Two methods for using period length to study rhythmic phenomena

Summary We have developed two distinct methods of biological rhythm analysis. The procedures are based on existing techniques for analysis of time series, Enright's periodogram and autocorrelation, and both of the new methods use the parameter, period length (), for defining oscillatory phenomena. We empirically evaluated the two types of analyses using real biological data from circadian rhythm studies in salamanders and sparrows.The first method permits us to make a statistical comparison of period lengths between groups of animals in given treatments. This method is useful for data where the signal-to-noise ratio of the suspected rhythm is very low; and the method is not adequate for making a definitive judgment from single animals. It can best be applied to the question of whether a signal is entraining a rhythm or not and to questions of group differences in period length.With the second method, we determined period length versus time. Using this procedure, we took into consideration the observation that the period length of many biological oscillations changes with time. The method is applicable to records from individual animals, and it can be used to compare treatment effects in individual animals. The technique can also be used to answer the common question of whether periodicityper se exists within a defined range in a time series.We thank Dr, T. J. Crovello, Mr. Kilian, Mr. B. Bailey, Mr. E. Kluth, Mr. G. Wyche, and the Notre Dame Computer Center. Support was provided by postdoctoral fellowship (l F02-HD-52858) from NIH to S. Binkley; grants to K. Adler (NSF GB-30547 and NIH FR-07 033-05); and NSF postdoctoral fellowship (GU-2058) and an Indiana Academy of Science grant to D. Taylor. Sparrow data used in this report were gathered while S. Binkley was a graduate student at the U. of Texas in Austin (NIH traineeship 5T01 GM-00836-08) and with funds from an NIH program project grant (HD-03803-02) to M. Menaker.     

Pineal N-acetyltransferase in chickens: Rhythm persists in constant darkness

Summary The daily rhythm in an enzyme, pineal serotonin N-acetyltransferase activity was studied in chickens kept in conditions of constant dark. The rhythm persisted and had a period length of approximately 24 hours which are characteristics of truly circadian rhythms. The detailed documentation of the rhythm (Fig. 1) shows the shape of the oscillation and clear anticipation of the time of lights on. Both the rise and fall of the rhythm occur without stimulation by light or dark.We thank Robert Weiner, William Finlay, Jay Freedman, Kathy Hall, Sylvia Goddes, Dr. S. K. Roberts, and the Temple University Computer Activity. Supported by NSF grant GB-43215, NSF Institutional Award, and Temple Grant-in-Aid to S. Binkley.     

Linear demasking techniques are unreliable for estimating the circadian phase of ambulatory temperature data.

Clinical investigators often use ambulatory temperature monitoring to assess the endogenous phase and amplitude of an individual's circadian pacemaker for diagnostic and research purposes. However, an individual's daily schedule includes changes in levels of activity, in posture, and in sleep-wake state, all of which are known to have masking or evoked effects on core body temperature (CBT) data. To compensate for or to correct these masking effects, many investigators have developed "demasking" techniques to extract the underlying circadian phase and amplitude data. However, the validity of these methods is uncertain. Therefore, the authors tested a variety of analytic methods on two different ambulatory data sets from two different studies in which the endogenous circadian pacemaker was not synchronized to the sleep-wake schedule. In both studies, circadian phase estimates calculated from CBT collected when each subject was ambulatory (i.e., free to perform usual daily activities) were compared to those calculated during the same study when the same subject's activities were controlled. In the first study, 24 sighted young and older subjects living on a 28-h scheduled "day" protocol were studied for approximately 21 to 25 cycles of 28-h each. In the second study, a blind man whose endogenous circadian rhythms were not synchronized to the 24-h day despite his maintenance of a regular 24-h sleep-wake schedule was studied for more than 80 consecutive 24-h days. During both studies, the relative phase of the endogenous (circadian) and evoked (scheduled activity-rest) components of the ambulatory temperature data changed progressively and relatively slowly, enabling analysis of the CBT rhythm at nearly all phase relationships between the two components. The analyses of the ambulatory temperature data demonstrate that the masking of the CBT rhythm evoked by changes in activity levels, posture, or sleep-wake state associated with the evoked schedule of activity and rest can significantly obscure the endogenous circadian component of the signal, the object of study. In addition, the masking effect of these evoked responses on temperature depends on the circadian phase at which they occur. These nonlinear interactions between circadian phase and sleep-wake schedule render ambulatory temperature data unreliable for the assessment of endogenous circadian phase. Even when proposed algebraic demasking techniques are used in an attempt to reveal the endogenous temperature rhythm, the phase estimates remain severely compromised.     

