Adaptive arousal regulation: Pharmacologically shifting the peak of the Yerkes–Dodson curve by catecholaminergic enhancement of arousal

Significance

Performance peaks at moderate arousal levels, as described by the Yerkes–Dodson law. We investigated the neuromodulatory underpinnings of this law by measuring decision-making accuracy and arousal fluctuations (via pupillometry) while pharmacologically enhancing humans’ overall arousal state. The catecholaminergic agent atomoxetine increased overall arousal (e.g., heart rate, blood pressure) but left the inverted U-shaped arousal–performance curve intact. This shows that human performance is optimized at a mean arousal level, irrespective of overall arousal state, a phenomenon reminiscent of normalization observed in other neuroscience domains. Computational modeling suggested that catecholaminergic enhancement modulated neural circuits responsible for sensory evidence accumulation. The model generated testable predictions about the underlying mechanisms and involved brain areas, further elucidating how performance flexibly adapts to arousal state changes.

Abstract

Performance typically peaks at moderate arousal levels, consistent with the Yerkes–Dodson law, as confirmed by recent human and mouse pupillometry studies. Arousal states are influenced by neuromodulators like catecholamines (noradrenaline and dopamine) and acetylcholine. To investigate their contributions to this law, we pharmacologically enhanced arousal while measuring human decision-making and spontaneous arousal fluctuations via pupil size. The catecholaminergic agent atomoxetine increased overall arousal and shifted the entire arousal–performance curve, suggesting a relative arousal mechanism where performance adapts to arousal fluctuations within arousal states. In contrast, the cholinergic agent donepezil did not measurably affect arousal or the curve. We modeled these findings in a neurobiologically plausible computational framework, showing how catecholaminergic modulation alters a disinhibitory neural circuit that encodes sensory evidence for decision-making. This work suggests that performance adapts flexibly to arousal fluctuations, ensuring optimal performance in each and every global arousal state.

Behavioral performance typically peaks during mid-level arousal—a relationship described by the classic Yerkes–Dodson law and recently confirmed in humans and mice (pupillometry) studies (1–7). Arousal fluctuates continuously across several time scales (e.g., days, hours, minutes, seconds) and these fluctuations are primarily influenced by the catecholaminergic (CA) and cholinergic (ACh) neurotransmitter systems (5, 8–10), which regulate the balance between sympathetic (fight or flight mode) and parasympathetic nervous system activity (rest and digest mode). The neuromodulator systems that regulate arousal also modulate pupil dilation (5, 8, 11–16), making non-luminance-mediated changes in pupil size a robust marker of spontaneous fluctuations of arousal, often referred to as “pupil-linked arousal” (5, 17–19).

Given that pupil size reflects the combined influence of various neuromodulatory systems (besides ACh and catecholamines e.g., also serotonin and orexin) (8, 11, 12, 14, 15, 20), previous work using pupil-linked arousal could not effectively distinguish the individual contributions of each neuromodulator to the Yerkes–Dodson law. Precise manipulation of these systems is crucial for unraveling their distinct roles in arousal–performance dynamics. Clarifying these mechanisms is not just a fundamental question in neuroscience, it also has significant implications for treating conditions like attention deficit hyperactivity disorder, anxiety, and sleep disturbances, which all involve arousal dysregulation (21, 22). Additionally, disentangling the influence of neuromodulators on performance could enhance human performance in high-stakes environments (e.g., aviation, emergency response) by informing strategies to optimize arousal levels.

Here, we pharmacologically increase neuromodulation using two different drugs that each enhance one main neuromodulatory driver of cortical arousal (5, 9, 23) to assess their relative roles in the inverted U-shaped arousal–performance relationship. The first drug, Donepezil (DNP), is a selective cholinesterase inhibitor that increases ACh levels by hindering the breakdown of acetylcholine (24). The second drug, atomoxetine (ATX), increases noradrenaline (NA) and dopamine (DA) levels by blocking their reuptake into the presynaptic terminal via NA transporters, serving as a relatively selective noradrenaline reuptake inhibitor (as both NA and DA are CAs, we refer to ATX as a catecholaminergic drug) (25). Both neuromodulators have been shown to affect overall performance in simple decision-making tasks [ACh: (26–28), catecholamines: (27, 29–33)]. By comparing the relationship between pupil-linked arousal fluctuations and performance in these enhanced neuromodulation states to a placebo control condition (PLC), we aim to test their respective roles in the pupil-linked arousal–performance relationship. While our study was designed to assess the influence of both CAs and ACh, our results primarily inform the role of catecholamines, because DNP had no measurable effect on arousal or the arousal–performance curve.

In addition, this pharmacological approach allows us to address another key open question about the Yerkes–Dodson law: whether it is absolute (and fixed) or relative (and adaptive). The common conception is that there is a fixed relationship between arousal and performance, with optimal performance during moderate arousal states, and inferior performance during states of low and high arousal. In this scenario, performance depends on the absolute arousal level and therefore the Yerkes–Dodson curve spans the entire arousal spectrum (absolute arousal scenario). Consequently, once arousal surpasses the moderate (“optimal”) level, performance will keep declining with increasing arousal, due to the selective sampling of only the right (descending) half of the curve (Fig. 1A). Alternatively, when an organism moves from a relaxed context to a more stressful context, the neural circuitry may adapt to these new circumstances. In this relative arousal scenario, the relationship between arousal fluctuations and task performance is inverted U-shaped within each context (Fig. 1B). In other words, even though the position of the pupil-linked arousal–performance relationship might change due to overall arousal changes, its shape remains intact. Such flexible adjustments to environmental conditions, reminiscent of (divisive) normalization (34–36), have been observed in other domains in neuroscience as well. For example, neuronal responses in V1 to a stimulus can adapt based on the average contrast in the visual field (35), and in mouse hippocampal network activity, neurons can dynamically scale their firing range depending on the size of the surrounding environment of the animal (37). We combine pharmacologically induced arousal state manipulations with simultaneous and continuous measurement of pupil-linked arousal fluctuations and behavioral psychophysics to arbitrate between the absolute and relative arousal scenario in humans. In addition, we use computational modeling to gain a better understanding of the empirical results.

Fig. 1.

Scenarios, tasks, arousal modulation, and pupil analysis. (A) Schematic of the absolute and (B) relative arousal scenario. (C) Outline of a session including drug administration scheme. (D) Schematic stimuli of the detection and discrimination tasks. (E) Histogram of prestimulus pupil size split by drugs. (F) Mean prestimulus pupil size modulation for DNP and ATX as compared to PLC. (G) Prestimulus pupil variance (standard error of the mean: SEM) modulation for DNP and ATX as compared to PLC. (H) HR modulation and (I) BP modulation for DNP minus PLC and ATX minus PLC (referred to as ATX and DNP respectively on the x-axis). (J) Example of the continuous pupil signal of seven trials with baseline windows [−0.5 s to 0 s to stimulus onset] divided over five bins. Colors indicate pupil size bins; see legend in (K). (K) Example data of three sessions of the discrimination task of a sample participant. Note that bins are determined for each task run (240 to 300 trials, depending on the task) separately, and that the boundaries of the bins thus differ between runs. Each dot represents the baseline pupil size of a trial, and the colors indicate bin membership (1 to 5). Black vertical lines indicate mean pupil size of each run. ***P < 0.001, **P < 0.01, statistics in text.

