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Memory consolidation refers to the stabilization of labile memory traces, possibly including intrahippocampal synaptic reinforcement

and the transfer of information initially encoded in the hippocampal system to the neocortex for long-term storage1–3. The consolidation process has been proposed to occur during post-learning rest or sleep3,4 by reactivation of memory traces in short bouts of neuronal activity associated with SPW-R events3,5–7, which can be temporally biased by neocortical slow oscillations8–10. Although numerous studies provide compelling correlative links between hippocampal SPW-Rs and memory consolidation3,5–7, a causal relationship has not yet been demonstrated. To examine the consequences of SPW-R elimi-nation on performance in a hippocampus-dependent, spatial-refer-ence memory task11 (Supplementary Methods and Supplementary Fig. 1), we selectively suppressed SPW-Rs during post-learning sleep. All of our experiments were conducted in accordance with institu-tional (CNRS Comité Opérationnel pour l’Ethique dans les Sciences de la Vie) and international (US National Institutes of Health guide-lines) standards and legal regulations (certificat no. 7186, Ministère de l’Agriculture et de la Pêche).

The onset of SPW-Rs was detected online by filtering the signal in the ripple-band and thresholding it. Threshold crossing triggered single-pulse stimulation of the ventral hippocampal commissure12 (n = 17 rats). This

Selective suppression of hippocampal ripples impairs spatial memoryGabrielle Girardeau1,3, Karim Benchenane1,3, Sidney I Wiener1, György Buzsáki2 & Michaël B Zugaro1

Sharp wave–ripple (SPW-R) complexes in the hippocampus-entorhinal cortex are believed to be important for transferring labile memories from the hippocampus to the neocortex for long-term storage. We found that selective elimination of SPW-Rs during post-training consolidation periods resulted in performance impairment in rats trained on a hippocampus-dependent spatial memory task. Our results provide evidence for a prominent role of hippocampal SPW-Rs in memory consolidation.

1Laboratoire de Physiologie de la Perception et de l’Action, Collège de France, CNRS, Paris, France. 2Center for Molecular and Behavioral Neuroscience, Rutgers University, Newark, New Jersey, USA. 3These authors contributed equally to this work. Correspondence should be addressed to M.B.Z. (michael.zugaro@college-de-france.fr) or G.B. (buzsaki@axon.rutgers.edu).

Received 20 May; accepted 9 July; published online 13 September 2009; doi:10.1038/nn.2384

Figure 1 Ventral hippocampal commissural stimulation interrupts SPW-Rs and hippocampal cell discharges without changing global sleep architecture. (a) Interruption of SPW-R and spiking activity in the hippocampus. Local field potential (LFP, black) in the hippocampus and spiking activity (vertical ticks) of pyramidal cells (pyr; hippocampus, dark blue; sensorimotor cortex, red) and interneurons (int; hippocampus, light blue; sensorimotor cortex, orange). Left, an intact ripple and the associated spiking activity. Vertical dashed lines and arrowheads represent stimulation times. (b) Duration of unit activity suppression as a function of the magnitude of the evoked field response. Pseudo-color plots show the z scores of multiple unit activity with increasing levels of stimulation (ordinate). Note the transient, evoked response magnitude–dependent suppression of spiking activity in the hippocampus with no observable effect on global neocortical activity. The increased activity before the stimulus is a result of the buildup of ripple-associated discharge. (c) SPW-R blocking by ventral hippocampal commissural stimulation (arrowheads). Example SPW-R in a test rat and a control rat (left). SPW-R was blocked after a few cycles in the test rat (upper right). For illustration purposes, the SPW-R–detection threshold was set higher for this example than in sleep sessions (inset). In the control rat (lower right), stimulation was triggered after a delay. Scale bars represent 20 ms and 0.2 mV. (d) Cross-correlograms of stimulations and offline-detected SPW-Rs in test and control rats. Virtually all SPW-Rs were suppressed in test rats, but were preserved in control rats, as a result of the 80–120-ms delay introduced between the ripples (blue peak) and the stimulations (time zero). (e) Average random eye movement (REM) sleep/slow-wave sleep (SWS) ratios in a random subset of test and control sessions (n = 24 and n = 27, respectively; t test, not significant (P > 0.05), error bars represent s.e.m.).

