Theta-gamma phase-amplitude coupling in psychosis and healthy controls: Predicting working memory capacity across different tasks

Highlights

• •Cortical theta-gamma phase-amplitude coupling (PAC) was found in different tasks.
• •PAC did not differ between patients with psychosis and healthy control groups.
• •PAC was a strong predictor of individual differences in working memory capacity.
• •This association remained strong even for PAC measured during a passive viewing task.
• •PAC may be a stable predictor of cognitive potential in patients and healthy controls.

Abstract

Theta-gamma phase-amplitude coupling has been proposed as a possible mechanism underlying working memory. Here, we assess whether cortical theta-gamma phase-amplitude coupling is related to working memory deficits in patients with psychosis, and whether any group differences observed in this neural measure are specifically related to group differences in working memory performance or instead reflect more general differences in brain dynamics. To address these issues, we collected 61-channel EEG data from 32 psychiatric patients with psychosis (including patients with schizophrenia, schizoaffective disorder, and bipolar disorder with psychotic features) and 35 age-matched healthy controls, and calculated the Phase Locking Value, a measure of theta-gamma phase-amplitude coupling across three tasks: a working memory task (Active WM+), a visual search task (Active WM−), and a passive viewing task (Passive WM−). We found significant theta-gamma phase-amplitude coupling across all tasks, including during a pre-stimulus baseline period. No significant differences between the PSY and HC groups were found, although the two groups did show some small differences in the specific patterns of coupling. However, surprisingly, we found that frequency dynamics in coupling strongly and significantly predicted individual differences in working memory capacity in both groups. This was true even when the coupling was assessed during a passive viewing paradigm that did not involve a working memory component. Taken together, these findings suggest that cortical theta-gamma phase-amplitude coupling may reflect behaviorally-relevant differences in structural or functional connections that persist regardless of stimuli, task or time window in both those with and without psychosis.

1. Introduction

Working memory, or the short term storage and manipulation of information, is thought to be fundamental to almost all conscious cognitive processing (Papaioannou and Luck, 2022). Reflecting its foundational role in cognition, working memory is related to overall cognitive capacity (Luciano et al., 2001, Johnson et al., 2013). Some psychiatric patient populations, such as individuals with psychosis (PSY), have significant working memory deficits (Johnson et al., 2013, Lee and Park, 2005, Gold et al., 2019, Erickson et al., 2021), although the neural processes that give rise to these impairments are not yet clear. One potential mechanism underlying this deficit is altered coordination between theta (4–7 Hz) and gamma (30–100 Hz) oscillations—namely, theta-gamma phase-amplitude coupling (PAC), whereby the amplitude of gamma oscillations is modulated by phases of the corresponding theta oscillations (see Fig. 1 for an illustration). Results from intracranial recordings during working memory tasks show that, during maintenance of the memory trace, cortical gamma power consistently increases at specific hippocampal theta phases, corresponding to an increase in measures of PAC between the hippocampus and the cortex (Lisman and Jensen, 2013, Axmacher et al., 2010, Bahramisharif et al., 2018). This increase in subcortical-cortical PAC shows a high degree of working memory specificity; that is, it seems to occur exclusively during working memory tasks and increases as working memory content increases (Axmacher et al., 2010, Bahramisharif et al., 2018). Altogether, such work suggests that cross-frequency coupling between theta phase and gamma amplitude may be a core mechanism involved in working memory maintenance among psychiatrically healthy individuals (Lisman, 2010, Lisman and Idiart, 1995) – and, in turn, that abnormal coupling may account for the reduced working memory capacity observed in PSY.

Fig. 1.

