Time of day and sleep effects on motor acquisition and consolidation

We investigated the influence of the time-of-day and sleep on skill acquisition (i.e., skill improvement immediately after a training-session) and consolidation (i.e., skill retention after a time interval including sleep). Three groups were trained at 10 a.m. (G10am), 3 p.m. (G3pm), or 8 p.m. (G8pm) on a finger-tapping task. We recorded the skill (i.e., the ratio between movement duration and accuracy) before and immediately after the training to evaluate acquisition, and after 24 h to measure consolidation. We did not observe any difference in acquisition according to the time of the day. Interestingly, we found a performance improvement 24 h after the evening training (G8pm), while the morning (G10am) and the afternoon (G3pm) groups deteriorated and stabilized their performance, respectively. Furthermore, two control experiments (G8awake and G8sleep) supported the idea that a night of sleep contributes to the skill consolidation of the evening group. These results show a consolidation when the training is carried out in the evening, close to sleep, and forgetting when the training is carried out in the morning, away from sleep. This finding may have an important impact on the planning of training programs in sports, clinical, or experimental domains.


INTRODUCTION
Motor learning is essential for the development of new motor skills and the perfection or preservation of existing ones 1 .Practice is fundamental to the acquisition of a profuse motor repertoire.The positive effects of practice on skill acquisition can be observed through different timescales, from a single session to several days, weeks, or months 2 .Typically, a single practice session leads to a rapid increase in accuracy and/or speed until one attains an asymptotic level of performance 3 .This fast learning process, defined as motor acquisition, is the first step to the formation of new motor memories.With additional practice sessions and during the rest period between them, a consolidation process transforms the new initially labile motor memory into a robust motor memory (for instance, the performance in a motor sequence enhances after a period of rest, defined as off-line learning) 4,5 .Notably, several studies, including diurnal and nocturnal sleep groups, have highlighted the key role of sleep on motor skill consolidation [6][7][8][9] .Both acquisition and consolidation processes are associated with neural adaptations and plastic modulations at several levels of the central nervous system 2 .
Optimization of skill learning is important for many activities and the literature on this topic is abundant.For example, the amount of training 10,11 , the distribution of rest periods during a training session 12,13 , or the variation of skills within a single training session 14,15 have been the topic of dedicated investigations.Astonishingly, although several studies have shown that motor and mental performances fluctuate across the day, following a circadian basis (∼24 h) [16][17][18] , the search for the optimal time-of-day for motor learning has not yet retained great attention.Daily variations were observed for maximal voluntary contractions 19 , spontaneous motor tempo 20 , speed/accuracy tradeoff of actual and mental movements 21 , handwriting 22 , and tennis service 23 .In all studies, better performances in strength or skill were consistently reported in the late afternoon than early in the morning.
Sporadic and contradictory information regarding the time-ofday influence on motor learning can be found in the literature.For example, some investigations did not find differences in skill learning between morning and evening training [24][25][26][27] .Others tempered this finding by showing that the time-of-day positively affects the expression of motor learning [28][29][30] .These studies, however, specifically focused on the role of sleep in motor learning, and therefore they cannot provide a direct and compelling investigation of the time-of-day effect on motor learning.
Here, we designed a specific experimental protocol to explore the influence of time-of-day in skill acquisition and consolidation.In the main experiment, we tested three groups that practiced at different times-of-day: 10 a.m., 3 p.m., and 8 p.m., on a fingertapping task.We measured skill acquisition, namely the enhancement in skill performance during and immediately after practice, and skill consolidation, i.e., the enhancement in skill performance 24 h later.Following the time-of-day literature 16 , we hypothesized that skill acquisition and consolidation should be better in the afternoon compared to the morning.We also motivated this premise by neurophysiological findings showing that physiological mechanisms are modulated throughout the day, such as the cortisol diurnal secretion related to LTP-like plasticity in the motor cortex 31 and the degree of hippocampus activation 32,33 , associated with consolidation 34,35 .We also designed two control experiments to specifically elucidate the effects of sleep on motor skill consolidation.

