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Circadian rhythms are endogenously generated physiological and molecular rhythms with a cycle length of about 24 h. Bioluminescent reporters have been exceptionally useful for studying circadian rhythms in numerous species. Here, we report development of a reporter mouse generated by modification of a widely expressed and highly rhythmic gene encoding D-site albumin promoter binding protein ( Dbp ). In this line of mice, firefly luciferase is expressed from the Dbp locus in a Cre recombinase-dependent manner, allowing assessment of bioluminescence rhythms in specific cellular populations. A mouse line in which luciferase expression was Cre -independent was also generated. The Dbp reporter alleles do not alter Dbp gene expression rhythms in liver or circadian locomotor activity rhythms. In vivo and ex vivo studies show the utility of the reporter alleles for monitoring rhythmicity. Our studies reveal cell-type-specific characteristics of rhythms among neuronal populations within the suprachiasmatic nuclei ex vivo. In vivo studies show Dbp -driven bioluminescence rhythms in the liver of Albumin-Cre;Dbp KI/+ "liver reporter" mice. After a shift of the lighting schedule, locomotor activity achieved the proper phase relationship with the new lighting cycle more rapidly than hepatic bioluminescence did. As previously shown, restricting food access to the daytime altered the phase of hepatic rhythmicity. Our model allowed assessment of the rate of recovery from misalignment once animals were provided with food ad libitum. These studies confirm the previously demonstrated circadian misalignment following environmental perturbations and reveal the utility of this model for minimally invasive, longitudinal monitoring of rhythmicity from specific mouse tissues.

Circadian rhythms are driven by daily oscillations of gene expression. An important tool for studying cellular and tissue circadian rhythms is the use of a gene reporter, such as bioluminescence from the reporter gene luciferase controlled by a rhythmically expressed gene of interest. Here we describe methods that allow measurement of circadian bioluminescence from a freely moving mouse housed in a standard cage. Using a LumiCycle In Vivo (Actimetrics), we determined conditions that allow detection of circadian rhythms of bioluminescence from the PER2 reporter, PER2::LUC, in freely behaving mice. The LumiCycle In Vivo applies a background subtraction that corrects for effects of room temperature on photomultiplier tube (PMT) output. We tested delivery of d-luciferin via a subcutaneous minipump and in the drinking water. We demonstrate spikes in bioluminescence associated with drinking bouts. Further, we demonstrate that a synthetic luciferase substrate, CycLuc1, can support circadian rhythms of bioluminescence, even when delivered at a lower concentration than d-luciferin, and can support longer-term studies. A small difference in phase of the PER2::LUC bioluminescence rhythms, with females phase leading males, can be detected with this technique. We share our analysis scripts and suggestions for further improvements in this method. This approach will be straightforward to apply to mice with tissue-specific reporters, allowing insights into responses of specific peripheral clocks to perturbations such as environmental or pharmacological manipulations.

We developed a method for single-cell resolution longitudinal bioluminescence imaging of PERIOD (PER) protein and TIMELESS (TIM) oscillations in cultured male adult Drosophila brains that captures circadian circuit-wide cycling under simulated day/night cycles. Light input analysis confirms that CRYPTOCHROME (CRY) is the primary circadian photoreceptor and mediates clock disruption by constant light (LL), and that eye light input is redundant to CRY; 3-h light phase delays (Friday) followed by 3-h light phase advances (Monday morning) simulate the common practice of staying up later at night on weekends, sleeping in later on weekend days then returning to standard schedule Monday morning [weekend light shift (WLS)]. PER and TIM oscillations are highly synchronous across all major circadian neuronal subgroups in unshifted light schedules for 11 d. In contrast, WLS significantly dampens PER oscillator synchrony and rhythmicity in most circadian neurons during and after exposure. Lateral ventral neuron (LNv) oscillations are the first to desynchronize in WLS and the last to resynchronize in WLS. Surprisingly, the dorsal neuron group-3 (DN3s) increase their within-group synchrony in response to WLS. In vivo , WLS induces transient defects in sleep stability, learning, and memory that temporally coincide with circuit desynchrony. Our findings suggest that WLS schedules disrupt circuit-wide circadian neuronal oscillator synchrony for much of the week, thus leading to observed behavioral defects in sleep, learning, and memory., (Copyright © 2021 Nave, Roberts et al.)

