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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

Our model correctly predicts majority of peaks in power spectrum of fly locomotion. a Power spectra of individual wild type and clock mutants of Drosophila measured in constant darkness for 5–7 days. X-axis given as ratio , with the circadian period  indicated in each case. Increasing values indicate shorter periods of oscillation. For each , prominent secondary peaks are found at  accompanied by lower power Dirichlet kernel peaks. b Comparison of peaks detected in the data to peaks predicted by the model was obtained by analyzing wt (N = 29), perS (N = 22) and perL (N = 19) flies. Only peaks higher than  were used in the analysis.  is shown as a solid line, 10 % deviation shown as dashed lines. For wild type and clock mutants more than 88 % of the data peaks for T = 2–35 h can be explained by the model with ± 10 % error. c Power spectra of a wild type fly measured in LL and a per0 mutant measured in DD. Neither spectrum shows peaks higher than  significance level (dashed line). For both graphs   h was used for scaling the abscissa
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Fig3: Our model correctly predicts majority of peaks in power spectrum of fly locomotion. a Power spectra of individual wild type and clock mutants of Drosophila measured in constant darkness for 5–7 days. X-axis given as ratio , with the circadian period indicated in each case. Increasing values indicate shorter periods of oscillation. For each , prominent secondary peaks are found at accompanied by lower power Dirichlet kernel peaks. b Comparison of peaks detected in the data to peaks predicted by the model was obtained by analyzing wt (N = 29), perS (N = 22) and perL (N = 19) flies. Only peaks higher than were used in the analysis. is shown as a solid line, 10 % deviation shown as dashed lines. For wild type and clock mutants more than 88 % of the data peaks for T = 2–35 h can be explained by the model with ± 10 % error. c Power spectra of a wild type fly measured in LL and a per0 mutant measured in DD. Neither spectrum shows peaks higher than significance level (dashed line). For both graphs  h was used for scaling the abscissa

Mentions: We noticed that the majority of peaks that appear in the power spectra of wild-type flies measured in LD occur at multiples of the primary period . To test if the secondary peaks result from the externally imposed light/dark cycle, we measured fly (N = 29) locomotion in constant darkness (DD) for 5–7 days. This analysis revealed that together with the 24 h peak reflecting the circadian clock, the power spectrum still has the same additional peaks that appear at multiples of (Fig. 3a, top), suggesting that the additional periodicities in the power spectra of fly activity are simply harmonics of the endogenous circadian period .Fig. 3


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

Lazopulo A, Syed S - BMC Neurosci (2016)

Our model correctly predicts majority of peaks in power spectrum of fly locomotion. a Power spectra of individual wild type and clock mutants of Drosophila measured in constant darkness for 5–7 days. X-axis given as ratio , with the circadian period  indicated in each case. Increasing values indicate shorter periods of oscillation. For each , prominent secondary peaks are found at  accompanied by lower power Dirichlet kernel peaks. b Comparison of peaks detected in the data to peaks predicted by the model was obtained by analyzing wt (N = 29), perS (N = 22) and perL (N = 19) flies. Only peaks higher than  were used in the analysis.  is shown as a solid line, 10 % deviation shown as dashed lines. For wild type and clock mutants more than 88 % of the data peaks for T = 2–35 h can be explained by the model with ± 10 % error. c Power spectra of a wild type fly measured in LL and a per0 mutant measured in DD. Neither spectrum shows peaks higher than  significance level (dashed line). For both graphs   h was used for scaling the abscissa
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Fig3: Our model correctly predicts majority of peaks in power spectrum of fly locomotion. a Power spectra of individual wild type and clock mutants of Drosophila measured in constant darkness for 5–7 days. X-axis given as ratio , with the circadian period indicated in each case. Increasing values indicate shorter periods of oscillation. For each , prominent secondary peaks are found at accompanied by lower power Dirichlet kernel peaks. b Comparison of peaks detected in the data to peaks predicted by the model was obtained by analyzing wt (N = 29), perS (N = 22) and perL (N = 19) flies. Only peaks higher than were used in the analysis. is shown as a solid line, 10 % deviation shown as dashed lines. For wild type and clock mutants more than 88 % of the data peaks for T = 2–35 h can be explained by the model with ± 10 % error. c Power spectra of a wild type fly measured in LL and a per0 mutant measured in DD. Neither spectrum shows peaks higher than significance level (dashed line). For both graphs  h was used for scaling the abscissa
Mentions: We noticed that the majority of peaks that appear in the power spectra of wild-type flies measured in LD occur at multiples of the primary period . To test if the secondary peaks result from the externally imposed light/dark cycle, we measured fly (N = 29) locomotion in constant darkness (DD) for 5–7 days. This analysis revealed that together with the 24 h peak reflecting the circadian clock, the power spectrum still has the same additional peaks that appear at multiples of (Fig. 3a, top), suggesting that the additional periodicities in the power spectra of fly activity are simply harmonics of the endogenous circadian period .Fig. 3

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