Retinal and extraretinal photoreceptors mediate entrainment of the circadian locomotor rhythm in lizards

Summary The circadian locomotor activity rhythms of 7 species of lizards can readily be entrained (synchronized) toLD12: 12 (30–50 lux: 0) fluorescent light cycles after complete surgical removal of both eyes. Removal of the parietal eye and pineal organ does not prevent entrainment of blinded lizards. Appropriate control experiments established that lightper se, and not low amplitude temperature cycles or other obvious environmental variables, was the entraining stimulus for blinded lizards. In some cases, blocking the penetration of light to the brains of blinded lizards caused them to free-run (express their endogenous circadian rhythm) in the presence of a dim green light cycle, to which they had previously entrained, suggesting that the brain is the site of the extraretinal photoreceptor(s) mediating entrainment. The extraretinal photoreceptor(s) is capable of intensity discrimination since changing the intensity of aLD 12: 12 fluorescent light cycle caused a change in the phase-relationship between the entrained activity rhythm and the light cycle in a blinded gekko. The lateral eyes are also involved in mediating entrainment since removal of the lateral eyes of thoseSceloporus olivaceus which previously entrained to a dim green light cycle [LD 12: 12 (0.05 lux: 0)] caused them to free-run. Also, blinding had noticeable effects on the entrained activity patterns of some species of lizards.I thank Michael Menaker, Jeffrey Elliott, Sue Binkley, Joseph Silver, Ed Kluth, George Wyche, Bruee Rouse, Nancy Leshikar, Lili Mostafavi, Janet Alvis, Celeste Cromack, A. L. Mackey and Jean Rogers for their suggestions and technical assistance. Support for this work was provided by NIH grant HD-03803-02 (to M. Menaker); NSP grant GB-8138 (to M. Menaker); NSF traineeship GZ-1336 (to H. Underwood); and MH traineeship 5T01GM00836-09 (to H. Underwood).     

Analysis method and experimental conditions affect computed circadian phase from melatonin data

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.     

AII amacrine neurons of the rat retina show diurnal and circadian rhythms of parvalbumin immunoreactivity

We investigated parvalbumin immunoreactivity (PA-IR) in the retinas of rats maintained on a 12:12 h light:dark cycle, or after being placed in constant darkness for 24–72 h. Retinas were harvested at zeitgeber and circadian times 02:00, 06:00, 10:00, 14:00, 18:00 and 22:00 h. PA-IR was found primarily in retinal amacrine cells of the AII subtype. In a light/dark cycle, PA-IR showed a clear rhythm, with a low near zeitgeber time (ZT) 10:00 h and a peak near ZT 18:00 h. The ratio of immunofluorescence intensities at these timepoints was >15-fold. When animals were kept in complete darkness for 1–3 days, the rhythm of PA-IR was still preserved, but was progressively reduced in amplitude. The rhythm of PA-IR inferred from immunohistochemical data was confirmed by Western blots. We conclude that PA-IR in the rat retina shows an underlying circadian rhythm that is enhanced by cyclic light. The regulation may involve translocation of the protein between cell compartments and/or new protein synthesis.This study was supported by an OTKA grant (T 34160), NIH grants NS 37919 (R.S.) and ET 03570, NSF grant IBN-96418886 (R.S.), and grants from the Helen Hoffritz Charitable Trust and Research to Prevent Blindness, Inc. R.G. was also in receipt of a János Bolyai fellowship     

pyActigraphy: Open-source python package for actigraphy data visualization and analysis

