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Light is the most effective environmental stimulus for shifting the mammalian circadian pacemaker. Numerous studies have been conducted across multiple species to delineate wavelength, intensity, duration, and timing contributions to the response of the circadian pacemaker to light. Recent studies have revealed a surprising sensitivity of the human circadian pacemaker to short pulses of light. Such responses have challenged photon counting-based theories of the temporal dynamics of the mammalian circadian system to both short- and long-duration light stimuli. Here, we collate published light exposure data from multiple species, including gerbil, hamster, mouse, and human, to investigate these temporal dynamics and explore how the circadian system integrates light information at both short- and long-duration time scales to produce phase shifts. Based on our investigation of these data sets, we propose 3 new interpretations: (1) intensity and duration are independent factors of total phase shift magnitude, (2) the possibility of a linear/log temporal function of light duration that is universal for all intensities for durations less than approximately 12 min, and (3) a potential universal minimum light duration of ~0.7 sec that describes a "dead zone" of light stimulus. We show that these properties appear to be consistent across mammalian species. These interpretations, if confirmed by further experiments, have important practical implications in terms of understanding the underlying physiology and for the design of lighting regimens to reset the mammalian circadian pacemaker.

BACKGROUND. In humans, a single light exposure of 12 minutes and multiple-millisecond light exposures can shift the phase of the circadian pacemaker. We investigated the response of the human circadian pacemaker to a single 15-second or 2-minute light pulse administered during the biological night. METHODS. Twenty-six healthy individuals participated in a 9-day inpatient protocol that included assessment of dim light melatonin onset time (DLMO time) before and after exposure to a single 15-second ( n = 8) or 2-minute ( n = 12) pulse of bright light (9,500 lux; 4,100 K fluorescent) or control background dim light (<3 lux; n = 6). Phase shifts were calculated as the difference in clock time between the two phase estimates. RESULTS. Both 15-second and 2-minute exposures induced phase delay shifts [median (± SD)] of -34.8 ± 47.2 minutes and -45.4 ± 28.4 minutes, respectively, that were significantly ( P = 0.04) greater than the control condition (advance shift: +22.3 ± 51.3 minutes) but were not significantly different from each other. Comparisons with historic data collected under the same conditions confirmed a nonlinear relationship between exposure duration and the magnitude of phase shift. CONCLUSIONS. Our results underscore the exquisite sensitivity of the human pacemaker to even short-duration single exposures to light. These findings may have real-world implications for circadian disruption induced by exposure to brief light stimuli at night. TRIAL REGISTRATION. The study was registered as a clinical trial on www.clinicaltrials.org, NCT #01330992. FUNDING. Funding for this study was provided by NSBRI HFP02802 and NIH P01-AG09975, R01-HL114088 (EBK), RC2-HL101340-0 (EBK, SWL, SAR, REK), K02-HD045459 (EBK), K24-HL105664 (EBK), T32-HL07901 (MSH, SAR), HL094654 (CAC), and AG044416 (JFD). The project described was supported by NIH grant 1UL1 TR001102-01, 8UL1TR000170-05, UL1 RR 025758, Harvard Clinical and Translational Science Center, from the National Center for Advancing Translational Science., Competing Interests: Conflict of interest: Possible conflicts of interest for all authors are disclosed in the online supplement (https://doi.org/10.1172/jci.insight.89494DS1).

The photic resetting response of the human circadian pacemaker depends on the timing of exposure, and the direction and magnitude of the resulting shift is described by a phase response curve (PRC). Previous PRCs in humans have utilized high-intensity polychromatic white light. Given that the circadian photoreception system is maximally sensitive to short-wavelength visible light, the aim of the current study was to construct a PRC to blue (480 nm) light and compare it to a 10,000 lux white light PRC constructed previously using a similar protocol. Eighteen young healthy participants (18-30 years) were studied for 9-10 days in a time-free environment. The protocol included three baseline days followed by a constant routine (CR) to assess initial circadian phase. Following this CR, participants were exposed to a 6.5 h 480 nm light exposure (11.8 μW cm(-2), 11.2 lux) following mydriasis via a modified Ganzfeld dome. A second CR was conducted following the light exposure to re-assess circadian phase. Phase shifts were calculated from the difference in dim light melatonin onset (DLMO) between CRs. Exposure to 6.5 h of 480 nm light resets the circadian pacemaker according to a conventional type 1 PRC with fitted maximum delays and advances of -2.6 h and 1.3 h, respectively. The 480 nm PRC induced ∼75% of the response of the 10,000 lux white light PRC. These results may contribute to a re-evaluation of dosing guidelines for clinical light therapy and the use of light as a fatigue countermeasure.