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blocked further development of the oscillation and transiently silenced hippocampal spiking activity12 (Fig. 1a,b and Supplementary Fig. 2), thus preventing potential replay of place-cell13 sequences5,6 previously activated during waking. In contrast with hippocampal cells, firing of neocortical neurons was not interrupted at the stimulus intensities that we used for abolishing ripples (Fig. 1a,b and Supplementary Fig. 3 shows data from anterior cingulated and prelimbic/infralimbic prefrontal cor-tices, two major candidates of hippocampal-neocortical information transfer during spatial memory consolidation2).

Next, we tested the role of SPW-Rs on memory consolidation. Three groups of rats (test group, n = 7; stimulated controls, n = 7; unimplanted controls, n = 12) were trained to find food rewards on an eight-arm radial maze in which the same three arms were baited every day (Supplementary Fig. 1). The rats performed three trials per day, after which they were allowed to sleep for 1 h.

During post-training rest and sleep, all of the online-detected ripples were suppressed by commissural stimulations in test rats (average online detection rate was 86.0 ± 1.3% (s.e.m.) of post hoc detected SPW-Rs; Fig. 1c,d and Supplementary Methods). Stimulated control rats underwent the same protocol, except that a random delay (80–120 ms) was introduced between SPW-R detection and stimulation, ensuring that the stimulations occurred mainly outside of the ripple episodes (Fig. 1c,d). Thus, these control rats received the same number of stimu-lations as test rats (t test, not significant, P > 0.05), but their hippocampal ripples were left largely intact. The global architecture of sleep and the local field potential power in distinct sleep stages were not modified by the suppression of SPW-Rs (Fig. 1e and Supplementary Fig. 4). Because reactivations of previously active cell assemblies occur preferentially during the first half-hour of sleep after exploration5, we blocked SPW-Rs for 1 h following training sessions. As stimulation outside SPW-Rs had no detectable effect on task performance (no significant difference between stimulated control and unimplanted rats, two-factor ANOVA, day × group, P > 0.05; Fig. 2), the two control groups were pooled and compared with test rats. Performance of the test rats was significantly impaired compared with control rats (two-factor ANOVA day × group, P < 0.001 for main factors, P < 0.01 for interaction; Fig. 2). In control rats (stimulated and unimplanted groups combined), performance exceeded the upper chance level after 5 d of training, whereas test rats

continued to perform at chance level until the eighth day of training (t tests, P < 0.05). Test rats did not develop stereotyped turning strate-gies (Supplementary Fig. 5) and working memory errors remained very low (less than one error per trial on average) in the three groups (Supplementary Fig. 6).

Suppression of SPW-Rs and associated neuronal discharges resulted in deterioration of memory consolidation. The behavioral effect was specifically related to suppression of SPW-Rs, rather than to non-specific consequences of the stimulation, as SPW-R–yoked control stimulation had no detectable effect on behavior. The observed defi-cit is all the more notable, as we suppressed the SPW-Rs for only 1 h and ripple incidence returned to normal levels after the stimula-tion period (Supplementary Fig. 4). The magnitude of impairment in the ripple-suppressed rats was comparable to that reported in a previous study on hippocampus-lesioned rats11. The slight perform-ance improvement in the test group could be the result of the spared small-amplitude SPW-Rs, of the SPW-Rs occurring after the stimu-lation period or of other, nonhippocampal learning mechanisms, as has been reported previously11. Our findings therefore indicate that SPW-Rs are critical for memory consolidation, possibly because, by temporally compressing reactivations of waking firing sequences3,5,6 in the hippocampus, they allow spikes to occur in a time window that is compatible with activation of the NMDA receptors and spike timing–dependent plasticity. In addition or alternatively, they would enable the reactivated ensembles to exert a strong effect on downstream target neurons7. Moreover, hippocampal SPW-Rs are coordinated in time with neocortical unit firing, slow oscillations and sleep spindles8–10,14,15, suggesting that they have a widespread effect on cortical function underlying long-term memory consolidation.