Main experiment
Thirty-six healthy adults, all right-handed, performed a finger sequential tapping task using their non-dominant hand on a computer keyboard (Fig. 1a).The participants were randomly divided into three groups: the G10 am (trained at 10 a.m.), the G3 pm (trained at 3 p.m.) and the G8 pm (trained at 8 p.m.).We evaluated the acquisition process during the training on day 1 (i.e., the improvement in motor skill), with the initial two trials (1 and 2, pre-test, T1), as well as the final two trials (47 and 48, post-test, T2).The remaining trials (3-46, n = 44) constituted the training phase.To measure the consolidation process, all participants carried out two additional trials 24 h later on day 2 (T3) (Fig. 1b).Throughout the experiment, we recorded the accuracy and speed of the sequence execution and defined the motor skill as the combination of both (see Fig. 1a).
Hereafter, we provided the main results for the skill parameter.A similar analysis for both speed and precision is reported in Supplementary notes 1.
The post-hoc analysis did not show any significant difference between groups in T1 (p > 0.7 in all cases).In addition, all Bayesian equivalence tests between groups in T1 showed the overlapping hypothesis Bayes Factor (BF OH 01 ) was superior to 2.45 and the non-overlapping hypothesis Bayes Factor (BF NOH 01 ) was superior to 2.85, meaning that the data are 2.5 times more likely to validate the null hypothesis than the alternative one and 2.9 times more likely to lie in the equivalence than in the non-equivalence region.Overall, these results suggest that the initial level was comparable between groups.
Skill significantly enhanced after training (T2) for all groups (T1 versus T2 post-hoc comparisons: p < 0.001 in all cases; see Fig. 2a). Figure 2b illustrates the average (+SD) acquisition gains (T1_T2) in skill.The T1_T2 gain was not significantly different between groups (one-way ANOVA: F 2,33 = 0.41, p = 0.67, η 2 = 0.02; Bayesian equivalence tests: BF OH 01 > 2.12 and BF NOH 01 > 2.38 in all cases).The comparison with the reference value zero (0) confirmed significant improvement for all groups Each key was assigned to a specific finger: 0-thumb, 1-index, 2-middle, 3-ring, and 4-little.One trial included 6 successive sequences: 1 -4 -2 -3 -1 -0.At the beginning of each trial, participants pressed the key '0' with their thumb to start the chronometer and they accomplished the 6 sequences in succession.Pressing the key '0' at the end of the 6 th sequence stopped the chronometer and ended the trial.We recorded the number of false sequences and the duration of the whole trial (MD).b Experimental procedure.On Day 1, participants performed a training-session at 10 a.m.(G10 am ), 3 p.m. (G3 pm ), and 8 p.m. (G8 pm , G8 sleep , G8 awake ).All participants carried out 48 trials (12 blocks of 4 trials, with 5-s rest between trials and 30-s rest between blocks).The pre-test (T1) and the post-test (T2) were composed, respectively, of the first two trials (1 and 2) and the last two trials (47 and 48).Then, for the retest-session, all participants accomplished two supplementary trials (T3).The G10 am , G3 pm, and G8 pm were tested 24 h after the training (Day 2).The G8 sleep and the G8 awake were tested 14 h after the training (Day 2 at 10 a.m.) and 2 h after the training (Day 1 at 10 p.m.), respectively.
To further explore acquisition, we examined the skill learning curves adjusted according to power function (Fig. 2c).The analysis did not reveal a significant difference between groups (factor b: F 2,33 = 0.54, p = 0.54, η 2 = 0.04; Bayesian equivalence tests: BF OH 01 > 1.69 and BF NOH 01 > 1.82 in all cases), indicating that the learning rate did not differ according to the time-ofday.Additionally, we did not find any modulation of the moment at which the skill enhancement reached an asymptote (G10 am : 26 ± 5 trials; G3 pm : 27 ± 3 trials; G8 pm : 27 ± 3 trials; F 2,33 = 0.37, p = 0.69, η 2 = 0.02; Bayesian equivalence tests: BF OH 01 > 2.12 and BF NOH 01 > 2.33 in all cases), whatever the threshold chosen (see also Supplementary notes 2).Overall, the above results indicate that skill improvement during the training sessions does not differ between groups, suggesting that the acquisition process is independent of the time-of-day.