Advances in imaging technology, combined with the development of bioluminescent reporters for core clock genes, has enabled the observation of spatiotemporal patterns of circadian rhythms in the suprachiasmatic nuclei (SCN). In particular, the PERIOD2::luciferase (PER2::LUC) knockin mouse has led to novel approaches for studying the heterogeneous circadian network in the SCN. This chapter describes how to automate the processing of PER2::LUC imaging data from SCN slices for generating spatiotemporal maps of circadian parameters like phase, period, and amplitude. These maps can be aligned and averaged to produce composite maps displaying common features across multiple slices. In addition, we describe a method for automated detection of cell-like regions of interest, to support the study of the neural network in the SCN.

A single phase advance of the light:dark (LD) cycle can temporarily disrupt synchrony of neural circadian rhythms within the suprachiasmatic nucleus (SCN) and between the SCN and peripheral tissues. Compounding this, modern life can involve repeated disruptive light conditions. To model chronic disruption to the circadian system, we exposed male mice to more than a month of a 20-hr light cycle (LD10:10), which mice typically cannot entrain to. Control animals were housed under LD12:12. We measured locomotor activity and body temperature rhythms in vivo, and rhythms of PER2::LUC bioluminescence in SCN and peripheral tissues ex vivo. Unexpectedly, we discovered strong effects of the time of dissection on circadian phase of PER2::LUC bioluminescent rhythms, which varied across tissues. White adipose tissue was strongly reset by dissection, while thymus phase appeared independent of dissection timing. Prior light exposure impacted the SCN, resulting in strong resetting of SCN phase by dissection for mice housed under LD10:10, and weak phase shifts by time of dissection in SCN from control LD12:12 mice. These findings suggest that exposure to circadian disruption may desynchronize SCN neurons, increasing network sensitivity to perturbations. We propose that tissues with a weakened circadian network, such as the SCN under disruptive light conditions, or with little to no coupling, for example, some peripheral tissues, will show increased resetting effects. In particular, exposure to light at inconsistent circadian times on a recurring weekly basis disrupts circadian rhythms and alters sensitivity of the SCN neural pacemaker to dissection time., (© 2018 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

The first aim of this research is to compare computational models of multi-alternative, multi-attribute choice when attribute values are explicit. The choice predictions of utility (standard random utility & weighted valuation), heuristic (elimination-by-aspects, lexicographic, & maximum attribute value), and dynamic (multi-alternative decision field theory, MDFT, & a version of the multi-attribute linear ballistic accumulator, MLBA) models are contrasted on both preferential and risky choice data. Using both maximum likelihood and cross-validation fit measures on choice data, the utility and dynamic models are preferred over the heuristic models for risky choice, with a slight overall advantage for the MLBA for preferential choice. The response time predictions of these models (except the MDFT) are then tested. Although the MLBA accurately predicts response time distributions, it only weakly accounts for stimulus-level differences. The other models completely fail to account for stimulus-level differences. Process tracing measures, i.e., eye and mouse tracking, were also collected. None of the qualitative predictions of the models are completely supported by that data. These results suggest that the models may not appropriately represent the interaction of attention and preference formation. To overcome this potential shortcoming, the second aim of this research is to test preference-formation assumptions, independently of attention, by developing the models of attentional sampling (MAS) model family which incorporates the empirical gaze patterns into a sequential sampling framework. An MAS variant that includes attribute values, but only updates the currently viewed alternative and does not contrast values across alternatives, performs well in both experiments. Overall, the results support the dynamic models, but point to the need to incorporate a framework that more accurately reflects the relationship between attention and the preference-formation process., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Circadian rhythms of mammalian physiology and behavior are coordinated by the suprachiasmatic nucleus (SCN) in the hypothalamus. Within SCN neurons, various aspects of cell physiology exhibit circadian oscillations, including circadian clock gene expression, levels of intracellular Ca 2+ ([Ca 2+ ] i ), and neuronal firing rate. [Ca 2+ ] i oscillates in SCN neurons even in the absence of neuronal firing. To determine the causal relationship between circadian clock gene expression and [Ca 2+ ] i rhythms in the SCN, as well as the SCN neuronal network dependence of [Ca 2+ ] i rhythms, we introduced GCaMP3, a genetically encoded fluorescent Ca 2+ indicator, into SCN neurons from PER2::LUC knock-in reporter mice. Then, PER2 and [Ca 2+ ] i were imaged in SCN dispersed and organotypic slice cultures. In dispersed cells, PER2 and [Ca 2+ ] i both exhibited cell autonomous circadian rhythms, but [Ca 2+ ] i rhythms were typically weaker than PER2 rhythms. This result matches the predictions of a detailed mathematical model in which clock gene rhythms drive [Ca 2+ ] i rhythms. As predicted by the model, PER2 and [Ca 2+ ] i rhythms were both stronger in SCN slices than in dispersed cells and were weakened by blocking neuronal firing in slices but not in dispersed cells. The phase relationship between [Ca 2+ ] i and PER2 rhythms was more variable in cells within slices than in dispersed cells. Both PER2 and [Ca 2+ ] i rhythms were abolished in SCN cells deficient in the essential clock gene Bmal1 . These results suggest that the circadian rhythm of [Ca 2+ ] i in SCN neurons is cell autonomous and dependent on clock gene rhythms, but reinforced and modulated by a synchronized SCN neuronal network., Competing Interests: Authors report no conflict of interest.