Note: Supplementary information is available on the Nature Neuroscience website.

AcKnoWledGMentSWe thank S. Sara, A. Larrieu, L. Hazan, A. Fruchart, P. Ruther, S. Kisban, S. Herwik, S. Doutremer, M.-A. Thomas, Y. Dupraz, M. Ehrette and S. Rateau for advice and technical support. This work was supported by the International Human Frontiers Science Program Organization (CDA0061/2007-C), the US National Institutes of Health (NS34994), European Projects NeuroProbes (IST-027017) and Integrating Cognition, Emotion and Autonomy (FP6-IST 027819), and a Collège de France Visiting Professor Fellowship.

AUtHoR contRIBUtIonSG.B. and M.B.Z. designed the study. G.G. carried out the majority of the experiments, K.B. and M.B.Z. carried out the remaining experiments. M.B.Z., G.G. and K.B. analyzed the data. All of the authors contributed to writing the manuscript.

Published online at http://www.nature.com/natureneuroscience/. Reprints and permissions information is available online at http://www.nature.com/reprintsandpermissions/.

1. Squire, L.R. & Bayley, P.J. Curr. Opin. Neurobiol. 17, 185–196 (2007).2. Maviel, T., Durkin, T.P., Menzaghi, F. & Bontempi, B. Science 305, 96–99

(2004).3. Buzsáki, G. Neuroscience 31, 551–570 (1989).4. Marshall, L., Helgadóttir, H., Mölle, M. & Born, J. Nature 444, 610–613 (2006).5. Kudrimoti, H.S., Barnes, C.A. & McNaughton, B.L. J. Neurosci. 19, 4090–4101

(1999).6. Wilson, M.A. & McNaughton, B.L. Science 265, 676–679 (1994).7. Chrobak, J.J. & Buzsáki, G. J. Neurosci. 16, 3056–3066 (1996).8. Battaglia, F.P., Sutherland, G.R. & McNaughton, B.L. Learn. Mem. 11, 697–704

(2004).9. Siapas, A.G. & Wilson, M.A. Neuron 21, 1123–1128 (1998).10. Sirota, A., Csicsvari, J., Buhl, D. & Buzsáki, G. Proc. Natl. Acad. Sci. USA 100,

2065–2069 (2003).11. Jarrard, L.E. Behav. Brain Res. 71, 1–10 (1995).12. Zugaro, M.B., Monconduit, L. & Buzsáki, G. Nat. Neurosci. 8, 67–71 (2005).13. O’Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Oxford University

Press, Oxford, 1978).14. Eschenko, O., Ramadan, W., Mölle, M., Born, J. & Sara, S.J. Learn. Mem. 15,

222–228 (2008).15. Peyrache, A., Khamassi, M., Benchenane, K., Wiener, S.I. & Battaglia, F. Nat.

Neurosci. 12, 919–926 (2009).

