Santucci et al. (1996) have demonstrated that the CB1 antagonist SR141716A dose-dependently increased the time spent awake with a parallel suppression of NREMS and REMS in rats. Goonawardena et al. (2011) could not confirm these findings in rats with applying AM-251 in 2-mg/kg dose, although they have observed an increased REMS latency that suggests an inhibition of REMS generation. However, testing AM-251 and ABD459 (another CB1 antagonist) in 3-mg/kg dose showed that both drugs produced REMS-decreasing effect in mice, while wakefulness was increased by AM-251 only (Goonawardena et al., 2015). In a recent study, dronabinol, a nonselective agonist of CB1/CB2 receptors, has been shown to decrease the percent time of REMS, and this effect was not reversible by either AM-251 or the CB2 receptor antagonist AM-630. Also, none of the CB1 and CB2 receptor antagonists could modify the sleep–wake pattern and the bout durations of NREMS and REMS items by applying alone (Calik and Carley, 2017). All these studies drew their conclusion by classifying vigilance states to REMS, NREMS, and wakefulness. For statistical comparisons, the authors used basic statistical tools, which, in principle, are applicable only for continuous variables (Santucci et al., 1996; Goonawardena et al., 2011; Goonawardena et al., 2015; Calik and Carley, 2017). This is the so-called standard or conventional approach (McShane et al., 2010), which is widely criticized for not being sensitive enough and therefore leading to information loss. Several authors (Bizzotto et al., 2010; Kostyalik et al., 2014, Diniz Behn et al., 2010, Stephenson et al., 2013) suggested sophisticated models to overcome this problem. However, the proposed models require estimating a number of parameters, which is not an easy mathematical problem. The mathematical difficulties are multiplying in the presence of a drug effect that introduces additional time-dependent variations. This explains why these sophisticated models are very rarely used to assess drug effects. However, the simple approach proposed by McShane et al. (2010) seemed to provide a bypass from this deadlock, so we decided to test it using our data obtained with AM-251. First, we confirmed, in line with the literature, that AM-251 dose-dependently increases the time spent in AW at the expense of the amount of other states ( Figure 1 ). Figure 1 represents our results obtained by the standard approach, and we started our exploratory investigations with plotting the histograms of bout durations ( Figure 2 ). Figure 2 confirms that the distribution of bout durations in rats shows the same “spike and slab” characteristics described originally by McShane et al. (2010) in mice. This mixture distribution feature was the most pronounced for REMS, so we relabeled the REMS episodes as short and long REMS (REMS-S and REMS-L, respectively) using 16 s (four epochs) as a cutoff. Note that the standard practice is to exclude all short REMS data from the analysis (Kitka et al., 2009). Figure 2 gives the impression that the shape of bout distributions in different vigilance stages remains unaffected by the treatments. If AM-251 had any effect on the average length of bout episodes, then, this effect would be apparent in Figure 2 by observing that the histograms of the treated groups are shifted horizontally relative to the control. However, such an effect could not be observed, which suggests that the frequencies rather than the duration times of bouts were affected. Therefore, in the next step, we focused on the relationships between time, drug treatment, and the frequencies of state transitions. Figure 3 shows the observed number of bouts by time and treatments. Strong time and dose dependency can be observed, practically for all vigilance states except PW. It is also noteworthy that, particularly in the first hour, several vigilance states, such as REMS-S, REMS-L, S2, and IS, are completely suppressed by the treatments. The ratio of bout numbers compared to the vehicle group is a plausible measure to assess the drug effect. We estimated this parameter using negative binomial regression ( Figure 4 ). Figure 4 shows that the smaller dose of AM-251 selectively suppressed the REMS-L bouts, while increased the AW frequency moderately. With the double dose, the frequency of AW bouts is roughly doubled, while the frequency of all other states drops by 25–60% except PW. The effect of the drug on REMS-L is not significant, because the confidence interval width is too wide. The probable reason of the wide confidence interval for REMS-L is that both REMS-S and REMS-L bouts are suppressed even in the vehicle-treated group, due to circadian factors in the regulation of the normal sleep–wake pattern. For this reason, the first hour of the study is uninformative (there is nothing to suppress), and there are too