Results

Participants (N = 28) took part in three all-day (9 am to 4 pm) experimental sessions in which they either received PLC, DNP (5 mg), or ATX (40 mg) in randomized order (Fig. 1C). The administration scheme ensured that blood concentration levels for DNP and ATX peaked when the tasks commenced (Methods). All participants performed four different visual decision-making tasks: two Gabor detection tasks (presence/absence judgment) and two Gabor orientation discrimination tasks (left/right tilt judgment, Fig. 1D). We recorded on average 6,337 trials per participant, resulting in a total of 177.460 trials. Performance was matched across all tasks and titrated to 75% correct (mean accuracy across tasks was 75.7% for the Placebo (PLC)).

First, we assessed whether the pharmacological agents ATX and DNP had increased physiological arousal as compared to PLC. To index arousal, we measured prestimulus pupil size, prestimulus pupil size variation, heart rate (HR) and mean arterial blood pressure (BP). We observed a clear increase in mean prestimulus pupil size, indicative of a heightened arousal state, after ingestion of ATX as compared to PLC [t(27) = 4.78, P < 0.001; Fig. 1 E and F; more statistical tests in SI Appendix]. In addition, ATX increased the range (i.e., variance) of arousal fluctuations, evidenced by a larger variation in prestimulus pupil size [t(27) = 3.43, P = 0.002; Fig. 1G]. Last, ATX increased HR and BP [HR: t(27) = 4.11, P < 0.001; BP: t(27) = 4.33, P < 0.001; Fig. 1 H and I]. DNP did not affect any of these measures (more details in SI Appendix, also see ref. 32). Previous nonclinical studies that report physiological responses of 5 mg DNP (38, 39) also did not observe consistent subjective or physiological effects of DNP. However, even in the absence of such autonomic markers, 5 mg DNP has been shown to induce changes in task behavior and associated neural activity patterns (26, 28, 32, 38–45). Therefore, and because DNP may still alter the shape of the arousal–performance curve, we still performed the intended analyses for DNP.

Next, we confirmed that the arousal–performance relationship was indeed inverted U-shaped in the PLC condition, as we previously showed for both visual as well as auditory sensory input (1). Identical to our previous study, we used mean pupil size in the 500 ms leading up to target onset as a proxy for arousal. We initially assigned each trial to 1 of 20 equally populated bins based on prestimulus pupil size (Fig. 1J; visualized for five bins). We performed this binning procedure for each run of all tasks separately, thereby focusing on arousal fluctuations that occur over the course of single experimental runs (i.e., blocks, Fig. 1K). For each pupil bin we calculated Signal Detection Theoretic (SDT) sensitivity [d’ (46); SDT’s criterion effects are reported in SI Appendix, Fig. S1] and mean reaction times (RT). Note that an increase in performance is equivalent to a decrease in RT, which means that the expected relationship between arousal and RT is U-shaped (not inverted) (1). We used linear mixed models (LMM) and formal model comparison to assess whether the pupil–performance relationship was linear or quadratic. A difference in Akaike Information Criterion (AIC) (47) or Bayesian Information Criterion (BIC) (48) values of more than 10 (i.e., ΔAIC or ΔBIC > 10) is considered evidence that the winning model captures the data significantly better (49). Both ΔAIC and ΔBIC were strongly in favor of a quadratic pupil–performance relationship for d’ and RT (all ΔAIC > 20.1, all ΔBIC > 15.8; Fig. 2 A and D, green dots; SI Appendix, Table S3) in the PLC condition, in line with previous work (1, 17–19, 50, 51).

Fig. 2.

Arousal–performance curves. (A) Perceptual sensitivity (d’) for small to large prestimulus pupils for all tasks combined (20 bins), (B) for discrimination tasks (5 bins) and (C) for detection tasks split for PLC, DNP, and ATX. (D) RT for small to large prestimulus pupils for all tasks combined (20 bins), (E) for discrimination tasks (5 bins) and (F) for detection tasks. Polynomial regression lines for first- and second-order fits (only significant fits are shown; significance is indicated in the Bottom Right of each panel, shading reflects SEM across subjects). Error bars represent SEM across subjects after first demeaning the bin-wise data points separately per subject (52). Brackets above the curves indicate significant pupil size differences between drug conditions, indicating the rightward shift for ATX vs. the rest. ***P < 0.001, **P < 0.01, *P < 0.05, means and statistics in SI Appendix. The consistency of the inverted U-shaped arousal–performance relationship across subjects is further shown in SI Appendix, Fig. S3 (showing second-order beta coefficients per subject).

If ACh or catecholamines play a significant role in the modulation of performance, we expect DNP or ATX to change the shape and/or position of the pupil-linked arousal–performance relationship. In the DNP condition, for which pupil-linked arousal seemed unmodulated (i.e., position on the arousal spectrum was unaltered), the shape of the arousal–performance curves appeared unaffected and formal model comparison favored the quadratic model for d’ and RT (all ΔAIC > 30.1, all ΔBIC > 25.8; Fig. 2 A and D, blue dots; SI Appendix, Table S3). For ATX, ΔAIC and ΔBIC were also strongly in favor of the quadratic model for both sensitivity and RT in the ATX condition (all ΔAIC > 36.6, all ΔBIC > 32.2; Fig. 2 A and D, red dots; see also SI Appendix, Table S3). Strikingly, the shape of the arousal–performance relationship seemed unaffected under ATX even though the position of the entire quadratic curve was now shifted to the right due to the overall increase in pupil size as compared to PLC (and other physiological arousal measures; indicative of a heightened arousal state; Fig. 1 E and F).

Finally, eye trackers can misestimate pupil size when an eye rotates away from the camera, a phenomenon known as the pupil foreshortening error, potentially leading to an overestimation of pupil size of ~4% when participants’ gaze deviates more than 8° (horizontally and vertically) from fixation (53). In principle, increased pupil size under ATX versus PLC could reflect a measurement artifact caused by drug-induced changes in saccade characteristics. However, in all our previous analyses, the influence of saccades on pupil size was removed from the data (54) and horizontal eye movements were restricted to 1.5° during task performance. Although the remaining small deviations are unlikely to explain the 13% increase in prestimulus pupil size under ATX (53), we performed an additional control analysis to further rule out eye-movement confounds. Specifically, excluding all trials with even very small eye movements during the prestimulus baseline period (velocity > 35°/s or acceleration > 9,500°/s², spanning 0.37° on average, 30.0% of trials) revealed highly similar results (SI Appendix, Fig. S2), making it unlikely that eye-movement confounds account for the observed pattern of results.