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Selective suppression of hippocampal ripples impairs spatial memory

Gabrielle Girardeau, Karim Benchenane, Sidney I. Wiener, György Buzsáki, Michaël B. Zugaro

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Nature Neuroscience: doi:10.1038/nn.2384

Supplementary Methods

Surgery. Fourteen male Long Evans rats (René Janvier, Le Genest, St Isle, France) were bilaterally implanted with four independently movable single-wire electrodes (70 µm stainless steel, n=11) or two 9-site silicon probes (NeuroProbes1-3, 200 µm spacing, n=3) in the dorsal hippocampus (ML ±2.5, AP -3.5 relative to bregma). Three additional rats were implanted, two with tetrodes (groups of four twisted 12 µm nichrome wires) in the hippocampus and overlying neocortex, and one with electrodes in hippocampus and anterior cingulate and prefrontal cortices (AP +2.7, ML +0.5), for preliminary experiments (shown in Fig. 2 and Supplementary Fig. 3). Bipolar stimulation electrodes (60 µm stainless steel) were implanted in the ventral hippocampal commissural pathway (ML ±1.1, AP -1.3, DV -3.8 relative to bregma). During recovery from surgery (minimum 3 days), the rats received food and water ad libitum. The recording electrodes were then progressively lowered until they reached the CA1 pyramidal layer, where ripples were recorded. Meanwhile, rats were habituated to the 8-arm radial maze, and maintained on food restriction at 85% of their normal weight. All experiments were in accord with institutional (CNRS Comité Opérationnel pour l'Ethique dans les Sciences de la Vie), international (NIH guidelines) standards and legal regulations (Certificat no. 7186, Ministère de l'Agriculture et de la Pêche) regarding the use and care of animals.

Training sessions. The rats were trained to find food rewards on an 8-arm radial maze where three of the arms were baited. Training occurred during the light cycle, either in the morning (9:00) or in the afternoon (14:30) with equal distribution in all groups. The same spatial configuration of rewards was used for all rats in all training sessions (Supplementary Fig. 1). Salient visual cues suspended on the walls of the room served as spatial reference cues. Each session consisted of three trials on the maze, separated by 3 min rest periods when the rat was secluded in a flowerpot in the center of the maze. On each trial, the rat was removed from the maze as soon as it had found the three rewarded arms, or after a maximum of three minutes of exploration. After completion of the three trials, the animals were placed in the flowerpot in the center of the maze for the immobility/sleep stimulation session (1 hour). During training and post-training recording sessions, the experimenter remained outside the maze area enclosed by black curtains, and behavior was monitored using an overhead video camera.

Recording and stimulation. Brain signals were preamplified (unity-gain, Noted Bt, Pécs, Hungary), amplified 1000x (Neuralynx L8, Bozeman, MT, USA), acquired and digitized using two synchronized Power1401 systems (CED, Cambridge, UK). Online detection of the ripples (threshold crossing on the bandpass-filtered signal) automatically triggered a single-pulse (0.5 ms) commissural stimulation. This recruited principal cells and interneurons throughout both hippocampi and dentate gyri (via commissural fibers bilaterally connecting CA3-CA3, CA3-DG and DG-DG, and Schaffer collaterals connecting CA3-CA1), inducing transient silencing of the hippocampal network due to a combination of GABA receptor-mediated inhibition, Ca2+-dependent K+ conductance increase and disfacilitation. In test rats the stimulation was triggered by the onset of the ripples (detection-stimulation) whereas in control rats stimulation was delayed by a random interval of 80 to 120 ms (detection-delay-stimulation, Fig. 1), so that the stimulation occurred outside the detected ripple. Hence, our stimulation protocol ensured that any potential performance deficit of the test rats could be specifically attributed to the selective suppression of ripples rather than to other non-specific effects of hippocampal stimulation. Online detection rate for test rats was calculated as N/(n+N) where N is the number of on-line ripple-triggered stimulations, and n is the number of remaining ripples detected offline using the same LFP (see below). In both cases (test and control) the number of stimulations was limited to 5 per second. Because at lower stimulus intensities, silencing of hippocampal activity lasted for less than ~100 ms (Fig. 1), in the behavioral

Nature Neuroscience: doi:10.1038/nn.2384

experiments we used low intensities for selective and transient perturbation of the hippocampal network activity. The stimulation voltage was thus adjusted for each animal to the minimum value necessary to interrupt the ripples (5~30 V). Recordings were visualized and processed using NeuroScope and NDManager4

(http://neuroscope.sourceforge.net, http://ndmanager.sourceforge.net). Spike sorting was done using the semi-automatic spike classifier KlustaKwik (http://klustakwik.sourceforge.net) and the graphical spike sorting application Klusters4 (http://klusters.sourceforge.net).