Light exposure in the early night induces phase delays of the circadian rhythm in melatonin in humans. Previous studies have investigated the effect of timing, intensity, wavelength, history and pattern of light stimuli on the human circadian timing system. We present results from a study of the duration–response relationship to phase-delaying bright light. Thirty-nine young healthy participants (16 female; 22.18±3.62 years) completed a 9-day inpatient study. Following three baseline days, participants underwent an initial circadian phase assessment procedure in dim light (<3 lux), and were then randomized for exposure to a bright light pulse (∼10,000 lux) of 0.2 h, 1.0 h, 2.5 h or 4.0 h duration during a 4.5 h controlled-posture episode centred in a 16 h wake episode. After another 8 h sleep episode, participants completed a second circadian phase assessment. Phase shifts were calculated from the difference in the clock time of the dim light melatonin onset (DLMO) between the initial and final phase assessments. Exposure to varying durations of bright light reset the circadian pacemaker in a dose-dependent, non-linear manner. Per minute of exposure, the 0.2 h duration was over 5 times more effective at phase delaying the circadian pacemaker (1.07±0.36 h) as compared with the 4.0 h duration (2.65±0.24 h). Acute melatonin suppression and subjective sleepiness also had a dose-dependent response to light exposure duration. These results provide strong evidence for a non-linear resetting response of the human circadian pacemaker to light duration.

The phase resetting response of the human circadian pacemaker to light depends on the timing of exposure and is described by a phase response curve (PRC). The current study aimed to construct a PRC for a 1 h exposure to bright white light (∼8000 lux) and to compare this PRC to a <3 lux dim background light PRC. These data were also compared to a previously completed 6.7 h bright white light PRC and a <15 lux dim background light PRC constructed under similar conditions. Participants were randomized for exposure to 1 h of either bright white light (n=18) or <3 lux dim background light (n=18) scheduled at 1 of 18 circadian phases. Participants completed constant routine (CR) procedures in dim light (<3 lux) before and after the light exposure to assess circadian phase. Phase shifts were calculated as the difference in timing of dim light melatonin onset (DLMO) during pre- and post-stimulus CRs. Exposure to 1 h of bright white light induced a Type 1 PRC with a fitted peak-to-trough amplitude of 2.20 h. No discernible PRC was observed in the <3 lux dim background light PRC. The fitted peak-to-trough amplitude of the 1 h bright light PRC was ∼40% of that for the 6.7 h PRC despite representing only 15% of the light exposure duration, consistent with previous studies showing a non-linear duration–response function for the effects of light on circadian resetting.

Accurate determination of circadian phase is necessary for research and clinical purposes because of the influence of the master circadian pacemaker on multiple physiologic functions. Melatonin is presently the most accurate marker of the activity of the human circadian pacemaker. Current methods of analyzing the plasma melatonin rhythm can be grouped into three categories: curve-fitting, threshold-based and physiologically-based linear differential equations. To determine which method provides the most accurate assessment of circadian phase, we compared the ability to fit the data and the variability of phase estimates for seventeen different markers of melatonin phase derived from these methodological categories. We used data from three experimental conditions under which circadian rhythms - and therefore calculated melatonin phase - were expected to remain constant or progress uniformly. Melatonin profiles from older subjects and subjects with lower melatonin amplitude were less likely to be fit by all analysis methods. When circadian drift over multiple study days was algebraically removed, there were no significant differences between analysis methods of melatonin onsets (P = 0.57), but there were significant differences between those of melatonin offsets (P<0.0001). For a subset of phase assessment methods, we also examined the effects of data loss on variability of phase estimates by systematically removing data in 2-hour segments. Data loss near onset of melatonin secretion differentially affected phase estimates from the methods, with some methods incorrectly assigning phases too early while other methods assigning phases too late; missing data at other times did not affect analyses of the melatonin profile. We conclude that melatonin data set characteristics, including amplitude and completeness of data collection, differentially affect the results depending on the melatonin analysis method used.