Our previous work indicated that the inverted U-shaped pupil–performance relationship does not depend on decision type (detection vs. discrimination) under neutral circumstances (1). Yet, because the pharmacological manipulation may have affected discrimination and detection decisions differently, we split up our data according to decision type. To accommodate to the lowered statistical power after splitting the data, we now used five pupil bins combined with polynomial regression, identical to our previous work (1). Again, the pupil–performance relationship was overall quadratically shaped for both sensitivity and RT for all drugs and decision-types (Fig. 2 B, C, E, and F), although there was also evidence for linear relationships in two cases (likely due to lower trial counts and fewer bins used for fits, details in SI Appendix). While no overall drug effect on d’ was observed [F(1, 54) = 1.05, P = 0.36], as can be seen in Fig. 2B, besides an overall rightward shift of the arousal–performance curve for ATX, ATX also selectively improved overall sensitivity on the discrimination tasks as compared to PLC [t(27) = 2.42, P = 0.02], reflected in an overall upward shift of curve. We reported this overall performance benefit under ATX previously based on independent analyses on the two separate discrimination datasets (32, 33). The improvement in d’ under ATX was driven by the cued discrimination task involving a spatial attention manipulation [P = 0.02, (32)], with a weaker effect for the discrimination task without this attention manipulation [P = 0.08; (33); see SI Appendix, Fig. S4; see Methods for task details]. This boost in overall performance was not present for detection tasks [t(27) = 0.06, P = 0.95] nor was it reflected in mean RTs on any task (both P > 0.27; see SI Appendix, Fig. S4; more statistics in SI Appendix). DNP did not affect mean sensitivity or RTs for either decision type (all P > 0.17; see SI Appendix).

To ensure that we captured slow, tonic arousal fluctuations rather than pupil responses associated with the previous trial, we conducted four control analyses. First, we tested whether the quadratic arousal–performance relationship persisted when using the previous trial’s task-evoked pupil response as the pupil measure (SI Appendix, Fig. S5A and Supplementary Methods). Second, we controlled for the influence of the previous trial’s task-evoked pupil response by regressing it out from the current trial’s prestimulus pupil size (SI Appendix, Fig. S5B). Third, we reanalyzed the data after removing posterror trials (SI Appendix, Fig. S5C). Fourth, we filtered out frequencies associated with task-evoked pupil responses, sparing only the very slow pupil size fluctuations (<0.1 Hz) in the data (SI Appendix, Fig. S5 D–F). Collectively, these analyses confirm that the reported inverted U-shaped arousal–performance relationships are not driven by lingering effects of the previous trial, indicating that prestimulus pupil size captures slow and ongoing tonic arousal fluctuations, even in relatively fast-paced experimental designs.

In all conditions, the intact pupil–performance curve under ATX was shifted rightward on the pupil size axis in line with the relative arousal scenario (Fig. 1B). Given that catecholamines are extensively linked to Yerkes–Dodson-like relationships (16, 27, 30), that pharmacological manipulation of catecholamines has been shown to affect behavioral decision-making [i.e., Fig. 2B and (27, 29–33)], and that we observed a clear increase of the arousal state of our participants after ingestion of ATX, including increases in HR and BP (Fig. 1 H and I), it seems likely that catecholamines are involved in maintaining the inverted U-shaped arousal–performance relationship, but apparently not in the most straightforward manner. To mechanistically explain how ATX could shift the arousal–performance curve on the arousal axis, essentially normalizing performance within each arousal state, we extended a neurobiologically plausible model that we have previously developed (1). With this model, we have demonstrated that the Yerkes–Dodson curve can be achieved by the influence of arousal fluctuations on two types of interneurons (vasoactive intestinal peptide; VIP, and somatostatin; SST) that together form a disinhibitory pathway for the excitatory neural populations that encode the available sensory evidence (E_A and E_B encoding the evidence for choice A and B; Fig. 3A; details in Methods). The model delineates a cortical circuit performing a detection or discrimination task under the influence of an arousal signal that is highly correlated to pupil size. It furthermore incorporates a nonselective population of parvalbumin (PV) interneurons, whose role is to provide a baseline level of inhibition and to mediate the competition between excitatory populations E_A and E_B. Both excitatory populations receive sensory input, prompting them to increase their own activity and suppress the activity of the other excitatory population—a process mediated by the inhibitory population PV. A decision is made when the firing rate of one of the excitatory populations reaches a certain predefined threshold, giving rise to a winner-take-all decision process (55), for a detection (A: present, B: absent) or a discrimination decision (choice A, choice B).

Fig. 3.

Computational modeling. (A) Schematic description of the first model. Arousal is determined by the combination of arousal fluctuations and the ATX signal (no/low/high ATX). Excitatory populations E_A and E_B encode two possible choices in a decision-making task (choice A and B). E_A and E_B are modulated by the arousal signal to VIP and SST cells. PV interneurons mediate the competition between E_A and E_B. Connectivity follows electrophysiological evidence and previous modeling approaches. Lines with arrows/dots indicate excitatory/inhibitory connections, respectively. (B) Arousal–performance curves derived from the first model, expressed in d’ and RT (C) as a function of arousal plotted for no/low/high ATX. (D) Schematic description of the second model. ATX increases arousal, but also excites neural population X, which subsequently inhibits the inhibitory chain of VIP and SST cells. (E) Arousal–performance curves of the second model for d’ and RT (F).

We extended the model with a neuromodulation (ATX) signal to gain a better understanding of the mechanism behind the observed shift of the arousal–performance curve after ingestion of ATX. As a first step, we implemented what we considered to be the simplest solution: an ATX signal that selectively increases arousal (Fig. 3A) in line with the influence of ATX on physiological arousal measures that we observed (Fig. 1 E–I). Note that the model now has two “arousal inputs” that together determine arousal: arousal fluctuations as well as ATX induced arousal (state) enhancement. These two arousal inputs are summed into the arousal node (lilac in Fig. 3A), whose output is plotted on the x-axis of our modeling results figures, as it directly translates to the arousal state that we measure with pupil size in our experimental studies.