This article is part of a Journal of Biological Rhythms series exploring analysis and statistics topics relevant to researchers in biological rhythms and sleep research. The goal is to provide an overview of the most common issues that arise in the analysis and interpretation of data in these fields. In this article on time series analysis for biological rhythms, we describe some methods for assessing the rhythmic properties of time series, including tests of whether a time series is indeed rhythmic. Because biological rhythms can exhibit significant fluctuations in their period, phase, and amplitude, their analysis may require methods appropriate for nonstationary time series, such as wavelet transforms, which can measure how these rhythmic parameters change over time. We illustrate these methods using simulated and real time series.

Light is the primary signal that calibrates circadian neural circuits and thus coordinates daily physiological and behavioral rhythms with solar entrainment cues. Drosophila and mammalian circadian circuits consist of diverse populations of cellular oscillators that exhibit a wide range of dynamic light responses, periods, phases, and degrees of synchrony. How heterogeneous circadian circuits can generate robust physiological rhythms while remaining flexible enough to respond to synchronizing stimuli has long remained enigmatic. Cryptochrome is a short-wavelength photoreceptor that is endogenously expressed in approximately half of Drosophila circadian neurons. In a previous study, physiological light response was measured using real-time bioluminescence recordings in Drosophila whole-brain explants, which remain intrinsically light-sensitive. Here we apply analysis of real-time bioluminescence experimental data to show detailed dynamic ensemble representations of whole circadian circuit light entrainment at single neuron resolution. Organotypic whole-brain explants were either maintained in constant darkness (DD) for 6 days or exposed to a phase-advancing light pulse on the second day. We find that stronger circadian oscillators support robust overall circuit rhythmicity in DD, whereas weaker oscillators can be pushed toward transient desynchrony and damped amplitude to facilitate a new state of phase-shifted network synchrony. Additionally, we use mathematical modeling to examine how a network composed of distinct oscillator types can give rise to complex dynamic signatures in DD conditions and in response to simulated light pulses. Simulations suggest that complementary coupling mechanisms and a combination of strong and weak oscillators may enable a robust yet flexible circadian network that promotes both synchrony and entrainment. A more complete understanding of how the properties of oscillators and their signaling mechanisms facilitate their distinct roles in light entrainment may allow us to direct and augment the circadian system to speed recovery from jet lag, shift work, and seasonal affective disorder., (© 2016 The Author(s).)