Idealized example of theta-gamma phase-amplitude coupling. (A) shows what the gamma (blue) and theta (green) traces might look like over time, and (B) shows the average gamma amplitude at particular theta phases (grey line). Note that the latter is a more complex relationship than a simple correlation between gamma and theta amplitude. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Given the inherent difficulty in acquiring intracranial recordings, interest in finding a non-invasive analogous marker that can be measured in a broader population (including psychiatric clinical populations) has grown. One such approach is to measure cortical theta-gamma PAC using electroencephalography (EEG). As EEG is recorded noninvasively from scalp electrodes, this method only reflects PAC within the cortex itself, and cannot measure associations with subcortical structures (e.g. the hippocampus). Nevertheless, promising results have emerged, with some studies showing increased cortical PAC in healthy controls (HC) during a working memory task compared to a pre-trial baseline (Sauseng et al., 2009, Papaioannou et al., 2022). Barr and colleagues (Barr et al., 2017) expanded on this work, examining theta-gamma PAC as a correlate of cognitive deficits in patients with schizophrenia and dementia. The authors reported that patients exhibited lower theta-gamma PAC during the response period of an n-back working memory task compared to controls, suggesting that these differences in neural dynamics might be related to working memory capacity deficits seen in these patients.

Interestingly, however, disruptions in PAC have been found even during non-working memory tasks. For example, Allen and colleagues (Allen et al., 2011) found that patients with schizophrenia had lower cross-frequency modulation between theta and gamma during an oddball task compared to matched healthy controls. Similarly, Grove and colleagues (Grove et al., 2021) found that patients with schizophrenia had both lower theta power, and lower theta-gamma PAC, during a gaze discrimination task. Note that the interaction between overall power and phase-amplitude-coupling is complex (Hülsemann et al., 2019), so it is difficult to know if these two effects are separable or not.

The presence of similar effects in these tasks calls into question the specificity of the measure. That is, it could be that these differences in theta-gamma PAC reflect more general neural disruptions that are not related to, or specifically induced by, working memory processes. Indeed, in a previous study we showed that, among HC, similar levels of cortical theta-gamma PAC can be observed during tasks that require working memory and tasks that do not (Papaioannou et al., 2022), suggesting that cortical theta-gamma may be less task specific than subcortical-cortical coupling. As such, it is not yet clear whether cortical theta-gamma PAC measures are indexing functions specific to working memory as opposed to more generalized neurophysiological processes, or whether such measures would track working memory deficits in PSY.

In the present study, we build on the previous research to a) investigate the specificity of cortical theta-gamma PAC as a working memory marker, b) test the hypothesis that theta-gamma PAC is correlated with behavioral measures of working memory capacity, and c) examine the degree to which group differences in cortical theta-gamma PAC dynamics are related to working memory deficits in PSY. To do this, we recorded EEG from 32 PSY and 35 matched HC, and calculated theta-gamma PAC across three tasks: a change detection task, which requires active attention and relies heavily on working memory maintenance (Active WM+), a color detection task, which requires active attention but does not rely on working memory maintenance (Active WM-), and a passive perception task, where participants are not required to make any response, thus requiring neither active attention nor working memory maintenance (Passive WM-). If cortical theta-gamma PAC is specific to working memory processes, then we would expect an increase in PAC during the Active WM+ task only. Similarly, if theta-gamma PAC is behaviorally meaningful, then we would expect that individual differences in PAC will correlate with individual differences in working memory capacity. Lastly, if cortical theta-gamma PAC is directly related to working memory deficits observed in PSY, then we would expect PAC to be abnormal in PSY in a manner that is proportional to the working memory deficit commonly observed in participants with psychosis.

