Caroline I Jahn

Chiara Varazzani

Jérôme Sallet

Mark E Walton

Sébastien Bouret
email: sebastien.bouret@icm-institute.org

Noradrenergic but not dopaminergic neurons signal task state changes and predict re-engagement after a failure

The two catecholamines, noradrenaline and dopamine, have been shown to play comparable roles in behaviour. Both noradrenergic and dopaminergic neurons respond to salient cues predicting reward availability and to stimulus novelty, and shape action selection strategies. However, their roles in motivation have seldom been directly compared. We therefore examined the activity of noradrenergic neurons in the locus coeruleus and putative midbrain dopaminergic neurons in monkeys cued to perform effortful actions for rewards. The activity in both regions correlated with the likelihood of engaging with a presented option. By contrast, only noradrenaline neurons were also (i) predictive of engagement in a subsequent trial following a failure to engage and (ii) sensitive to the task state change, the discovery of the new task condition in unrepeated trials. This indicates that while dopamine is primarily important for the promotion of actions directed towards currently available rewards, noradrenergic neurons play a crucial complementary role in mobilizing resources to promote future engagement.

Introduction

Catecholaminergic neuromodulation is thought to be critical for numerous aspects of behaviour, including motivation, learning, decision-making and behavioural flexibility [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. Indeed, LC neurons are reliably activated when animals initiate an action [START_REF] Bouret | Reward expectation, orientation of attention and locus coeruleus-medial frontal cortex interplay during learning[END_REF][START_REF] Rajkowski | Activation of monkey locus coeruleus neurons varies with difficulty and performance in a target detection task[END_REF][START_REF] Kalwani | Phasic Activation of Individual Neurons in the Locus Ceruleus/Subceruleus Complex of Monkeys Reflects Rewarded Decisions to Go But Not Stop[END_REF]. Critically, the magnitude of this activation seems to be related to the amount of effort necessary to trigger the action [START_REF] Bouret | Sensitivity of Locus Ceruleus Neurons to Reward Value for Goal-Directed Actions[END_REF][START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. In line with this interpretation, we recently used a pharmacological manipulation to demonstrate directly that, on top of its role in behavioural flexibility, noradrenaline was also causally involved in motivation [START_REF] Jahn | Dual contributions of noradrenaline to behavioural flexibility and motivation[END_REF]. One interpretation of the dual role of noradrenergic LC neurons in behavioural flexibility and motivation is that flexibility relies upon their response to unexpected stimuli whereas their role in motivation relies upon their activation at the triggering of effortful actions. Alternatively, the response of LC neurons to unexpected stimuli could be directly related to motivation.

Since the tripartite relationship among LC activity, processing of expected vs unexpected stimuli, and motivation remain unexplored, we re-analysed a data set of noradrenergic neurons in the LC recorded in monkeys presented with cues signalling how much effort they would need to expend to gain rewards of various sizes [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. The task was designed such that rejecting an offer caused it to be represented on the subsequent trial, and the analyses reported by [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF] deliberately excluded such repeated trials. Here, by including those trials, we could investigate separately (i) the sensitivity to task state changes in unrepeated vs. repeated trials and (ii) the encoding of motivational processes, by examining the modulation of LC activity by willingness to perform the presented option (engagement) in the current or in the future trials.

Moreover, to gain further insight on the specific role of noradrenaline as compared to dopamine neurons, we compared the activity of LC neurons to that of putative DA neurons recorded from substantia nigra pars compacta and ventral tegmental area (SNc/VTA) in the same paradigm. Indeed, dopamine is also implicated in novelty and information seeking [START_REF] Horvitz | Burst activity of ventral tegmental dopamine neurons is elicited by sensory stimuli in the awake cat[END_REF][START_REF] Schultz | Predictive Reward Signal of Dopamine Neurons[END_REF][START_REF] Costa | Dopamine modulates novelty seeking behavior during decision making[END_REF][START_REF] Bromberg-Martin | Midbrain Dopamine Neurons Signal Preference for Advance Information about Upcoming Rewards[END_REF][START_REF] Naudé | Nicotinic receptors in the ventral tegmental area promote uncertainty-seeking[END_REF], as well as playing a prominent role in motivation and action initiation [START_REF] Walton | What Is the Relationship between Dopamine and Effort?[END_REF]. As for LC noradrenergic neurons, we could examine separately the relation between dopaminergic neurons and sensitivity to task state changes and willingness to perform the presented option.

We found that that although the magnitude of the neuronal response at the cue predicted the engagement in effortful actions similarly in the two catecholaminergic systems, only noradrenaline neurons were sensitive to changes in task state, i.e. to the difference between repeated (and therefore perfectly expected) and unrepeated (and therefore informative) stimuli. Moreover, while dopamine neurons only reflected the engagement at the cue onset, noradrenaline cells were also activated by erroneous fixation breaks, in a manner that predicted the likelihood of future engagement after erroneous trials. Taken together, our analyses demonstrate complementary but distinct roles for noradrenaline and dopamine in signalling new states of the world and in motivating current or future engagement with effortful actions.

Results

Behaviour

Three monkeys were trained to perform a task in which visual cues indicated the amount of effort (3 effort levels) that was required to obtain a reward (3 reward levels) (fig 1A andB). Effort and reward levels were manipulated independently across the 9 task conditions. On a given trial, monkeys could either engage in the effortful action (whether action is correct or not) or fail to engage by breaking fixation (the proportion of trials where monkeys maintained fixation and omitted the response was negligible). Importantly, unsuccessful trials, which effectively represent a failure, were repeated (see Material and Methods and figure 1 for details).

D) Weights of the task parameters in the decision to engage with the effortful action. Multi-level logistic regression of the decision to initiate the action by the three experimental task parameters: effort level,

reward level and trial number. Significant negative effect of effort level (p<0.001) and trial number (p<0.001) and significant positive effect of reward level (p<0.001) in both NA and DA session (no difference between NA and DA sessions for all three parameters (p<0.05)). *** p ≤ 0.001.

Noradrenergic and dopaminergic neurons' activity reflects monkeys' engagement in the task

We have seen previously that the task factors (i.e. effort level, reward level and trial number) influenced the probability of monkeys to engage with the effortful action.

Therefore, we first measured the influence of these task factors on neurons' activity at the time of cue. Dopaminergic neurons' activity was significantly positively modulated by reward level (β=0.05±0.01, t(83)=3.67, p<0.001) and negatively modulated by the effort level (β=-0.02±0.001, t(83)=-2.01, p=0.05), as well as by trial number (β=-0.06±0.03, t(83)=-2.53, p=0.01) (fig. 2A). Noradrenergic neurons' activity was only significantly modulated by the reward size (β=0.04±0.001, t(91)=4.05, p<0.001) but not reliably modulated by either the effort level (β=-0.01±0.01, t(91)=-1.15, p=0.25) nor trial number (β=-0.03±0.03, t(91)=-1.02, p=0.31) (fig 2A). However, we found no significant difference between the encoding of the effort level and the trial number between dopaminergic and noradrenergic neurons (p=0.42 and p=0.37 respectively). Critically, there was a significant difference between the weights of effort and reward in the firing rates of both noradrenergic and dopaminergic neurons (2-way ANOVA measuring the effect of task factor (effort and reward) and recording type (NA or DA) onto -β(effort) and β(reward): main effect of task factor F(1,348)=9.71, p=0.02) but no main effect of recording session type (F(1,348)=0.61, p=0.4) and no interaction (F(2,348)=0.04, p=0.8). This means that the relative sensitivity of noradrenergic and dopaminergic neurons to the task factors was similar, with a greater sensitivity for reward than effort (post-hoc T-test on the distribution of -β(effort) and β(reward): t(350)=-3.13, p=0.002).

After having considered the relation between neuronal activity and task factors, we looked at the relationship between neuronal activity and the engagement in the effortful action. First, we did it across the nine task conditions (defined by a combination of effort and reward levels) by using an aggregate measure of the engagement for each condition (the probability to engage given the task condition). This tested whether neuronal activity directly reflected the probability for the monkeys to engage in a particular task condition. For each recording, we regressed this z-scored probability of engagement on neurons' activity and found a significant positive effect at the population level, for both noradrenergic and dopaminergic neurons (NA: β=0.04±0.01, t(91)=3.70, p<0.001, DA: β=0.03±0.01, t(83)=2.16, p=0.03) (fig 2B). Again, there was no difference in the strength of this signal encoding between populations (p=0.50).

Moreover, this activity was specific to the onset of the cue as there was no significant encoding of this probability before the cue onset (pre-cue period) even in repeated trials, in which monkeys already knew which cue was coming (500ms window before cue onset: NA: p=0.17, DA: p=0.71). We also examined the relation between neuronal activity and engagement on a trial by trial basis. We found that both noradrenergic and dopaminergic responses were predictive of engagement on a trial by trial basis (NA: β=0.06±0.03, t(91)=2.47, p=0.01; DA: β=0.06±0.03, t(83)=2.36, p=0.02) (fig 2C). Here again, there was no difference in the strength of this signal encoding between dopaminergic and noradrenergic neurons (p=0.96). Moreover, the activity was specific to the onset of the cue, with no encoding of engagement in the pre-cue period (NA: p=0.08, DA: p=0.88).

Overall, we found that even if, contrary to behaviour, the activity of the noradrenergic and dopaminergic systems is biased toward the encoding of reward compared to effort the firing of these neurons reflected the engagement in the effortful action in a similar fashion at the time of the cue.

Both noradrenergic and dopaminergic neurons encode monkeys' engagement, but only noradrenergic neurons are sensitive to changes in task state

In order to understand if catecholaminergic neurons also encode changes in task states (i.e. when their responses to cues differed between repeated and non-repeated trials) and to determine the relationship between this factor and motivation (engagement), we compared the encoding of these two variables at the time of cue.