Data analysis. In accordance with standard procedures to perform ANOVAs on proportion data, behavioral performance was computed as p=2/π.arcsin(√(n/N)), where n is the number of baited arms visited by the rat, and N is the total number of visits. Data were analyzed using custom software developed in Matlab (The Mathworks, Inc., Natick, MA, USA). Spectrograms were constructed using chronux (http://www.chronux.org). Chance performance was computed using a bootstrap procedure. Because chance performance depends on the number of working memory (WM) errors, which is a priori unknown, we estimated its lower and upper bounds. These correpond to the following two scenarios. In the first scenario (lower chance level), the rat randomly chooses any one arm on each sequential visit (indefinite number of WM errors). In the second scenario (upper chance level), the rat chooses each sequential arm randomly but never visits the same arm twice (no WM errors). The actual chance performance lays between these two bounds. Analyses used the more conservative upper chance level.Offline ripple detection was performed by band-pass filtering (100~200 Hz), squaring and normalizing, then thresholding the field potential recorded in CA1 pyramidal layer. Ripples were defined as events peaking at >5 standard deviations and lasting <100 ms. Sleep stages (SWS/REM) were determined by automatic K-means clustering of the theta/delta ratio extracted from the power spectrograms during the episodes where the animal was immobile (linear velocity < 3 cm/s for at least 30 s, with brief movements < 0.5 s).

Supplementary References

1. Herwik, S., Kisban, S., Aarts, A. A. A., Seidl, K., Girardeau, G., Benchenane, K., Zugaro M. B.,Wiener, S. I., Paul, O., Neves, H. P. & Ruther, P. Fabrication technology for silicon-based microprobe arrays used in acute and sub-chronic neural recording. J. Micromech. Microeng. 19, (2009)2. Neves, H.P., Orban, G.A., Koudelka-Hep, M., Stieglitz, T. & Ruther, P. Development of modular multifunctional probe arrays for cerebral applications. Neural Engineering, CNE '07. 3rd International IEEE/EMBS Conference, 104-9 (2007).3. Ruther, P., Aarts, A.A., Frey, O., Herwik, S., Kisban, S., Seidl, K., Spieth, S., Schumacher, A., Koudelka-Hep, M., Paul, O., Stieglitz, T., Zengerle, R., & Neves, H. The NeuroProbes project - multifunctional probe arrays for neural recording and stimulation. Biomed. Tech., 53 (suppl.1), 238-240 (2008).4. Hazan, L., Zugaro, M. & Buzsáki, G. Klusters, Neuroscope, NDManager: a free software suite for neurophysiological data processing and visualization. J. Neurosci. Methods 155, 207-216 (2006).

Nature Neuroscience: doi:10.1038/nn.2384

777CELEC Biol Res (2004) 37 S: 777-782Biol Res 37: 777-782, 2004 BRAnalysis of rhythmic variance – ANORVA. A new simplemethod for detecting rhythms in biological time series

PETER CELEC (1, 2, 3, 4)

1 Institute of Pathophysiology, Faculty of Medicine, Comenius University, Bratislava, Slovakia2 Department of Molecular Biology, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia3 Department of Banking and International Finance, Faculty of National Economy, Economic University,Bratislava, Slovakia4 BiomeD research & publishing group

ABSTRACT

Cyclic variations of variables are ubiquitous in biomedical science. A number of methods for detectingrhythms have been developed, but they are often difficult to interpret. A simple procedure for detecting cyclicvariations in biological time series and quantification of their probability is presented here. Analysis ofrhythmic variance (ANORVA) is based on the premise that the variance in groups of data from rhythmicvariables is low when a time distance of one period exists between the data entries. A detailed stepwisecalculation is presented including data entry and preparation, variance calculating, and difference testing. Anexample for the application of the procedure is provided, and a real dataset of the number of papers publishedper day in January 2003 using selected keywords is compared to randomized datasets. Randomized datasetsshow no cyclic variations. The number of papers published daily, however, shows a clear and significant(p<0.03) circaseptan (period of 7 days) rhythm, probably of social origin.