Over the past 40 years, actigraphy has been used to study rest-activity patterns in circadian rhythm and sleep research. Furthermore, considering its simplicity of use, there is a growing interest in the analysis of large population-based samples, using actigraphy. Here, we introduce pyActigraphy, a comprehensive toolbox for data visualization and analysis including multiple sleep detection algorithms and rest-activity rhythm variables. This open-source python package implements methods to read multiple data formats, quantify various properties of rest-activity rhythms, visualize sleep agendas, automatically detect rest periods and perform more advanced signal processing analyses. The development of this package aims to pave the way towards the establishment of a comprehensive open-source software suite, supported by a community of both developers and researchers, that would provide all the necessary tools for in-depth and large scale actigraphy data analyses.     

Non-stationary time series and the robustness of circadian rhythms

Circadian rhythms are regular oscillations in the value of behavioral and physiological variables of organisms that recur on a daily basis. The purpose of this study was to evaluate the extent of non-stationarity of circadian rhythms over several days, to determine how damaging is the violation of the assumption of stationarity in the analysis of circadian rhythms, and to formalize the concept of "rhythm robustness" as an index of oscillatory ("weak") stationarity. Simulated (computer-generated) and experimental data sets (rhythms of body temperature and running-wheel activity in several rodent species) were analysed. Tests of stationarity based on the variance of the daily means and the variance of the daily variances revealed that most experimental data sets are not stationary. Analysis of linear trends indicated that significant trends are rare in experimental data sets. Although the non-stationarity of the experimental data sets reduced the spectral energy of the Enright periodogram used to assess rhythmicity, detection of circadian rhythmicity was not prevented in any of the rhythmic data sets. The results of the various analyses allow the inference that, after high-frequency noise is filtered out, the value of the periodogram's Q(P) statistic reflects the extent of stationarity of the time series. Thus, the "robustness" of a circadian rhythm (i.e. the magnitude of the empirical Q(P) value as compared to the Q(P) value associated with a perfectly rhythmic time series) can serve as an index of the stationarity of the rhythm.     

The statistical analysis of circadian phase and amplitude in constant-routine core-temperature data.

Accurate estimation of the phases and amplitude of the endogenous circadian pacemaker from constant-routine core-temperature series is crucial for making inferences about the properties of the human biological clock from data collected under this protocol. This paper presents a set of statistical methods based on a harmonic-regression-plus-correlated-noise model for estimating the phases and the amplitude of the endogenous circadian pacemaker from constant-routine core-temperature data. The methods include a Bayesian Monte Carlo procedure for computing the uncertainty in these circadian functions. We illustrate the techniques with a detailed study of a single subject's core-temperature series and describe their relationship to other statistical methods for circadian data analysis. In our laboratory, these methods have been successfully used to analyze more than 300 constant routines and provide a highly reliable means of extracting phase and amplitude information from core-temperature data.     

The molecular mechanism regulating the autonomous circadian expression of Topoisomerase I in NIH3T3 cells

To identify whether Topoisomerase I (TopoI) has autonomous circadian rhythms regulated by clock genes, we tested mouse TopoI (mTopoI) promoter oscillation in NIH3T3 cells using a real-time monitoring assay and TopoI mRNA oscillations using real-time RT-PCR. Analysis of the mTopoI promoter region with Matlnspector software revealed two putative E-box (E1 and E2) and one DBP/E4BP4-binding element (D-box). Luciferase assays indicated that mTopoI gene expression was directly regulated by clock genes. The real-time monitoring assay showed that E-box and D-box response elements participate in the regulation of the circadian expression of mTopoI. Furthermore, a gel-shift assay showed that E2 is a direct target of the BMAL1/CLOCK heterodimer and DBP binds to the putative D-site. These results indicate that TopoI is expressed in an autonomous circadian rhythm in NIH3T3 cells.     