Importantly, skill improvement for the G8 pm at T3 was not due to a simple continuation of the practice, namely to the improvement that this group would obtain if two more trials Fig. 2 Skill performance for the G10 am , G3 pm , and G8 pm groups.a Average values and standard deviations (+SD) of skill in T1, T2, and T3 for each group.Repeated measures ANOVA and Newman-Keuls post hoc comparisons were applied to the data.b Violin plots for the percentage of acquisition gain in skill (T1_T2).Thick and thin horizontal lines mark mean and SD, respectively.Dots represent individual data.No significant difference was found with a one-way ANOVA between groups.c Trial-by-trial plotting of skill evaluation during the training.Dots correspond to the group means for each trial and curves correspond to the power law functions using the mean point for each trial.Diamonds are the extrapolation to the two additional trials composing the T3 pred .d Violin plots for the percentage of consolidation gain in skill (T2_T3) for each group and the G8 pred (prediction of gain by extrapolation for G8 pm ).Thick and thin horizontal lines mark mean and SD, respectively.Dots represent individual data.A one-way ANOVA and Newman-Keuls post hoc comparisons were applied between G10 am , G3 pm , and G8 pm .Additionally, an independent sample T-test was performed between G8 pm and G8 pred .Stars indicate significant differences between groups or sessions.✧ p < 0.001, ✦ p < 0.05.Triangles indicate significant differences from the value zero (T-test).Δ p < 0.001, ▴ p < 0.05.would be carried out on Day 1 (50 trials instead of 48), but rather to offline learning.Indeed, the T2_T3 gain of G8 pm was significantly different from the T2_T3 pred gain (t = 2.21, p = 0.04, d = 0.90; see Fig. 2c and d).Note that, due to inter-trial variability in T2, we observed negative and positive values in individual T2_T3 pred gains.Although the gain results of the G8 pm were similarly affected by T2 inter-trial variability, all participants showed positive gains.
Despite group differences in offline skill improvement after training (T2 versus T3), all groups showed better skill performance one-day later (T3) compared to their initial performance (T1 versus T3; post-hoc comparisons: p < 0.001 in all cases).To exclude any effects of different chronotypes, we conducted the same statistical analyses without the extreme and moderate chronotypes and we obtained the same results (see Supplementary notes 3).
Overall, the consolidation process (i.e., skill measured 24 h later) was affected by the time of day wherein the training was carried out.This finding suggests that physical training scheduled in the evening, close to the night of sleep, may enable offline learning, while that scheduled in the morning may lead to forgetting.Before asserting such a premise, we controlled for alternative issues.

Control experiment 1
In the main experiment, the groups were retested (T3) at different times on Day 2, to respect a 24 h delay.Precisely, the participants of the G8 pm were retested twelve hours after waking up (8 a.m.-8 p.m.), whilst those of the other groups were tested 2 h (G10 am ; 8 a.m.-10 a.m.) or 7 h (G3 pm ; 8 a.m.-3 p.m.) after waking up.Hence, we controlled for a possible effect of the time being awake the day after training (Day 2), which could positively contribute to skill consolidation.The G8 sleep performed the training at 8 p.m. and was retested the next day at 10 a.m.(i.e., a total of 14 h after the training but 2 h after waking up; see Fig. 1b).If offline learning is due to training close to the night of sleep and not to the time of being awake the day after, the individuals of the G8 sleep should show comparable improvement with those of the G8 pm .
According to these results, skill consolidation seems to be independent of the time one is awake the day after the trainingsession, further reinforcing the premise that sleep significantly better contributes to skill consolidation if the acquisition is performed closer to sleep time.

Control experiment 2
To directly attribute the skill consolidation to sleep, one must also examine for any positive effect of the passage of time between training and sleep.Approximately, 4 h elapsed between the beginning of training (8 p.m.) and time of sleep (12 a.m.) for the G8 pm , and therefore, one could not exclude any improvement/ consolidation in skill performance during this period.To evaluate such an effect, the G8 awake carried out the training at 8 p.m. and was retested 2 h later at 10 p.m.

