Introduction

Cognitive performance follows an inverted-U relationship with arousal (Yerkes and Dodson 1908; Hebb 1955). This relationship is thought to be driven, at least in part, by different patterns of activation of the locus coeruleus-norepinephrine (LC-NE) neuromodulatory system (Aston-Jones and Cohen 2005; Cools and Arnsten 2022). According to this hypothesis, baseline LC activity tracks overall arousal level and shapes the strength of task-evoked LC responses (including “phasic” and “tonic” modes of activation), which in turn influence attention, memory, and other higher-order functions (Figure 1A). Low arousal (drowsiness) corresponds to low baseline activity, weak evoked responses, and relatively poor performance. Moderate arousal (optimal engagement) corresponds to moderate baseline activity, strong evoked responses, and relatively high performance (phasic mode). High arousal (distractibility) corresponds to high baseline activity, weak evoked responses, and relatively poor performance (tonic mode). Thus, the difference between phasic and tonic mode involves an inverse relationship between baseline (lower for phasic, higher for tonic mode) and evoked (higher for phasic, lower for tonic mode) LC activity.

Figure 1:

Experimental support for this hypothesis has been largely indirect. The LC’s small size and position deep in the brainstem make it difficult to directly measure its activity patterns. Instead, studies often use indirect proxies for LC activity, including non-luminance-mediated modulations of pupil size. Under certain conditions, baseline and evoked pupil modulations are related directly to baseline and evoked LC activity, respectively (Joshi et al. 2016). LC microstimulation can also drive pupillary responses (Joshi et al. 2016). Pupil modulations can reflect presumed functional effects of LC activation, including changes in functional connectivity, LC BOLD responses, and certain EEG potentials (Eldar et al. 2013; Murphy et al. 2011, 2014). Moreover, like for phasic and tonic LC modes, baseline and evoked pupil size tend to be related inversely to each other, such that as baseline increases, evoked responses tend to diminish (Gilzenrat et al. 2010). Accordingly, pupil changes have been interpreted in terms of phasic and tonic modes of LC activation, including using evoked pupil responses (which can be easier to calibrate across individuals and sessions than measurements of baseline pupil size, which depend on camera position, ambient lighting, and other factors; Mathôt et al. 2018) to infer baseline LC activity and relate to certain theories of LC function (Eldar et al. 2013; Koss 1986; Gilzenrat et al. 2010).

However, this kind of cross-modal inference about LC firing modes is likely to be complicated by several factors. Pupil size is modulated by multiple neural systems, not just the LC (Joshi and Gold 2020). Moreover, the inverse relationship between baseline and evoked pupil size likely reflects not only neural drive but also the pupil’s limited physical dynamic range, which causes response saturation at large baseline diameters (Chen and Kardon 2013) Thus, more direct measurements are needed to better understand if and how pupil-size modulations can be interpreted in terms of phasic and tonic modes of LC activation.

Here we report such measurements and show that they should be interpreted with caution. We first replicated previously reported within-epoch relationships between baseline LC activity and pupil size and between evoked LC activity and pupil size, as well as cross-epoch relationships within a single modality. We then show that, despite these well-established features of pupil and LC activation patterns, there were no reliable relationships across both modalities and epochs (i.e., baseline LC vs. evoked pupil or baseline pupil vs. evoked LC). These findings further clarify the limitations inherent to interpreting patterns of pupil modulation in terms of neural activity in the LC and elsewhere in the brain.

Results

We compared measurements of baseline and evoked LC spiking activity (N = 42 single units from 32 sessions in monkey Oz and 63 units from 51 sessions in monkey Ci; an example session is shown in Figure 1B) and pupil diameter from monkeys performing a passive fixation task with occasional startling beeps (a reanalysis of data from Joshi et al., 2016). All training, surgery, and experimental procedures were in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and were approved by the University of Pennsylvania Institutional Animal Care and Use Committee (protocol # 803740).

