Ultradian regulation of rest and activity bouts in mice

The suprachiasmatic nucleus (SCN), which serves as the central pacemaker in mammals, regulates the 24-hour rhythm in behavioral activity. However, it is currently unclear whether and how bouts of activity and rest are regulated within the 24-hour cycle (i.e., over ultradian time scales). Therefore, we used passive infrared sensors to measure behavior in mice housed under either a light-dark (LD) cycle or continuous darkness (DD). We found that a probabilistic Markov model captures the ultradian changes in the behavioral state over a 24-hour cycle. In this model, the animal’s behavioral state in the next time interval is determined solely by the animal’s current behavioral state and by the “toss” of a proverbial “biased coin”. We found that the bias of this “coin” is regulated by light input and by the phase of the clock. Moreover, the bias of this “coin” for an animal is related to the average length of rest and activity bouts in that animal. In LD conditions, the average length of rest bouts was greater during the day compared to during the night, whereas the average length of activity bouts was greater during the night compared to during the day. Importantly, we also found that day-night changes in the rest bout lengths were significantly greater than day-night changes in the activity bout lengths. Finally, in DD conditions, the activity and rest bouts also differed between subjective night and subjective day, albeit to a lesser extent compared to LD conditions. The persistent differences in bout length over the circadian cycle following loss of the external LD cycle indicate that the central pacemaker plays a role in regulating rest and activity bouts on an ultradian time scale.


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Introduction 28 Ultradian regulation of rest and activity bouts 2 In most organisms, the circadian clock facilitates adaptation to the natural periodic light cycle. This 29 clock regulates a wide range of physiological processes, including behavior (Herzog, 2007). 30 Therefore, behavior has been used to determine the state of the clock in vivo since the early days of 31 the field of chronobiology (Pittendrigh, 1960;Pittendrigh and Daan, 1976). In mammals, the 32 circadian clock is located in the suprachiasmatic nucleus (SCN) at the base of the hypothalamus 33 (Ralph et al., 1990). The neurons in the SCN have near 24-hour oscillations in both protein 34 expression and neuronal firing (Nakamura et al., 2002;Quintero et al., 2003;Schaap et al., 2003;35 Yamaguchi et al., 2003;Hastings et al., 2018). 36 Recording the frequency of action potential firing in the SCN of freely moving animals has allowed 37 researchers to measure the degree of correspondence between SCN firing and behavioral activity 38 (Houben et al., 2009(Houben et al., , 2014. These studies showed that the onset and offset of behavioral activity are 39 regulated probabilistically by differences in firing between high levels of firing activity during the 40 day and low levels during the night (Houben et al., 2009). Moreover, the waveform of the SCN's 41 firing patterns is correlated with the distribution of behavioral activity within the active phase 42 (Houben et al., 2009(Houben et al., , 2014. However, whether-and to what extent-temporal behavior is regulated 43 within the circadian cycle (i.e., over ultradian time scales) is largely unknown. 44 Here, we examined whether bouts of activity and rest (i.e., prolonged stretches of activity and rest, 45 respectively) are regulated at ultradian time scales in mice. We fit a simple probabilistic model of the 46 transitions between behavioral states to behavioral data collected under a light-dark (LD) cycle or 47 The estimates of transition probability obtained from the behavioral data were stable over the course 107 of acquisition. The estimates of and obtained from the first half of each acquisition were highly 108 correlated with the estimates obtained from the second half (Figure S1A, : r(96)=0.85, p<.001; : 109 r(96)=0.69, p<.001). Thus, the data can be considered stationary for the purposes of this model. 110 The data also support the Markov assumption made in the probabilistic model, which can be 111 paraphrased as the "the future is independent of the past, given the present". Estimates derived from 112 the data regarding dependence (via mutual information) between the next state ( !!! ) and the 113 previous state ( !!! ), given the current state ( ! ), were all close to zero ( Figure S1B), indicating near 114 independence. In summary, our model provides a consistent representation of the data and produces 115 robust estimates of the average duration of activity and rest bouts. 116 3.2 Activity and rest in mice are not restricted to night and day, respectively 117 Next, we examined the distribution of activity during the day and night under 22-hour, 24-hour, and 118 26-hour T-cycles (i.e., LD cycles consisting of 11 hours light/11 hours dark, 12 hours light/12 hours 119 dark, and 13 hours light/13 hours dark, respectively). 120 We defined average activity as the average fraction of time an animal was active in an interval; the 121 interval is the length of the day for the average activity during the day. The average activity across 122 day and night (the interval here is the T-cycle period) was similar between the 22-hour and the 24-123 hour T-cycles, but was significantly higher in the 26-hour T-cycle compared to the 24-hour T-cycle 124 ( Figure S2, F(2, 29)=4.95, p=0.01, Tukey post-hoc test). The mice were more active at night than 125 during the day, consistent with their nocturnal nature ( Figure 2A). The mice spent about ~30% of the 126 night and about ~10% of the day being active. Thus, the mice were active for a minority of the time 127 not only in their rest phase (day), but also in their active phase (night). Moreover, in the rest phase, 128 the mice were not inactive, but rather active for 10% of the time. 129 The night to day change in average activity was similar among the three T-cycles. Specifically, the 130 average activity during the day was one-third of the levels during the night for all three T-cycles 131 indistinguishable from the night to day change in the other two T-cycles.