To examine the effect of changes in task states, we compared cue-evoked activity in repeated ('non-informative cue') versus non-repeated ('informative cue') trials. Since erroneous trials were repeated, and monkeys knew the structure of the task, they could predict following an error that the same condition (with the same visual cue) would be presented again, such that the visual cue provided no information about the task state.

By contrast, after a correct trial, any of the nine task conditions could be pseudorandomly presented to the monkey, such that visual cues now provided information about the upcoming reward and effort levels (task state). Erroneous trials were mainly of two types: (i) monkeys broke the fixation (no engagement) and (ii) monkeys engaged (tried to squeeze the clamp) but did not execute the action correctly. Therefore, as not all trials in which monkeys engaged were successful, we were able to look conjointly at the effect of engagement and the information being presented on neuronal activity.

First, we found no interaction between the linear encoding of the effort, reward levels and trial number with whether the trial was repeated or not in either noradrenergic neurons or dopaminergic neurons (see Materials and Methods, NA: p=0.24, p=0.26 and p=0.58 respectively; DA: p=0.26, p=0.27 and p=0.10 respectively). This means that the task condition was encoded in a similar fashion whether the cue was informative or not.

To examine the effect of engagement and task state change above and beyond the effect of a particular task condition (effort and reward levels), we regressed out the effect of the task condition on the firing rate of neurons and looked at the effect of engagement and task state change (unrepeated vs. repeated trials) on the remaining neuronal activity (see Material and Methods). Here, we found an important dissociation between the activity of noradrenergic and dopaminergic neurons (fig 3). For a given trial condition, noradrenergic neurons were more active either when the action was initiated (vs not) or when the cue provided information about the new task condition (in unrepeated vs repeated trials) in a given experimental condition (β(engagement)=0.11±0.03, t(91)=3.40, p<0.001; β(task state change)=0.16±0.04, t(91)=4.23, p<0.001). We also found a significant negative interaction (β(interaction)=-0.06±0.02, t(91)=-3.02, p=0.003), which indicates that engagement and information effects were not perfectly additive: when both factors were combined, the firing rate increased less than by the sum of the two separate effects. On the other hand, while dopaminergic neurons were on average more active when monkeys engaged in a given condition (β=0.08±0.04, t(83)=2.05, p=0.04), they were not sensitive to the task state change (p=0.56). There was also no significant interaction between the two effects (p=0.36), and the main effects were similar when we removed the interaction.

A direct comparison of these effects between noradrenergic and dopaminergic neurons confirmed that, while there was no difference in the strength of their encoding of engagement in the task (p=0.59) noradrenergic neurons encoded significantly more task state change than dopaminergic neurons (p<0.001).

Here again, this effect was specific of the onset of the cue as when we examined the 500ms pre-cue period, there was neither an effect of engagement (NA: p=0.17, DA: p=0.77) nor an effect of task state change (NA: p=0.96, DA: p=0.07). There was also no effect of engagement in the pre-cue period if we only examined repeated trials where monkeys already knew the task condition (NA: p=0.31, DA: p=0.47). In short, when comparing the encoding of engagement and task state change (unrepeated vs. repeated trials) variables over and above the task variables, both noradrenergic and dopaminergic neurons encoded the engagement in the task, but only noradrenergic neurons encoded the task state change (whether the cue was informative or not). In addition, these effects were unaffected by the addition of trial number to the analyses, which captures the influence of fatigue and satiety (main effects of engagement and task state change remained as described before; main effect of trial number: NA: p=0.47, DA: p=0.02; interaction of engagement and task state change with trial number did not reach significance in either noradrenergic or dopaminergic neurons, NA: p(engagement)=0.84, p(task state change)=0.97, DA: p(engagement)=0.91, p(task state change)=0.19) (see supplemental figure 1A). Thus, engagement and task state change had specific effects on neurons' firing rates, which in turn were independent of the progression in the session.

Only noradrenergic neurons were activated after a failure to engage and are sensitive to the task condition

We next examined the activity of dopaminergic and noradrenergic neurons time-locked to fixation break, which resulted in trial abortion. We focused our analysis on three epochs: a baseline epoch from -600 to -300ms prior to fixation; a pre-fixation break epoch corresponding to the 300ms prior to fixation break, and post fixation break epoch corresponding to the 300ms following fixation break. There was neither a significant activation of dopaminergic neurons before fixation break (p=0.62) nor after the fixation break (p=0.49). By contrast, noradrenergic neurons were significantly activated after (mean difference=0.30±0.09 spikes/s, t(83)=3.31, p=0.001), but not before (p=0.81) the fixation break had occurred. This activation corresponds to an average change of 16.5%±0.04 of activity between before (average firing rate = 2.83 spikes/s) and after (average firing rate = 3.12 spikes/s) the fixation break (fig 4A). At the single neuron level, 18.1% noradrenergic neurons were activated at the fixation break (one-tailed Ttest: firing rate(pre fixation break) < firing rate(post fixation break), p<0.05 were considered as significant). Note that all results hold true if we removed fixation break events that occurred less than 500ms after the cue onset.

We then looked at the modulation of fixation-break related activity across task conditions. The firing of dopaminergic neurons did not show any significant modulation across task conditions (probability to engage with the task condition: p=0.97) or behavioural responses (engagement in the next trial: p=0.45) and it will not be described further. By contrast, noradrenergic neurons' evoked activity was positively modulated by the reward size (β=0.06±0.02, t(83)=3.64, p<0.001) but neither by the effort level nor by the trial number (β(effort level)=-0.01±0.02, t(83)=-0.91, p=0.37; β(trial number)=-0.04±0.03, t(83)=-1.31, p=0.20) (fig 4B). Note however, that the difference between the sensitivity to effort and reward did not reach significance (t-test on -β(effort) and β(reward): t(166)=1.88, p=0.06). This activity was specific to the onset of the fixation break as there was no modulation of the activity by these task factors in the 300ms before the fixation break (effort level: p=0.50; reward level: p=0.15; trial number: p=0.9).

C) Example noradrenergic neurons at fixation break for each reward level. Neuronal activity representative of noradrenergic neuron around fixation break (pink vertical line). Trials are sorted by decreasing latency between cue onset (grey dots) and fixation break. Cue onset is only visible for bottom trials, with latencies shorter than the displayed 1 sec. Spike activity (raster and spike density function)

of a noradrenergic neuron showing an increase after the fixation break. In addition, its activity is modulated by the reward level (p<0.001).

Noradrenergic neurons activity predicted the engagement on the next trial

Finally, we examined the relationship between fixation-break evoked activity and the probability, across sessions, that the monkeys engaged on the next trial. Here again, we only looked at fixation break events that occurred after cue onset, meaning that the monkeys always knew the task condition at the time of the fixation break.

We found a significant positive effect of the probability to engage given the task condition on LC activity at the time of the fixation break (β=0.05±0.02, t(83)=2.79, p=0.007). In other words, the more monkeys tended to engage in a specific task condition, the more noradrenergic neurons would be active if a fixation break occurred in this task condition. This effect was also present in the pre-fixation break activity (-300-0ms to fixation break) (β=0.15±0.06, t(83)=2.55, p=0.01), suggesting that it appeared after cue onset, in line with the fact that noradrenergic neurons also displayed a positive relation with task engagement at the time of the cue onset (fig 2B). Indeed, we found a significant positive correlation (r=0.33, p=0.002) between the strength of the encoding of the probability to engage at the time of cue and at the time of the post-fixation break (fig 5B). In short, noradrenergic neurons were activated both at cue onset and at the fixation break when it occurred. They tended to be more active in conditions associated with a greater probability of engagement, both at the cue onset and at the time of fixation break, and these two responses were correlated across the population of LC neurons.

Given this strong relation between LC activity and probability of engagement in the current trial when monkeys erroneously break fixation, we were interested to examine whether this activity could also predict monkeys' likelihood of engagement in the following trial. After a fixation break, two things could happen on the next trial (and therefore in the same task condition): monkeys could now choose to engage with the same task condition or could again reject the offer (fig 5A). We therefore examined if LC activity at the time of fixation break could provide information about engagement in the next trial, over and above task condition.

In fact, the magnitude of the fixation-break activation of noradrenergic neurons (controlled for task condition) was predictive of subsequent engagement in the next trial (β=0.12±0.003, t(83)=3.84, p<0.001; effect calculated on the z-scored distributions of firing rates and translating to an average difference of 25.1%±0.1 of activity between non-engage and engage on the next trial conditions) (fig 5C). At the single neuron level, only 6.5% of neurons showed a significant effect (compared to 7.6% of neurons showing a significant sensitivity to reward at fixation break and 20.6% at cue). Hence, although the effects seen at the fixation break are relatively weak at the single neuron level, they are very consistent across the population, such that at the population level the effect clearly reaches significance. In fact 66.3% of neurons showed small but consistently greater activation in trials in which monkeys engage on the next trial, which is comparable to the proportion of neuron displaying a positive relation with reward at the fixation break (63%) or at the cue (66.3%). We controlled for potential interactions with confounding factors such as task state change (whether the erroneous trial was itself a repeated or not), trial number and their interactions with the effect of the engagement in the next trial, but none of them were significant (main effects: p(information)=0.18, p(trial number)=0.15; interactions with engagement with next trial: p(information)=0.27, p(trial number)=0.81). As previously mentioned, this activity was specific of noradrenergic neurons as dopaminergic neurons were not activated postfixation break and did not signal the engagement in the next trial (p=0.45) (see supplemental figure 1B).

Finally, we looked whether the effect of the engagement in the next trial could be found before the cue of the next trials. In other words, we looked if we could predict the engagement before the cue (-500 -0ms) for trials where a fixation break occurred. We found that it was not the case (p=0.25) and could therefore only conclude that noradrenergic neurons predict the engagement on a trial-by-trial basis.

