A Computational Error and Restricted Use of Time-series Analyses Underlie the Failure to Replicate period-Dependent Song Rhythms in Drosophila.

From 1980 to 1991, Kyriacou, Hall, and collaborators (K&H) reported that the Drosophila melanogaster courtship song has a 1-min cycle in the length of mean interpulse intervals (IPIs) that is modulated by circadian rhythm period mutations. In 2014, Stern failed to replicate these results using a fully automated method for detecting song pulses. Manual annotation of Stern's song records exposed a ~50% error rate in detection of IPIs, but the corrected data revealed period-dependent IPI cycles using a variety of statistical methods. In 2017, Stern et al. dismissed the sine/cosine method originally used by K&H to detect significant cycles, claiming that randomized songs showed as many significant values as real data using cosinor analysis. We first identify a simple mathematical error in Stern et al.'s cosinor implementation that invalidates their critique of the method. Stern et al. also concluded that although the manually corrected wild-type and perL mutant songs show similar periods to those observed by K&H, each song is usually not significantly rhythmic by the Lomb-Scargle (L-S) periodogram, so any genotypic effect simply reflects "noise." Here, we observe that L-S is extremely conservative compared with 3 other time-series analyses in assessing the significance of rhythmicity, both for conventional locomotor activity data collected in equally spaced time bins and for unequally spaced song records. Using randomization of locomotor and song data to generate confidence limits for L-S instead of the theoretically derived values, we find that L-S is now consistent with the other methods in determining significant rhythmicity in locomotor and song records and that it confirms period-dependent song cycles. We conclude that Stern and colleagues' failure to identify song cycles stems from the limitations of automated methods in accurately reflecting song parameters, combined with the use of an overly stringent method to discriminate rhythmicity in courtship songs.

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.

Melatonin increases the regularity of cardiac rhythmicity in the Drosophila heart in both wild-type and strains bearing pathogenic mutations.

Melatonin is a hormone that is critical for normal circadian and seasonal rhythmicity in a wide range of different animals. It is a powerful antioxidant commonly used to prevent reperfusion injury to the heart after infarction. We show here it has other more far-reaching effects on cardiac function. Using the Drosophila model, we show that injection of melatonin increases the regularity of heartbeat significantly and can rescue rhythmicity in flies bearing mutations that adversely affect cardiac function. Notably, melatonin increases cardiac regularity independent of alteration of heart rate. We provide compelling evidence that melatonin's action as an antioxidant is not the mechanism underlying improved cardiac performance. We have strong evidence that melatonin's action on the heart is mediated via a specific G-Protein-coupled receptor encoded by the CG 4313 gene that our results implicate as a candidate melatonin receptor. These results open a line of questioning about fundamental aspects of cardiac pacemaking.

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.

Sleep-wake behavior in the rat: ultradian rhythms in a light-dark cycle and continuous bright light.

Ultradian rhythms are a prominent but little-studied feature of mammalian sleep-wake and rest-activity patterns. They are especially evident in long-term records of behavioral state in polyphasic animals such as rodents. However, few attempts have been made to incorporate ultradian rhythmicity into models of sleep-wake dynamics, and little is known about the physiological mechanisms that give rise to ultradian rhythms in sleep-wake state. This study investigated ultradian dynamics in sleep and wakefulness in rats entrained to a 12-h:12-h light-dark cycle (LD) and in rats whose circadian rhythms were suppressed and free-running following long-term exposure to uninterrupted bright light (LL). We recorded sleep-wake state continuously for 7 to 12 consecutive days and used time-series analysis to quantify the dynamics of net cumulative time in each state (wakefulness [WAKE], rapid eye movement sleep [REM], and non-REM sleep [NREM]) in each animal individually. Form estimates and autocorrelation confirmed the presence of significant ultradian and circadian rhythms; maximum entropy spectral analysis allowed high-resolution evaluation of multiple periods within the signal, and wave-by-wave analysis enabled a statistical evaluation of the instantaneous period, peak-trough range, and phase of each ultradian wave in the time series. Significant ultradian periodicities were present in all 3 states in all animals. In LD, ultradian range was approximately 28% of circadian range. In LL, ultradian range was slightly reduced relative to LD, and circadian range was strongly attenuated. Ultradian rhythms were found to be quasiperiodic in both LD and LL. That is, ultradian period varied randomly around a mean of approximately 4 h, with no relationship between ultradian period and time of day.

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.

Analyses for physiological and behavioral rhythmicity.