Daily rhythms in mammals are controlled by the circadian system, which is a collection of biological clocks regulated by a central pacemaker within the suprachiasmatic nucleus (SCN) of the anterior hypothalamus. Changes in SCN function have pronounced consequences for behaviour and physiology; however, few studies have examined whether individual differences in circadian behaviour reflect changes in SCN function. Here, PERIOD2::LUCIFERASE mice were exposed to a behavioural assay to characterize individual differences in baseline entrainment, rate of re-entrainment and free-running rhythms. SCN slices were then collected for ex vivo bioluminescence imaging to gain insight into how the properties of the SCN clock influence individual differences in behavioural rhythms. First, individual differences in the timing of locomotor activity rhythms were positively correlated with the timing of SCN rhythms. Second, slower adjustment during simulated jetlag was associated with a larger degree of phase heterogeneity among SCN neurons. Collectively, these findings highlight the role of the SCN network in determining individual differences in circadian behaviour. Furthermore, these results reveal novel ways that the network organization of the SCN influences plasticity at the behavioural level, and lend insight into potential interventions designed to modulate the rate of resynchronization during transmeridian travel and shift work., (© 2015 The Author(s) Published by the Royal Society. All rights reserved.)

The duper mutation in Syrian hamsters shortens the free-running period of locomotor activity (τDD) to about 23 h and results in a type 0 phase-response curve (PRC) to 15-min light pulses. To determine whether exaggerated phase shifts are specific to photic cues and/or restricted to subjective night, we subjected hamsters to novel wheel confinements and dark pulses during subjective day. Small phase shifts elicited by the nonphotic cue were comparable in mutant and wild-type (WT) hamsters, but dark pulses triggered larger shifts in dupers. To assess further the effects of the duper mutation on light-dark transitions, we transferred hamsters between constant light (LL) and constant dark (DD) or between DD and LL at various circadian phases. Duper hamsters displayed significantly larger phase shifts than WT hamsters when transferred from LL to DD during subjective day and from DD to LL during subjective night. The variability of phase shifts in response to all light/dark transitions was significantly greater in duper hamsters at all time points. In addition, most duper hamsters, but none of the WTs, displayed transient ultradian wheel-running patterns for 5 to 12 days when transferred from light to dark at CT 18. The χ(2) periodogram and autocorrelation analyses indicate that these ultradian patterns differ from the disruption of rhythmicity by SCN lesions or exposure to constant bright light. We conclude that the duper mutation specifically amplifies phase shifts to photic cues and may destabilize coupling of circadian organization upon photic challenge due to weakened coupling among components of the circadian pacemaker. Mathematical modeling of the circadian pacemaker supports this hypothesis., (© 2015 The Author(s).)

Circadian neural circuits generate near 24-hr physiological rhythms that can be entrained by light to coordinate animal physiology with daily solar cycles. To examine how a circadian circuit reorganizes its activity in response to light, we imaged period (per) clock gene cycling for up to 6 days at single-neuron resolution in whole-brain explant cultures prepared from per-luciferase transgenic flies. We compared cultures subjected to a phase-advancing light pulse (LP) to cultures maintained in darkness (DD). In DD, individual neuronal oscillators in all circadian subgroups are initially well synchronized but then show monotonic decrease in oscillator rhythm amplitude and synchrony with time. The small ventral lateral neurons (s-LNvs) and dorsal lateral neurons (LNds) exhibit this decrease at a slower relative rate. In contrast, the LP evokes a rapid loss of oscillator synchrony between and within most circadian neuronal subgroups, followed by gradual phase retuning of whole-circuit oscillator synchrony. The LNds maintain high rhythmic amplitude and synchrony following the LP along with the most rapid coherent phase advance. Immunocytochemical analysis of PER shows that these dynamics in DD and LP are recapitulated in vivo. Anatomically distinct circadian neuronal subgroups vary in their response to the LP, showing differences in the degree and kinetics of their loss, recovery and/or strengthening of synchrony, and rhythmicity. Transient desynchrony appears to be an integral feature of light response of the Drosophila multicellular circadian clock. Individual oscillators in different neuronal subgroups of the circadian circuit show distinct kinetic signatures of light response and phase retuning., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

