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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 results make quantitative predictions about biochemical signals that may shape fly locomotor patterns. a Cartoon showing circadian genes and their products oscillate in a sinusoidal fashion (top row, left) and produce a power spectrum with a single peak (top row, right). We propose that efferent signal from the clock impinges on exponential processes that turn on/off stochastically in time. An example may be neuromodulator accumulation and release (middle rows, left). Without circadian regulation, the exponential process should result in noisy power spectra (middle rows, right). Integration of the sinusoidal with the exponential processes together with other signals (not shown) result in the observed shape of fly locomotion (bottom row, left). The resulting time series has multiple peaks in power spectrum by virtue of its non-sinusoidal shape (bottom row, right). b We suggest that the exponential processes that may underlie the observed shape in locomotion are temporally gated by the circadian clock. If so, then changing rhythm of the clock should cause corresponding changes both in the oscillatory period and the peak–peak amplitude of the gated signal. Shortening period of the clock () predicts speeding up of the periodic exponential process and decrease of its amplitude of oscillation (). In these cartoons, it is assumed that the rate at which the exponential process occurs, for instance, the rate of neuromodulator release, is not affected by the circadian clock speed. To underscore the constant rate, the first decay phase of the fast and slow exponential waves are overlaid
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Fig6: Our results make quantitative predictions about biochemical signals that may shape fly locomotor patterns. a Cartoon showing circadian genes and their products oscillate in a sinusoidal fashion (top row, left) and produce a power spectrum with a single peak (top row, right). We propose that efferent signal from the clock impinges on exponential processes that turn on/off stochastically in time. An example may be neuromodulator accumulation and release (middle rows, left). Without circadian regulation, the exponential process should result in noisy power spectra (middle rows, right). Integration of the sinusoidal with the exponential processes together with other signals (not shown) result in the observed shape of fly locomotion (bottom row, left). The resulting time series has multiple peaks in power spectrum by virtue of its non-sinusoidal shape (bottom row, right). b We suggest that the exponential processes that may underlie the observed shape in locomotion are temporally gated by the circadian clock. If so, then changing rhythm of the clock should cause corresponding changes both in the oscillatory period and the peak–peak amplitude of the gated signal. Shortening period of the clock () predicts speeding up of the periodic exponential process and decrease of its amplitude of oscillation (). In these cartoons, it is assumed that the rate at which the exponential process occurs, for instance, the rate of neuromodulator release, is not affected by the circadian clock speed. To underscore the constant rate, the first decay phase of the fast and slow exponential waves are overlaid

Mentions: Our mathematical model also permits a number of general predictions to be made about candidate neurobiological processes that may underlie our model parameters (Fig. 6). First, we propose that the candidate process can be described, for simplicity, in terms of linear or exponential growth-decay kinetics. Second, the processes are presumably sporadic when averaged over many neurons. Their random nature would imply they have noisy power spectra (Fig. 6a, middle row) and considering the processes are key modulators of behavior, their average stochastic nature should result in arrhythmic behavior in the absence of the circadian clock (Fig. 3c). Third, we suggest that the underlying processes have kinetics on the time-scale of tens of minutes. This constraint is based on the magnitude of the model rate constants, which are ~1.5 h−1 on average, suggesting that the processes they represent persist for ~40 min. At the molecular level, this is a long time-scale and suggests that neurotransmitter activity or electrical pulses, which also have exponential kinetics but act on the time-scale of seconds or less, are unlikely to be direct contributors to the exponents in . However, neuropeptide half-life in the brain and accumulation in synaptic boutons happen over span of ~30 min, making these substrates attractive candidates in our model [50]. Lastly, we suggest that on the time-scale of hours the circadian clock is likely the sole pacemaker (Fig. 6a, top row) to temporally gate the relevant neurobiological processes. The circadian gating imposes rhythm on otherwise stochastic processes and when integrated with additional downstream signals, ultimately produces rhythmic patterns in locomotion (Fig. 6a, bottom row). Related to the circadian gating are two additional features that the hypothetical processes might display (Fig. 6b). We suggest that changes in the period of the clock may cause not only parallel changes in the rhythm of the processes but, importantly, also changes in the amplitude of their oscillation. For instance, if and are indeed related to PDF activity, our model predicts that compared to perL animals, in perS animals both the period and the peak–peak amplitude of PDF oscillation is smaller. This prediction is based on our assumption that such changes in the amplitude of the underlying processes likely causes the correlation observed in our data between the average locomotor amplitude and the circadian period, which is predicted surprisingly well by our model (Fig. 4b, c). Together, these characterizations should facilitate experimental identification of the key neurobiological processes that our model parameters represent.Fig. 6