DISCUSSION
In the current study, we examined the influence of the time-of-day on motor skill acquisition and consolidation on a finger-tapping task.Our findings did not show any effect of the time-of day (10 a.m., 3 p.m., and 8 p.m.) in the acquisition process (i.e., skill improvement during the training session) as all groups equally improved their skill performance.Consolidation, however, significantly differed according to the time-of-day.Precisely, we observed a deterioration in skill performance 24 h after training in the morning (G10 am ), a stabilization after training in the afternoon (G3 pm ), and an improvement after training in the evening (G8 pm ).In addition, the findings from the two control groups suggest that offline gains in skill performance for the evening group were mainly due to the night of sleep and not to the awakening time between training and sleep or the amount of time passed awake after sleep (G8 awake and G8 sleep , respectively).
As in many previous findings 6, 25,26,[36][37][38][39] , all participants in our study increased skill performance following a single session of practice.Interestingly, the total skill improvement was comparable between the different times-of-day in which training was provided (morning, afternoon, or evening).Furthermore, the skill learning rate (see learning curves, Fig. 2c) was also similar among groups and thus according to the time-of-day.These findings indicate that skill acquisition is independent of the time-of-day in which training is administrated.
These results may be surprising since clear influences of the time-of-day on behavioral and neural processes have been described 16,18 .For instance, the maximal voluntary contraction 19 , speed/accuracy tradeoff of actual and mental movements 21 , handwriting 22 , and badminton serve accuracy 40 fluctuate through the day.It is proposed that the naturally higher values of body temperature in the late evening compared to the morning may enhance motor performance due to hormonal and muscular adaptations 41,42 .It must be noted that in these studies, which did not evaluate the motor learning process, performances were already acquired at the moment of the tests, possibly explaining the differences with our results.In addition, neurophysiological mechanisms, such as Long-Term Potentiation (LTP-like plasticity) and intracortical inhibition within the primary motor cortex (M1), which are both involved in skill acquisition [43][44][45][46] , are also modulated by the time of day.For example, Sale et al. 31 showed that these neural mechanisms seem to vary across the day according to the cortisol hormonal circadian fluctuation.Furthermore, Lang et al. 47 showed that the inhibitory networks on M1 (notably by GABA-B mediated), influencing neural plasticity 48 , also fluctuated throughout the day.
In the present study, such plastic neural changes within M1 did not seem to affect skill acquisition.Possibly, daily fluctuations of plastic neural changes influence consolidation rather than the acquisition of motor skills.In addition, the acquisition of motor sequences is a complex process, which is not limited to the M1 area but includes different cortico-subcortical networks such as cortico-striatal (CS) and cortico-cerebellar (CC) networks 3,49 .It is also important to note that skill acquisition includes multiple mechanisms 50,51 and reflects the sum of different learning components, such as implicit and explicit learning 1,[52][53][54] .In the present study, we did not explore these mechanisms analytically.Isolating these components to examine their evolution across the day may provide a better understanding of our results.
While the time of day did not influence the acquisition, we discovered different outcomes concerning consolidation.A majority of studies have shown offline learning, i.e., additional improvement of performance without practice after a night of sleep 6,25,27,36,38,[55][56][57] .Here, we found that this offline learning occurs only if the training takes place in the evening, followed by a night of sleep.More precisely, we observed different amounts of consolidation according to the training schedule, with a deterioration of motor skill for the morning group (10 a.m.), a stabilization for the afternoon group (3 p.m.), and an improvement for the evening group (8 p.m.) 24 h after the training.Notably, our results showed that the offline skill improvement of the evening group was due to a consolidation process (see Fig. 2c with the T3 pred and Fig. 2d with the gain of G8pred), and not due to a simple continuation of the learning 12 .In such a case, one should observe the same amount of improvement from 24 h later (T3) to the extrapolation of learning (T3 pred ).Despite restructuring our experimental protocol to reduce the potential biases 58 , a part of the supplementary improvement observed may also be attributed to the dissipation of reactive inhibition that occurs during the acquisition process 12 .However, it is important to note that this does not alter the conclusion about the different consolidations observed.