Activity and rest bouts are inversely regulated during the day and night 136
Next, we examined whether the average duration of the activity and rest bouts were different between 137 the day (i.e., the resting phase) and the night (i.e., the active phase) for the three different T-cycles. 138 We observed higher activity during the night than during the day (Figure 2A). This could result from 139 three different scenarios: (i) rest bouts are longer during the day than during the night, but activity 140 bouts are unchanged between day and night (ii) activity bouts are longer during the night than during 141 the day, but rest bouts are unchanged between day and night (iii) rest bouts are shortened and activity 142 bouts are lengthened from day to night. In this section, we identify the scenario that is most 143 consistent with the data. 144 According to our analysis, on average, the rest bouts were longer during the day compared to during Thus, both rest and activity bouts are indeed regulated reciprocally between day and night. 155

Day-night changes in rest bouts dominate day-night changes in activity bouts 156
This section compares the relative durations of rest and activity bouts during the day and during the 157 night. 158 We observed that the average rest bout was always longer than the average activity bout ( Figure  159 2B,C, ratio rest/activity =2.53, CI: [2.25, 2.86]). This agrees with mice having more rest than activity 160 (average activity < 0.5) during both day and night (Figure 2A). The average rest bout was about 161 twice as long as the average activity bout in the night (ratio rest/activity = 2.28, CI: [2.08, 2.49], Figure 2D). The ratio increased to about eight-fold in the day (ratio rest/activity = 8.06, CI: [7.37, 8.81]) and was 163 significantly greater under the 24-hour T-cycle (ratio = 1.17, CI: [1.05, 1.31]). 164 It appears therefore that the average rest bout is always longer than the average activity bout and the 165 absolute day-night change in the rest bouts is also greater than the absolute day-night change in the 166 activity bouts ( Figure 2B,C,D). We therefore hypothesize that the day-night changes in rest bouts 167 dominate the day-night changes in activity bouts. Quantifying the day-night change in the number of 168 bouts can help test this hypothesis. 169 Given that "rest" is defined as the lack of activity, bouts of rest and bouts of activity always alternate 170 ( Figure 1B,C); therefore, the number of rest and activity bouts in any given time interval is equal (or 171 differs by no more than one). As a result, we only report the total number of bouts in an interval. If 172 rest bouts were to dominate the day-night change, then the number of bouts would be expected to be 173 higher during the night than during the day (rest bouts are shorter during the night). If, on the other 174 hand, the activity bouts dominate, then the number of bouts would be expected to be lower during the 175 night than during the day. Since the total number of bouts during the night was higher than during the 176 day ( Figure S3A), we conclude that rest bouts rather than activity bouts dominate the day-night 177 change in activity. Mean rest bout and mean activity bout lengths changed inversely between subjective day and 195 subjective night also in DD ( Figure 3B,C). The mean length of the rest bouts increased 1.5-fold from 196 the subjective night to the subjective day ( Figure 3B, Table 1), whereas the mean length of the 197 activity bouts decreased by 20% from the subjective night to the subjective day ( Figure 3C, Table 1 The mean rest bouts were longer than the mean activity bouts during both the subjective day and the 204 subjective night in DD ( Figure 3D). The day-night changes in the rest bout lengths and the activity 205 bout lengths result in different ratios of mean rest bout and mean activity bout lengths between 206 subjective day and subjective night. The ratio of rest bout lengths to activity bout lengths during the 207 night was significantly greater under DD than under a LD cycle ( Figure 3D, Table 1). However, the 208 ratio of rest bout lengths to activity bout lengths during the day was similar in DD and LD (Table 1). 209 As a result, the ratio of rest bout lengths to activity bout lengths varied less in DD than in LD. 210 Day-night changes in the rest bouts rather than in the activity bouts predominantly contributed to the 211 day-night changes in activity. The number of total bouts was higher during the subjective night 212 compared to the subjective day, which coincides with the shorter rest bouts during the subjective 213 night ( Figure 3B). However, the day-night difference in the total number of bouts was smaller in DD 214 than in LD ( Figure S3B). 215

Model underestimates the number of very short and very long rest bouts 216
The probabilistic model fitting ensures that the mean bout lengths in the behavioral data and the 217 model are identical (fitting probability parameters is tantamount to fitting the means). In this section, 218 the observed distribution of the rest and activity bout lengths is contrasted against the distribution 219 predicted by the model. The model-derived rest bout length distribution deviates from the observed distribution. Under the 221 probabilistic model (Figure 1A), bout lengths follow a geometric distribution with a mean given by 222 the model parameters. The model predicts fewer extremely short and extremely long rest bouts than 223 those observed in the data (Figure 4). Nevertheless, the activity bout distribution in the data closely 224 matched the predicted distribution. This predicted rest bout distribution consistently differed from the 225 data across the three T-cycles and constant darkness. 226