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

Lazopulo A, Syed S - BMC Neurosci (2016)

Our results make quantitative predictions about biochemical signals that may shape fly locomotor patterns. a Cartoon showing circadian genes and their products oscillate in a sinusoidal fashion (top row, left) and produce a power spectrum with a single peak (top row, right). We propose that efferent signal from the clock impinges on exponential processes that turn on/off stochastically in time. An example may be neuromodulator accumulation and release (middle rows, left). Without circadian regulation, the exponential process should result in noisy power spectra (middle rows, right). Integration of the sinusoidal with the exponential processes together with other signals (not shown) result in the observed shape of fly locomotion (bottom row, left). The resulting time series has multiple peaks in power spectrum by virtue of its non-sinusoidal shape (bottom row, right). b We suggest that the exponential processes that may underlie the observed shape in locomotion are temporally gated by the circadian clock. If so, then changing rhythm of the clock should cause corresponding changes both in the oscillatory period and the peak–peak amplitude of the gated signal. Shortening period of the clock () predicts speeding up of the periodic exponential process and decrease of its amplitude of oscillation (). In these cartoons, it is assumed that the rate at which the exponential process occurs, for instance, the rate of neuromodulator release, is not affected by the circadian clock speed. To underscore the constant rate, the first decay phase of the fast and slow exponential waves are overlaid
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig6: Our results make quantitative predictions about biochemical signals that may shape fly locomotor patterns. a Cartoon showing circadian genes and their products oscillate in a sinusoidal fashion (top row, left) and produce a power spectrum with a single peak (top row, right). We propose that efferent signal from the clock impinges on exponential processes that turn on/off stochastically in time. An example may be neuromodulator accumulation and release (middle rows, left). Without circadian regulation, the exponential process should result in noisy power spectra (middle rows, right). Integration of the sinusoidal with the exponential processes together with other signals (not shown) result in the observed shape of fly locomotion (bottom row, left). The resulting time series has multiple peaks in power spectrum by virtue of its non-sinusoidal shape (bottom row, right). b We suggest that the exponential processes that may underlie the observed shape in locomotion are temporally gated by the circadian clock. If so, then changing rhythm of the clock should cause corresponding changes both in the oscillatory period and the peak–peak amplitude of the gated signal. Shortening period of the clock () predicts speeding up of the periodic exponential process and decrease of its amplitude of oscillation (). In these cartoons, it is assumed that the rate at which the exponential process occurs, for instance, the rate of neuromodulator release, is not affected by the circadian clock speed. To underscore the constant rate, the first decay phase of the fast and slow exponential waves are overlaid
Mentions: Our mathematical model also permits a number of general predictions to be made about candidate neurobiological processes that may underlie our model parameters (Fig. 6). First, we propose that the candidate process can be described, for simplicity, in terms of linear or exponential growth-decay kinetics. Second, the processes are presumably sporadic when averaged over many neurons. Their random nature would imply they have noisy power spectra (Fig. 6a, middle row) and considering the processes are key modulators of behavior, their average stochastic nature should result in arrhythmic behavior in the absence of the circadian clock (Fig. 3c). Third, we suggest that the underlying processes have kinetics on the time-scale of tens of minutes. This constraint is based on the magnitude of the model rate constants, which are ~1.5 h−1 on average, suggesting that the processes they represent persist for ~40 min. At the molecular level, this is a long time-scale and suggests that neurotransmitter activity or electrical pulses, which also have exponential kinetics but act on the time-scale of seconds or less, are unlikely to be direct contributors to the exponents in . However, neuropeptide half-life in the brain and accumulation in synaptic boutons happen over span of ~30 min, making these substrates attractive candidates in our model [50]. Lastly, we suggest that on the time-scale of hours the circadian clock is likely the sole pacemaker (Fig. 6a, top row) to temporally gate the relevant neurobiological processes. The circadian gating imposes rhythm on otherwise stochastic processes and when integrated with additional downstream signals, ultimately produces rhythmic patterns in locomotion (Fig. 6a, bottom row). Related to the circadian gating are two additional features that the hypothetical processes might display (Fig. 6b). We suggest that changes in the period of the clock may cause not only parallel changes in the rhythm of the processes but, importantly, also changes in the amplitude of their oscillation. For instance, if and are indeed related to PDF activity, our model predicts that compared to perL animals, in perS animals both the period and the peak–peak amplitude of PDF oscillation is smaller. This prediction is based on our assumption that such changes in the amplitude of the underlying processes likely causes the correlation observed in our data between the average locomotor amplitude and the circadian period, which is predicted surprisingly well by our model (Fig. 4b, c). Together, these characterizations should facilitate experimental identification of the key neurobiological processes that our model parameters represent.Fig. 6

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