In summary, we found that noradrenergic but not dopaminergic neurons' activity at fixation break reflected the probability to engage both in the current and in the subsequent trial, over and above cost-benefit task conditions.

B) Correlation between noradrenergic neurons' encoding of the probability to engage for each task condition at the cue onset and the fixation break across sessions. Significant correlation (r=0.33, p<0.01). C) Noradrenergic neurons' activity at fixation break is predictive of engagement in the next trial above

and beyond the task condition. Linear regression, significant effect (p<0.001). % difference between the firing rate distribution for no engagement in next trial and engagement in next trial in the null space of task conditions (mixed effect linear regressions on non-z-scored distributions). The distribution is represented on a log-scale. Significant difference (p<0.001). *** p ≤ 0.001.

D) Example noradrenergic neurons at fixation break for no engagement (left) and engagement (right) in the next trial. Neuronal activity (raster and spike density function) is displayed around fixation break (t=0, pink vertical line). Trials are sorted by decreasing latency between cue onset (grey dots) and fixation break. Cue onset is only visible for bottom trials, with latencies shorter than the displayed 1 sec. As a majority of LC neurons, this one shows a stronger activation when monkeys engaged on the next trial (p<0.001).

Discussion

In this task, monkeys were presented with informative (non-repeated) and noninformative (repeated) cues instructing them to produce actions of different intensities to gain rewards of different magnitudes. The probability that monkeys would try to produce the action (engagement) depended on the task condition (effort and reward levels) but failing to engage would only lead to the repetition of the same task condition.

Repeated trials constituted series of actions towards the same goal: the reward. This goal directed behaviour ended when the goal was reached. From that perspective, there is a clear transition in behaviour after a correct trial, as animals get started on another trial, another goal directed behaviour [START_REF] Bouret | Relation of Locus Coeruleus Neurons in Monkeys to Pavlovian and Operant Behaviors[END_REF]. Hence, given the structure of the task, unrepeated trials are more likely to constitute a task state changes than repeated ones from a goal-directed behaviour perspective. We used this task structure to reveal the precise roles of noradrenergic and dopaminergic neurons in encoding motivation to engage in the task and in signalling task state changes. We used the engagement in a task condition on a specific trial as a measure of motivation and found that both noradrenergic and dopaminergic neurons' activities were predictive of the engagement. Their activities were not only correlated with the sessionaverage probability to engage in a particular task condition, but also with the trial-bytrial engagement. Furthermore, their activities were correlated with engagement over and above the specific task condition. This strengthens the role of both catecholaminergic systems in motivating effortful, reward directed actions.

However, the activity of noradrenergic and dopaminergic neurons differed significantly when it came to signalling task state changes. First, only noradrenergic neurons' activity was sensitive to whether or not the visual cue was providing information about the new task state (which was the case only in non-repeated trials), over and above its relation with upcoming reward and effort levels. Moreover, noradrenergic, but not dopaminergic, neurons displayed activity after a fixation break, which ended the trial and represented a failure to engage. This activity scaled with the probability of engagement given the task condition and it was positively correlated with the engagement in the next trial. Hence, noradrenaline, contrary to dopamine, plays a role both in signalling information about task state and in promoting current and future effortful actions given this information.

Similarities and dissimilarities of the role of the catecholaminergic systems in motivation

This study builds on experiments presented in [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF], but here includes both repeated and non-repeated, and correct and incorrect trials, rather than just the non-repeated correct trials reported in [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. This allowed us to examine the influence of information about task state changes and motivation to engage, and not just the cost-benefit parameters of the presented cues, on neural activity. The inclusion of these additional trials did lead to slight differences in the strength of encoding of task parameters to those reported previously. However, importantly the overall pattern of effects was comparable, and any differences were negligible compared to the difference in terms of sensitivity in noradrenaline and dopamine neurons to changes in task state.

Both noradrenergic and dopaminergic neurons' activity was related to the engagement in the effortful actions. Dopaminergic neurons' activity was tightly linked with the engagement in the rewarded course of action independently of whether the trial was repeated or not. Dopaminergic neurons were also activated at the time of producing the action, but contrary to noradrenergic neurons, they did not correlate with the actual force produced [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. The causal role of dopamine in incentive processes has been shown in different species, with an emphasis on its role in controlling reward sensitivity [START_REF] Denk | Differential involvement of serotonin and dopamine systems in cost-benefit decisions about delay or effort[END_REF] Noradrenergic neurons' activity was also linked to the engagement in the effortful course of action as well as to the actual production of the action [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. This is in line with previous demonstrations that LC neurons respond to stimuli predicting future rewards and action initiation responses [START_REF] Bouret | Reward expectation, orientation of attention and locus coeruleus-medial frontal cortex interplay during learning[END_REF][START_REF] Bouret | Relation of Locus Coeruleus Neurons in Monkeys to Pavlovian and Operant Behaviors[END_REF], 2015;[START_REF] Kalwani | Phasic Activation of Individual Neurons in the Locus Ceruleus/Subceruleus Complex of Monkeys Reflects Rewarded Decisions to Go But Not Stop[END_REF]). Contrary to dopamine, causal manipulation of the noradrenergic system does not seem to affect incentive processes (Hoskins et al. 2014;[START_REF] Jahn | Dual contributions of noradrenaline to behavioural flexibility and motivation[END_REF]. Indeed, our recent study showed that the noradrenergic system controls the amount of force produced during the action, but not the selection nor the initiation of the action [START_REF] Jahn | Dual contributions of noradrenaline to behavioural flexibility and motivation[END_REF]). Hence, the noradrenergic system might be critical to ensure that the effortful action is appropriately performed once a decision to engage has been taken [START_REF] Bouret | Sensitivity of Locus Ceruleus Neurons to Reward Value for Goal-Directed Actions[END_REF][START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF], whereas dopamine is instead key for signalling the subjective future reward to be gained by performing an action and promoting that response (Ishiwari et al., 2017) and to be implicated in novelty seeking [START_REF] Costa | Dopamine modulates novelty seeking behavior during decision making[END_REF]). Therefore, it may initially seem surprising that in our task, dopaminergic neurons were not sensitive to the novelty of the presented task condition information. However, there are a number of important differences between these experiments and the current one. For instance, in previous experiments examining novelty seeking, it is unclear whether dopaminergic neurons are encoding new information based on the change in uncertainty about the world, independent of choice, or as a variable driving the behaviour. While Bromberg-Martin and Hikosaka showed that dopaminergic neurons were sensitive to the advanced information about the size of the reward, importantly in their study, monkeys showed a preference for obtaining this information, implying that it was therefore relevant for guiding the behaviour (Bromberg-Martin & Hikosaka 2009; [START_REF] Charpentier | Valuation of knowledge and ignorance in mesolimbic reward circuitry[END_REF]). In another experiment, Naudé and colleagues showed that mice preferred a probabilistic outcome to a deterministic outcome, and that this preference was controlled by the dopaminergic system [START_REF] Naudé | Nicotinic receptors in the ventral tegmental area promote uncertainty-seeking[END_REF]). These two studies show that dopaminergic neurons are sensitive to information as a variable that can influence choices through preferences, since it acted as a reward [START_REF] Charpentier | Valuation of knowledge and ignorance in mesolimbic reward circuitry[END_REF]). In our task, as the cost-benefit cues were all well known, information (as provided by the cues in non-repeated, but not in repeated trials) would neither cause sensory surprise (as cues themselves were not novel) nor be relevant for modulating future choices.

Therefore, although we cannot rule out that some individual dopamine neurons do code for this factor, it seems that dopamine neurons as a population do not encode the information about task state changes when this is not relevant to guide the behaviour.

Noradrenergic neurons' activity reflects the role of noradrenaline in information processing and engagement after a failure

The crucial difference between dopaminergic and noradrenergic neurons was that noradrenergic neurons were sensitive to the repetition of a trial at cue. Because task state changes only occur after a successful trial, lower activation of LC neurons at cue on repeated trials could reflect the fact that an error just occurred. However, we found no significant effect of error on the previous trial in baseline activity before the cue. Therefore, it is unlikely that there is a carry-over effect of error on the next trial. This lower activation in repeated trials could also be simply due to the repetition of a visual cue. However, there was no significant difference in the sensitivity to the task factors (effort and reward levels) in repeated and non-repeated trials. Hence, there is no evidence in our data for a simple stimulus repetition suppression effect. Moreover, from a goal directed behavior perspective, there is much more likely to be a state transition after a sequence ended with a reward, which would argue against a simple cue repetition response. Therefore, we attributed this lower activation to the fact that the monkeys already knew the task condition in repeated trials. Noradrenergic neurons would be sensitive to the information about task state changes, which corresponds to the discovery of a new state of the world either at the time of cue (i.e., which task condition has been selected for the current trial) but also at fixation break (an error means that the trial is terminated and that the same task condition is coming next).This is in line with the long-stated, if underspecified, role of noradrenaline in signalling important events in the environment [START_REF] Kety | The possible role of the adrenergic systems of the cortex in learning[END_REF] Crucially, only noradrenergic neurons were activated following a break in fixation, which represents a failure to engage in the effortful action. Similar patterns of activity at the break of fixation have also been observed in mid-cingulate cortex (MCC), here modulated by how close to reward delivery the error occurred or how much effort was already invested in the task [START_REF] Amiez | Anterior cingulate error-related activity is modulated by predicted reward[END_REF]. Given the connections between LC and MCC, this suggests that MCC and LC might well interact when required to signal salient events. A break of fixation was an important event not only as it signalled the end of the trial, but also the re-occurrence of same task condition in the next one. This post-fixation break activity was tightly linked to firing rates at the time of cue, which in turn reflected the probability of engagement in the effortful action. A potential scenario is that if the activity at the cue was too small to enable maintenance of the fixation and the engagement in the trial, then activity at the fixation break reflects a prospective update to enable performance of the action on the subsequent trial. Indeed, we found that when we controlled for task condition, noradrenaline neurons were more active after fixation break when monkeys then engaged in the subsequent trial. Finally, as we were never able to predict the engagement in the trial from the baseline activity at the cue, even for repeated trials and even for trials following a fixation break, we only conclude that noradrenergic neurons predict the engagement on a trial-by-trial basis but have no evidence that they do so through a slow fluctuation of activity that lasts beyond the range of a trial.

