tube with food on one end and cotton on the other (Fig. 1a). An infrared beam crosses the tube in the middle in a perpendicular direction. When a fly interrupts the beam, the monitor receives a signal which is accumulated over time and sent to the computer every 20 s (Fig. 1b). Power spectra for activity data were calculated using maximum entropy spectral analysis (MESA) and Lomb–Scargle periodogram (LS) (Fig. 1c). Spectra obtained by each method show the expected 24 h peak. Additionally, there is a series of statistically significant peaks at smaller periods () with peak values from the two methods agreeing with each other to within 2 %. Unlike MESA, the Lomb–Scargle periodogram has an easily computable significance metric, which allows one to distinguish between significant and insignificant periodicities in the power spectra. Departing from the practice of filtering data prior to spectral analysis, we determine all power spectra directly from raw data. A number of past studies on ultradian rhythms adopted digital filtering as a standard procedure in their analyses [18, 21, 37–39]. However, as we demonstrate in this work (see “Methods”; Additional file 1: Fig. S9 and associated text), application of digital filters can irrevocably modify statistical properties of a time series and can give rise to artifacts in its power spectrum.Fig. 1


A mathematical model provides mechanistic links to temporal patterns in Drosophila daily activity.

Lazopulo A, Syed S - BMC Neurosci (2016)

Power spectrum of fly locomotor activity shows multiple peaks. a Schematic representation of fly activity measurement. Each time the enclosed fly crosses an IR beam, the computer receives a “1”. b Activity of a single wild type fruit fly measured in constant darkness. Subjective day/night time is shown in white/grey bars. c Power spectrum of the fly activity. Spectrum from 0 to 30 h is shown on top, dashed rectangle is enlarged in the lower panel. Power spectra calculated with Lomb–Scargle (LS, black) and maximum entropy spectral analysis (MESA, red) methods show the expected ~24 h circadian peak and additionally show a series of statistically significant peaks at lower . Dashed horizontal line represents statistical significance of 0.005 for the Lomb–Scarge spectrum. Peak positions detected by LS and MESA agree to within 2 %
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4835852&req=5

Fig1: Power spectrum of fly locomotor activity shows multiple peaks. a Schematic representation of fly activity measurement. Each time the enclosed fly crosses an IR beam, the computer receives a “1”. b Activity of a single wild type fruit fly measured in constant darkness. Subjective day/night time is shown in white/grey bars. c Power spectrum of the fly activity. Spectrum from 0 to 30 h is shown on top, dashed rectangle is enlarged in the lower panel. Power spectra calculated with Lomb–Scargle (LS, black) and maximum entropy spectral analysis (MESA, red) methods show the expected ~24 h circadian peak and additionally show a series of statistically significant peaks at lower . Dashed horizontal line represents statistical significance of 0.005 for the Lomb–Scarge spectrum. Peak positions detected by LS and MESA agree to within 2 %
Mentions: Fruit fly activity was measured using the standard Drosophila Activity Monitor (DAM). Each fly is placed in an individual tube with food on one end and cotton on the other (Fig. 1a). An infrared beam crosses the tube in the middle in a perpendicular direction. When a fly interrupts the beam, the monitor receives a signal which is accumulated over time and sent to the computer every 20 s (Fig. 1b). Power spectra for activity data were calculated using maximum entropy spectral analysis (MESA) and Lomb–Scargle periodogram (LS) (Fig. 1c). Spectra obtained by each method show the expected 24 h peak. Additionally, there is a series of statistically significant peaks at smaller periods () with peak values from the two methods agreeing with each other to within 2 %. Unlike MESA, the Lomb–Scargle periodogram has an easily computable significance metric, which allows one to distinguish between significant and insignificant periodicities in the power spectra. Departing from the practice of filtering data prior to spectral analysis, we determine all power spectra directly from raw data. A number of past studies on ultradian rhythms adopted digital filtering as a standard procedure in their analyses [18, 21, 37–39]. However, as we demonstrate in this work (see “Methods”; Additional file 1: Fig. S9 and associated text), application of digital filters can irrevocably modify statistical properties of a time series and can give rise to artifacts in its power spectrum.Fig. 1

Bottom Line: In the time domain, we find the timescales of the exponentials in our model to be ~1.5 h(-1) on average.Our results indicate that multiple spectral peaks from fly locomotion are simply harmonics of the circadian period rather than independent ultradian oscillators as previously reported.From timescales of the exponentials we hypothesize that model rates reflect activity of the neuropeptides that likely transduce signals of the circadian clock and the sleep-wake homeostat to shape behavioral outputs.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, University of Miami, 1320 Campo Sano Avenue, Coral Gables, FL, 33146, USA.

ABSTRACT

Background: Circadian clocks are endogenous biochemical oscillators that control daily behavioral rhythms in all living organisms. In fruit fly, the circadian rhythms are typically studied using power spectra of multiday behavioral recordings. Despite decades of study, a quantitative understanding of the temporal shape of Drosophila locomotor rhythms is missing. Locomotor recordings have been used mostly to extract the period of the circadian clock, leaving these data-rich time series largely underutilized. The power spectra of Drosophila and mouse locomotion often show multiple peaks in addition to the expected at T ~ 24 h. Several theoretical and experimental studies have previously used these data to examine interactions between the circadian and other endogenous rhythms, in some cases, attributing peaks in the T < 24 h regime to ultradian oscillators. However, the analysis of fly locomotion was typically performed without considering the shape of time series, while the shape of the signal plays important role in its power spectrum. To account for locomotion patterns in circadian studies we construct a mathematical model of fly activity. Our model allows careful analysis of the temporal shape of behavioral recordings and can provide important information about biochemical mechanisms that control fly activity.

Results: Here we propose a mathematical model with four exponential terms and a single period of oscillation that closely reproduces the shape of the locomotor data in both time and frequency domains. Using our model, we reexamine interactions between the circadian and other endogenous rhythms and show that the proposed single-period waveform is sufficient to explain the position and height of >88 % of spectral peaks in the locomotion of wild-type and circadian mutants of Drosophila. In the time domain, we find the timescales of the exponentials in our model to be ~1.5 h(-1) on average.

Conclusions: Our results indicate that multiple spectral peaks from fly locomotion are simply harmonics of the circadian period rather than independent ultradian oscillators as previously reported. From timescales of the exponentials we hypothesize that model rates reflect activity of the neuropeptides that likely transduce signals of the circadian clock and the sleep-wake homeostat to shape behavioral outputs.

No MeSH data available.


Related in: MedlinePlus