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Discussion 227 The central pacemaker in mammals contributes to the daily rhythmic patterns of behavioral activity. 228 This paper set out to test whether behavioral activity is also regulated within the 24h circadian cycle. 229 Using data on spontaneous behavioral activity of mice under LD and DD, we quantified activity in 230 terms of rest and activity bouts in the day and in the night using a probabilistic model. We Mice were inactive for a majority of the day and the night, but with significant activity even during 255 the day. Nevertheless, the mice showed more activity in the night versus the day. Spontaneous 256 behavior (measured using passive IR sensors) is not as clearly segregated into an active phase and a 257 rest phase as is wheel-running activity (Schwartz and Zimmerman, 1990). The mean rest bouts were 258 shortened and the mean activity bouts lengthened in the night relative to the day in the 22-hour, 24-259 hour and 26-hour T-cycles. The different T-cycles affect clock function under the entrained 260 conditions studied here. Since the day-night differences in bout lengths were unaltered across T-261 cycles, we conclude that light regulates the length of rest and activity bouts independent of the central 262 clock. To fully support the latter conclusion, we may study ultradian behavioral regulation in animals 263 under short and long photoperiod, as an additional modifier of clock function. 264 We observed that, on average, rest bouts were always longer than activity bouts. Moreover, the day-265 night changes in mean rest bout lengths were about two-fold larger than the changes in mean activity 266 bout lengths in LD. Taken together, the day-night changes in rest bouts (in minutes) is significantly 267 larger than day-night changes in activity bouts. Therefore, we conclude that regulation of rest bouts 268 predominantly underlies the differences between the active and rest phases. If this were true, we 269 would expect higher number of bouts (rest and activity) in the night compared to the day. This is 270 indeed the case. Thus, the LD environment regulates rest bouts rather than activity bouts over the 24h 271

cycle. 272
Under a LD cycle, both light and the central clock affect behavioral activity. To determine the effects 273 of the central clock on behavior, animals are routinely exposed to constant darkness, and in the 274 absence of all potential time cues. In DD, mice continued to show the same qualitative changes in 275 mean bout lengths between subjective day and subjective night. The persistence of bout regulation in 276 DD between subjective day and night suggests that the central clock also regulates bout length. 277 The day-night difference in activity and rest bout duration was larger in LD cycles than in DD. Given 278 the enhanced difference between the day and night under LD cycles, we conclude that environmental 279 light cycles reinforce the SCN effect on bout regulation. In other words, exposure to LD cycles increases the "amplitude" of circadian regulation of bouts. Interestingly, the amplitude of the 281 circadian rhythm is also increased under LD as compared to DD conditions. This is the case both at 282 the level of behavioral activity and also at the level of SCN electrical discharge rate (Coomans et al., 283 2013). It is possible therefore, that even the influence of light on ultradian behavior involves the 284 SCN. At least, and given our results obtained from DD conditions, we suggest that the SCN is a node 285 in the central regulation of ultradian behavioral activity, and is a regulator of the duration of ultradian 286 bouts. Thus, in the absence of the SCN, ultradian bouts will still be present, but the day-night 287 difference in their duration will be completely lost. This interpretation is in line with the ongoing 288 presence of ultradian behavioral rhythmicity in transgenic clockless animals (Vitaterna et al., 1994;289 Horst et al., 1999;Blum et al., 2014), as well as in voles with SCN lesions (Gerkema et al., 1990). (not shown). The deviation of the rest bout distribution might be due to the presence of different 313 types of rest bouts, such as a "pause" in activity explaining the very short bouts, and the existence of 314 other processes regulating rest bouts, such as homeostatic sleep drive. 315 Our conclusions must be viewed in the context of our analysis methodology. The model treats 316 behavior within the dark and light phases as homogeneous, which is not often the case (Houben et al., 317 2014). The simplified data capture the duration of activity, but ignore the intensity of activity. Thus, 318 there could be differences in intensity of activity across LD cycles or between DD and LD, which our 319 analysis overlooked. All these limitations provide interesting avenues for further study. Finally, the 320 behavioral activity was collected in 10s bins and although bout lengths were of the order of minutes, 321 the effect of bin size on the results cannot be excluded. 322  behavioral activity data is encoded into sequences of "activity" (behavioral activity>0) and "rest" 430 (behavioral activity = 0) bins. The encoded sequences are inputs to the model in (A). One or more 431 contiguous occurrences of "activity" and "rest" bins are termed activity and rest bouts, respectively. 432 (C) The behavioral activity of an animal is recorded as raw counts in 10s bins (shown here for a 433 mouse under 24h light-dark cycles). The corresponding encoded sequence is shown with the same 434 color-coding in (B) for rest and activity. Inset zooms into a 400s interval during the night (active 435 phase). 436