Together, these results are compatible with the idea that noradrenergic neurons signal and potentially facilitate the need to engage resources to undertake and complete effortful actions [START_REF] Bouret | Complementary neural correlates of motivation in dopaminergic and noradrenergic neurons of monkeys[END_REF][START_REF] Walton | What Is the Relationship between Dopamine and Effort?[END_REF]). In both cases, they do it as a function of new information about the state of the world: about the start of a new and unpredictable experimental condition that will bring a reward at the cue, and about the failure to complete a trial that might has been worth it, since they re-engage immediately at fixation break.

To conclude, our data show the specific and complementary roles of dopamine and noradrenaline in motivation and behavioural flexibility. The former would promote actions directed towards currently available rewards, while the latter could play a critical role in facing challenging situations by mobilizing resources based on new information about the environment.

Materials and Methods

Monkeys

Task

The behavioural paradigm has previously been described in detail in [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF]. In brief, each monkey sat in a primate chair positioned in front of a monitor on which visual stimuli were displayed. A pneumatic grip (M2E Unimecanique, Paris, France) was mounted on the chair at the level of the monkey's hands. Water rewards were delivered from a tube positioned between the monkey's lips. Behavioural paradigm was controlled using the REX system (NIH, MD, USA) and Presentation software (Neurobehavioral systems, Inc, CA, USA).

The task consisted of squeezing the grip to a minimum imposed force threshold to obtain rewards, delivered at the end of each successful squeeze (fig 1A andB). At the beginning of each trial, subject had to fixate a red dot at the centre of the screen before a cue appeared. The cue indicated the minimum amount of force to produce to obtain the reward (3 force levels) and the amount of reward at stake (3 reward levels: 1, 2 and 4 drops of water). After a variable delay (1500±500ms from cue display), the dot at the centre of the cue turned green (Go signal) and subject had 1000ms to initiate the action, meaning squeezing the clamp very little (threshold set to detect any attempt to perform the action). If the monkey reached the minimum force threshold indicated by the cue, the dot tuned blue and remained blue if the effort was sustained for 500±100ms. At the end of this period, if at least the minimum required effort had been maintained, the water reward was delivered.

Fixation of the central dot had to be maintained through the different phases of the task. A trial was incorrect if: (i) the monkey broke fixation before the reward delivery, (ii) he squeezed the clamp before the go signal, (iii) he failed to squeeze the clamp at all or (iv) at the minimum force threshold or (v) didn't maintain the effort long enough.

After an error the same trial was repeated until it was successfully completed. Within a session, the nine combinations of effort and reward conditions were selected with equal probability and presented in a random order. As erroneous trials were repeated, the policy with the highest reward rate was to always engage until satiety.

Monkeys were trained for several months on this task. They first learned to distinguish and perform two different force levels and the difficulty of the task was progressively increased until they were could do so with the nine experimental conditions. Finally, they learned that they had to fixate the central dot to go through a trial.

Electrophysiological recordings

Single unit recording using vertically movable single electrodes was carried out using conventional techniques. The electrophysiological signals were acquired, amplified (x10,000), digitized, and band-pass filtered (100 Hz to 2 kHz) using the OmniPlex system (Plexon). Precise description of the recording procedures can be found in the article where LC and SNc/VTA data used here were originally reported [START_REF] Varazzani | Noradrenaline and dopamine neurons in the reward/effort trade-off: a direct electrophysiological comparison in behaving monkeys[END_REF] In all our analyses we only considered trials (correct and incorrect) in which monkeys did not break the fixation before the onset of the cue (NA: 324 trials on average for monkey A and 281 for monkey D, DA: 314 trials on average for monkey D and 274 for monkey E). We took all those trials and computed the probability that for a given effort and reward level (or a given task condition), subjects would engage with the trial. We considered that monkeys engaged if they maintained fixation throughout the trial and initiated the action even if it occurred before the Go signal, (5% of trials in both noradrenergic (NA) and dopaminergic (DA) neurons recording sessions), not strongly (0% and 0.1% of trials in NA and DA sessions respectively) or long enough (8% and 10% of trials in NA and DA sessions respectively). Although it was possible to fail to engage with a trial by maintaining fixation but not squeezing the clamp, this type of mistake was rare (2% and 1% of trials in NA and DA sessions respectively) and monkeys mostly rejected a trial by breaking fixation (20% of all trials in both NA and DA sessions). Erroneous trials were therefore mainly of two types: i) monkeys broke the fixation and failed to engage with the trial (no engagement and no new information as the same trial type is presented again: 20% of all trials in both NA and DA sessions) and ii) monkeys engaged (tried to squeeze the clamp) but did not complete the correct action (engagement but no new information: 17% and 20% of engaged trials, which corresponds to 13% and 15% of all trials in NA and DA sessions respectively).

We examined the effects of effort, reward and trial number on the engagement in the action using a multi-level logistic regression for each session. The three variables were z-scored so that we could compare their weights across sessions. We then went on to examine task conditions influenced neuronal activity. To assess the effect of task conditions on neurons' activity at the time of cue onset, we used a window from 0 to 500ms from cue onset. When we looked at these effects in the pre-cue period, we used a window from -500 to 0ms from cue onset. Neurons' activity was measured in firing rates (spikes per second) and were z-scored scored for each session to compare the activity across neurons. First, the effects of the task factors: effort, reward and trial number in a session on neurons' activity were estimated using a multi-level linear regression for each neuron. Second, we assessed the relationship between neurons' firing rates and engagement in a given trial by running a logistic regression of neurons' firing rates on engagement. Finally, we looked at the linear encoding of the z-scored probability to engage given the task condition on neurons' firing rates using a linear regression.

When we looked at the effect of the novelty of the trial state (here referred to as "task state change") on neuronal activity, we first looked at whether the fact that a cue was informative (I=1) or not (I=0) changed the sensitivity of neurons for the task factor (E, R, N) at the time cue by regressing the task factors and the interaction between the task factors and the informativity (I=0 or 1) onto the trial-by-trial neurons' activity. A significant interaction would mean that an informative cue (signalling the new task state) would increase of decrease the sensitivity for the task factor. We then wanted to assess the conjoint effect of engagement and task state change on neurons' firing rates above and beyond the effect of effort and reward levels. To do so, we ran a multilevel linear regression taking into account the task condition variability. In other words, we removed from neurons' firing rates the effect of the task condition using a mixed model: 𝑁𝑒𝑢𝑟𝑜𝑛𝑠 ( 𝑓𝑖𝑟𝑖𝑛𝑔 𝑟𝑎𝑡𝑒𝑠 = 𝛽 1 + 𝛽 1 (𝑡𝑎𝑠𝑘 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛) + 8 𝛽 9 . 𝑥 9 9 where β0 a constant, β0(task condition) a constant fitted for each combination of effort and reward level (9 possibilities), xi the experimental factors and βi their weights in the linear regression (e.g. engagement, task state change, interaction). When looking at the effect of engagement and task state change at cue, we tested the following experimental factors: engagement, task state change and interaction between effect.

We then added to the regression the following confounds: trial number, interaction between trial number and engagement and interaction between trial number and task state change. All results hold when adding the confounds.

We then moved on to assess whether noradrenergic and dopaminergic neurons were activated before the fixation break. We only considered fixation breaks that occurred after the display of the cue. We compared firing rates from 600ms before the fixation break to 300ms after (in 300ms windows). For all analyses at fixation break, we only included sessions during which there were more than 20 fixation break events after the onset of the cue (91 % of NA sessions and 89 % of DA sessions). Delays between the onset of the cues and fixation break events followed a Poisson-like distribution of median 845ms for NA session and 713ms for DA sessions (statistically different, t-test on the mean of the log-transformed distributions: p<0.001). To ensure that the activity at the fixation break was not contaminated by the cue response, we also looked only at fixation break events that occurred at least 500ms after the cue onset (83 % of NA sessions and 75 % of DA sessions). However, all main results were similar both with and without exclusion of the early fixation break events. To assess whether neurons were activated at the fixation break, we compared the difference in firing rate before and after the fixation break and the % of change in firing rate (by dividing by the firing rate before the fixation break). We ran a similar analysis to assess whether neurons were activated before the fixation break. When looking at the modulation of the evoked activity a fixation break, we used the same methodological approach as for the analysis of activity at cue onset. When looking at the effect of engagement in the next trial at fixation break cue, we tested the following experimental factors: engagement in the next trial. We then added to the regression the following confounds: task state change (in the current trial), trial number, interaction between the effect of engagement in the next trial and task state change and interaction between the effect of engagement in the next trial and trial number. All results hold when adding the confounds. To assess the size of the effect of engagement in the next trial, we ran the linear regression of the effect of engaging in the next trial while taking into account the task condition on the non-z-scored firing rate of neurons at fixation break and divided the regression coefficient (difference between engage and non-engage conditions) by the fixed intercept (mean firing rate across both conditions).