We first recapitulated previous findings showing reliable relationships between LC activity and pupil diameter when measured separately for baseline (during fixation prior to an auditory beep stimulus) or evoked (during fixation just after an auditory beep stimulus) response epochs (four example units/sessions and population summaries are shown in Figure 2, rows 1 and 2). Specifically, trial-by-trial measurements of baseline LC activity were positively correlated with simultaneously recorded measurements of baseline pupil diameter over the course of a session (using residuals, after correcting for linear drifts in both over the session to minimize spurious correlations, as illustrated in Figure 1B; Wilcoxon rank-sum test for H₀: median partial Spearman correlation coefficient across sessions = 0, p = 8.6×10^-4 for monkey Oz, p = 9.85×10^-6 for monkey Ci). Likewise, baseline-subtracted evoked LC responses were positively correlated with baseline-subtracted evoked pupil responses (p = 0.0135 for monkey Oz, p = 0.0018 for monkey Ci). These results are consistent with those reported previously and illustrate the coupling between LC activity and pupil size when measured simultaneously.

Figure 2:

During moderate to high levels of arousal, evoked responses are expected to decrease as baseline increases for each respective modality. Accordingly, in our dataset baseline-subtracted evoked pupil responses were negatively correlated with baseline pupil diameter (using residuals; p = 1.16×10^-6 for monkey Oz, p = 5.02×10^-9 for monkey Ci; Figure 2, row 3). Similarly, baseline-subtracted evoked LC responses were negatively correlated with baseline LC activity (using residuals; p = 5.88×10^-7 for monkey Oz, p = 1.04×10^-11 for monkey Ci; Figure 2, row 4).

Having recapitulated previous findings, we sought to determine whether similar cross-modal (LC and pupil) inferences can be made across different epochs (from baseline to task-evoked and vice versa). We first sought to test the specific hypothesis that evoked pupil responses could be used as an inverse approximation of baseline LC activity and corresponding phasic/tonic mode. As shown in Figure 2 (row 5), evoked pupil responses were rarely positively or negatively related to baseline LC activity in a reliable manner (Wilcoxon rank-sum test for H₀: median Spearman correlation coefficient across sessions = 0, p = 0.894 for monkey Oz, p = 0.904 for monkey Ci). Likewise, baseline pupil diameter was rarely positively or negatively related to evoked LC responses reliably across monkeys (Figure 2, bottom row) (p = 0.915 for monkey Oz, p = 0.008 for monkey Ci). Thus, despite consistent relationships between LC activity and pupil size within each epoch, there were no reliable relationships between the two when comparing across epochs (i.e., baseline versus evoked).

We conducted several additional analyses to address possible sources of these null results. First, the startling auditory beep was likely insufficient to evoke the full dynamic range of LC and pupil responses, potentially limiting the magnitude of the observed correlations. To assess the potential impact of this limitation, we related the correlation coefficients between evoked pupil responses and baseline LC activity (and vice versa) to the range of observed LC firing rates or pupil responses in each session. We found that the relationship between baseline pupil diameter and evoked LC responses was not systematically impacted by the range of evoked LC responses for either monkey (Spearman’s rho = 0.02, p = 0.89 for monkey Oz; rho = 0.07, p = 0.589 for monkey Ci). Similarly, the relationship between baseline LC activity and evoked pupil responses was not systematically impacted by the range of evoked pupil responses for monkey Ci (rho = 0.18, p = 0.16). However, we did observe a modest impact for monkey Oz (rho = -0.33, p = 0.03), suggesting that evoked pupil diameter may be inversely proportional to baseline LC activity for some conditions that evoke a sufficiently wide range of evoked pupil responses.

Second, our conservative approach to calculating baseline, by regressing out any linear relationship with elapsed time, could eliminate or reduce genuine correlations. However, this effect was minimal in our dataset, and we obtained similar results when using raw baseline measurements as opposed to residuals (see Supplemental Figure 1).