few observations. The analysis of the bout frequencies is based on the assumption that the multiplying effect of AM-251 on bout frequencies does not change with time. This is a reasonable assumption but could not be verified, because the regression procedure did not converge when the time × treatment interaction was included into the model. The probable reason of this, as shown in Figure 6 , is that, particularly in the first hour, some type of bout events never happened or happened only for a very few times. For these vigilance states, the estimates are on the boundaries of the allowable parameter space and the optimization procedure is deemed to fail (Williamson et al., 2013). Retrospectively, setting the time of drug administration at periods when the REMS activity is high would have been better to estimate the drug effect on the REMS periods. Indeed, we followed vigilance states only for 3 h after drug administration, which seems to be a limitation of our study compared to Santucci et al. (1996) and Goonawardena et al. (2015) who applied longer periods, 4 and 6 h, respectively. However, we used AM-251 only as a tool to study the sleep effects of CB1 blockade effect. From this perspective, the change in concentration from pharmacokinetic reasons is a disturbing factor which interferes with the correct the evaluation of data. The estimated half-life of AM-251 is quite long (22 h) in rats (McLaughlin et al., 2013). Assuming a simple one-compartment model, this value gives that the relative difference between the initial maximum and the minimal concentration at the end of the observation period is 9.01%. Therefore, it is reasonable assuming that during the three-hour observation period, the plasma levels were relatively constant, and the time-dependent effects seen in Figures 3 , 5 , and 6 are not the result of the drug elimination.

The results presented so far suggested that the effect of AM-251 only modulates the between-states transitions. To check the lack of effect on bout duration, a regression analysis was conducted between bout duration and by treatment for each vigilance state. The effect of AM-251 on the bout duration of PW was highly significant, which is surprising, as PW is the only vigilance state that was completely resistant to the effect AM-251 so far. However, we do not believe that this is a direct effect of AM-251 on neural circuits that are responsible for PW. We think this effect is a compensatory response as the difference from the control increases with time ( Figure 5 ). If this were a direct dose-related effect, then the time course would be the opposite. Essentially, the same effect was observed for S1. However, in this case, the compensatory decrease in bout duration was much more moderate ( Figure 5 ).

McShane et al. (2013) introduced and demonstrated the usefulness of conditional analysis that is computing bout characteristics conditionally on the previous state. Since we have already known that AM-251 affects only the transition frequencies but not the state lengths, we investigated only the conditional dependence of transition frequencies. In the first step of the conditional analysis, we made a 7 × 7 table where the number in row i and column j showed the bout number of state j when the predecessor was state i. The “7” comes from the fact that we distinguished seven vigilance states, and states i and j can be any of them. This kind of table is known as a contingence table in statistics, and many methods were developed to visualize it. The goal of the visualization is to find connection between categorical variables which translates them, in the current context as that state i and state j (variables) are connected if state i precedes state j. We measured the strength of the connection with the help of z-statistics. High z_ij statistics means that state_j is preferred over other states to “jump to” from the current state “i.” Large negative z means just the opposite—namely, the transition from “i” to “j” is not likely. When the matrix of z-s was visualized by mapping the z_ij -s to color, the resulting “transition heatmaps” turned to be very informative ( Figure 6 ). Most of the z values were significantly positive and significantly negative (above 2 or below -2, respectively). Therefore, transitions between states generally cannot be considered random. In fact, we identified several regular features, characteristics for each map regardless of time or drug treatment. The heatmaps helped us easily discover highly connected vigilance stages and derive the likely bout trajectories. The drug, time, and circadian effect can be easily spotted on them. Taken together, we recommend using the transition heatmaps as explorative aids for the visualization of transitions between vigilance stages that can be a useful in the microstructure analysis of sleep research.