When we simulated performance of this version of the model with two levels of ATX (low/high ATX) and compared this to baseline (no ATX), we observed that the relationship between performance measures and arousal became linear while shifting on the arousal axis (Fig. 3 B and C), and this implementation of the model was therefore not able to mimic our findings. We thus considered a second, more elaborate model architecture in which ATX enhances arousal, but simultaneously influences other brain areas, which may have additional modulatory effects on neural circuits involved in the task. More concretely, we introduced a nonspecific catecholamine-selective population that is excited by ATX but downregulates activity of both VIP and SST neurons (region “X”, Fig. 3D). Note that we assume that the (negative) modulation strength from the catecholamine-selective area X to VIP and SST is stronger than the (positive) modulation strength of summed arousal to population VIP and SST (i.e., thicker purple lines from X to VIP/SST in Fig. 3B), otherwise the opposing effects of these connections would cancel each other out or be overcompensated. This new version of the model nicely echoes our experimental observations. First, when ATX increases above baseline (no ATX/PLC; Fig. 3 E and F) levels, arousal is increased as observed experimentally in pupil size. Second, the firing of SST and VIP cells is weakly excited via the increased arousal level, but strongly inhibited by the catecholamine-selective population X that is activated by ATX. This means that the working point of the VIP-SST-pyramidal cell disinhibitory pathway is altered, providing more inhibition to the excitatory populations than under no ATX/PLC. In other words, the net effect of (low/high) ATX is stronger inhibition of the excitatory populations as compared to no ATX/PLC. As a result, the shape of the arousal–performance curves will remain intact but peak performance under ATX will occur at higher levels of arousal as compared to PLC. With the administration of ATX, the arousal–performance curve thus shifts to the right on the arousal (i.e., pupil size) axis, and more ATX equals a larger shift (Fig. 3 C and D). Taken together, we present a model in which ATX causes a rightward shift of the arousal–performance relationship via a population of catecholamine-selective neurons that inhibit VIP and SST populations. In the discussion section we will elaborate on which brain region (or neural population) may fulfill the role of node X in our model.

Discussion

Here, we demonstrated that the relationship between pupil-linked arousal and task performance is inverted U-shaped, even when the arousal state is heightened due to the administration of the catecholaminergic drug ATX. Strikingly, ATX shifted the arousal–performance curve rightward on the (pupil-linked) arousal axis without altering its overall shape. This suggests that task performance is not simply tied to the absolute level of arousal, but it is rather optimized relative to fluctuations within a given arousal state, supporting the relative arousal scenario (Fig. 1B). The relationship between arousal and performance may thus be more adaptive than previously understood, potentially operating through mechanisms similar to well-known normalization processes in neuroscience (34–36). Arousal typically fluctuates around a midpoint, producing a normal distribution of arousal fluctuations within each arousal state, even in high arousal states (i.e., red curve in Fig. 1E and see refs. 5 and 6). By centering the arousal–performance curve around this midpoint, organisms optimize performance for the most frequently encountered arousal levels within each state, ensuring overall higher performance compared to a flat or linear relationship. Previous research has indeed demonstrated that organisms can adapt their overall arousal state to maximize performance (6, 56, 57), in line with the adaptive gain theory (16). For example, mice adjust their arousal state to an optimal level in high-utility task contexts, partially by suppressing irrelevant locomotor behavior (6). Together, these findings underscore the flexibility and efficiency of neural circuits responsible for shaping the arousal–performance relationship, both within and across arousal states.

At first glance, our findings may seem at odds with the common interpretation of the Yerkes–Dodson law, which states that performance should always peak during states of (global) moderate arousal. There is indeed evidence in animals, humans, and computational modeling that performance is impaired during very low (i.e., drowsiness) or very high (i.e., locomotion) arousal states as compared to neutral states (5, 6, 51, 58–62). Yet, this body of work often reduces low and high arousal states to one or two data points, neglecting the shape of the arousal–performance relationship within these states, or more subtle arousal fluctuations in general. The Yerkes–Dodson law and the relative arousal scenario can coexist, as (relative) arousal fluctuations may shape performance within states on top of overall performance differences that occur between arousal states.

Important, yet open questions are how relative arousal shapes performance over time and how changes in overall arousal state are demarcated. In our study, we manipulated arousal state across sessions, on different days, allowing participants to establish a new equilibrium for optimal performance in each session. At present, it is unclear how long an organism must spend in a new arousal state for the neural circuitry to adapt, and thus for the inverted U-shaped arousal–performance relationship to shift. Future studies could address this by comparing session-wise arousal state manipulations, as in our experiment, to block-wise manipulations (e.g., alternating blocks of stationarity and locomotion within a session). This approach would help determine whether the inverted U-shaped arousal–performance relationship, and a shift therein, emerges only after extended exposure to a given arousal state. Relatedly, how could researchers disambiguate whether a measured change in pupil/arousal reflects a shift within a given arousal state (within the inverted-U curve) or an overall shift across states (entire shift of the inverted-U curve)? The answer to this question partly depends on how one defines and labels arousal states. Whether a given shift in arousal is interpreted as a transition between distinct states or a fluctuation within a continuous state is determined, at least in part, by the criteria we impose [e.g., based on neural or behavioral measures (10, 63)]. Studies in freely behaving animals, particularly mice, may provide direct insight into these questions. Mice can perform tasks while sitting on a wheel, allowing them to alternate between stationary and locomotive states, continuously self-regulating their arousal levels (6). We encourage researchers using such paradigms to post hoc sort stationary and locomotive trials and investigate the pupil-linked arousal–performance relationship within these states. If stationary and locomotive states correspond to distinct arousal states, we would expect to see two similar but shifted arousal–performance curves when analyzing them separately. Conversely, if no such shift is observed, locomotion and stationary behavior may be part of a single arousal state within the context of this task and time scale, suggesting that global state transitions might require longer timescales to emerge. This approach could help clarify whether such behavioral state changes reflect discrete transitions or a continuous modulation within the same state.

Possibly surprisingly, ATX selectively improved mean task performance for the discrimination tasks compared to PLC, while the Yerkes–Dodson law would predict the opposite. However, with only two arousal states (PLC and ATX) one cannot establish the relative positions of those states on the Yerkes–Dodson curve. It is notoriously difficult to establish the (starting) point of individuals on the Yerkes–Dodson curve and some auxiliary measures have been proposed as proxies (e.g., working memory capacity) (27, 30, 64), but so far not fully satisfactorily. The observed data pattern suggests that participants were slightly underaroused during the PLC condition, which is common during long experiments, and closer to peak performance in the ATX condition. Further, the performance increase in the discrimination tasks was only observed for d’ and not RT, and was most pronounced in a task involving a voluntary spatial attention manipulation (SI Appendix, Fig. S4), suggesting a potential interaction between ATX and selective attention reported previously (32). Given the diversity of tasks in our study, pinpointing the potential source of this performance difference between tasks is challenging. Therefore, it was not incorporated in the computational model, which was designed to capture commonalities across tasks and the general arousal–performance relationship as reflected in both performance (d’) and speed (RT). However, once this sensitivity improvement under ATX—whether specific to discrimination tasks or common across tasks—is firmly established, future computational models based on the one we propose here should be able to account for both the vertical and horizontal shift of the arousal–performance curve.

