Maximum entropy spectral analysis for circadian rhythms: theory, history and practice

There is an array of numerical techniques available to estimate the period of circadian and other biological rhythms. Criteria for choosing a method include accuracy of period measurement, resolution of signal embedded in noise or of multiple periodicities, and sensitivity to the presence of weak rhythms and robustness in the presence of stochastic noise. Maximum Entropy Spectral Analysis (MESA) has proven itself excellent in all regards. The MESA algorithm fits an autoregressive model to the data and extracts the spectrum from its coefficients. Entropy in this context refers to "ignorance" of the data and since this is formally maximized, no unwarranted assumptions are made. Computationally, the coefficients are calculated efficiently by solution of the Yule-Walker equations in an iterative algorithm. MESA is compared here to other common techniques. It is normal to remove high frequency noise from time series using digital filters before analysis. The Butterworth filter is demonstrated here and a danger inherent in multiple filtering passes is discussed

Advanced analysis of a cryptochrome mutation's effects on the robustness and phase of molecular cycles in isolated peripheral tissues of Drosophila

BACKGROUND: Previously, we reported effects of the cry(b) mutation on circadian rhythms in period and timeless gene expression within isolated peripheral Drosophila tissues. We relied on luciferase activity driven by the respective regulatory genomic elements to provide real-time reporting of cycling gene expression. Subsequently, we developed a tool kit for the analysis of behavioral and molecular cycles. Here, we use these tools to analyze our earlier results as well as additional data obtained using the same experimental designs. RESULTS: Isolated antennal pairs, heads, bodies, wings and forelegs were evaluated under light-dark cycles. In these conditions, the cry(b) mutation significantly decreases the number of rhythmic specimens in each case except the wing. Moreover, among those specimens with detectable rhythmicity, mutant rhythms are significantly weaker than cry(+) controls. In addition, cry(b) alters the phase of period gene expression in these tissues. Furthermore, peak phase of luciferase-reported period and timeless expression within cry(+) samples is indistinguishable in some tissues, yet significantly different in others. We also analyze rhythms produced by antennal pairs in constant conditions. CONCLUSIONS: These analyses further show that circadian clock mechanisms in Drosophila may vary in a tissue-specific manner, including how the cry gene regulates circadian gene expression

Signal analysis of behavioral and molecular cycles

BACKGROUND: Circadian clocks are biological oscillators that regulate molecular, physiological, and behavioral rhythms in a wide variety of organisms. While behavioral rhythms are typically monitored over many cycles, a similar approach to molecular rhythms was not possible until recently; the advent of real-time analysis using transgenic reporters now permits the observations of molecular rhythms over many cycles as well. This development suggests that new details about the relationship between molecular and behavioral rhythms may be revealed. Even so, behavioral and molecular rhythmicity have been analyzed using different methods, making such comparisons difficult to achieve. To address this shortcoming, among others, we developed a set of integrated analytical tools to unify the analysis of biological rhythms across modalities. RESULTS: We demonstrate an adaptation of digital signal analysis that allows similar treatment of both behavioral and molecular data from our studies of Drosophila. For both types of data, we apply digital filters to extract and clarify details of interest; we employ methods of autocorrelation and spectral analysis to assess rhythmicity and estimate the period; we evaluate phase shifts using crosscorrelation; and we use circular statistics to extract information about phase. CONCLUSION: Using data generated by our investigation of rhythms in Drosophila we demonstrate how a unique aggregation of analytical tools may be used to analyze and compare behavioral and molecular rhythms. These methods are shown to be versatile and will also be adaptable to further experiments, owing in part to the non-proprietary nature of the code we have developed

Data from: Failure to reproduce period-dependent song cycles in Drosophila is due to poor automated pulse-detection and low-intensity courtship

