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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

Analysis reveals quantitative relations between model parameters and circadian period. a Parameters extracted from fitting locomotor data of wild type (N = 11), perS (N = 22), perL (N = 19) and timUL (N = 11) flies measured in constant darkness for 5–7 days. Plotted parameter is indicated in the adjacent box for each graph, with curvatures shown for . The data show that the exponential rate constants are independent of , while parameters  and  grow roughly linearly with . Dashed lines are visual guides (top and middle panels) or linear fits (bottom panels). b Sketch of two locomotor patterns where the red locomotion is driven by a faster clock (shorter ). If increase in  results in lengthening of activity peak widths from  to  without altering the exponential rates, our model predicts that the activity amplitude must also increase from  to . The first M peaks are shown to overlap to emphasize constancy of the exponential rates. The red sketched activity has been vertically shifted for visual clarity. c Data from flies in a demonstrate a positive correlation between average activity amplitude h and the circadian period . Dashed line is a linear fit to the data giving
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Fig5: Analysis reveals quantitative relations between model parameters and circadian period. a Parameters extracted from fitting locomotor data of wild type (N = 11), perS (N = 22), perL (N = 19) and timUL (N = 11) flies measured in constant darkness for 5–7 days. Plotted parameter is indicated in the adjacent box for each graph, with curvatures shown for . The data show that the exponential rate constants are independent of , while parameters and grow roughly linearly with . Dashed lines are visual guides (top and middle panels) or linear fits (bottom panels). b Sketch of two locomotor patterns where the red locomotion is driven by a faster clock (shorter ). If increase in results in lengthening of activity peak widths from to without altering the exponential rates, our model predicts that the activity amplitude must also increase from to . The first M peaks are shown to overlap to emphasize constancy of the exponential rates. The red sketched activity has been vertically shifted for visual clarity. c Data from flies in a demonstrate a positive correlation between average activity amplitude h and the circadian period . Dashed line is a linear fit to the data giving

Mentions: In order to understand what factors affect the model parameters, we determined their values for different clock mutants and tested for their relation to the circadian period . Wild-type, perS, and perL animals introduced above together with timUL flies (N = 11) with average T0 ~ 27 h were used in these analyses (Additional file 1: Fig. S10). Given our mathematical description of fly activity, we hypothesized two possibilities: one, in which the rate constants do not vary but and adjust with and another, in which both sets of parameters change with . Interestingly, the data show that the rate constants , , , do not depend strongly on ( for linear fits), whereas the parameters and that determine width of the morning and evening peaks, increase with (Fig. 5a). Assuming the measured parameters represent characteristics of underlying biological processes, the robustness of the rate constants suggests that the pace of the clock likely does not alter the kinetics of these processes. On the contrary, tight association between and and clock speed suggests that the clock may regulate when these processes are initiated and terminated. The rate constants typically range between ±5 h−1 for and , and between 0 and 1.5 h−1 for and , with average , , , (mean ± standard deviation). The mean ± standard deviation of the magnitude of the four rate constants from all flies tested in constant darkness is . Lastly, linear fits of the versus data reveal and ( and , respectively) (Fig. 5a, bottom panels).Fig. 5


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

Lazopulo A, Syed S - BMC Neurosci (2016)

Analysis reveals quantitative relations between model parameters and circadian period. a Parameters extracted from fitting locomotor data of wild type (N = 11), perS (N = 22), perL (N = 19) and timUL (N = 11) flies measured in constant darkness for 5–7 days. Plotted parameter is indicated in the adjacent box for each graph, with curvatures shown for . The data show that the exponential rate constants are independent of , while parameters  and  grow roughly linearly with . Dashed lines are visual guides (top and middle panels) or linear fits (bottom panels). b Sketch of two locomotor patterns where the red locomotion is driven by a faster clock (shorter ). If increase in  results in lengthening of activity peak widths from  to  without altering the exponential rates, our model predicts that the activity amplitude must also increase from  to . The first M peaks are shown to overlap to emphasize constancy of the exponential rates. The red sketched activity has been vertically shifted for visual clarity. c Data from flies in a demonstrate a positive correlation between average activity amplitude h and the circadian period . Dashed line is a linear fit to the data giving
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4835852&req=5

Fig5: Analysis reveals quantitative relations between model parameters and circadian period. a Parameters extracted from fitting locomotor data of wild type (N = 11), perS (N = 22), perL (N = 19) and timUL (N = 11) flies measured in constant darkness for 5–7 days. Plotted parameter is indicated in the adjacent box for each graph, with curvatures shown for . The data show that the exponential rate constants are independent of , while parameters and grow roughly linearly with . Dashed lines are visual guides (top and middle panels) or linear fits (bottom panels). b Sketch of two locomotor patterns where the red locomotion is driven by a faster clock (shorter ). If increase in results in lengthening of activity peak widths from to without altering the exponential rates, our model predicts that the activity amplitude must also increase from to . The first M peaks are shown to overlap to emphasize constancy of the exponential rates. The red sketched activity has been vertically shifted for visual clarity. c Data from flies in a demonstrate a positive correlation between average activity amplitude h and the circadian period . Dashed line is a linear fit to the data giving
Mentions: In order to understand what factors affect the model parameters, we determined their values for different clock mutants and tested for their relation to the circadian period . Wild-type, perS, and perL animals introduced above together with timUL flies (N = 11) with average T0 ~ 27 h were used in these analyses (Additional file 1: Fig. S10). Given our mathematical description of fly activity, we hypothesized two possibilities: one, in which the rate constants do not vary but and adjust with and another, in which both sets of parameters change with . Interestingly, the data show that the rate constants , , , do not depend strongly on ( for linear fits), whereas the parameters and that determine width of the morning and evening peaks, increase with (Fig. 5a). Assuming the measured parameters represent characteristics of underlying biological processes, the robustness of the rate constants suggests that the pace of the clock likely does not alter the kinetics of these processes. On the contrary, tight association between and and clock speed suggests that the clock may regulate when these processes are initiated and terminated. The rate constants typically range between ±5 h−1 for and , and between 0 and 1.5 h−1 for and , with average , , , (mean ± standard deviation). The mean ± standard deviation of the magnitude of the four rate constants from all flies tested in constant darkness is . Lastly, linear fits of the versus data reveal and ( and , respectively) (Fig. 5a, bottom panels).Fig. 5

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