Two factors constrain the interpretability of our results. First, the inclusion of only male subjects limits the generalizability of our findings. While our study focuses on a fundamental aspect of perceptual decision-making, sex differences in arousal regulation and neuromodulatory dynamics may influence the observed relationship between arousal and performance. Future studies should investigate whether similar effects are present in female participants and explore potential mechanisms underlying sex-specific differences in arousal-mediated cognitive processes. Second, we did not observe a behavioral or physiological arousal-related (pupil size, HR, BP) effect of 5 mg of DNP. The lack of a physiological effect is difficult to interpret. While ACh is considered a key driver of arousal (5, 9), many studies investigating DNP’s cognitive effects do not measure, analyze, or report physiological changes (28, 40–45, 65–67). Nevertheless, many studies with sample sizes similar to ours have found behavioral or neural effects of a 5 mg DNP dose in healthy participants [(26, 28, 32, 33, 38–40, 42–45), but see refs. 65 and 67). To our knowledge, aside from our own work based on subsets of these data (32, 33), only two studies analyze physiological effects of arousal: Pfeffer et al. report that 5 mg of DNP affects HR variability (HRV), but found no effect on HR and pupil diameter (38, 39). The latter finding aligns with our results, though we did not collect HRV data. The absence of both physiological and behavioral effects in our study leaves two possible interpretations regarding acetylcholine’s role: 1) the cholinergic manipulation was ineffective, or 2) DNP was effective, but acetylcholine does not alter the shape of the arousal–performance relationship. With many studies reporting behavioral and neural effects of 5 mg DNP in the absence of arousal effects (26, 28, 38–40, 42–45), we cautiously consider the second explanation more likely. However, future work with a higher dose of DNP, other cholinergic agents (e.g., galantamine, rivastigmine), or optogenetics should provide clarity into the role of acetylcholine in the arousal–performance relationship (for more discussion see refs. 9, 32, and 33).

To provide a potential neural mechanism that explains our observations, we extended a computational model that we posited in previous work in two ways (1): 1) we added a neuromodulation signal that heightened (summed) arousal, and 2) we included an additional brain region (called X), which strongly inhibits the activity of SST and VIP cells. There are several lines of evidence suggesting that the prefrontal cortex (PFC) could potentially fulfill the role of region X in our model. First, acute administration of ATX mainly increases extracellular levels of noradrenaline and dopamine in PFC, and leaves extracellular catecholamine levels in other catecholamine-responsive regions (e.g., striatum and nucleus accumbens) unaffected in rodents (68, 69). Second, PFC, and in particular the orbitofrontal (OFC) and anterior cingulate cortex (ACC), plays an important role in the evaluation of task utility (16, 70). More specifically, these regions monitor the costs and benefits of task performance, which is essential for adapting neuromodulation levels to optimize performance. Moreover, OFC and ACC send strong convergent projections to the noradrenergic locus coeruleus (LC) in monkeys (12, 16, 71). This connectivity allows LC to adapt neuromodulation (and consequently arousal) levels to task utility information that comes from high-level structures. PFC may direct similar information about task utility to the disinhibitory chain of VIP/SST interneurons, analogous to the role of population X in our model. Indeed, top–down projections from frontal/motor cortices are known to target SST and VIP cells in rodents leading to disinhibitory effects in sensory areas (72). Such top–down modulation to SST/VIP is dependent on behavioral strategies (73), again suggesting the involvement of high association areas like PFC. By modulating the activity of these interneurons, PFC can effectively influence the arousal–performance relationship, ensuring that performance remains optimal within different arousal states. The workings and predictions of the model can be tested experimentally. Specifically, the role of the VIP-SST-pyramidal circuit as a potential mechanistic basis for the Yerkes–Dodson law, both under controlled conditions (1) and within enhanced arousal states, can be investigated in rodents using optogenetic inactivation of VIP and/or SST cells. According to our hypothesis, this would disrupt the inverted U-shape of the arousal–performance relationship. Second, the model predicts that the observed shift in the arousal–performance relationship requires the involvement of additional brain regions (such as region X), which are modulated by ATX to provide top–down inhibitory control over decision-making areas. Studies in human or nonhuman animals in which PFC (and other candidate areas) are pharmacologically suppressed might serve to test these results.

The computational model presented here considers inhibition and disinhibition as fundamental ingredients for the effect of arousal on performance. Besides its importance in the Yerkes–Dodson law (1), inhibition has been highlighted as a key component in arousal-mediated regulation of visual processing (74, 75) and normalization of activity in attention models in vision (34, 35). Mapping normalization models to concrete biophysical implementations is a difficult and unresolved problem, although subtractive, divisive, and nonlinear transformations needed for normalization effects to occur, may emerge from a combination of inhibition and noise (76), both existing ingredients of our model. Exploring our proposed mechanism in more detailed models including PV, SST, and VIP cells (77–79) should shed more light onto the particular circuits and layers involved in arousal-regulated perception.

Methods

Subjects.

30 right-handed Dutch speaking male participants (aged between 18 and 30) were recruited from the University of Amsterdam for this study. Because this study involved a pharmacological manipulation, all participants underwent extensive medical and psychological screening to rule out any medical or mental illnesses. All participants gave written consent for participation and received monetary compensation. This study was approved both by the local ethics committee of the University of Amsterdam and the Medical Ethical Committee of the Amsterdam Medical Centre (protocol NL64341.018.18). All participants provided written informed consent after explanation of the experimental protocol. Two participants decided to withdraw from the experiment after the first experimental session. The data from these participants were excluded from further analyses, resulting in N = 28 for the results presented here. Nonoverlapping results of parts of this dataset, focusing on specific conditions in specific tasks, are reported elsewhere (1, 32, 33).

Note that we limited participation to male subjects. Although we initially planned to include both sexes, the medical ethics committee required invasive blood pregnancy tests for women before each session due to the pharmacological agents used. Combined with logistical challenges, additional costs, and uncertainties about interactions with hormonal cycles, this led us to restrict the study to men.

Screening Procedure.

After completing the registration process, potential participants were contacted via e-mail to communicate the inclusion criteria, specific procedures, and potential risks associated with the study. Additionally, they were provided with the contact information of an independent physician whom they could reach out to for any inquiries or further clarifications. Following a contemplation period of 7 d, candidates were contacted again to invite them for a preliminary phone discussion. This preintake conversation aimed to verify that the candidate indeed fulfilled all the necessary inclusion and exclusion criteria (a comprehensive list of criteria can be found in SI Appendix). If the requirements were met, candidates were then invited to participate in an on-site intake session at the research facility of the University of Amsterdam. During this face-to-face intake session, the experimental protocol was thoroughly explained, including the subsequent physical and mental evaluations, after which candidate participants were asked to provide their written consent. The intake process also encompassed a range of physiological measurements such as body mass index, HR, BP, and an electrocardiogram. Additionally, a psychiatric questionnaire was administered to assess the candidates’ mental well-being. The information gathered during the intake was carefully reviewed by a physician, who subsequently determined the eligibility of each candidate participant. Finally, participants performed the staircasing procedure for the behavioral tasks (for more details, see Staircasing procedure).