The challenging problems presented by noisy biological oscillators have led to the development of a great variety of methods for accurately estimating rhythmic parameters such as period and amplitude. This chapter focuses on wavelet-based methods, which can be quite effective for assessing how rhythms change over time, particularly if time series are at least a week in length. These methods can offer alternative views to complement more traditional methods of evaluating behavioral records. The analytic wavelet transform can estimate the instantaneous period and amplitude, as well as the phase of the rhythm at each time point, while the discrete wavelet transform can extract the circadian component of activity and measure the relative strength of that circadian component compared to those in other frequency bands. Wavelet transforms do not require the removal of noise or trend, and can, in fact, be effective at removing noise and trend from oscillatory time series. The Fourier periodogram and spectrogram are reviewed, followed by descriptions of the analytic and discrete wavelet transforms. Examples illustrate application of each method and their prior use in chronobiology is surveyed. Issues such as edge effects, frequency leakage, and implications of the uncertainty principle are also addressed., (© 2015 Elsevier Inc. All rights reserved.)

Background: Hepatocytes, the parenchymal cells of the liver, express core clock genes, such as Period2 and Cryptochrome2, which are involved in the transcriptional/translational feedback loop of the circadian clock. Whether or not the liver is capable of sustaining rhythms independent of a central pacemaker is controversial. Whether and how circadian information may be shared among cells in the liver in order to sustain oscillations is currently unknown., Results: In this study we isolated primary hepatocytes from transgenic Per2(Luc) mice and used bioluminescence as a read-out of the state of the circadian clock. Hepatocytes cultured in a collagen gel sandwich configuration exhibited persistent circadian rhythms for several weeks. The amplitude of the rhythms damped, but medium changes consistently reset the phase and amplitude of the cultures. Cry2(-/-) Per2(Luc) cells oscillated robustly and expressed a longer period. Co-culturing with wildtype cells did not significantly shorten the period, indicating that coupling among hepatocytes is insufficient to synchronize cells with significantly differing periods. However, spatial patterns revealed by cellular imaging of wildtype cultures provided evidence of weak local coupling among the hepatocytes., Conclusions: Our results with primary hepatocyte cultures demonstrate that cultured hepatocytes are weakly coupled. While this coupling is not sufficient to sustain global synchrony, it does increase local synchrony, which may stabilize the circadian rhythms of peripheral oscillators, such as the liver, against noise in the entraining signals.

Interactions among suprachiasmatic nucleus (SCN) neurons are required for robust circadian rhythms entrained to local time. To investigate these signaling mechanisms, we developed a functional coupling assay that uniquely captures the dynamic process by which SCN neurons interact. As a population, SCN neurons typically display synchronized rhythms with similar peak times, but will peak 6-12 hr apart after in vivo exposure to long days. Once they are removed from these conditions, SCN neurons resynchronize through a phase-dependent coupling process mediated by both vasoactive intestinal polypeptide (VIP) and GABAA signaling. Notably, GABAA signaling contributes to coupling when the SCN network is in an antiphase configuration, but opposes synchrony under steady-state conditions. Further, VIP acts together with GABAA signaling to couple the network in an antiphase configuration, but promotes synchrony under steady-state conditions by counteracting the actions of GABAA signaling. Thus, SCN neurons interact through nonredundant coupling mechanisms influenced by the state of the network., (Copyright © 2013 Elsevier Inc. All rights reserved.)