Second-level analyses were performed by comparing the distributions of regression coefficients against zero or other distributions (paired t-test and unpaired t-test respectively or ANOVA). Statistical reports include means of the distribution ± standard

(

  Robbins & Roberts 2007; Doya 2008; Sara 2009; Robbins & Arnsten 2009; Sara & Bouret 2012). Both noradrenaline and dopamine neurons respond to novel and salient stimuli and signal predictions of future reward (Schultz 1998; Bouret & Sara 2004; Ravel & Richmond 2006; Berridge 2007; Ventura et al. 2007; Matsumoto & Hikosaka 2009; Bromberg-Martin et al. 2010) and both systems have been implicated in motivating action (Robbins & Everitt 2007; Nicola 2010; Bouret et al. 2012; Varazzani et al. 2015; Jahn et al, 2018; Walton & Bouret, 2019). Nonetheless, the specific contributions of dopamine and noradrenaline to these functions remain unclear, in part as their roles have seldom been compared in the same task (but see Bouret et al. 2012 and Varazzani et al. 2015). Locus coeruleus (LC) noradrenergic-containing neurons have a long-stated role in signalling new information about the state of the world, specifically a change in predictability of the environment (Swick et al, 1994; Vankov et al, 1995; Dalley et al, 2001; Aston-Jones & Cohen, 2005; Bouret & Sara, 2005; Yu & Dayan, 2005). LC neurons are particularly sensitive to unexpected and/or novel stimuli (Kety 1972; Foote et al. 1980; Aston-Jones & Bloom 1981; Grant et al, 1988; Sara & Segal, 1991; Vankov et al, 1995; Bouret & Sara, 2004; Bouret et al, 2012), and the transient activation of LC neurons in response to unexpected stimuli is often thought to facilitate adaptation through an increase in behavioural flexibility (Bouret & Sara, 2005; Dayan & Yu, 2006, Einhauser et al, 2008; Nassar et al, 2012, Urai et al. 2017; Muller et al. 2019). In that frame, the magnitude of LC responses to sensory stimuli increases when these stimuli are unexpected, and therefore provide information about the state of the world that may be useful to guide subsequent behaviour. By contrast, perfectly expected stimuli provide little information, and so their presentation should not require the updating of behaviour. In other words, such a function could allow the activation of LC neurons to promote the adaptation of behaviour in response to a change in the state of the world (Aston-Jones & Cohen, 2005; Bouret & Sara, 2005; Yu & Dayan, 2005). Such a role for noradrenaline in behavioural flexibility has received strong support from pharmacological studies (Devauges & Sara, 1990; Tait et al, 2007; McGaughy et al, 2008; Jahn et al, 2018; Jepma et al, 2018). More recently, noradrenaline function has been extended to include the promotion of effortful actions (Ventura et al. 2008; Bouret & Richmond 2009; Zénon et al. 2014;

  The monkeys' willingness to engage in the task -measured as the attempt to squeeze the clamp after seeing the cue -was clearly affected by the information about the upcoming effort and reward levels (task condition) of the trial (fig 1C-D). In both sessions when noradrenergic (NA) or dopaminergic (DA) neurons were recorded from, the likelihood of engagement in the effortful action was negatively affected by the effort level (NA: β=-0.19±0.03, t(91)=-6.19, p<0.001; DA: β=-0.26±0.03, t(83)=-8.43, p<0.001) and positively modulated by the reward level (NA: β=0.27±0.04, t(91)=6.93, p<0.001; DA: β=0.31±0.04, t(83)=8.78, p<0.001). Moreover, monkeys' engagement was negatively modulated by the trial number (NA: β=-0.13±0.03, t(91)=-4.11, p<0.001; DA: β=-0.12±0.05, t(83)=-2.58, p<0.001) (fig 1D). Note that there was no significant difference between effort level, reward level and trial number weights in engagement across for NA and DA recording sessions (p=0.13, p=0.52 and p=0.88 respectively). This was confirmed by a 2-way ANOVA measuring the effect of task factor (effort and reward) and recording type (NA or DA) onto -β(effort) and β(reward): main effect of task factor F(1,348)=3.35, p=0.07) but no main effect of recording session type (F(1,348)=2.14, p=0.15) and no interaction (F(2,348)=0.23, p=0.63), meaning that engagement was affected in the same way by the two task factors in both types of recordings.

Figure 1 :

 1 Figure 1: Task and behaviour A) Task structure. Monkeys had to squeeze a clamp with a certain minimum intensity to obtain reward of a certain magnitude. During the whole trial, monkeys had to maintain fixation on a dot at the centre of the screen. If they broke the fixation, the trial restarted from the start after an inter-trial interval delay. A trial started with monkeys fixating the red dot, then a cue appeared indicating the effort and reward levels for the current trial. The dot turned green (Go signal) and monkeys had to squeeze the clamp to the minimum force threshold indicated by the cue. Upon reaching this threshold, the dot turned blue (Feedback) and remained blue as long as monkeys had to keep on squeezing. If monkeys maintain the effort long enough, they received the amount of reward indicated by the cue. B) Task design. Each trial corresponded to one of nine experimental conditions, defined by three levels of effort and three levels of reward. C) Probability to engage with the action as a function of effort and reward levels. Computed for all NA and DA sessions together.

Figure 2 :

 2 Figure 2: noradrenergic and dopaminergic neurons encoding of the task parameters and engagement at the time of cue A) Encoding of task parameters at the time of cue (0-500ms from cue onset). Dopaminergic neurons were sensitive to all three task parameters (effort level: p=0.05; reward level: p<0.001; trial number: p=0.01). Noradrenergic neurons were only significantly sensitive to the reward level (p<0.001). No significant difference between the encoding of effort level and trial number in noradrenergic and dopaminergic neurons (p>0.05). * p < 0.05; ** p ≤ 0.01; *** p ≤ 0.001. B) Noradrenergic and dopaminergic neurons reflect the engagement in a task condition. Linear regression of the probability to engage in a given task condition (effort and reward levels) for each session. Both populations encode significantly the probability to engage (p<0.05), no difference between the strength of encoding across populations (p>0.05). * p < 0.05; ** p ≤ 0.01; *** p ≤ 0.001. C) Noradrenergic and dopaminergic neurons' activity reflects the engagement on a trial-by-trial basis throughout the session. Logistic regression of Noradrenergic and dopaminergic neurons' activity on engagement in the action. Both populations predict the engagement in the action (p<0.05). * p < 0.05; ** p ≤ 0.01; *** p ≤ 0.001.

Figure 3 :

 3 Figure 3: Change in task condition is encoded by noradrenergic but not dopaminergic neurons A) Encoding of engagement and trial repetition in null space of task condition at cue (0-500ms from cue onset). Noradrenergic neurons encoded significantly the change in trial condition, the engagement and the interaction (all p<0.01). Dopaminergic neurons encoded only significantly the engagement (p<0.05). * p < 0.05; ** p ≤ 0.01; *** p ≤ 0.001 B) Example noradrenergic and dopaminergic neurons. Neuronal activity of two representative neurons around the cue onset (grey vertical line). Top: spike activity (raster and spike density function) of a noradrenergic neuron showing a strong activation at cue. The activation is stronger in engaged vs. nonengaged trials (all experimental conditions pooled together) and for informative vs. non-informative cues. Bottom: same but for a dopaminergic neuron showing an intermediate activation at cue onset. Its activity was greater for engaged than non-engaged trials but was not modulated by the task state change of the cue. Note, even though the baseline firing appears different in these example neurons, there was no reliable effect of engagement before cue onset. Each panel corresponds to a different number of trials (each trial is a line in the raster plot).

Figure 4 :

 4 Figure 4: Noradrenergic but not dopaminergic neurons were activated after the fixation break A) Only noradrenergic neurons population is activated at fixation break. Firing rate pre (-300 -0ms) and post (0 -300s) fixation break for both noradrenergic (left) and dopaminergic neurons (right). Points and error bars are mean ± SEM. Solid points indicate a significant activation (One-tailed T-test, p<0.05). For illustration purposes only, we have removed two dopaminergic neurons (with a non-significant activation at fixation break), whose firing rates were above 20 spikes/s from the display. B) Noradrenergic and Dopaminergic neurons' change in firing rate evoked by activity after fixation break (0-300ms from fixation break). The distributions are represented on a log-scale. Noradrenergic neurons population was significantly activated after the fixation break (p=0.001) but not dopaminergic neurons population (p=0.49). *** p ≤ 0.001.

Figure 5 :

 5 Figure 5: Noradrenergic neurons' activity predicts the engagement on the next trial A) Task structure after a fixation break.

  2004; Gan et al. 2010; Pasquereau & Turner 2013; Varazzani et al. 2015; Papageorgiou et al., 2016; Salamone et al. 2016). Why are dopaminergic neurons not sensitive to the information about task state change in our task? Dopamine neurons have long been reported to respond to salient novel stimuli (Strecker & Jacobs 1985; Ljunberg et al. 1992; Horvitz et al. 1997; Menegas et al.

  ; Foote et al. 1980; Aston-Jones & Bloom 1981; Abercrombie & Jacobs 1987; Berridge & Waterhouse 2003; Vazey et al. 2018). Noradrenaline has been implicated in signalling a need to provoke or facilitate a cognitive shift to adapt to the environment (Bouret & Sara 2005; Yu & Dayan 2005; Glennon et al. 2019). Here, noradrenergic neurons' sensitivity to change in task state at the time of cue could reflect a need to process the information about the current task condition.

  Three male rhesus monkeys (Monkey D, 11 kg, 5 years old; Monkey E, 7.5 kg, 4 years old; Monkey A, 10 kg, 4 years old) were used as subjects for the experiments. During testing days (Monday to Friday), they received all their water as reward on testing days and they received water according to their physiological needs on non-testing days. All experimental procedures were designed in association with the Institut du Cerveau et de la Moelle Epiniere (ICM) veterinarians, approved by the Regional Ethical Committee for Animal Experiment (CREEA IDF no. 3) and performed in compliance with the European Community Council Directives (86/609/EEC).

  standard deviation to the mean.

  deviation to the mean, t-values or F-values and p-values. 80. Zénon A, Sidibé M, Olivier E. Pupil size variations correlate with physical effort perception. Front Behav Neurosci [Internet]. 2014 [cited 2017 Apr 18];8.