Key terms: chronobiology, time series, method, ANORVA, analysis of rhythmic variance, circaseptan, cycle,rhythm.

Corresponding Author: Peter Celec, MD, Ing., B.Sc., Galbavého 3, 841 01 Bratislava, Slovakia, Telephone: (421) 903-507822, E-mail: petercelec@hotmail.com

Received: June 16, 2004. In revised form: July 12, 2004. Acepted: August 18, 2004.

INTRODUCTION

Cycles and periodicities can be foundnearly everywhere in nature. Nevertheless,chronobiology still has the reputation ofsomething strange and curious. Mostrhythms in biomedicine can be classifiedaccording to their period lengths intocircadian (period ~ 24 h), ultradian (period< 24 h), and infradian (period > 24 h). Thebest known is the circadian rhythm, e.g. thesleep-wake cycle. Its genetic basis and theinteractions between the internal Zeitgeber(pacemaker) and external influences arewell understood. Interested readers can findcomprehensive information in a number ofrecent reviews (2; 4; 9; 10; 15; 21). Anexample for ultradian cycles is the variationof gonadotropin releasing hormone levels(8). Infradian rhythms include circannualvariations and the circalunar menstrualcycle in women (13; 16). In a narrow

interpretation, infradian characterizes thecycles with shorter periods than thecircalunar cycle. These infradian rhythmsare rarely described. One possible reasonfor this is the number of methodologicalproblems regarding cycle detection (7; 17).A growing number of statistical methodsexist that should make the search for cyclesin datasets easier (9; 11; 17; 18; 20). On theother hand, the variety of statisticalprocedures used indicates that there is noclear answer regarding which method iscorrect. I would like to add some entropy tothis chaos and present a new method that iseasy to use and understand for detectingperiodicities in biological time series.

METHODS

Most methods are very difficult tounderstand and use without specific

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commercial software. Moreover, thecomplexity of the procedures makes itdifficult to accurately interpret the results,particularly when considering that everymethod has its own characteristics andrequires specific data conditions. Mymethod is based on the premise that groupsof values from cycling time series have alow variance (theoretically zero) if the timedistance between the data entries is oneperiod of the cycle. That is why I call themethod Analysis of Rhythmic Variance(ANORVA). The detailed step-by-stepprocedure is presented here so it can bereproduced and used by other scientists.

Step 1 – Data entry and preparation

The minimum number of subjects/objectsor datasets is 5. The quantity of observeddata in every dataset determines theprovable period lengths. Minimumprovable period length (Min PPL) is triplethe time distance between the two closestdata entries in one subject/object, and themaximum provable period length (MaxPPL) is half of the whole minimum

observation period. Therefore, when adataset consisting of daily measurementsfor 30 days, possible period lengthsbetween 3 (3x1) and 15 (30/2) days can beproven. Randomized number sets representthe negative control used for thecomparison with the real data. To showhow this method works, two negativecontrols are used here and compared toeach other. The randomized datasetsshould have the same dimensions as theproven variable. The positive control usedwas the number of papers published dailyin January 2003 using selected keywordsaccording to the PubMed Medlinedatabase. See Figure 1 for details.

Datasets must be full; no blank dataentries are feasible. If no other possibilityexists, entries should be filled usinginterpolation and averages of the datasurrounding the blank entry. Datasets arenot required to be of the same extent inevery subject, although similar extents aredesirable. Values that are clearly differentfrom the rest should be excluded if they areaffected by external influence of a knownnon-cyclic factor.