Additionally, we showed that offline learning did not occur with the simple passage of time just after training (G8 awake ; see control experiment 2) and that sleep is the key factor for off-line learning.We also found comparable offline improvement when the retest was scheduled in the morning or the evening of Day 2 (G8 sleep vs G8 pm ; see control experiment 1), excluding the possible contribution of the retest schedule and, thus, the time being awake after the night of sleep.Indeed, many studies have reported changes in non-rapid-eye-movement (NREM) stage-2 sleep as well as reactivations of task-related memory networks during sleep following a training session 59,60 .Moreover, it appears that sleep facilitates skill consolidation with a favorable molecular and cellular environment for plasticity 61 , which is the key process of motor learning to improve performance and memory 11,44,62 .Note that sleep quantification would undeniably add complementary information regarding the effects of sleep stages on motor consolidation in the present study.Our qualitative analysis of sleep, however, via the Pittsburgh sleep quality index, showed that all participants had good sleep quality without any differences between groups.
Overall, our findings support the specific contribution of sleep in skill consolidation when the training is administrated in the evening.Thus, there may be a temporal window after training where sleep may provide consolidation benefits.A training session close to sleep could protect against memory deterioration induced by additional memories (retroactive interferences 63,64 ).The morning group, spending more time awake than the afternoon and evening groups, could be more exposed to interferences.As discussed in a previous study 30 , however, these different consolidations may result from variations in neural correlates during acquisition, which is essential for consolidation.Albouy et al. 39 found that the interaction between hippocampoand striato-networks during acquisition was associated with offline gains observed during re-testing.On the other hand, Dolfen et al. 65 showed that increased cortisol levels through stress induction resulted in a gradual disengagement of hippocampal networks during acquisition, which was unfavorable for consolidation.Therefore, the natural fluctuation in cortisol levels, which are typically higher in the morning than in the evening 66 , could potentially harm the consolidation process.However, these explanations need to be further explored to determine whether it is the time of day or the proximity between training and sleep that influences consolidation, particularly through experimental protocols involving nap designs.For instance, it would be interesting to investigate whether taking a nap after morning training can enable offline learning.
Another hypothesis for the deterioration of the morning group may be the involvement of different memory systems during the training.The learning of a sequential finger-tapping task requires both procedural (for skill) and declarative (for knowledge) memories 67 .While procedural memory appears to consolidate during wakefulness 68,69 , the combination of procedural and declarative memories consolidate during sleep 6,25,27,36,37 .More interestingly, Brown et al. 70 showed a conflictual interaction between declarative and procedural memories, leading to a deterioration of performance.This conflict may be due to common cerebral structures (medial temporal lobe) or a mediating structure (the dorsolateral prefrontal cortex) being engaged in both types of memories 64,70,71 .In our study, the worst consolidation for the morning group could be due to the competition between both memories engaging in our finger-tapping task.Further investigation is needed to provide a better understanding of the underlying mechanisms contributing to the time-of-day influence on consolidation processes.
Skill consolidation according to the time of day does not appear to be population-specific but is a robust phenomenon occurring regardless of age and chronotype.Better consolidation was found after evening training in both adolescent 29 and elderly 72 populations.Moreover, although our study mainly included intermediate-type chronotypes (see also Supplementary notes 3 with only intermediate-type participants), we found a similar conclusion as the study of Korman et al. 72 , which showed an advantage in consolidation when the practice was scheduled in the evening for participants with a morning-type chronotype.It should be noted that in their study the advantage in speed observed in the evening group was associated with a decrease in the time between sequences rather that the time within sequences.
Finally, the current study suggests that the timing of practice is an important factor for motor consolidation, which is better after training in the evening than in the morning.Even if new investigations are necessary to generalize these results and to better understand the underlying neural mechanisms, our findings may help in planning effective interventions in sports and rehabilitation.This conclusion applies primarily to individuals with an intermediate chronotype, as the majority of participants in the study belonged to this type.It would be interesting to expand this research to include populations with different chronotypes to broaden our recommendations.and as fast as possible with their non-dominant hands in the following sequence: 1-4-2-3-1-0.Each key was affected by a specific finger: 0-thumb, 1-index, 2-middle, 3-ring, and 4-little.One trial was composed of six sequences performed in a row.At the beginning of each trial, participants pressed the key '0' with their thumb to start the chronometer and they accomplished the 6 sequences continuously.Pressing the key '0' at the end of the 6 th sequence stopped the chronometer and ended the trial (Fig. 1a).