In humans, modulation of circadian rhythms by light is thought to be mediated primarily by melanopsin-containing retinal ganglion cells, not rods or cones. Melanopsin cells are intrinsically blue light-sensitive but also receive input from visual photoreceptors. We therefore tested in humans whether cone photoreceptors contribute to the regulation of circadian and neuroendocrine light responses. Dose-response curves for melatonin suppression and circadian phase resetting were constructed in subjects exposed to blue (460 nm) or green (555 nm) light near the onset of nocturnal melatonin secretion. At the beginning of the intervention, 555-nm light was equally effective as 460-nm light at suppressing melatonin, suggesting a significant contribution from the three-cone visual system (lambda(max) = 555 nm). During the light exposure, however, the spectral sensitivity to 555-nm light decayed exponentially relative to 460-nm light. For phase-resetting responses, the effects of exposure to low-irradiance 555-nm light were too large relative to 460-nm light to be explained solely by the activation of melanopsin. Our findings suggest that cone photoreceptors contribute substantially to nonvisual responses at the beginning of a light exposure and at low irradiances, whereas melanopsin appears to be the primary circadian photopigment in response to long-duration light exposure and at high irradiances. These results suggest that light therapy for sleep disorders and other indications might be optimized by stimulating both photoreceptor systems.

Mathematical models have become vital to the study of many biological processes in humans due to the complexity of the physiological mechanisms underlying these processes and systems. While our current mathematical representation of the human circadian pacemaker has proven useful in many experimental situations, it uses as input only a direct effect of light on the circadian pacemaker. Although light (a photic stimulus) has been shown to be the primary synchronizer of the circadian pacemaker across a number of species, studies in both animals and humans have confirmed the existence of non-photic effects that also contribute to phase shifting and entrainment. We modified our light-based circadian mathematical model to reflect evidence from these studies that the sleep-wake cycle and/or associated behaviors have a non-photic effect on the circadian pacemaker. In our representation, the sleep-wake cycle and its associated behaviors provides a non-photic drive on the circadian pacemaker that acts both independently and concomitantly with light stimuli. Further experiments are required to validate fully our model and to understand the exact effect of the sleep-wake cycle as a non-photic stimulus for the human circadian pacemaker.

Human expeditions to Mars will require adaptation to the 24.65-h Martian solar day-night cycle (sol), which is outside the range of entrainment of the human circadian pacemaker under lighting intensities to which astronauts are typically exposed. Failure to entrain the circadian time-keeping system to the desired rest-activity cycle disturbs sleep and impairs cognitive function. Furthermore, differences between the intrinsic circadian period and Earth's 24-h light-dark cycle underlie human circadian rhythm sleep disorders, such as advanced sleep phase disorder and non-24-hour sleep-wake disorders. Therefore, first, we tested whether exposure to a model-based lighting regimen would entrain the human circadian pacemaker at a normal phase angle to the 24.65-h Martian sol and to the 23.5-h day length often required of astronauts during short duration space exploration. Second, we tested here whether such prior entrainment to non-24-h light-dark cycles would lead to subsequent modification of the intrinsic period of the human circadian timing system. Here we show that exposure to moderately bright light ( approximately 450 lux; approximately 1.2 W/m(2)) for the second or first half of the scheduled wake episode is effective for entraining individuals to the 24.65-h Martian sol and a 23.5-h day length, respectively. Estimations of the circadian periods of plasma melatonin, plasma cortisol, and core body temperature rhythms collected under forced desynchrony protocols revealed that the intrinsic circadian period of the human circadian pacemaker was significantly longer following entrainment to the Martian sol as compared to following entrainment to the 23.5-h day. The latter finding of after-effects of entrainment reveals for the first time plasticity of the period of the human circadian timing system. Both findings have important implications for the treatment of circadian rhythm sleep disorders and human space exploration.