2. Methods

2.1. Participants

A total of 34 PSY and 36 HC were recruited from the community surrounding the University of Chicago. 2 PSY and 1 HC were rejected due to excessive EEG artifacts (>50 % of trials; see preprocessing below), resulting in a final sample of 32 PSY and 35 HC. The two groups were similar with respect to gender (χ² = 0.003; p = 0.952), race (χ² = 2.29; p = 0.319), age (t = 0.09; p = 0.925), and parental education (t = 0.60; p = 0.553), a proxy measure of socioeconomic status (see Table 1). Diagnosis was confirmed using the Structured Clinical Interview for DSM-5 Disorders (SCID, 2015) and review of medical records where appropriate. The PSY group included participants with schizophrenia (n = 17), schizoaffective disorder (n = 6), and bipolar disorder with a history of psychotic features (n = 9). Participants reported stable medication doses in the last 4 weeks (mean Chlorpromazine dose equivalent = 492 mg/d; 7 participants reported no use of any antipsychotic medication). HC were free from a current mood disorder, past mood episodes, or a lifetime history of psychosis, and denied having any first degree relatives with a psychotic disorder. All participants were between the ages of 18–60, had normal or corrected to normal vision, and reported no history of epilepsy or a traumatic brain injury. All participants were also free from a current substance use disorder (i.e., they had not experienced 2 or more symptoms of substance use disorder in the past 3 months). All recruiting and experimental methods were approved by the University of Chicago Institutional Review Board.

Table 1.

Participant demographic information, and clinical scale scores for patients with psychosis (PSY) and healthy controls (HC). * denotes a significant difference between groups after correcting for multiple comparisons.

	HC		PSY
Gender:	Male	19 (54 %)	Male	18 (56 %)
	Female	16 (46 %)	Female	14 (44 %)
Race:	African American	11 (31 %)	African American	15 (47 %)
	Caucasian	16 (46 %)	Caucasian	13 (41 %)
	Other	8 (23 %)	Other	4 (12 %)
Handedness:	Right	32 (91 %)	Right	29 (91 %)
	Left	3 (9 %)	Left	3 (9 %)
	Mean	SD	Mean	SD
Age:	35.09	10.64	34.84	10.57
Education, Self:	15.03	2.04	13.74	2.22
Parental Education:	13.38	4.02	13.86	2.20
BPRS Positive:	N/A	N/A	2.74	1.42
BRPS Negative	N/A	N/A	1.82	0.74
BPRS Disorganized	N/A	N/A	1.54	0.49
BPRS Combined	N/A	N/A	2.03	0.53
SLOF:	N/A	N/A	4.32	0.45
MCCB:	46.01	10.16	35.73*	10.18
WASI:	104.66	12.26	99.60	12.98
WTAR:	106.57	11.74	104.68	12.49
PRECIS	35.22	9.02	52.23*	17.25

2.2. Clinical and cognitive assessments

To measure current and premorbid cognitive functioning, the following battery of cognitive tasks was used: i) the MATRICS Consensus Cognitive Battery (MCCB (Nuechterlein et al., 2008), ii) the Wechsler Test of Adult Reading (WTAR (Test, 2012), and iii) the Wechsler Abbreviated Scale of Intelligence (WASI-II (Wechsler and Scale, 2012). PSY participants were also administered the Brief Psychiatric Rating Scale (BPRS (Overall and Gorham, 1962) to measure symptom severity and the Specific Level of Functioning Scale (SLOF (Schneider and Struening, 1983) to measure social and occupational functioning. All participants also completed a self-report questionnaire assessing perceived cognitive impairment (Patient Reported Evaluation of Cognition Scale – PRECiS (Patchick et al., 2016). As expected, we found that PSY reported more severe cognitive symptoms than HC, as evidenced by a significantly lower objective performance in the MCCB (t(62) = 4.04, p < 0.001), and significantly more subjective difficulties reported in the PRECIS (t(62) = 4.99, p < 0.001).

2.3. Experimental paradigm

The trial sequence for the three tasks is shown in Fig. 2. Each trial began with a 1500 ms blank screen, to act as an ITI. Following that, a 300 ms sample array appeared that consisted of one to five colored squares, each measuring 0.66 degrees on each side and arranged around an invisible circle with a radius of 4.1 degrees of visual angle. Each square was a different color selected randomly from the following nine color list: dark brown (140,81,10), tan (216,179,101), magenta (197,27,125), light pink (233,163,201), yellow (255,255,0), sage (161,2,106), teal (77,146,33), midnight blue (1,102,94), and sky blue (90,180,172). This sample array was followed by another blank display lasting 1700 ms.