The experiments included two sessions, scheduled on two consecutive days (Day 1 and Day 2), except for the G8 awake (tested only on Day 1, see Fig. 1b).On Day 1, participants were tested at 10 a.m.(G10 am ), 3 p.m. (G3 pm ) or 8 p.m. (G8 pm , G8 awake , and G8 sleep ).They carried out 48 trials (12 blocks of 4 trials, with 5-s rest between trials and 30-s rest between blocks).The score in the first two trials (1 and 2) and the last two trials (47 and 48) constituted the pre-test (T1) and the post-test (T2), respectively.The remaining trials (n = 44; from the 3 rd to the 46 th trial) constituted the training trials.To familiarize themselves with the protocol, all participants accomplished two trials at a natural speed.For the retest-session (consolidation), all participants carried out two trials (T3).The G10 am , G3 pm, and G8 pm were re-tested 24 hours (Day 2) after the first training-session.
When testing skill consolidation following different training times, one is faced with a double problem: the effect of the passage of time and the effect of sleep, since both could contribute to motor consolidation 68,76 .For that reason, we included two supplementary groups to specifically test whether the time being awake before and after the night of sleep affects skill consolidation.The G8 sleep was re-tested 14 h (Day 2 at 10 a.m.) after the first training-session.The G8 awake was re-tested 2 h (Day 1 at 10 p.m.) after the first training-session.If only the night of sleep contributes to the development of off-line learning, we should not observe changes in skill performance before sleep (G8 awake ), while offline gains should be observed immediately after sleep (G8 sleep ).
The vision of the non-dominant hand was hidden using a box during the whole protocol.The sequence's order, however, was displayed on the box and thus visible to the participants during the whole experiment.No information concerning motor performance (i.e., time or typing errors) was provided to the participants.

Data recording and analysis
For each trial, movement accuracy and duration were computed.The accuracy ('Error rate') was defined as the number of false sequences throughout one trial (0 = no false trial; 6 = all trials false).If the participants made one or more mistake(s) in one of the sequences, this sequence was counted as false (see Fig. 1a).The error rate was defined as the percentage of the number of errors during a trial: Movement duration was defined as the time interval (in seconds) between the start of the trial (when the participant pressed the key '0') and the end of the trial (when the participant pressed the key '0' at the end of the 6 th sequence).
These two parameters (Movement duration and Error rate) are related by the speed-accuracy tradeoff function 77 .Ascertaining, thus, that motor skill (i.e., the training-related change in the speedaccuracy trade-off function) has been improved is not possible when duration and accuracy change in opposite directions.For that reason, we compute a composite ratio (a.u) to describe motor skills as follows: In that formula, skill increases if the duration decreases and/or if the number of errors decreases.

Statistical analysis
Based on a previous study 30 using the same experimental design, an a priori G*POWER analysis for total sample size estimation (parameters: Effect size f = 0.30; α = 0.05; power = 0.90; groups = 3; number of measurements = 3; correlation among the repeated measures = 0.5), indicated 8 participants per group (n = 33).While this analysis indicated that twelve (n = 12) participants per group were sufficient for our study, we are aware that increasing the sample size would yield more reliable and robust results.For all data, we verified the normality and sphericity using Shapiro-Wilk test and Mauchly's test, respectively.For all statistical analyses, the significance level was fixed at 0.05 and the observed power was superior to 0.8.
First, we compared the G10 am , G3 pm , and G8 pm .For skill, we applied repeated measures (rm) ANOVA with group as betweensubjects factor (G10 am , G3 pm , and G8 pm ) and session as withinsubjects factor (T1, T2, and T3).Gains in motor skills (T1_T2 and T2_T3) were analyzed by one-way ANOVA between groups.When necessary, the post-hoc analyses were performed by applying Newman-Keuls tests.Moreover, each gain was compared with the reference value zero (T-test).
We performed the same analyses on the movement duration (see Supplementary notes 1).As the error rate did not follow a normal distribution (Shapiro-Wilk test, p < 0.05), we used twotailed permutation tests (5000 permutations; MATLAB function mult_comp_perm_t1).P-values were corrected for multiple comparisons using the Benjamini-Hochberg False Discovery Rate (MATLAB function fdr_bh) (see Supplementary notes 1).