Mathematical models of neurobehavioral function are useful both for understanding the underlying physiology and for predicting the effects of rest-activity-work schedules and interventions on neurobehavioral function. In a symposium titled "Modeling Human Neurobehavioral Performance I: Uncovering Physiologic Mechanisms" at the 2006 Society for Industrial and Applied Mathematics/Society for Mathematical Biology (SIAM/SMB) Conference on the Life Sciences, different approaches to modeling the physiology of human circadian rhythms, sleep, and neurobehavioral performance and their usefulness in understanding the underlying physiology were examined. The topics included key elements of the physiology that should be included in mathematical models, a computational model developed within a cognitive architecture that has begun to include the effects of extended wake on information-processing mechanisms that influence neurobehavioral function, how to deal with interindividual differences in the prediction of neurobehavioral function, the applications of systems biology and control theory to the study of circadian rhythms, and comparisons of these methods in approaching the overarching questions of the underlying physiology and mathematical models of circadian rhythms and neurobehavioral function. A unifying theme was that it is important to have strong collaborative ties between experimental investigators and mathematical modelers, both for the design and conduct of experiments and for continued development of the models.

Entrainment of the circadian pacemaker to the light:dark cycle is necessary for rhythmic physiological functions to be appropriately timed over the 24-h day. Nonentrainment results in sleep, endocrine, and neurobehavioral impairments. Exposures to intermittent bright light pulses have been reported to phase shift the circadian pacemaker with great efficacy. Therefore, we tested the hypothesis that a modulated light exposure (MLE) with bright light pulses in the evening would entrain subjects to a light:dark cycle 1 h longer than their own circadian period (tau). Twelve subjects underwent a 65-day inpatient study. Individual subject's circadian period was determined in a forced desynchrony protocol. Subsequently, subjects were released into 30 longer-than-24-h days (daylength of tau + 1 h) in one of three light:dark conditions: (i) approximately 25 lux; (ii) approximately 100 lux; and (iii) MLE: approximately 25 lux followed by approximately 100 lux, plus two 45-min bright light pulses of approximately 9,500 lux near the end of scheduled wakefulness. We found that lighting levels of approximately 25 lux were insufficient to entrain all subjects tested. Exposure to approximately 100 lux was sufficient to entrain subjects, although at a significantly wider phase angle compared with baseline. Exposure to MLE was able to entrain the subjects to the imposed sleep-wake cycles but at a phase angle comparable to baseline. These results suggest that MLE can be used to entrain the circadian pacemaker to non-24-h days. The implications of these findings are important because they could be used to treat circadian misalignment associated with space flight and circadian rhythm sleep disorders such as shift-work disorder.

A new focus for mathematical models of the circadian pacemaker involves the encapsulation within the models of detailed biological processes responsible for generating those circadian rhythms. Representing greater biological detail requires more mathematical equations, which pose a greater challenge for the analysis of such systems. Development of a method that retains the predominant dynamics while still providing biologically detailed information is advantageous. Two high-dimension mathematical models of intracellular mammalian circadian pacemakers, Leloup-Goldbeter and Forger-Peskin, with 19 and 73 differential equations, respectively, have been published. The authors projected each of these high-dimension models onto their respective manifold using proper orthogonal functions (POFs) obtained from the empirical decomposition of the model's phase space to obtain a 2-dimension model. The resulting 2-dimension model, represented by 2 differential equations, predicts most of the salient characteristics of a biological clock including approximately 24-h oscillations, entrainment to an LD cycle, phase response curves, and the amplitude recovery dynamics that emerge following amplitude suppression. The manifold representation simplifies the mathematical analysis, since only 2 variables need to be observed and analyzed to understand the behavior of the biological clock. This reduced model derived from a model based on biological variables can be used for the development and analysis of mathematical models of the coupled mammalian oscillators to understand the dynamics of the integrated circadian pacemaker.

The light-dark cycle is the primary synchronizing factor that keeps the internal circadian pacemaker appropriately aligned with the environmental 24-h day. Although it is known that ocular light exposure can effectively shift the human circadian pacemaker and do so in an intensity-dependent manner, the curve that describes the relationship between light intensity and pacemaker response has not been fully characterized for light exposure in the late biological night. We exposed subjects to 3 consecutive days of 5 h of experimental light, centered 1.5 h after the timing of the fitted minimum of core body temperature, and show that such light can phase advance shift the human circadian pacemaker in an intensity-dependent manner, with a logistic model best describing the relationship between light intensity and phase shift. A similar sigmoidal relationship is also observed between light intensity and the suppression of plasma melatonin concentrations that occurs during the experimental light exposure. As with a simpler, 1-day light exposure during the early biological night, our data indicate that the human circadian pacemaker is highly sensitive even to typical room light intensities during the late biological night, with approximately 100 lux evoking half of the effects observed with light 10 times as bright.