Fig. 2.

Experimental paradigm showing the trial structures across the three tasks: (A) Active WM+, (B) Active WM- and (C) Passive WM-. Blue text summarizes the task demands at each screen. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

In the Active WM+ task (Fig. 2A), participants were instructed to hold the colors and location of the sample array in memory, as in a typical change detection task (e.g., (Vogel and Machizawa, 2004). A test array was presented immediately following the 1700 ms delay that consisted of a single square matching the location of one of the squares in the sample array. In 50 % of trials, the color of the square remained the same, whereas in the other 50 % of trials the color of the square changed to a new color not previously used on that trial. Participants were instructed to indicate by button-press response with their right hand whether the color of the square remained the same or had changed.

The Active WM- task followed the same sequence (Fig. 2B): a sample array containing 1 to 5 colored squares was presented for 300 ms followed by a blank delay of 1700 ms. In this task, participants were instructed to make a button press response with their right hand when they detected a randomly selected target color (e.g. turquoise) within the sample array. Only trials without a response (i.e. without the target color) were used in EEG analyses. To help participants remember the target color, which remained constant throughout the task, the static fixation cross was set to match the target color. As there was no memory component for the Active WM- task, no test array appeared after the 1700 ms delay interval.

Lastly, the Passive WM− task again followed the same sequence of a 300 ms sample array followed by a 1700 ms blank delay (Fig. 2C). In this task, participants were instructed to passively view the stimuli. To ensure adequate task engagement, participants completed a secondary irrelevant task in which they were asked to rate the pleasantness of neutral images that were presented every 30 Passive WM- trials. These images were unrelated to the stimuli, and were followed by a brief break, to ensure that the rating task did not interfere with the main stimulus arrays. The order of the conditions was randomized across participants, and did not systematically vary between groups. All participants completed 160 trials of each of the three tasks (32 trials per set size of each condition).

The three tasks were thus designed so that the stimulus sequence remained approximately the same while cognitive demands differed by task instruction. Thus, if theta-gamma PAC is specifically tied to WM processes, we expect that it would be highest in the Active WM+ task, where the task relies heavily on working memory processes, and lowest in the Passive WM- condition, where there is no explicit task demands aside from passive perception.

2.4. EEG recording and pre-processing

EEG data was collected at 1000 Hz from 61 scalp electrodes using the Brain Products actiCHamp system (Brain Products GmbH, Gilchin, Germany). These electrodes were distributed across the scalp evenly, following standard 10-20 electrode placement. All electrode placements are indicated in Fig. 4. Additionally, 3 electrooculogram (EOG) electrodes were used (one below the right eye and one on each side of the external canthi) to measure vertical and horizontal EOG, respectively. All electrodes were referenced online to P9, and later re-referenced offline to the average of P9/P10, which is comparable to the average mastoid (Zhang et al., 2024). EOG channels were re-referenced offline to create two bipolar channels: a horizontal EOG channel (HEOG; Left EOG minus Right EOG) and a vertical channel (VEOG; Lower EOG minus Fp2). An online 200 Hz antialiasing filter was applied throughout the recording.

Fig. 4.