Stern has criticized a body of work from several groups that have independently studied the so-called “Kyriacou and Hall” courtship song rhythms of male Drosophila melanogaster, claiming that these ultradian ∼60-s cycles in the interpulse interval (IPI) are statistical artifacts that are not modulated by mutations at the period (per) locus [Stern DL (2014) BMC Biol 12:38]. We have scrutinized Stern’s raw data and observe that his automated song pulse-detection method identifies only ∼50% of the IPIs found by manual (visual and acoustic) monitoring. This critical error is further compounded by Stern’s use of recordings with very little song, the large majority of which do not meet the minimal song intensity criteria which Kyriacou and Hall used in their studies. Consequently most of Stern’s recordings only contribute noise to the analyses. Of the data presented by Stern, only perL and a small fraction of wild-type males sing vigorously, so we limited our reanalyses to these genotypes. We manually reexamined Stern’s raw song recordings and analyzed IPI rhythms using several independent time-series analyses. We observe that perL songs show significantly longer song periods than wild-type songs, with values for both genotypes close to those found in previous studies. These per-dependent differences disappear when the song data are randomized. We conclude that Stern’s negative findings are artifacts of his inadequate pulse-detection methodology coupled to his use of low-intensity courtship song records

Solitary and Gregarious Locusts Differ in Circadian Rhythmicity of a Visual Output Neuron

ABSTRACT Locusts demonstrate remarkable phenotypic plasticity driven by changes in population density. This density dependent phase polyphenism is associated with many physiological, behavioural and morphological changes, including observations that cryptic solitarious (solitary-reared) individuals start to fly at dusk, whereas gregarious (crowd-reared) individuals are day-active. We have recorded for 24-36h from an identified visual output neuron, the descending contralateral movement detector (DCMD) of Schistocerca gregaria, in solitarious and gregarious animals. DCMD signals impending collision and participates in flight avoidance manoeuvres. The strength of DCMD's response to looming stimuli, characterised by the number of evoked spikes and peak firing rate, varies approximately sinusoidally with a period close to 24h under constant light in solitarious locusts. In gregarious individuals the 24h pattern is more complex, being modified by secondary ultradian rhythms. DCMD's strongest responses occur around expected dusk in solitarious locusts, but up to 6h earlier in gregarious locusts, matching the times of day at which locusts of each type are most active. We thus demonstrate a neuronal correlate of a temporal shift in behaviour that is observed in gregarious locusts. Our ability to alter the nature of a circadian rhythm by manipulating the rearing density of locusts under identical light-dark cycles may provide important tools to investigate further the mechanisms underlying diurnal rhythmicity

Solitary and Gregarious Locusts Differ in Circadian Rhythmicity of a Visual Output Neuron

Locusts demonstrate remarkable phenotypic plasticity driven by changes in population density. This density dependent phase polyphenism is associated with many physiological, behavioral, and morphological changes, including observations that cryptic solitarious (solitary-reared) individuals start to fly at dusk, whereas gregarious (crowd-reared) individuals are day-active. We have recorded for 24-36 h, from an identified visual output neuron, the descending contralateral movement detector (DCMD) of Schistocerca gregaria in solitarious and gregarious animals. DCMD signals impending collision and participates in flight avoidance maneuvers. The strength of DCMD's response to looming stimuli, characterized by the number of evoked spikes and peak firing rate, varies approximately sinusoidally with a period close to 24 h under constant light in solitarious locusts. In gregarious individuals the 24-h pattern is more complex, being modified by secondary ultradian rhythms. DCMD's strongest responses occur around expected dusk in solitarious locusts but up to 6 h earlier in gregarious locusts, matching the times of day at which locusts of each type are most active. We thus demonstrate a neuronal correlate of a temporal shift in behavior that is observed in gregarious locusts. Our ability to alter the nature of a circadian rhythm by manipulating the rearing density of locusts under identical light-dark cycles may provide important tools to investigate further the mechanisms underlying diurnal rhythmicity

perLmanual

manual analysis of perL song

first25CSsongs

Manual analysis of first 24 CS songs plus cong CS7

TullyCS

Manual analysis of CSTully songs from Arthur et al 201

interobserver

results on inter-observer analyses of 3 song