Drug Administration.

This study employed a randomized, double-blind crossover design. ATX (40 mg), DNP (5 mg), and PLC were administered on different experimental sessions, all separated by a minimum of 7 d. The sequence in which the drugs were given was counterbalanced among the participants. The experimental days commenced at 9 am and concluded at 4 pm. Since ATX (~2 h) and DNP (~4 h) reach their peak plasma levels at distinct times, they were administered prior to the initiation of the behavioral tasks at different intervals (Fig. 1C). To maintain the integrity of the double-blind setup, participants were instructed to orally consume a pill 4 h before the commencement of the initial behavioral task. This pill could either contain DNP or PLC. Subsequently, a second pill was ingested 2 h prior to the start of the same task, which could contain either ATX or PLC. This ensured that participants received either PLC along with an active pharmaceutical or two PLCs during each experimental session. Additional details regarding ATX and DNP can be found in SI Appendix.

Procedure.

Participants performed multiple tasks during a single experimental session. During the first 2 h of each session, participants performed auditory discrimination and detection tasks that are not part of this study (1). In the second half of all sessions, participants performed four versions of visual detection and discrimination tasks. The order of the tasks was randomized between participants, but constant over sessions for each participant.

Below, we provide a brief description of the behavioral tasks, for additional results please see ref. 32. During all tasks, participants were seated 80 cm from a computer monitor (69 × 39 cm, 60 Hz, 1,920 × 1,080 pixels) in a darkened, sound isolated room. To minimize head movements, participants rested their heads on a head-mount with chinrest. All tasks were programmed in Python 2.7 using PsychoPy (80) and in-house scripts.

Behavioral Tasks.

Participants performed four visual tasks. Two of these were variations of a discrimination task, in which participants were asked to discriminate the orientation of a Gabor patch hidden in dynamic visual noise as being rotated clockwise (CW: 45°, 50% of trials) or counterclockwise (CCW: −45°, 50% of trials; Fig. 1D). The other two tasks were visual detection tasks in which participants had to indicate whether they believed a Gabor patch (CCW or CW) to be present or absent (50% present trials). The two detection tasks differed in terms of response bias manipulation (conservative versus liberal; see below). Besides these main task characteristics, there were some additional instructions and manipulations that are discussed below. During all tasks, the online measurement of gaze position ensured that participants maintained fixation. Trials in which gaze deviated by more than 1.5° from fixation on the horizontal axis were excluded from subsequent analyses.

Cued visual discrimination task.

The first visual discrimination task was an adaptation of the Posner cueing task (81). Target stimuli were presented unilaterally for a duration of 200 ms, appearing either on the left or right side of the screen in equal proportions (50% left, 50% right). 1,300 ms prior to target presentation, a spatial cue that was predictive of the target stimulus location was presented for 300 ms (80% cue validity). Participants were instructed to use this spatial cue to covertly shift their attention toward the cued location. Participants had the opportunity to respond within 1,400 ms after the onset of the target stimulus by pressing one of two buttons on the keyboard (S for CCW Gabor patches, K for CW). A variable intertrial interval (ITI) randomly drawn from a uniform distribution between 250 and 350 ms started directly after a response or the end of the response window if no response was given. Participants performed 560 trials per session of this task, distributed over two runs of 280 trials, which were subdivided in shorter blocks of 70 trials, in between which participants could rest.

Uncued visual discrimination task.

The other discrimination task took the form of a classical visual discrimination task. Target stimuli were presented centrally for a duration of 200 ms without any additional manipulations. In addition to identifying the orientation of the target stimulus, participants were also required to provide their level of confidence in their decision. Prior to engaging in the task, participants received instructions to evenly distribute their confidence reports, a measure taken to ensure a balanced reporting of low and high confidence answers and prevent bias toward low confidence responses in this challenging task. Participants conveyed their orientation judgment and confidence simultaneously by pressing one of four designated buttons on the keyboard (A for high confidence CCW Gabor patches, S for low confidence CCW, K for low confidence CW, L for high confidence CW). Once again, participants had a time window of 1,400 ms to make their response, followed by a 250 to 350 ms ITI. Participants completed a total of 600 trials for the uncued visual discrimination task, divided across two sets of 300 trials each (3 miniblocks of 100 trials).

Liberal visual detection task.

In the liberal visual detection task, target stimuli were presented centrally for 200 ms as well. On every trial, the noise stimulus (a circle containing dynamic noise) was presented, while the target stimuli (Gabor patches) were only exhibited in 50% of the trials. Participants were instructed to determine whether they perceived a target stimulus or not, and they indicated their response by pressing S (for target absent) or K (for target present). These target stimuli retained the same CCW and CW orientations as in the discrimination tasks, but the orientation was not task-relevant and could be disregarded. The response window was again 1,400 ms from stimulus onset, followed by a 250 to 350 ms ITI. Response bias was manipulated toward more liberal answers by means of negative auditory feedback in the form of a buzzer sound after missed target stimuli (i.e., misses in signal detection theory), presented immediately after the response. Participants performed 480 trials of the liberal visual detection task on each session, distributed over two runs of 240 trials (3 miniblocks of 80 trials).

Conservative visual detection task.

The conservative detection task was like the liberal detection task, differing solely in the manipulation of response bias toward more conservative responses. In this case, negative auditory feedback was provided after falsely reporting the presence of a target stimulus (i.e., false alarms in signal detection theory). Again, participants performed 480 trials (two runs of 240 trials, 3 miniblocks of 80 trials) per session of this task.

Staircasing procedure.

We titrated performance on all tasks to 75% correct in a separate intake session that preceded the three experimental sessions discussed here (32). To this end, the opacity of the Gabor patches (i.e., signal strength) was varied according to the weighted transformed up/down method proposed by Kaernbach (82), while the visual noise was kept constant.

Eye-Tracking Acquisition and Preprocessing.

Gaze position and pupil size were recorded with an EyeLink 1000 eye tracker (SR Research, Canada) during the experiment at 500 Hz. Nine-point calibration was performed at the start of each run to ensure high data quality. Additionally, a head-mount with a chinrest was employed to minimize any potential head movements from participants. Participants were given explicit instructions to keep head movements to a minimum and to try to avoid blinking during trials.