Mean PLV (y-axis) split by group (HC − green lines, PSY – blue lines), cluster (Frontal –left plot, Posterior − right plot), task (Active WM+, Active WM-, and Passive WM- from left to right in each plot), frequency (25–35 Hz– light lines, 45–55 Hz − dark lines) and time window (x-axis). Error bars represent 95 % confidence intervals. The scalp maps show the placement of the two electrode clusters. AU refers to arbitrary units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Offline processing was done using the MATLAB software suite (MathWorks, Inc., Natick, MA) and the EEGLAB (Delorme and Makeig, 2004) and ERPLAB (Lopez-Calderon and Luck, 2014) packages. Following re-referencing, bad channels were identified via visual inspection and marked for interpolation. Artifact correction was performed on all remaining channels via independent component analysis (ICA) by removing components related to eye blinks and eye movements. All channels previously marked as bad were then interpolated from the corrected channel data using a circular interpolation algorithm. The data was then segmented to 4 s epochs (−1500 to 2500 ms from the onset of the sample array) and baseline adjusted with respect to the average of the pre-stimulus activity. Segments with remaining artifacts were identified using built-in EEGLAB and ERPLAB functions. These functions marked any epochs containing activity exceeding ±200 μV or voltage changes exceeding ±150 μV within a 200 ms moving window. Finally, a visual inspection was conducted and trials containing artifacts were removed. We disqualified any participants with less than 50 % trials remaining after artifact rejection in any of the tasks. Most participants fell well under that threshold (PSY: M = 17.8 %, SD = 17.4 %; HC: M = 17.9,% SD = 14.8 %).

2.5. Theta-gamma phase-amplitude coupling

Theta-gamma phase-amplitude coupling calculations were adapted from Sauseng et al. (2009) and have also been described in Papaioannou et al. (2022). Briefly, EEG segments were first converted from voltage to current-source density using the ERPLAB (Lopez-Calderon and Luck, 2014) MATLAB package (m-constant = 4, lambda = 0.00001, head radius rescaling factor = 10 cm). The FieldTrip MATLAB package (Oostenveld et al., 2010) was used to apply a 5-cycle Morlet wave convolution to each epoch at theta (6 Hz) and gamma (20–70 Hz, sampled at 1 Hz intervals) frequencies, producing a complex data series representing the instantaneous phase and amplitude at each frequency. Note that the gamma frequency band we use here includes frequencies that are lower than the traditional gamma range (typically > 30 Hz). We included these lower frequencies to maintain continuity with previous studies looking at PAC (Sauseng et al., 2009, Papaioannou et al., 2022).

To isolate coupling between theta phase and gamma amplitude, we took the following steps: first, we extracted the theta phase at each time point by calculating the angle of the complex time–frequency signal at 6 Hz. We then extracted the amplitude of gamma at each frequency within the gamma range and each timepoint by taking the absolute value of the complex indices. Gamma amplitude was then normalized (to a mean of 0 and SD of 1) within each trial to remove any impact of overall gamma power differences across frequencies and trials. Lastly, to quantify coherence between the two measures, we calculated the phase-locking value (PLV) of the theta phase with the phase angle of the gamma amplitude envelope. This was done by calculating the angle of the Hilbert transform of the filtered gamma amplitude data, giving us the instantaneous phase of the gamma amplitude (i.e. the pattern of amplitude changes in the time window). Comparing the theta phase to this instantaneous phase of gamma amplitude gives us the PLV, which is defined as follows:

$$\mathit{PLV}=\left|\frac{1}{N}\sum _{n=1}^N\mathrm{e}\mathrm{x}\mathrm{p}(i{\phi }_{\theta }\left(n\right)-i{\phi }_y\left(n\right))\right|$$

where $i=\sqrt{-1}$, ${\phi }_{\theta }\left(n\right)$ is the instantaneous theta phase at timepoint n, ${\phi }_y\left(n\right)$ is the instantaneous phase of the filtered gamma amplitude at time point n, and N is total number of timepoints. The resulting PLV value is a value between 0 and 1, where 0 reflects no phase coupling, and 1 reflects perfect coupling (Aydore et al., 2013). Note that previous research has shown that PLV is relatively modest in real-world EEG signal, but higher than what would be expected by chance (Sauseng et al., 2009, Papaioannou et al., 2022).