Figure 1. The keywords ‘DNA,’ ‘Heart,’ ‘PCR,’ ‘Brain,’ ‘RNA,’ and ‘Kidney’ were chosen foranalysis. The number of papers published on these topics each day in January 2003 were estimatedusing the PubMed Medline database search. Data from January 1-2, 2003 were excluded due to theextremely high values probably influenced due to the retention of the papers during Christmasholidays. Following data show a 7-day cyclic variation with clear nadirs on weekends, particularlyon Sundays as indicated by arrows.

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The values of January 1-2, 2003 wereexcluded as they were higher by order ofmagnitude in comparison with other dataentries, probably due to the accumulation ofthe papers over the Christmas holidays. Asthis exclusion affects the size of the testednegative control dataset, the randomizeddatasets must be cut off in the same way.

If needed, the original data must betransformed to achieve normal distribution inbiological data, often by the log-normaltransformation. Data must be transformed intoa non-dimensional variable by dividing thedata entries through their average value. Thus,the average value of the new dataset must be 1.Moreover, if a significant trend is present, thetime series must be detrended using the resultsof the relevant regression analysis.

Step 2 – Variance calculating

The process begins with the Min PPL,calculating the variance of a groupconsisting of data entries with the Min PPLtime distance between them. The same isrepeated for the remaining phase shifts untilthe first phase shift is reached.

The first group of data will consist ofour example of the 1, 4, 7, 10, …, 3n+1data entry. The second group (next phaseshift) will consist of the 2, 5, 8, 11, …,3n+2. With 3 as the Min PPL, the thirdgroup (3, 6, 9, 12, … , 3n) is the last group.

The average variance is calculated fromthe results of all phase shiftsand is repeatedwith every subject/object. The entireprocedure is repeated for every periodlength between Min PPL and Max PPL.

Subjects/objects are represented in ourexample by the keywords. With MinPPL=3, the average variance can becalculated from 3 variances that respond to3 possible phase shifts. This must berepeated with every keyword. Testing forthe 4-day period is the same except thatthere are 4 possible phase shifts (4n+1,4n+2, 4n+3 and 4n). Other periods aretreated in the same way with an increasingnumber of possible phase shifts up to theMax PPL=15.

To obtain a similar dispersion of theresults in randomized and real datasets, theresulting mean variances must be divided by

the average variance and the dynamic weightof the results increased. A similar calculationwas done in Step 1. Repeat the entireprocedure with the randomized dataset. Theresults are the dynamic weighted averagevariances for phase shifts of every provableperiod for every subjects/object.

Step 3 – Testing the difference

If n is the number of subjects/objects in thedataset, then for every tested period p there isa set of n dynamic weighted averagevariances for real data and n dynamicweighted average variances for randomizeddata. These two new groups of values must becompared using a simple Student t-test or anon-parametric test such as the Mann-Whitney U test. The t-test is preferred due toits statistical power and robustness; the one-tailed t-test is used here, although the choiceof test type used in this step is not crucial forANORVA. The resulting p-value is aquantification of the probability that apossible observed cycle is based only oncoincidence. Thus, a low p-value, particularlyone lower than 0.05, indicates a low periodicvariance and a high probability for theexistence of a cycle with the given periodlength in the proved dataset. Calculating p-values for every period makes it possible tocompare the probabilities of the potentialcycles and to find a cycle with a period lengthbetween Min PPL and Max PPL.