Third, it is possible that these relationships are more consistent with a non-linear (e.g., Yerkes-Dodson inverted-U) form that was not well identified by our analysis approaches (e.g., the Spearman correlation coefficient). We therefore fit both linear and quadratic curves for all across-epoch relationships illustrated in Figure 2 and computed the log-likelihood ratios for the corresponding fits (Supplemental Figure 2). The relationship between baseline and evoked pupil responses was better described by a non-linear fit for a minority of sessions (LLR > critical value of 3.841: 7/32 sessions for monkey Oz, 6/51 sessions for monkey Ci). Similarly, LC neuronal responses were rarely better characterized using a non-linear fit (2/42 neurons for monkey Oz, 3/63 for monkey Ci). Accordingly, across-epoch comparisons showed similar trends that favored a linear relationship (baseline LC versus evoked pupil: 4/42 for monkey Oz, 4/63 for monkey Ci; baseline pupil versus evoked LC: 2/42 for monkey Oz, 5/63 for monkey Ci). These results suggest our null findings were not attributable to a potentially non-linear relationship between baseline and evoked responses in our dataset.

Supplemental Figure 1:

Supplemental Figure 2:

Fourth, the monkeys were exposed to a relatively limited number of trials with startling auditory beeps to evoke LC and pupil responses, which could have underpowered the per-session analyses. To address this possibility, we applied our single-unit analyses (Figure 2) to data pooled across all trials, sessions, and units (Figure 3). The results are qualitatively similar for the pooled and single-unit analyses, in neither case showing a reliable relationship between baseline pupil and evoked LC responses or baseline LC activity and evoked pupil responses across monkeys. This result also held when LC units were separated based on the direction of their baseline relationship with pupil size (i.e., whether baseline LC activity was reliably associated with larger (Figure 3; green) or smaller (Figure 3; orange) baseline pupil measurements).

Figure 3:

Discussion

Arousal, measured in terms of physiological (e.g., pupil size) or neurophysiological (e.g., the LC-NE system) mechanisms, can interact with higher brain function over multiple timescales. These interactions are often reduced to two primary categories: 1) those that occur over relatively long timescales, which involve fluctuations in arousal that are not tied directly to specific external events but instead represent an internal state that can vary over seconds, minutes, hours, or days (“baseline”); and 2) those that occur over relatively short timescales, which involve abrupt changes in arousal triggered by specific internally or externally generated events that last around a second or less (“evoked”). Both baseline and evoked changes in arousal have been linked to different features of higher brain function (Berridge and Waterhouse 2003; Cools and Arnsten 2022; Joshi and Gold 2022; Aston-Jones and Cohen 2005) and, critically, with each other: evoked changes are often strongest at intermediate baseline values and substantially weaker otherwise, corresponding to the “inverted-U” Yerkes-Dodson relationship. Thus, the role of arousal in higher brain function is often studied and interpreted in terms of coupled variations in baseline and evoked activation patterns.

These studies are dominated by measures of pupil size, which is much easier to measure than LC-NE neural activity (Eldar et al. 2013; Gilzenrat et al. 2010; Usher et al. 1999; Laeng et al. 2012). Because of known relationships between the two, studies that measure pupil size are often interpreted in terms of LC-NE function. Here we reproduced previous findings that support links between the two measurement modalities when considering baseline or evoked activity separately. Specifically, variability in baseline values of LC activity and pupil size measured across trials lasting ∼2–4 s, and variability in evoked changes in LC activity and pupil size in response to a surprising stimulus, each tended to show positive correlations. These relationships were statistically reliable but imperfect, consistent with the idea that pupil changes are dynamically coupled with multiple neural systems in a manner that depends on an animals’ cognitive, behavioral, and physiological state (Berridge and Waterhouse 2003; Reimer et al. 2016; Joshi and Gold 2022; Yang et al. 2021; Weiss et al. 2026; Cazettes et al. 2021).