The pupillometry data of all tasks were preprocessed in the exact same way. Pupil traces were low-pass filtered at 10 Hz, blinks were linearly interpolated and the effects of blinks and saccades on pupil diameter were removed via finite impulse-response deconvolution (54). Note that EyeLink provides pupil size in arbitrary units, which we divided by 1,000 for plotting purposes.

Data Analysis.

Analysis for data collapsed across tasks.

To assess the overall shape of the relationship between prestimulus pupil-linked arousal and perceptual decision-making, we first combined the data of all tasks, split for the pharmacological manipulation. To quantify prestimulus pupil-linked arousal, we took the minimally preprocessed pupil traces of all tasks, and we calculated the average pupil size in the baseline window (−500 to 0 ms) before each stimulus onset (Fig. 1J). This baseline window includes the ITI (250 to 350 ms) between the response on the previous trial and the presentation of the stimulus on the current trial, as well as the motor response to the previous trial. Given this overlap, we performed several control analyses (SI Appendix, Supplementary Methods) to ensure that the effects of prestimulus arousal fluctuations did not actually reflect the lingering effects of the previous trial (SI Appendix, Fig. S5). Note that for the cued visual discrimination task, we also took the 500 ms before target presentation (not cue presentation) as the baseline window. We excluded all trials for which the eyes were closed during the entire baseline window, as well as trials for which pupil size during the baseline window was smaller or larger than three SD from a subjects’ mean baseline pupil size. Next, for each run of each task separately, we assigned each trial to one of 20 equally populated bins based on the average prestimulus pupil size (note that we use five bins for the analyses performed separately for decision type). The binning procedure was performed per run because it is not possible to assess whether pupil size differences between individual runs are the result of arousal fluctuations or small shifts in the exact head location (even though we used a head-mount). Therefore, we are looking at arousal fluctuations that occur within experimental runs (Fig. 1K, shown for five bins).

After having assigned all trials to 20 bins, we calculated Signal Detection Theoretic sensitivity [SDTs d’ (46)] and average RT as our dependent measures of perceptual decision-making for each bin. We also calculated the mean pupil size for each bin to replace (equally spaced) bin numbers with (not necessarily equally spaced) mean prestimulus pupil size values, to do justice to the true relationship between pupil size and decision behavior. Next, we subsequently averaged over runs and tasks, leaving us with mean d’ and RT for 20 bins for each subject and for each drug. To assess the shape of the relationship between arousal and perceptual decision-making, we next used mixed linear models (see below Mixed linear models).

Mixed linear models.

We used a mixed linear modeling approach implemented in the Python-package Statsmodels (83) to quantify the dependence of behavioral sensitivity and RT on pupil size (84). Specifically, we fitted two mixed models to test whether pupil response bin predominantly exhibited a monotonic effect (first-order), or a nonmonotonic effect (second-order) on the behavioral metric of interest (y). The fixed effects were specified as

$$\text{Model} 1:\mathrm{y}\sim {\beta }_{0}1+{\beta }_1{P}^1$$ [1]

$$\text{Model} 2:\mathrm{y}\sim {\beta }_{0}1+{\beta }_1{P}^1+{\beta }_2{P}^2$$ [2]

with β as regression coefficients and P as the average baseline pupil size in each bin. We included the maximal random effects structure justified by the design (85): Intercepts and pupil size coefficients could vary with participant. The mixed models were fitted through restricted maximum likelihood estimation. The two models were then formally compared based on AIC (47) and BIC (48).

Analyses performed separately for decision type.

After having assessed that the shape of the overall relationship between pupil-linked arousal and perceptual decision-making was quadratically shaped for all drugs separately, we investigated whether this relationship also held for the different decision types in our dataset. We collapsed the data of all tasks over the relevant features [i.e., detection (2 tasks), discrimination (2 tasks)], but kept the data split for the pharmacological manipulations. We next treated the data as before (see Analysis for data collapsed across all tasks), but this time we assigned the trials to five equally populated bins (instead of 20) to compensate for the lowered power after splitting the data (Fig. 1 J and K). Next, we performed polynomial regression (see below Polynomial regression) to assess the shape of the relationship between arousal and perceptual decision-making in the different decision types for each drug separately in our dataset.

Polynomial regression.

To assess the shape of the relationship between arousal and perceptual decision-making (quadratic or linear), we performed second-order polynomial regression. Because we were merely interested in the shape of the relationship, and for visualization purposes, we first normalized our data in the pupil dimension (i.e., essentially centering the data around a common mean). Next, we modeled the relationship between our observed behavior (d’ and RT) and prestimulus pupil size as a negative quadratic relationship, and as a (unsigned) linear relationship using ordinary least squares linear regression with freely varying intercepts. We extracted the relevant beta coefficient from each model (ß₁ for the linear model and ß₂ for the quadratic model) for each subject and tested whether the coefficients were significantly different from zero using one-sample t tests (α = 0.05). We first tested the significance of the linear model (two-sided), followed by the quadratic model. After having established that the overall relationship between prestimulus pupil and sensitivity/RT was negatively/positively quadratically shaped, respectively, we performed one-sided tests for the quadratic beta coefficients.

Methods: Computational Model.

Following and extending our previous efforts, we considered a population-based model of neural dynamics to describe a general decision-making task (55), which we adapted for our detection/discrimination tasks (1). The model simulates, in a first instance, the temporal evolution of global synaptic conductance variables corresponding to the NMDA and GABA receptors of two competing excitatory populations and one inhibitory (PV) population. The model is described by the following equations:

$$\frac{d{S}_A}{\mathit{dt}}=-\frac{S_A}{{\tau }_N}+\gamma \left(1-S_A\right)r_A$$ [3]

$$\frac{d{S}_B}{\mathit{dt}}=-\frac{S_B}{{\tau }_N}+\gamma \left(1-S_B\right)r_B$$ [4]

$$\frac{d{S}_C}{\mathit{dt}}=-\frac{S_C}{{\tau }_G}+{\gamma }_I{r}_C$$ [5]

Above, S_A and S_B correspond, respectively, to the NMDA conductances of selective excitatory populations A and B, and S_C corresponds to the GABAergic conductance of the inhibitory population. The parameters in these equations take the following values: τ_N = 60 ms, τ_G = 5 ms, γ = 1.282, and γ_I = 2. The variables r_A, r_B, and r_C are the mean firing rates of the two excitatory populations and one inhibitory population, respectively. We obtain their values by solving, at each time step, the transcendental equation $r_i={\varphi }_i(I_i)$, with $\varphi$ being a transfer function of the population (specified below) and I_i being the input to population “i,” given by

$$I_A=J_s{S}_A+J_c{S}_B+J_{\mathit{EI}}{S}_C+I_{0A}+I_{\mathit{SST}}^A+x_A\left(t\right)+I_{\mathit{sensory}}^A\left(t\right)$$ [6]

$$I_B=J_c{S}_A+J_s{S}_B+J_{\mathit{EI}}{S}_C+I_{0B}+I_{\mathit{SST}}^B+x_B\left(t\right)+I_{\mathit{sensory}}^B\left(t\right)$$ [7]

$$I_C=J_{\mathit{IE}}{S}_A+J_{\mathit{IE}}{S}_B+J_{\mathit{II}}{S}_C+I_{0C}+x_C\left(t\right)$$ [8]