  ; Hoskins et al. 2014; Le Bouc et al. 2016; Yohn et al. 2016; Zénon et al. 2016; Noritake et al, 2018). Moreover, our results are in line with studies demonstrating that dopamine release is strongly driven by the initiation of a purposeful action for reward (Phillips et al. 2003; Roitman et al., 2004; Syed et al. 2016).

  . Noradrenergic neurons recordings were performed on monkey A (29 neurons in 15 sessions) and monkey D (63 neurons in 38 sessions), midbrain dopaminergic neurons recordings were performed on monkey D (56 neurons in 38 sessions, sometimes simultaneously as noradrenergic neurons recordings) and monkey E (28 neurons in 19 sessions).

	Data analysis
	Data were analysed with Matlab software (MathWorks). Figures represent data ±

Acknowledgments

This research was funded by the ERC BIOMOTIV, the Paris Descartes University doctoral and mobility grants and the Wellcome Trust fellowships (MEW: 202831/Z/16/Z, JS: 105651/Z/14/Z). The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z).

Conflict of interest

The authors declare no competing financial interest.

Supplemental figure

Supplemental figure 1


Léo Dontot

Fernand Spiegelman

Sébastien Zamith

Mathias Rapacioli

Dependence upon charge of the vibrational spectra of small Polycyclic Aromatic Hydrocarbon clusters : the example of pyrene

Keywords: XX, XX, XX No code given

Infrared spectra are computed for neutral and cationic clusters of Polycyclic Aromatic Hydrocarbon clusters, namely (C16H10) (0/+) n=1,4 , using the Density Functional based Tight Binding scheme combined with a Configuration Interaction scheme (DFTB-CI) in the double harmonic approximation. Cross-comparison is carried out with DFT and simple DFTB. Similarly to the monomer cation, the IR spectra of cluster cations are characterized by a depletion of the intensity of the CH stretch modes around 3000 cm -1 , with a weak revival for n = 3 and 4. The in-plane CCC modes in the region 1400-2000 cm -1 are enhanced while the CH bending modes in the range 700-1000 cm -1 are significantly weakened with respect to the monomer cation, in particular for n = 2. Finally, soft modes corresponding to diedral fluctuations of the monomers within the central stack of the ion structure, possibly mixed with monomer folding, are also observed in the region 70-120 cm -1 .

Introduction

Clusters of Polycyclic Aromatic Hydrocarbons (PAHs) have been the subject of various experimental and theoretical investigations over the past decades due to their interest in several research fields. For instance, their role in flame chemistry is still under debate, as they could act as possible precursors of soot particles through oligomerization [1][2][3][4][5][6][7][8][9][10][11][12]. The optical and transport properties of PAH clusters are also investigated in the context of organic solar cell design [12][13][14][15][16][17][18][19][20][21]. Carbonaceous compounds involving PAH are studied as pollutants in both environmental and atmospheric science [22][23][24][25][26]. In astrophysics, PAHs have been proposed in the mid-eighties as precursors of mid-infrared emission bands [27,28] as well as contributors to the Diffuse Interstellar Bands (DIBs), a series of UV-Visible absorption bands [29][30][31][START_REF] Salama | Astrophys[END_REF]. Observations made with the Infrared Space Observatory and the Spitzer Space Telescope suggested that free flying PAHs result from the evaporation of larger grains, possibly PAH clusters [33][34][35]. PAH clusters are also suspected to contribute to some of the DIBs and the extended red emission and to play a role in the growth of interstellar PAHs [16,[START_REF] Rhee | Proc. Natl. Acad. Sci. Unit. States Am[END_REF][START_REF] Lemmens | [END_REF][38][39]. Not only there is a need for characterizing the spectral properties of neu-Correspondence to: mathias.rapacioli@irsamc.ups-tlse.fr tral clusters, but also to address their dependence upon charge, as previously done for free-flying PAH molecules, either ionized or protonated [40][41][42][43][44][45][46][47][48].

A number of studies focused on the characterisation of the structural properties of PAH clusters, in particular discussing the appearance of stack patterns [9,[49][50][51][52][53][54][55][56][57][58][59]. The structures of neutral clusters are governed by steric effects and long-range interactions. It is obviously necessary to use a methodology adequate to describe long range forces and in particular the dispersion forces. Unfortunately, highly accurate methods such as Coupled Cluster or MP4, fully relevant to deal with weakly bound closed shell molecular systems, are quite accurate if large basis sets are involved but computationally demanding and hence have not been used for PAH clusters larger than dimers. Their IR spectra have been investigated both experimentally and theoretically [59][60][61]. Ricca et al. gave a quite thorough IR theoretical harmonic characterization of various isomers of neutral pyrene clusters at the DFT+D3 level [59].

The theoretical investigation of cationic clusters is even more delicate. Indeed in addition to long range forces, the charge localization must me treated correctly. At the DFT level, traditional functionals undergo self-interaction artifacts leading to improper description of dissociated rad-ical cations [62]. Several schemes have been developed to correct those artifacts, such as the long-range shortrange schemes which allow to treat differently the short dynamical correlation and the long-range non-dynamical correlation [START_REF] Savin | Recent developments and applications of modern Density Functional Theory[END_REF][START_REF] Leininger | [END_REF][65][66]. Similar implementations have been done [67] with the context of Density Functional based Tight Binding (DFTB [68][69][70][71]), an approximation of DFT which is computationally more efficient than DFT and able to deal with larger systems. Other schemes can be used to avoid overdelocalization problems in charged molecular clusters. In the past decade, we have developed a model combining Configuration Interaction with the DFTB (hereafter labeled DFTB-CI) [72], which is an adaptation of the DFT-CI scheme [73] to the DFTB framework.

The coupling of DFTB and DFTB-CI with a global exploration scheme allowed us to obtain low energy structures for cationic and neutral pyrene clusters [74], providing binding energies and ionisation potentials in agreement with experimental measurements [75,76]. We report, in the present work, the IR spectra of cationic and neutral pyrene clusters, namely dimers, trimers and tetramers, obtained with DFTB-CI for cations and DFTB for neutrals. In particular, we address the IR spectra dependence upon size and charge. We also present comparison with first principle DFT spectra. In the next section, we briefly describe the scheme used to compute these spectra before presenting and discussing the results.

Method

The IR spectra presented for the most stable structures of pyrene clusters are computed here within the double harmonic approximation. Three electronic structure methods have been used to compute these spectra, namely DFTB for neutrals, DFTB and DFTB-CI for the ions and DFT for common reference calculations. The DFT calculations have been performed with the Gaussian09 [START_REF] Frisch | Gaussian 03 Revision A.1[END_REF] package using the B3LYP functional with D3 dispersion correction combined with the extended basis cc-pVDZ. We quickly summarize the essential ingredients of the DFTB scheme used here [68][69][70][71]. In its most common SCC (selfconsistent-charge) formulation [70], DFTB is derived from DFT through a second order expansion of the DFT energy around a reference density, taken as the sum of isolated atomic densities. The neglect of three-center integrals allows for building the DFTB Kohn Sham operator from two-center pre-tabulated DFT data, Mulliken definition of the atomic charges and Hubbard atomic parameters. In the present work, we use the set of matsci-0-3 parameters [START_REF] Frenzel | Semi-relativistic, self-consistent charge Slater-Koster tables for density-functional based tight-binding (DFTB) for materials science simulations[END_REF] as well as the weighted Mulliken (Wmull) charge scheme [START_REF] Simon | [END_REF]80], allowing for a better description of intermolecular coulomb interactions, and a dispersion correction scheme [50]. Note that the use of different charges also improves the dipole moments, a crucial quantity for the determination of IR spectra [81]. In the case of cationic clusters, we will also work in the framework of the configuration interaction DFTB-CI scheme [72] to properly describe the charge delocalization over different units. Briefly, the DFTB-CI scheme is implemented in a basis of valencebond type configurations Φ + Ak obtained via DFTB with a constraint of charge localization on a given molecule of the cluster. The DFTB-CI energies are thus the eigenvalues of a non-orthogonal CI problem whose size is equal (k=HOMO only) or scales (k=HOMO,HOMO-1...) as the number of molecules, corresponding to ground state eigenvectors Ψ + 0 incorporating charge delocalization as a combination over the charged localized configurations

Ψ + 0 = Ak c 0 Ak Φ + Ak (1)
Note that, in the case of the cationic monomer, DFTB-CI is reduced to simple DFTB. The DFTB and DFTB-CI calculations have been carried out with the deMonNano package [START_REF] Heine | deMon-Nano Experiment[END_REF]. In the following and for sake of simplicity, we will generally refer to DFT, DFTB or DFTB-CI, the previously mentioned calculation details (+D/ +D3/ Wmull/ SCC) being implicit. All presented spectra result from convolution of the lines originating from the diagonalisation of the weighted Hessian matrix with lorentzian functions with half-width 15 cm -1 .