We also examined relationships between baseline and evoked changes within and across each recording modality. Consistent with previous results, we found reliable within-modality relationships: baseline and evoked activity tended to be negatively correlated with each other when analyzed separately for pupil size or LC activity, such that evoked responses decreased as baseline increased. However, these relationships did not hold across modalities: baseline pupil size did not covary reliably with LC evoked activity, and baseline LC activity did not covary reliably with evoked changes in pupil size.

These findings imply that the two systems are insufficiently coupled to reliably use moment-to-moment changes in pupil size to predict “phasic/tonic” LC activity modes. This limitation likely results from not only the contribution of multiple neural systems on pupil changes, but also the different mechanisms that govern relationships between baseline and evoked activity patterns in the brain and the eye. These mechanisms include spike-generating processes in the LC and physical properties of sphincter muscles in the eye that introduce different saturating non-linearities that tend to reduce evoked responses as baseline increases. Thus, this limitation also likely depends on the ranges of baseline and evoked activity considered. In our study, the monkeys were generally engaged in the task, suggesting that they were operating around the peak of the inverted-U Yerkes-Dodson curve. Targeted experiments aimed at identifying the distinct contributions of different neuromodulatory systems, through both pharmacological and task-specific manipulations, will be crucial in developing a comprehensive understanding of the conditions under which pupil diameter can be used to make reliable inferences about LC-NE function.

Materials and Methods

Behavioral Task

The monkeys performed a fixation task that required them to maintain fixation for a variable duration of 1–5 sec. On ∼25% of the trials, selected at random, a loud auditory tone (1 kHz; 0.5 sec) was played after 1–1.5 sec of fixation. Successful fixation until fixation-point offset on beep and no-beep trials was followed by a liquid reward.

Pupillometry

A video-based eye-tracking system (Eyelink 1000, SR Research) was used to obtain measures of pupil diameter (see Joshi et al. 2016 for details). Briefly, fixation was measured monocularly (1000 Hz sample rate) and only included periods of stable fixation (those without saccadic eye movements) that were maintained for at least 200 ms. Raw pupil measurements were first z-scored for each session. To remove modulations related to fixation onset, the average trace aligned to fixation onset and measured across trials was subtracted from each trial. These standardized traces were then smoothed using a 151-ms wide boxcar filter. Baseline pupil diameter was quantified as the mean smoothed pupil trace throughout fixation for fixation-only trials, or until the onset of an auditory beep (minimum baseline duration of 100 ms) for beep trials. Evoked pupil diameter was quantified as the maximum change in pupil diameter (from mean values in 50 ms-wide sliding windows measured in 10-ms steps) relative to baseline following the onset of an auditory beep until 20 ms before the end of fixation.

Neuronal Recordings

Details of the neuronal recordings were reported previously (Kalwani et al. 2014; Joshi et al. 2016). Briefly, monkeys were implanted with circular recording cylinders (∼2 cm diameter) that allowed for custom microelectrodes to be lowered approximately dorsal-ventrally while electrical activity was recorded from multiple structures typically encountered leading to the pontine brainstem, including the superior colliculus, inferior colliculus, and the locus coeruleus. Recordings were filtered between 100 Hz and 8 kHz to extract spiking activity and were sorted offline using the Plexon Offline Sorter (Plexon, Inc.). For each single unit, baseline activity was quantified as the firing rate from fixation onset to 20 ms before the end of fixation for fixation-only trials or until the onset of an auditory beep (minimum baseline duration of 100 ms) for beep trials. Evoked activity was quantified as the baseline-subtracted firing rate 0–200 ms following an auditory beep.

Data availability

All data and analysis code necessary to generate figures is accessible at https://github.com/lwthompson2/Thompson2026_LCPupilAnalysis.git.

Additional information

Funding

HHS | NIH | National Institute of Mental Health (NIMH) (R01-MH-127566)

• Joshua I Gold