The parameters J_s, J_c are the self- and cross-coupling synaptic terms between excitatory populations, respectively. J_EI is the coupling from the inhibitory populations to any of the excitatory ones, J_IE is the coupling from any of the excitatory populations to the inhibitory one, and J_II is the self-coupling strength of the inhibitory population. The parameters I_0i with i = A, B, C are background inputs to each population. Parameters in these equations take the following values: J_s = 0.49 nA, J_c = 0.0107 nA, J_IE = 0.3597 nA, J_EI = −0.31 nA, J_II = −0.12 nA, I_0A = I_0B = 0.3294 nA, and I_0C = 0.26 nA. The term Iⁱ_SST denotes the input to each excitatory population from its corresponding SST population (see details about this term below).

The term x_i(t) with i = A, B, C is an Ornstein–Uhlenbeck process, which introduces some level of stochasticity in the system. It is given by

$${\tau }_{\mathit{noise}}\frac{d{x}_i}{\mathit{dt}}=-x_i+\sqrt{{\tau }_{\mathit{noise}}} {\sigma }_i {\xi }_i\left(t\right)$$ [9]

Here, ξ_i(t) is a Gaussian white noise, the time constant is τ_noise = 2 ms and the noise strength is σ_A,B = 0.03 nA for excitatory populations and σ_C = 0 for the inhibitory one.

The last term in Eqs. 6 and 7 represents the external sensory input arriving to both populations. Assuming a detection task in which the subject has to detect the sensory stimulus A, the input is given by

$$I_{\mathit{sensory}}^A\left(t\right)={\mu }_0, I_{\mathit{sensory}}^B\left(t\right)=0$$ [10]

The average stimulus strength is μ₀ = 0.0133 unless specified otherwise. The stimulus is present during the whole duration of the trial. The discrimination task can be simply simulated by alternating the population which receives the input in the equation above, and therefore provides equivalent results.

The transfer function ϕ_i(t) which transform the input into firing rates takes the following form for the excitatory populations:

$${\varphi }_{A,B}\left(I\right)=\frac{1}{2}\frac{aI-b}{1-\text{exp}[-d(aI-b\left)\right]}$$ [11]

The values for the parameters are a = 135 Hz/nA, b = 54 Hz, and d = 0.308 s. For the inhibitory population a similar function can be used, but for convenience we choose a threshold-linear function:

$${\varphi }_C\left(I\right)={\left[\frac{1}{g_I}\left(c_{1}I-c_0\right)+r_0\right]}_{0,20}$$ [12]

The notation ${\left[x\right]}_{0,20}$ denotes a minimum value of zero (rectification) and a maximum value at 20 spikes/s (saturation). The values for the parameters are g_I = 4, c₁ = 615 Hz/nA, c₀ = 177 Hz, and r₀ = 5.5 spikes/s. It is sometimes useful for simulations (although not a requirement) to replace the transcendental equation $r_i={\varphi }_i(I_i)$ by its analogous differential equation, of the form:

$${\tau }_r\frac{d{r}_i}{\mathit{dt}}=-r_i+{\varphi }_i\left(I_i\right)$$ [13]

The time constant can take a typical value of τ_r = 2 ms.

In addition to the two selective excitatory populations and the PV population, our model also includes the effects of top–down input mediated by selective VIP and SST populations. To introduce this, we assume that the firing rate activity of VIP and SST cells is determined, respectively, by the following equations:

$$r_{\mathit{VIP}}^i={\left[{\alpha }_{\mathit{VIP}}(z I_{\mathit{PS}}+I_{\mathit{bg}}+J_{\mathit{vx}}{R}_x)+{\beta }_{\mathit{VIP}}\right]}_{0,20}$$ [14]

$$r_{\mathit{SST}}^i={\left[{\alpha }_{\mathit{SST}}\left(g_{\mathit{SST}}(z{I}_{\mathit{PS}}+I_{\mathit{bg}}+J_{\mathit{sx}}{R}_x)+J_{\mathit{VIP}}{r}_{\mathit{VIP}}^i\right)+{\beta }_{\mathit{SST}}\right]}_{0,20}$$ [15]

The subindex “i” indicates the associated selective excitatory populations. Parameter values are α_VIP = 50, β_VIP = 0, α_SST = 20, β_SST = 32, g_SST = 2, J_VIP = −0.1, z = 0.1, and I_bg = 0.37. The variable R_x is the firing rate of unspecified, potentially neuromodulatory neurons (neural population X in Fig. 3D) modulated by ATX, which we assume to have an inhibitory effect over all SST and VIP populations (with synaptic couplings of J_sx = −0.06 and J_vs = −0.06, respectively) and follows the equation

$$R_x=z_x I_{\mathit{ATX}}$$ [16]

Here, z_x = 20 is a gain factor and I_ATX is the modulation of R_x by ATX, which is I_ATX = 0 for the control case, I_ATX = 0.05 nA for low ATX, and I_ATX = 0.1 nA for high ATX.

The parameter I_PS in Eqs. 12 and 13 indicates the variable associated with the pupil size, which is both influenced by the level of ATX and the underlying levels of arousal of the organism. It is given by

$$I_{\mathit{PS}}=I_{\mathit{internal}}+J_{\mathit{PS}}{I}_{\mathit{ATX}}$$ [17]

Here, we assume that the internally generated arousal levels are I_internal = 0.35 unless specified otherwise, and J_PS = 2 to capture the experimentally observed positive effect of ATX on pupil size.

Finally, we link the firing rate of the SST populations in Eq. 15 with the input to excitatory populations given in Eqs. 6 and 7 by assuming that:

$$I_{\mathit{SST}}^i=J_{\mathit{SST}} r_{\mathit{SST}}^i$$ [18]

The synaptic strength is given by J_SST = −0.001.

For each simulated trial, we consider that the circuit makes a detection when the firing rate of either the excitatory population A (or B, in the case of a discrimination task) reaches a threshold of 15 spikes/s. The duration of the trial is set to T_trial = 1.5 s. To compute sensitivity (d’) and RT, we averaged over 3,000 trials for each value of the pupil size considered. In Fig. 3 B–E, we plot performance for selected arousal ranges for each ATX level.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Computational modeling data have been deposited in ModelDB (original code published upon publication). Anonymized pupillometry and behavior data have been deposited in the Open Science Framework (OSF) repository (https://osf.io/bczku/) (86).