Circadian rhythms in cockroaches

Summary The driving oscillator, which mediates circadian locomotor rhythms in cockroaches, appears to reside in the protocerebrum of the brain. The evidence indicates that the optic lobes are crucial elements in this circadian system, and that control of rhythmicity is mediated through electrical, rather than hormonal, channels. Lesions were placed at various sites within the optic lobes in order to localize the areas controlling rhythmicity. It appears that the two innermost synaptic areas (the lobula and the medulla) constitute the crucial optic lobe elements. The outer synaptic area of the optic lobe (the lamina) is not necessary for the expression of rhythmicity, but does function as a coupling through which light cycles, transduced by the compound eyes, entrain the circadian clock.I would like to thank both Dr. Sue Binkley for her helpful comments in the preparation of this report, and Mr. Eli Levine for his assistance in photography. Support for this research was provided by a grant from the National Science Foundation (NS GB-30497).     

性信息素对斜纹夜蛾雄蛾嗅觉相关基因 abp,pbp 和 or 表达的影响

【目的】信息素是个体之间传递信息的重要分子,研究性信息素对斜纹夜蛾 Spodoptera litura 嗅觉相关基因表达的影响对于增加性信息素作用机理的认识及其应用有重要的意义。【方法】本研究通过实时定量PCR（qRT-PCR）技术探究在性信息素刺激处理条件下,斜纹夜蛾成虫嗅觉相关基因 abp, pbp 和 or 表达水平的变化;利用性信息素在田间诱捕斜纹夜蛾雄蛾,并通过自动计数器记录每小时诱虫量,从而间接显示其交配行为的节律性。【结果】斜纹夜蛾雄虫触角中嗅觉相关基因abp, pbp 和 or 的表达具有节律特性。经性信息素化合物(Z9, Z11-14:OAc+Z9, Z12-14:OAc)刺激处理后,abp, pbp 和 or 表达量也发生了显著的改变。通过记录田间性信息素诱捕器在一天中不同时间段内诱捕的雄蛾数量,发现诱捕到的斜纹夜蛾也具有节律特性。【结论】基因表达水平上的节律特性可能与雄虫交配活动的节律相关联,说明性信息素处理也在一定程度上改变了其节律及其对性信息素的神经反应。这一结果也首次从基因水平证明性信息素的刺激处理提高了周缘神经系统对性信息素反应的敏感性,有助于我们理解性信息素作用的分子机理,对迷向及性诱和测报应用具有指导意义。     

Simulated microgravity influences circadian rhythm of NIH3T3 cells

Gravity heavily influences living organisms on earth including their circadian rhythm, which is fundamentally important for coordinately physiology in organisms as diverse as cyanobacteria, fungus and humans. Numerous researches have revealed that microgravity in outer space can affect circadian rhythm of astronauts and rodent animals, but the mechanism remains unknown. Using rotary cell culture system to simulate microgravity environment, we investigated the role of simulated microgravity in regulating the circadian rhythm of NIH3T3 cells. Our experiments found that simulated microgravity can not only influence the mRNA level of some core circadian genes, but also modify the circadian rhythm of Per1 and Per2 synchronized after phorbol myristate acetate treatment. Remarkably, MEK/ERK pathway was transiently activated after a 2-h simulated microgravity treatment, with a significant upregulation of Kras, Raf1 and p-ERK1/ERK2. Moreover, U0126, a selective inhibitor of MEK/ERK pathway, could disrupt the circadian rhythm of Per1 and Per2 synchronized after simulated microgravity treatment. Together, our results unveil that simulated microgravity could act like a zeitgeber to influence the circadian rhythm of NIH3T3 by acting on MEK/ERK pathway, indicating that MEK/ERK pathway may act as a bridge which connects cells mechanotransduction pathway and circadian rhythm regulation.     

