Summary Interactions among suprachiasmatic nucleus (SCN) neurons are required for robust circadian rhythms entrained to local time. To investigate these coupling mechanisms, we developed a novel 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 6–12h apart after in vivo exposure to long days. Once 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 in an anti-phase configuration, but opposes synchrony under steady-state conditions. Further, VIP acts together with GABAA signaling to couple the network in an anti-phase configuration, but promotes synchrony under steady-state conditions by counteracting the actions of GABAA signaling. Thus, SCN neurons interact through non-redundant coupling mechanisms influenced by the state of the network.

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.

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.

Aging produces a decline in the amplitude and precision of 24h 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 jetlag 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 6h 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.

Abstract. Google's success derives in large part from its PageRank algorithm, which ranks the importance of web pages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this article as a project to more advanced students or spend one or two lectures presenting the material with assigned homework from the exercises. This material also complements the discussion of Markov chains in matrix algebra. Maple and Mathematica files supporting this material can be found at www.rose-hulman.edu/∼bryan.

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.

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.