At an organism level, the mammalian circadian pacemaker is a two-dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures--including plasma cortisol, plasma melatonin, and core body temperature (CBT)--all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A = 1), but are markedly different in the prediction of recovery rates when A < 0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.

It has been shown in animal studies that exposure to brief pulses of bright light can phase shift the circadian pacemaker and that the resetting action of light is most efficient during the first minutes of light exposure. In humans, multiple consecutive days of exposure to brief bright light pulses have been shown to phase shift the circadian pacemaker. The aim of the present study was to determine whether a single sequence of brief bright light pulses administered during the early biological night would phase delay the human circadian pacemaker. Twenty-one healthy young subjects underwent a 6.5-h light exposure session in one of three randomly assigned conditions: 1) continuous bright light of approximately 9,500 lux, 2) intermittent bright light (six 15-min bright light pulses of approximately 9,500 lux separated by 60 min of very dim light of <1 lux), and 3) continuous very dim light of <1 lux. Twenty subjects were included in the analysis. Core body temperature (CBT) and melatonin were used as phase markers of the circadian pacemaker. Phase delays of CBT and melatonin rhythms in response to intermittent bright light pulses were comparable to those measured after continuous bright light exposure, even though the total exposure to the intermittent bright light represented only 23% of the 6.5-h continuous exposure. These results demonstrate that a single sequence of intermittent bright light pulses can phase delay the human circadian pacemaker and show that intermittent pulses have a greater resetting efficacy on a per minute basis than does continuous exposure.

Circadian rhythms are endogenous rhythms with a cycle length of approximately 24 h. Rhythmic production of specific proteins within pacemaker structures is the basis for these physiological and behavioral rhythms. Prior work on mathematical modeling of molecular circadian oscillators has focused on the fruit fly, Drosophila melanogaster. Recently, great advances have been made in our understanding of the molecular basis of circadian rhythms in mammals. Mathematical models of the mammalian circadian oscillator are needed to piece together diverse data, predict experimental results, and help us understand the clock as a whole. Our objectives are to develop mathematical models of the mammalian circadian oscillator, generate and test predictions from these models, gather information on the parameters needed for model development, integrate the molecular model with an existing model of the influence of light and rhythmicity on human performance, and make models available in BioSpice so that they can be easily used by the general community. Two new mammalian models have been developed, and experimental data are summarized. These studies have the potential to lead to new strategies for resetting the circadian clock. Manipulations of the circadian clock can be used to optimize performance by promoting alertness and physiological synchronization.

A circadian pacemaker within the central nervous system regulates the approximately 24-h physiologic rhythms in sleep cycles, hormone secretion, and other physiologic functions. Because the pacemaker cannot be examined directly in humans, markers of pacemaker function must be used to study the pacemaker and its response to environmental stimuli. Core body temperature (CBT), plasma cortisol, and plasma melatonin are three marker variables frequently used to estimate the phase of the human pacemaker. Measurements of circadian phase using markers can contain variability due to the circadian pacemaker itself, the intrinsic variability of the marker relative to the pacemaker, the method of analysis of the marker, and the marker assay. For this report, we compared the mathematical variability of a number of methods of identifying circadian phase from CBT, plasma cortisol, and plasma melatonin data collected in a protocol in which pacemaker variability was minimized using low light levels and regular timing of both the light pattern and the rest/activity schedule. We hoped to assess the relative variabilities of the different physiological markers and the analysis methods. Methods were based on the crossing of an absolute threshold, on the crossing of a relative threshold, or on fitting a curve to all data points. All methods of calculating circadian phase from plasma melatonin data were less variable than those calculated using CBT or cortisol data. The standard deviation for the phase estimates using CBT data was 0.78 h, using cortisol data was 0.65 h, and for the eight analysis methods using melatonin data was 0.23 to 0.35 h. While the variability for these markers might be different for other subject populations and/or less stringent study conditions, assessment of the intrinsic variability of the different calculations of circadian phase can be applied to allow inference of the statistical significance of phase and phase shift calculations, as well as estimation of sample size or statistical power for the number of subjects within an experimental protocol.