Thyroid hormone and circadian regulation of the binding activity of a liver-specific protein associated with the 5'-flanking region of the S14 gene

Recent studies have described a DNase I hypersensitive site in the 5'-flanking region of the rat hepatic S14 gene that is closely associated with its expression. A 111-base pair subfragment (-389 to -279) of this region interacts specifically in a gel shift assay with a protein present in hepatic nuclear protein extracts. This protein, designated P1, was not present in extracts of other tissues, even those in which the gene is expressed and hormonally regulated. The binding activity of P1 is exceedingly low in extracts from hypothyroid rats and is markedly increased by administration of thyroid hormone. However, the slow accumulation of P1 after thyroid hormone administration indicates that increased levels of P1 are not necessary for the acute hormonal induction of S14 gene expression. The level of P1 binding activity increases in the evening, synchronous with circadian variation of hepatic mRNA S14. Since neither P1 binding activity nor circadian variation in mRNA-S14 levels are observed in the other tissues expressing the S14 gene, P1 may function to modulate the circadian rhythm observed in hepatic S14 gene expression. DNase I footprinting analysis revealed that P1 binds to a defined nucleotide sequence, 5'-AAAAGAGCTATTGATTGCCTGCA-3', located between -310 and -288 in the S14 gene.     

Circadian features of carbohydrate metabolism in domestic fowls exposed to weekly 120 degree-shifts of synchronizer schedule.

Effects of weekly 8 hr advance- or delay-shifts on the circadian rhythm of plasma glucose, liver glycogen and muscle glycogen in male domestic fowls, beginning at about 3 days of age, were examined. Circadian rhythm in the aforesaid indices of carbohydrate metabolism in control birds was also studied. Blood and tissue samples were collected from birds in all the three groups at 4 hr intervals over a single 24 hr time scale both at 6th and 12th week of age. Plasma glucose and glycogen content in the tissues were determined by employing standard techniques. Cosinor rhythmometry was used for analyzing time series data. In general, a statistically significant circadian rhythm was documented for all the three indices in control and advance-schedule birds, irrespective of age. In contrast, in delay-schedule birds, statistically significant circadian rhythm could not be detected, excluding in muscle glycogen at 12th week of age. The poor growth rate in the delay-schedule birds could be imputed to the disappearance of circadian rhythm in the indices of carbohydrate metabolism.     

Dysregulation of circadian rhythms following prolactin-secreting pituitary microadenoma

A patient who developed an irregular sleep-wake pattern following prolactin-secreting pituitary microadenoma is described. The patient reported difficulties in sleep onset and awakening at the desired time, which caused major dysfunction in his daily life activities. Despite these difficulties, the sleep-related complaints of the patient remained unrecognized for as long as three yrs. Statistical analyses of the patient's rest-activity patterns revealed that the disruption of the sleep-wake circadian rhythm originated from a disharmony between ultradian (semicircadian) and circadian components. The circadian component displayed shorter than 24 h periodicity most of the time, but the semicircadian component fluctuated between longer and shorter than 12 h periods. Additionally, desynchrony in terms of period length was found in the tentative analyses of the rest-activity pattern, salivary melatonin, and oral temperature. While the salivary melatonin time series data could be characterized by a best-fit cosine curve of 24 h, the time series data of oral temperature was more compatible with 28 h best-fit curve. The rest-activity cycle during the simultaneous measurements, however, was best approximated by a best-fit curve of 21 h. The dysregulation of circadian rhythms occurred concomitantly, but not beforehand, with the onset of pituitary disease, thus suggesting an association between the two phenomena. This association may have interesting implications to the modeling of the circadian time-keeping system. This case also highlights the need to raise the awareness to circadian rhythm sleep disorders and to consider disruptions of sleep-wake cycle in patients with pituitary adenoma.     

Statistical model building and model criticism for human circadian data

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.