Results

We start here with the monomer. The present subsection is not supposed to bring new information about the IR spectra of the pyrene monomer and its cation, abundantly documented in the literature but to measure the performance of DFTB as an approximate DFT method for the vibrational observables of this constituting molecule. The spectrum of neutral pyrene has been experimentally determined by a number of authors, either in cryogenic matrices [41,[START_REF] Joblin | [END_REF] or in gas phase [86,[START_REF] Joblin | [END_REF]. Joblin et al. [START_REF] Joblin | [END_REF] provided full range spectroscopy of pyrene in neon matrices at 4K, the lines with largest intensity occurring around peaks at 713, 844, 1087/1097, 1605 and 3053/3064 cm -1 while the gas phase experiments of Malteseva et al. [86] only concerned the range 3044-3118 cm 1 . Essentially, the region 700-900 cm -1 corresponds to CH out of plane bending modes, that between 1000 and 1800 cm -1 to in-plane CCC or CH bending (possibly coupled) modes and the features around 3000 cm -1 to CH stretching modes. Some weaker intensity patterns are also observed in the region 1405-1430 cm -1 . A number of theoretical studies, either at the HF level [41] or at the DFT level [40,42], were devoted to the IR bands assignments. In most calculations, the double harmonic approximation was used, corrected by scaling factors. Mackie et al. [87] and Mulas et al. [88] have explored theoretically the importance of anharmonicities. The work of Mulas et al. is based on a DFT potential surface with the B97-1 hybrid functional, which provides, after applying a scaling factor, harmonic lines (largest intensities at 713, 845, 1089, 1606 and 3057/3074 cm -1 ) in close correspondence with the experimental results. Anharmonicities are shown to induce small shifts of a few cm -1 depending on the spectral region. More significant C 16 H 10 DFTB IR wavenumber (cm -1 ) Fig. 1. Harmonic IR spectra of neutral and cationic pyrene monomer with DFT/B3LYP and DFTB. The vertical dashed lines indicate the experimental frequencies of the major intensity modes for neutral [START_REF] Joblin | [END_REF] and cationic [41,84,85] pyrene changes are observed for the intensities, due to mode mixing. We will take as reference here standard DFT calculations achieved using the hybrid B3LYP functional, the most commonly used to calculate IR spectra. Despite DFT calculations already exist [40,42,88] for the monomer, we have repeated them here to have a global common benchmark with the same functional and the same basis set for monomers and small clusters, neutral and singly charged. It can be seen in figure 1 that DFT/B3LYP yields lines at 746, 878, 1112/1196, 1455, 1648 and 3186/3196 cm -1 . The DFTB results of the neutral monomer reproduce reasonably the DFT spectrum, with three peaks at 722, 816 and 2929 cm -1 and very weak bumps at 1175 and 1858 cm -1 . The relative errors on the DFT peaks vs the experimental values are in the range of 3 to 10 percent. Fortuitously, the errors of DFTB on the three main peaks vs the corresponding experimental values above are found to be below 5 percent. One can however observe that in the region 900-1700 cm -1 (in plane CCC stretching modes), the intensities of the DFTB bands almost completely vanish, while the DFT peaks remain small but still visible, more consistent with the experimental results [41,[START_REF] Joblin | [END_REF]. Despite these differences, the qualitative assignment in DFT and DFTB is consistent. In the following, since we will be mostly interested in the changes induced by clustering effects, we will not apply any scaling factors.

The IR spectrum of the singly charged pyrene monomer has also been investigated experimentally either from ab-sorption in argon matrices [41] or in gas phase via the Single Photon Infra Red emission technique [84,85] (SPIRES). The spectrum is strongly different from that of neutral pyrene with a vanishing intensity for the stretching CH modes around 3000 cm -1 and lines with significant intensities at 685, 862, 961, 1125, 1217, 1245, 1362/1459, 1420, 1441 and 1550 (the most intense). This large change was reported theoretically [41,40,42] and interpreted by Torii et al. [89]. In their interpretation the collective inplane vibrational motion of the carbon atoms couples with strong fluctuations of the dipole moment over the molecule skeleton. This coupling induces significant charge fluxes which dominates the in-plane CH stretch intensity contributions to the spectrum. All together, these give rise to a much richer pattern in the 1000-2000 cm -1 region and vanishing intensity around 3000 cm -1 It can be seen in Figure 1 that these trends are correctly reproduced both at the DFT level, as previously reported [41,40] Fig. 2. Harmonic IR spectra of (C16H10)n=1,4 clusters from DFT/B3LYP (top) and DFTB (bottom) calculations. For each method, two zoom views in the 700-900 cm -1 range and around 3000 cm -1 regions, respectively, are shown below the full spectrum graph. We now comment results obtained for clusters. Crossed comparisons of the IR spectra computed at the various levels of theory are given for neutral and cationic pyrene clusters in supplementary materials. The spectra obtained for neutrals are reported in Fig. 2. Note that the geometries involved in the present work and shown in Figure 3 are the lowest ones found with DFTB global optimization simulations in our previous work [74](or the same consistently relaxed in the DFT/B3LYP approach). They are different from the ones explored by Ricca et al. [59]. The dimer and the trimer are stacks presenting twisting, while the tetramer consists of a deformed twisted stack with a side molecule. At both the DFTB and DFT levels, the IR spectra of the neutral clusters are very similar to those of the monomer and the size evolution is hardly visible on the upper plots of Figure 2 showing the full spectrum. The peak modes around 746 and 878 cm -1 in DFT are now associated with in-phase out of plane CH bending of the molecules in the stack, while the peak around 3190 cm -1 is actually a quite narrow band associated with various CH stretches on the different molecules. The bottom insets of the figure show that the lines in clusters present weak shifts with respect to the monomer lines. With DFT/B3LYP (resp DFTB), the peak maxima of the CH bending modes at 746 (resp 878 ) cm -1 are redshifted by -4 (resp -5) cm -1 for the dimer and -6 (resp -7) cm -1 for the trimer. This is qualitatively consistent although smaller than the redshifts previously calculated by Ricca et al. [59] for the components of those lines in various geometries (in the range -5/-8 cm -1 for dimers and -8/-13 cm -1 for the trimers) and the redshifts measured experimentally by Roser and Ricca [60]. The DFT peak maximum of the CH stretching band at 3190 cm -1 is almost not affected by size (± 2cm -1 ). The DFTB results are essentially consistent with the DFT results, with spectral shapes very weakly affected by size. Let us mention that the intensity weakness of the mode at 722 cm -1 observed for the monomer persists for larger sizes. The 816 cm -1 peak is also redshifted up to the trimer, (-4 cm -1 ), slightly less than the corresponding DFT peak (-7 cm -1 ) at 878 cm -1 . Note however that in the tetramer case, the shift with respect to the monomer is cancelled, certainly due to the hindrance induced by the side molecule. The peak position at 722 cm -1 is almost unaffected by size. In contrast, the maximum of the CH stretch band is shifted to the red from 2932 to 2927 cm -1 , a trend also observed experimentally [60]. Note that for the two peaks at 746 and 878 cm -1 (respectively 722 and 816 cm -1 with DFTB), DFT spectra seem to show a monotonic increase of the redshift with the addition of molecules, which is much less stringent at the DFTB level. This could stem from the different dispersion terms or also from the pointwise charge approximation used in the Coulomb contribution. Obviously, the present results must be taken with care because of the inherent approximations of DFTB. They do not include anharmonicity, whose magnitude is also of a few cm -1 on the monomer [88], certainly transferable and possibly enhanced in clusters. Finally one can also see that neither in DFT nor in DFTB, the intermolecular modes, associated with low frequencies, have significant intensities in the spectra, certainly because in the neutral species, those modes are characterized by vanishing dipole variations either within the monomers or over the cluster.

The geometries of the cationic clusters, taken from Dontot et al. [74], are shown in Figure 3. They are similar however not identical to those of neutral clusters, since the intermolecular twists within the stack are different. The spectra of cationic dimers (Figure 4) present the same main trends as the one of the cationic monomer, characterized by a weak intensity of the CH stretching mode in comparison with the neutrals. Concerning the relative intensities of the bands in the 700-1000 cm -1 region versus those in the 1000-2000 cm -1 region, the charge effect is even more pronounced in the dimer as compared to that previously reported for the monomer, as the bands in the range 700-1000 cm with and without the CI scheme. The first observation is that in cationic clusters, oppositely to neutral clusters, size effects have a non negligible influence on the spectra, as can be seen in Figure 4. In the dimer, obviously both the DFTB and DFTB-CI schemes lead to the same charge delocalization pattern, that is an equal sharing of the charge over the two units. The DFT intensities of the maxima at 1395 and 1459 cm -1 are inverted, producing a major peak located around 1432 cm -1 . The peak located in the monomer around 1613 cm -1 is now blueshifted by almost 30 cm -1 . The same merging is observed in the dimer with DFTB and DFTB-CI for the lines at 1528 and 1572 cm -1 merging into a single peak at 1590 cm -1 . The DFTB-CI band at 1781 cm -1 is also blueshifted to the region 1801-1826 cm -1 . A similar behaviour is observed for the larger sizes n=3 and 4. Let us notice nevertheless that for the trimer and the tetramer, the band intensities in the regions 698-762 and 816-826 cm -1 tend to increase, a trend that can probably be attributed to the fact that the charge (expressed in units of electrons) is now shared by several units and its average decreases on each one namely (DFTB-CI values) 0.46/0.27/0.26 in the trimer and 0.49/0.25/0.24/0.02, in the tetramer, the side molecule being almost neutral. When the cluster size increases, the contribution of neutral molecules should tend to increase. Interestingly, this can be observed (Figure 5, right) in the re-emergence for sizes n=3 and 4 of a weak feature around 2945 cm -1 , the region of the CH stretch mode, the most active in the neutral monomer and almost absent in the monomer cation. This feature is further enhanced in DFTB-CI calculation. In the tetramer, one may notice a triplet peak structure in the DFTB-CI spectrum at 2769, 2854 and 2939 cm -1 , due to the influence of the side molecule above the stack. Finally, another feature which is specific of the ions concerns the intermolecular modes and the appearance of a weak but visible intensity pattern at very low frequency around 122 cm -1 as can be seen in the left panel of Figure 5. In the trimer, a mode at 79 cm -1 (DFTB-CI) is associated with a change of the diedral angles between almost internally rigid monomers. The mode at 122 cm -1 couples this diedral fluctuation with folding of the monomer carbon skeleton. In the neutrals, those modes had vanishing intensities. In the cation, the small but existing intensities of those modes may reflect charge fluctuations between the various molecules. Similar modes are observed in the tetramer at 79 (diedral) and 129 cm -1 (diedral coupled with monomer folding).

