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.

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.

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.

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.

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 Ca2+ ([Ca2+]i), and neuronal firing rate. [Ca2+]i oscillates in SCN neurons even in the absence of neuronal firing. To determine the causal relationship between circadian clock gene expression and [Ca2+]i rhythms in the SCN, as well as the SCN neuronal network dependence of [Ca2+]i rhythms, we introduced GCaMP3, a genetically encoded fluorescent Ca2+ indicator, into SCN neurons from PER2::LUC knock-in reporter mice. Then, PER2 and [Ca2+]i were imaged in SCN dispersed and organotypic slice cultures. In dispersed cells, PER2 and [Ca2+]i both exhibited cell autonomous circadian rhythms, but [Ca2+]i rhythms were typically weaker than PER2 rhythms. This result matches the predictions of a detailed mathematical model in which clock gene rhythms drive [Ca2+]i rhythms. As predicted by the model, PER2 and [Ca2+]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 [Ca2+]i and PER2 rhythms was more variable in cells within slices than in dispersed cells. Both PER2 and [Ca2+]i rhythms were abolished in SCN cells deficient in the essential clock gene Bmal1. These results suggest that the circadian rhythm of [Ca2+]i in SCN neurons is cell autonomous and dependent on clock gene rhythms, but reinforced and modulated by a synchronized SCN neuronal network.

In Fall 2015, Amherst College students held a four-day sit-in in unity with student protests occurring all over the United States highlighting barriers to inclusion of underrepresented and marginalized students.Following appeals for action, students partnered with faculty and staff in science, technology, engineering, and mathematics (STEM) to develop the Being Human in STEM (HSTEM) Initiative. HSTEM involves exploring past diversity and inclusion efforts in STEM, sharing one’s own experiences in STEM with others, and developing student-driven projects to improve belonging in STEM. In this student, faculty, and staff co-authored paper, we describe the origin of HSTEM; share student, faculty and staff reflections on our experiences with HSTEM; and present two inquiry projects examining HSTEM impact. We discuss lessons learned and recommendations for diversity and inclusion efforts in higher education, both in and beyond STEM, emphasizing the power of an initiative that was originated by and remains driven by student partners.

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.

Genome biology approaches have made enormous contributions to our understanding of biological rhythms, particularly in identifying outputs of the clock, including RNAs, proteins, and metabolites, whose abundance oscillates throughout the day. These methods hold significant promise for future discovery, particularly when combined with computational modeling. However, genome-scale experiments are costly and laborious, yielding "big data" that are conceptually and statistically difficult to analyze. There is no obvious consensus regarding design or analysis. Here we discuss the relevant technical considerations to generate reproducible, statistically sound, and broadly useful genome-scale data. Rather than suggest a set of rigid rules, we aim to codify principles by which investigators, reviewers, and readers of the primary literature can evaluate the suitability of different experimental designs for measuring different aspects of biological rhythms. We introduce CircaInSilico, a web-based application for generating synthetic genome biology data to benchmark statistical methods for studying biological rhythms. Finally, we discuss several unmet analytical needs, including applications to clinical medicine, and suggest productive avenues to address them.