In addition, the trial-by-trial (n = 48) evolution of individual skill performance during the whole training session was analyzed by a power-law function: where a is the learning gain and the exponential b is the learning rate.We used one-way ANOVA between groups for the learning rate (b).To further analyze the form of each learning curve (represented by the power-law function), we determined the moment at which the skill performance reached an asymptote.Precisely, we computed the derivative of the fitted power function for each participant.To define the moment at which skill progression tends to plateau, we computed the time point at which the derivative (i.e., the difference between skill at t1 + 1 and skill at T1) reached 0.0001 above its minimum value for each participant.We compared these values between groups using a one-way ANOVA.Since our threshold was arbitrarily determined, we performed, as a control, the same analysis with threshold values of 0.0002, 0.0003, 0.0004, and 0.0005 (results of these analyses are presented in Supplementary notes 2).
To test whether a possible improvement in skill performance at T3 was due to offline learning rather than the continuation of training 58 , we extrapolated the individual skill performance during the 48 trials to an additional two trials (49 and 50) in G8 pm .For each participant, we determined the gain T2_T3 pred based on the post-test (T2) and the individual predicted evolution of training (T3 pred ) and compared it with the gain T2_T3 of G8 pm by independent samples T-test.

Fig. 1
Fig. 1 Experimental design.a Participants' hand position on the keyboard and the computerized version of the sequential finger-tapping task.Each key was assigned to a specific finger: 0-thumb, 1-index, 2-middle, 3-ring, and 4-little.One trial included 6 successive sequences: 1 -4 -2 -3 -1 -0.At the beginning of each trial, participants pressed the key '0' with their thumb to start the chronometer and they accomplished the 6 sequences in succession.Pressing the key '0' at the end of the 6 th sequence stopped the chronometer and ended the trial.We recorded the number of false sequences and the duration of the whole trial (MD).b Experimental procedure.On Day 1, participants performed a training-session at 10 a.m.(G10 am ), 3 p.m. (G3 pm ), and 8 p.m. (G8 pm , G8 sleep , G8 awake ).All participants carried out 48 trials (12 blocks of 4 trials, with 5-s rest between trials and 30-s rest between blocks).The pre-test (T1) and the post-test (T2) were composed, respectively, of the first two trials (1 and 2) and the last two trials(47 and 48).Then, for the retest-session, all participants accomplished two supplementary trials (T3).The G10 am , G3 pm, and G8 pm were tested 24 h after the training (Day 2).The G8 sleep and the G8 awake were tested 14 h after the training (Day 2 at 10 a.m.) and 2 h after the training (Day 1 at 10 p.m.), respectively.

Fig. 3
Fig. 3 Skill performance for the G8 sleep group.a Average values (+SD) of skill in T1, T2, and T3.Repeated measures ANOVA and Newman-Keuls post hoc comparisons were applied to the data.Stars indicate significant differences between sessions.✧ p < 0.001, ✦ p < 0.05.b Violin plots for the percentage of acquisition gain in skill (T1_T2).c Violin plots for the percentage of consolidation gain in skill (T2_T3).Thick and thin horizontal lines mark mean and SD, respectively.Dots represent individual data.Triangles indicate significant differences from the value zero (T-test).Δ p < 0.001.Hatched blue lines correspond to the mean of G8 pm .

Fig. 4
Fig. 4 Skill performance for the G8 awake group.a Average values (+SD) of skill in T1, T2, and T3.Open stars indicate significant differences between sessions.Repeated measures ANOVA and Newman-Keuls post hoc comparisons were applied to the data.Stars indicate significant differences between sessions.✧ p < 0.001.b Violin plots for the percentage of acquisition gain in skill (T1_T2).c Violin plots for the percentage of consolidation gain in skill (T2_T3).Thick and thin horizontal lines mark mean and SD, respectively.Dots represent individual data.The triangle indicates a significant difference from the value zero (T-test).Δ p < 0.001.Hatched blue lines correspond to the mean of G8 pm .