The process of calculating the p-valuesis simplified by using the built-in functionsof office software packages; sophisticatedstatistical software is not necessary forthese simple calculations, but an adjustmentfor multiplicity in testing, such as theBonferroni correction, is needed to controlthe type I error rate. The resulting p-valuesare shown in graphs (Fig. 2). Therandomized dataset is clearly free of cyclicvariations, data on the papers publisheddaily show an apparent and statisticallysignificant rhythm of 7 days. Thiscircaseptan cycle is the best-known rhythmof social origin (1, 6, 15). I believe that thiscycle can be explained by the variations ofpublications due to the work-free weekenddays, and indeed, the lowest number ofpublications coincides with Sundays.

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Figure 2a. Periodicities in random data. The P-values in this graph are the result of the Student t-test that compared average variances in period lengths between 2 sets of randomized data, eachrepresenting a negative control. Although the p-values express great variability (explained by thesmall amount of data), they do not reach the alpha level of 0.05.

Figure 2b. Periodicities in real data. The P-values in this graph are the result of the Student t-testthat compared average variances in period lengths between the dataset of daily published papersand of randomized data that represent a negative control. P-value for the 7-day period reaches thelevel of 0.0278. This means that the 7-day cycle variation is low enough to be presented assignificant. Low p-value for a 14-day period can easily be explained, as it is twice the significant 7-day period length. Larger datasets might prove its existence.

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It should be noted that further extensionsof the method can be also used forsynchronization of data and thus forpreparing periodograms with an averagecycle curve. The procedure is far morecomplicated, however, and beyond thescope of this article. The example containssynchronized data. The sole quantitativedetection of rhythmic variations usingANORVA is independent from the de-synchronization of the subjects/objects asall possible phase shifts are analyzed.

CONCLUSION

The aim of this article was to offer a simplepresentation of the basic principles and useof a new method for detecting cyclicvariations in biological t ime series.Although other methods do exist, such asthe widely-used Cosinor method andspecific procedures based on Fast Fouriertransformations (9; 11; 14;), they aredifficult to interpret because they aredependent upon the morphology of thecycle (comparison to sinus wave) or haveparticular problems with noisy data.ANORVA is straightforward and easy touse and is independent of the morphologyof the cycle curve. Its low specificityimproves with the higher dataset sizes, butit can also handle small datasets.

An earlier study indicating thepossibilities of the basic principle ofANORVA was the first to describe thecircavigintan (period of 20 days) andcircatrigintan (period of 30 days) cycles ofsalivary testosterone levels in men (5).Other studies on hormonal variations foundin our lab using ANORVA have beensubmitted and are currently underconsideration. Hopefully, the currentlycomplicated chronobiological analysis willsoon be easily understood and reproducedby interested scientists. Chronobiologicalresearch is a growing area of researchthroughout the world (19), and a simplemethod for the detection of periodicalcomponents of biological datasets is nowmore necessary than ever before.

Of course the ANORVA method muststill be subjected to an objective evaluation,

a detailed comparison with other methods,and have its weaknesses traced. However,this is a long-term process that requirestime and feedback from other groups withexperience using ANORVA on otherdatasets. Problems may occur with thenumber of randomized datasets, the choiceof arithmetical rather than geometrical orother averages, or sensitivity toward hiddencycles. Identifying the method’s limitationswill help improve it and make it moreuniversal, which is one of the reasons forproviding a detailed description of themethod’s relatively simple calculation stepshere. I believe that this clear and simpleexplanation will prove more helpful toreaders than a complicated manuscript thatcould obscure more than it shows.

ACKNOWLEDGMENTS

I would like to express my appreciation tomy mentors Assoc. Prof. DanielaOstatnikova, MD, PhD and Assoc. Prof.Bozena Chovancova, Ing, PhD for thesupport, to my co-workers Julius Hodosy,MD and Rastislav Kostka, Ing for thecontribution to this manuscript, to KatarinaMelisova, Ing, Michaela Prihodova, MDand Ingrid Jurkovicova, MD for theinspiration and especially to Matus Kudela,MSc for the fruitful discussions andsustained criticism, which were mostimportant in the development of ANORVA.This work was supported by Grant of theComenius University No. 116/2004.

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