Biological data that contain cycles require specialized statistical and analytical procedures. Techniques for analysis of time series from three types of systems are considered with the intent that the choice of examples is sufficiently broad that the processes described can be generalized to most other types of physiological or behavioral work. Behavioral circadian rhythms, acoustic signals in fly mating, and the Drosophila melanogaster cardiac system have been picked as typical in three broad areas. Worked examples from the fly cardiac system are studied in full detail throughout. The nature of the data streams and how they are acquired is first discussed with attention paid to ensuring satisfactory subsequent statistical treatment. Analysis in the time domain, namely simple and advanced plotting of data, autocorrelation analysis, and cross-correlation, is described. The search for periodicity is conducted through examples of analysis in the frequency domain, primarily spectral analysis. Nonstationary time series pose a particular problem, and wavelet analysis of Drosophila mating song is described in detail as an example. Conditioning of data to improve output with digital filters, Fourier filtering, and trend removal is described. Finally, two tests for noise levels and regularity are considered. All the nonproprietary software used throughout the work is available from the author free of charge and can be specifically tailored to the needs of individual systems.

Statistical analysis of biological rhythm data.

The author has developed an ensemble of digital signal analysis techniques applicable to biological time series containing circadian and ultradian periodicities that is of very high resolution and functions well even in the presence of extreme noise and trend. A method for quantifying the significance, strength, and regularity of the rhythmic process is included. To illustrate these techniques, the author presents analyses of artificial periodic data containing varying amounts of noise, trend, and multiple periodicities. The periods and amplitudes of circadian and, where included, ultradian periodicities, and all other components of the test signals are known exactly. Analyses are illustrated in a step-by-step manner and the results are compared with the known input parameters. Trends are removed; spectra, autocorrelation functions, and rhythmicity indices are produced and discussed. References covering theory and details of all analyses are supplied. All programs employed are available from the author free of charge.

Mutations in and deletions of the Ca2+ channel-encoding gene cacophony, which affect courtship song in Drosophila, have novel effects on heartbeating.

The cacophony (cac) locus of Drosophila melanogaster encodes the a-1 subunit of a voltage gated Ca(2+) channel, termed Dmca1A. A subset of mutations at this locus cause characteristic alterations in the male mating song, manifest as polycyclic pulses with higher than normal amplitude. This phenotype has been postulated to result from disruption of an oscillator involving the cac-encoded channel, nearly identical to a model proposed for the pacemaker of the Drosophila heart. We report here that flies bearing two intragenic mutations that affect song, cac(S) and cac(TS2), cause aberrant heartbeating. Hearts of both cac(S) and cac(TS2) mutants beat significantly more rapidly than wild type and the heartbeat is more regular across temperature. Deletions of the cac gene, heterozygous with cac(+), caused interestingly similar heartbeating anomalies. For the heart phenotypes, the mutations are dominant, unlike the effects of cac(S) on song. In sum, our results establish the hypothesis that the observed effects are a result of a reduced number of functional cac-encoded channels rather than any specific alteration in the protein, and that in addition to Dmca1A, a second Ca(2+) channel with different kinetics is also involved in pacemaking.

Resetting the circadian clock by social experience in Drosophila melanogaster.

Circadian clocks are influenced by social interactions in a variety of species, but little is known about the sensory mechanisms underlying these effects. We investigated whether social cues could reset circadian rhythms in Drosophila melanogaster by addressing two questions: Is there a social influence on circadian timing? If so, then how is that influence communicated? The experiments show that in a social context Drosophila transmit and receive cues that influence circadian time and that these cues are likely olfactory.

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.

SYMMETRY VERSUS ASYMMETRY IN SEXUAL ISOLATION EXPERIMENTS.

Two hypotheses predicting the ancestral or derived status of populations and based on asymmetrical mate discrimination (Kaneshiro, 1976; Watanabe and Kawanishi, 1979) were tested using nine laboratory populations of D. simulans, a highly outcrossed ancestral population, and eight populations derived from it via founder-flush-crash cycles. The data from individual mating tests using pairwise combinations of these populations fit the Kaneshiro hypothesis reasonably well, rejecting the Watanabe-Kawanishi hypothesis. However, more powerful tests rejected the Kaneshiro hypothesis for the data we analyzed. The values for derived females predicted by the Kaneshiro hypothesis were biased: they were consistently high for derived males and consistently low for ancestral males. We propose a hypothesis, based on variation in mating propensities and symmetrical mate discrimination. We assessed the power of Kaneshiro's and our hypotheses to predict the number of matings between derived females and derived males by plotting predicted vs. observed values and fitting these points to the expected line of unit slope passing through the origin. Predictions of our hypothesis explained more of the variance (r2 = 0.87) than predictions of the Kaneshiro model (r2 = 0.63). While asymmetrical sexual isolation undoubtedly occurs between some species, its existence cannot be determined simply by measuring mating frequencies in a single experiment.