At this point, it may be worth to comment about the difference for ions between DFTB and DFTB-CI. A partial relocalization of the charge is observed in DFTB-CI vs DFTB, namely 0.46/0.27/0.26 and 0.49/0.25/0.24/0.02 for the trimer and the tetramer respectively instead of 0.35/0.32/0.30 and 0.38/0.30/0.30/0.02 in simple DFTB. This does not considerably affect the cluster spectra. Nevertheless, the account of non-dynamical correlation vs mean field charge average and the avoidance of self-interaction in DFTB-CI, especially for extended systems, probably provides a better balance between neutral and ionized monomers. Indeed DFTB-CI explicitly considers the resonance of configurations with the charge based on a sin-gle monomers, while simple DFTB (and to some extent DFT, even though hybrid methods avoid a part of selfinteraction) intrinsically considers average charges on the monomers, which may not be equivalent in terms of dipole fluctuations. This seems to be responsible for a more pronounced account of the intensity of the very soft modes and of the triplet structure of the CH stretch mode of the tetramer.

We now focus on the distribution of vibrational frequencies. As can be seen in figure 6 (top) for dimers and tetramers, the distribution of these frequencies hardly depends on the cluster charge. The largest discrepancies occurs for the C-H stretching modes around 3000 cm -1 and are already present in the monomers. We compare now the computed vibrational frequencies with those resulting from an extrapolation model [75], allowing to address larger sizes. In this approach, one considers that the total number of modes 3nN at -6 of a given cationic cluster of size n can be simply separated in n inter = 6n -6 intermolecular modes and n intra = n(3N at -6) intramolecular modes, where N at is the number of atoms in the pyrene molecules. The intramolecular modes are obtained as the addition of the monomer cation modes ω + 1 , ω + 2 , ..., ω + 72 and those of n -1 neutral monomers (n -1) × ω 0 1 , ω 0 2 , ..., ω 0 72 . Intermolecular modes are linearly extrapolated between ω =13 cm -1 and the lowest frequency monomer mode :

ω i = ω + (ω + 1 -ω) (i -1) n inter , i = 1, n inter (2)
Despite the crudeness of this model (the charge fluctuation over several molecules is completely neglected, in-tramolecular modes are considered unperturbed, etc.), a fairly good agreement is obtained when constructing the modes of the dimer and tetramer and comparing them to the actual DFTB-CI calculation, as shown in the difference spectrum (Figure 6, bottom). For the dimer, the frequencies are well reproduced for the cation and the agreement is excellent for the neutral. Of course, the largest the cluster, the minor the contribution of the charge. For the tetramer both neutral and cation frequencies are equally well reproduced. However, a clear departure is observed for some of the high frequency CH modes: this is due to H atoms pointing towards the plane of the side pyrene molecule (see figure 3 for the structure of the tetramer) and such steric effects cannot be reproduced by this additive model. The model can however be applied to arbitrarily large clusters, thus approaching the bulk limit and can be used to determine heat capacities in the harmonic approximation for the frequencies. Figure 7 shows the evolution of the heat capacities from the small cluster cations and up to 2000 molecules. For this largest size, we find a heat capacity in reasonable good agreement with the pyrene bulk experimental one [90], as can be seen in figure 7, except obviously for the peak associated to a phase transition, out of reach by the present additive model. To some extent, this agreement of an intensive observable is somewhat consistent with the reasonable reliability of the present DFTB monomer vibrational structure discussed above despite the various approximations inherent to DFTB and the harmonic approximations.

Conclusion

We have reported a comparison of normal mode analysis for pyrene clusters containing up to 4 units, involving DFT, DFTB and DFTB-CI in the full range spectrum up to ≈ 3300 cm -1 . In the case of neutrals, little change is observed with size, both at the DFT and DFTB levels. The present DFTB IR spectra are generally consistent with the DFT/B3LYP ones and also with the previous results of Ricca et al. [59], even though quantitative shifts of a few cm -1 are quite delicate to estimate accurately, whatever the above methods. The situation of the pyrene cation clusters is significantly different from that of neutrals and essentially follows that of the cation monomer up to size n=4. The spectra show a strong attenuation of the CH stretch band around 3000 cm -1 and a strong reduction of the intensity between 700-1000 cm -1 , the region of the out of plane CH bending. The bands in the 1000-2000 cm -1 spectral range conserve their strong intensity from the cationic monomer to the tetramer. However, the CH stretch modes recover some perceptible intensity when the number of units increases. Another noticeable feature is that, while the intermolecular modes have almost no intensity in the neutrals, diedral fluctuation modes within the trimer stacks become somewhat active in the cationic clusters, possibly coupled with monomer folding motion.

Obviously, the question may arise about the challenge and ability of DFTB and DFTB-CI to address such small vibrational shifts induced by size or the transferability to different species. Indeed, while the qualitative change in the spectra due to charge are correctly accounted for as shown in the above results for the monomer, some absolute frequencies show errors of the order of 100-200 cm -1 . However, it was shown in a number of previous studies dealing with IR spectroscopy (harmonic and also including anharmonicities from molecular dynamics simulation) of various systems that spectral shifts are well accounted for, despite the discrepancies in the absolute line positions. This includes cases with significant spectral changes (varying the charge and/or the PAH size) as well as delicate shifts due to perturbations induced by clustering [91,81,92,93], chemical attachment [94,81] or matrix environment [95,96]. In neutral molecular clusters, clearly the bonding relies on a phenomenological dispersion contribution in DFTB (+D) or in DFT(+D3) and the present results seem to be reasonably consistent with the previous DFTB+D3 publication [59], despite the differences in the equilibrium structures. Thus it seems likely that the trends determined in the present work are correct and possibly transferable to other molecular clusters of the PAH family with larger units and/or larger sizes and possibly complexes, even though higher level calculations such as Coupled Cluster carried out in sufficiently large basis sets, nowadays out of reach with sufficiently extensive basis sets, are certainly desirable.

We hope that the present study brings some new insight in the spectroscopy of PAH-containing compounds and possibly help for the detection of PAH clusters or small grains in interstellar or circumstellar media. A perspective of the present work would be to investigate the anharmonic effects via molecular dynamics simulations which is possible either with DFTB or DFTB-CI and also potentially to explore the evolution of the IR spectra with temperature. Comparison of the bulk heat capacity (black line) [90] to the calculated ones using the extrapolation model for the vibration modes described in the text, for: the monomer (green dashed line), the tetramer (blue point line) and a cluster of 2000 pyrene molecules (red line).

Fig. 3 .

 3 Fig. 3. Geometries of neutral (top) and cationic (bottom) pyrene clusters, n=1-4 from left to right. For each structure, side (left) and top (right) views

Fig. 4 .

 4 Fig. 4. Harmonic IR spectra of (C16H10) + n=1,4 clusters from DFT/B3LYP (top), DFTB (medium) and DFTB-CI (bottom) calculations.

Fig. 5 .

 5 Fig. 5. Zoom views of the harmonic IR spectra of cationic pyrene clusters (n=1-4, from bottom to top) in regions 0-350 cm 1 (left) and 2700-3100 cm -1 (right), comparing DFTB and DFTB-CI calculations.

Fig. 6 .

 6 Fig. 6. Harmonic frequencies computed at the DFTB-CI level for neutral and cationic dimers (a) and tetramers (c). Differences between frequencies at the DFTB-CI level and from the extrapolation model for the dimer (b) and the tetramer (d) (see text).

  Fig.7. Comparison of the bulk heat capacity (black line)[90] to the calculated ones using the extrapolation model for the vibration modes described in the text, for: the monomer (green dashed line), the tetramer (blue point line) and a cluster of 2000 pyrene molecules (red line).

  , and DFTB level. The main DFT peaks are at 726, 895, 1256, 1395/1460 and 1613/1615 cm -1 . The main DFTB maxima point at 684, 841, 1323, 1529/1572 and 1781/1784 cm -1 . The analysis shows that the same types of modes are observed for the lines obtained at the DFT wavenumbers 726, 895, 1256 and 1613/1615 cm -1 and at the corresponding DFTB values at 684, 841, 1323 and 1781/1784 cm -1 respectively. The mixing of the analogous in-plane CCC and CH modes is however different for frequencies 1395/1460 in DFT cm -1 (1529/1572 in DFTB), due to de-

	IR Intensity (km/mol)	(C 16 H 10 ) n DFT/B3LYP	trimer dimer monomer
	0	500	1000	1500	2000	2500	3000	3500
				wavenumber (cm -1 )
	IR Intensity (km/mol)			IR Intensity (km/mol)	0 50 100 150 200
		750 800 850 900 950	3160 3180 3200 3220 3240
		wavenumber (cm -1 )			wavenumber (cm -1 )
	IR Intensity (km/mol)	(C 16 H 10 ) n DFTB		tetramer trimer dimer monomer
	0	500	1000	1500	2000	2500	3000	3500
				wavenumber (cm -1 )
	IR Intensity (km/mol)			IR Intensity (km/mol)	0 50 100 150 200
		700 750 800 850 900	2900 2920 2940 2960
		wavenumber (cm -1 )			wavenumber (cm -1 )

  -1 (CH out of plane bending modes) have very weak intensity. It is worth mentioning that these trends are well reproduced at the DFTB level, computed

	IR Intensity (km/mol)	0	(C 16 H 10 ) n + DFT/B3LYP	dimer monomer
		0	500	1000	1500	2000	2500	3000	3500
				wavenumber (cm -1 )
	IR Intensity (km/mol)	0	(C 16 H 10 ) n + DFTB		tetramer trimer dimer monomer
		0	500	1000	1500	2000	2500	3000	3500
				wavenumber (cm -1 )
	IR Intensity		(C 16 H 10 ) n + DFTB-CI	tetramer trimer dimer monomer
		0
		0	500	1000	1500	2000	2500	3000	3500
				wavenumber / cm -1

Acknowledgements

The authors thank the CALMIP HPC center for computational support. L. D. acknowledges ERC for support under grant ERC-2013-Syg-610256-NANOCOSMOS and EUR grant NanoX n 080876 in the framework of the "Programme des Investissements d'Avenir".