: We review time-frequency methods that can be useful in quantifying circadian and ultradian patterns in behavioral records. These records typically exhibit details that may not be captured through commonly used measures such as activity onset and so may require alternative approaches. For instance, activity may involve multiple bouts that vary in duration and magnitude within a day, or may exhibit day-to-day changes in period and in ultradian activity patterns. The discrete Fourier transform and other types of periodograms can estimate the period of a circadian rhythm, but we show that they can fail to correctly assess ultradian periods. In addition, such methods cannot detect changes in the period over time. Time-frequency methods that can localize frequency estimates in time are more appropriate for analysis of ultradian periods and of fluctuations in the period. The continuous wavelet transform offers a method for determining instantaneous frequency with good resolution in both time and frequency, capable of detecting changes in circadian period over the course of several days and in ultradian period within a given day. The discrete wavelet transform decomposes a time series into components associated with distinct frequency bands, thereby facilitating the removal of noise and trend or the isolation of a particular frequency band of interest. To demonstrate the wavelet-based analysis, we apply the transforms to a numerically-generated example and also to a variety of hamster behavioral records. When used appropriately, wavelet transforms can reveal patterns that are not easily extracted using other methods of analysis in common use, but they must be applied and interpreted with care.

A variety of methods to determine phase markers and period length from experimental data sets have traditionally assumed a rhythm of fixed period and amplitude. But most biological oscillations exhibit fluctuations in both period and amplitude, leading to the recent interest in the application of wavelet transforms that can measure how rhythms vary over time. Here we examine how wavelet-based methods can be extended to the analysis of conventional actograms, including the detection of onsets in circadian activity and temperature rhythms of rodents.

Precise determination of a noisy biological oscillator's period from limited experimental data can be challenging. The common practice is to calculate a single number (a point estimate) for the period of a particular time course. Uncertainty is inherent in any statistical estimator applied to noisy data, so our confidence in such point estimates depends on the quality and quantity of the data. Ideally, a period estimation method should both produce an accurate point estimate of the period and measure the uncertainty in that point estimate. A variety of period estimation methods are known, but few assess the uncertainty of the estimates, and a measure of uncertainty is rarely reported in the experimental literature. We compare the accuracy of point estimates using six common methods, only one of which can also produce uncertainty measures. We then illustrate the advantages of a new Bayesian method for estimating period, which outperforms the other six methods in accuracy of point estimates for simulated data and also provides a measure of uncertainty. We apply this method to analyze circadian oscillations of gene expression in individual mouse fibroblast cells and compute the number of cells and sampling duration required to reduce the uncertainty in period estimates to a desired level. This analysis indicates that, due to the stochastic variability of noisy intracellular oscillators, achieving a narrow margin of error can require an impractically large number of cells. In addition, we use a hierarchical model to determine the distribution of intrinsic cell periods, thereby separating the variability due to stochastic gene expression within each cell from the variability in period across the population of cells., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Aging produces a decline in the amplitude and precision of 24 h behavioral, endocrine, and metabolic rhythms, which are regulated in mammals by a central circadian pacemaker within the suprachiasmatic nucleus (SCN) and local oscillators in peripheral tissues. Disruption of the circadian system, as experienced during transmeridian travel, can lead to adverse health consequences, particularly in the elderly. To test the hypothesis that age-related changes in the response to simulated jet lag will reflect altered circadian function, we examined re-entrainment of central and peripheral oscillators from young and old PER2::luciferase mice. As in previous studies, locomotor activity rhythms in older mice required more days to re-entrain following a shift than younger mice. At the tissue level, effects of age on baseline entrainment were evident, with older mice displaying earlier phases for the majority of peripheral oscillators studied and later phases for cells within most SCN subregions. Following a 6 h advance of the light:dark cycle, old mice displayed slower rates of re-entrainment for peripheral tissues but a larger, more rapid SCN response compared to younger mice. Thus, aging alters the circadian timing system in a manner that differentially affects the re-entrainment responses of central and peripheral circadian clocks. This pattern of results suggests that a major consequence of aging is a decrease in pacemaker amplitude, which would slow re-entrainment of peripheral oscillators and reduce SCN resistance to external perturbation.

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude.

Analysis of circadian oscillations that exhibit variability in period or amplitude can be accomplished through wavelet transforms. Wavelet-based methods can also be used quite effectively to remove trend and noise from time series and to assess the strength of rhythms in different frequency bands, for example, ultradian versus circadian components in an activity record. In this article, we describe how to apply discrete and continuous wavelet transforms to time series of circadian rhythms, illustrated with novel analyses of 2 case studies involving mouse wheel-running activity and oscillations in PER2::LUC bioluminescence from SCN explants., (© 2011 The Author(s))

The mammalian pacemaker in the suprachiasmatic nucleus (SCN) contains a population of neural oscillators capable of sustaining cell-autonomous rhythms in gene expression and electrical firing. A critical question for understanding pacemaker function is how SCN oscillators are organized into a coherent tissue capable of coordinating circadian rhythms in behavior and physiology. Here we undertake a comprehensive analysis of oscillatory function across the SCN of the adult PER2::LUC mouse by developing a novel approach involving multi-position bioluminescence imaging and unbiased computational analyses. We demonstrate that there is phase heterogeneity across all three dimensions of the SCN that is intrinsically regulated and extrinsically modulated by light in a region-specific manner. By investigating the mechanistic bases of SCN phase heterogeneity, we show for the first time that phase differences are not systematically related to regional differences in period, waveform, amplitude, or brightness. Furthermore, phase differences are not related to regional differences in the expression of arginine vasopressin and vasoactive intestinal polypeptide, two key neuropeptides characterizing functionally distinct subdivisions of the SCN. The consistency of SCN spatiotemporal organization across individuals and across planes of section suggests that the precise phasing of oscillators is a robust feature of the pacemaker important for its function.

Circadian rhythms regulate most physiological processes. Adjustments to circadian time, called phase shifts, are necessary following international travel and on a more frequent basis for individuals who work non-traditional schedules such as rotating shifts. As the disruption that results from frequent phase shifts is deleterious to both animals and humans, we sought to better understand the kinetics of resynchronization of the mouse circadian system to one of the most disruptive phase shifts, a 6-h phase advance. Mice bearing a luciferase reporter gene for mPer2 were subjected to a 6-h advance of the light cycle and molecular rhythms in suprachiasmatic nuclei (SCN), thymus, spleen, lung and esophagus were measured periodically for 2 weeks following the shift. For the SCN, the master pacemaker in the brain, we employed high-resolution imaging of the brain slice to describe the resynchronization of rhythms in single SCN neurons during adjustment to the new light cycle. We observed significant differences in shifting kinetics among mice, among organs such as the spleen and lung, and importantly among neurons in the SCN. The phase distribution among all Period2-expressing SCN neurons widened on the day following a shift of the light cycle, which was partially due to cells in the ventral SCN exhibiting a larger initial phase shift than cells in the dorsal SCN. There was no clear delineation of ventral and dorsal regions, however, as the SCN appear to have a population of fast-shifting cells whose anatomical distribution is organized in a ventral-dorsal gradient. Full resynchronization of the SCN and peripheral timing system, as measured by a circadian reporter gene, did not occur until after 8 days in the advanced light cycle.

Experimental evidence points increasingly to the importance of posttranslational processes such as phosphorylation and translocation in the molecular circadian clocks of many organisms. We develop a mathematical model of the Drosophila circadian clock that incorporates the emerging details of the timing of nuclear translocation of the PERIOD and TIMELESS proteins. Most models assume that these proteins enter the nucleus as a complex, but recent experiments suggest that they in fact enter the nucleus separately. Our model reproduces observed patterns of intracellular localization of PERIOD and TIMELESS during light-dark cycles and in constant darkness, as well as phenotypes of several clock mutants. We also use the model to demonstrate how the Drosophila clock can exhibit robust oscillations with constant mRNA levels of period or timeless, and propose a possible mechanism for oscillations in double-rescue experiments of per(01)-tim(01) mutants. The model also explains (via posttranslational processes) the counter-intuitive observation that total dCLOCK levels are at their lowest at the circadian time when active nuclear dCLOCK must be peaking in order to activate transcription of other clock genes, implying that for dCLOCK a posttranslationally generated rhythm is more important than the transcriptionally generated rhythm. These results support the idea that posttranslational processes play key roles in generating as well as modulating robust circadian oscillations. While it appears that posttranslational mechanisms alone are not sufficient to generate rhythms in Drosophila, posttranslational mechanisms can greatly amplify a very weak transcriptional rhythm.