To examine fluctuations in theta-gamma PAC over the course of the trial, we split each epoch into eight overlapping segments (−900 to −300 ms, −600 to 0 ms, −300 to 300 ms, 0 to 600 ms, 300 to 900 ms, 600 to 1200 ms, 900 to 1500 ms and 1200 to 1800 ms from stimulus onset), calculating the mean PLV at each segment. This ensured that a) PAC measurements included activity well before the stimulus onset (−900 to −300 ms) to well after (1200 ms to 1800 ms), and b) all time windows had the same number of timepoints. This is important because measures of PAC, including PLV, are moderately sensitive to the number of samples used to calculate them (Tort et al., 2010), so any differences in time window length could lead to artifactual changes in PAC. These steps yielded a single PLV value for each time segment, trial, electrode, and gamma frequency. In order to reduce the number of statistical comparisons for our analysis, we averaged across all set sizes within a task. We then created two electrode clusters (one frontal and one posterior; see Fig. 4 for the specific electrode locations) and two frequency clusters (25–35 Hz and 45–55 Hz). These clusters were created based on a priori thresholds taken from the results of Papaioannou et al., 2022 (Papaioannou et al., 2022). Note that the electrode and frequency clusters were averaged after the PLV was extracted – i.e. theta-gamma amplitude coupling was measured independently at each electrode and frequency, but the resulting values were averaged to asses the overall strength of the coupling and produce more stable values.

2.6. Statistical analyses

Statistical analyses were conducted using the R language and R studio environment (R Core Team. R, 2022, RStudio Team, 2022). All ANOVAs were calculated using the “ez” package in R (Lawrence, 2016). A Huynh-Feldt correction for sphericity (Huynh and Feldt, 1976) was applied for repeated factors with 3 or more levels, which adjusted the degrees of freedom to account for non-spherical data structures. Where noted, within-subjects 95 % confidence intervals were calculated using the procedure described in Morey, (2008). A post-hoc power analysis based on our sample sizes shows that we were well-powered (1-β = 80 %) to detect a small-to-medium within-subjects effect (d ≥ 0.32 across our full sample; or, d ≥ 0.45 for PSY and d ≥ 0.44 for HC separately) or a medium-to-large between-subjects effect (d ≥ 0.62).

3. Results

3.1. Behavioral results

The main behavioral measure of interest was performance on the change detection task (Active WM + ); the Active WM- task was specifically designed to induce at-ceiling performance (mean d’ = 4.24), and the Passive WM- task did not have a relevant behavioral response. To assess performance in Active WM+, we extracted the working memory capacity (K) of each participant, using the procedure described in Rouder et al. (2011). Fig. 3A shows the distribution of K values for the HC (M = 2.73, SD = 0.99) and PSY (M = 2.62, SD = 1.00) groups. Surprisingly, there was no significant difference in K between the two groups (t₆₅ = 0.452, p = 0.653). We also calculated the more traditional derivation of K (Cowan, 2001), which needs to be estimated separately for each set size (see Fig. 3B). A mixed-effects ANOVA showed no significant main effect of group (F(1,65) = 1.68, p = 0.199), although the mean K is numerically higher in HC than in PSY in every case.

Fig. 3.

Behavioral performance during the Active WM+ task, measured as estimated working memory capacity (K). K was calculated using the Rouder et al. (2008) model (A) or using Cowan’s K at each set size (B). No significant difference between the two diagnostic groups was observed at any measurement, although HC had consistently higher mean K. The thicker middle line represents the median value, and the filled circle the mean. The upper and lower box boundaries represent the 25 % and 75 % quartiles respectively. Unfilled circles are outlier values that fall more than 1.5 times the interquartile range from the median.

To make sure that the lack of a behavioral difference was not due to heterogeneity in our diagnostic groups, we repeated the analysis separating the patient with bipolar disorder (BP; N = 9) from those with schizophrenia or schizoaffective disorder (SCZ; N = 23). The pattern remained the same, with no significant differences in K (F(2,64) = 0.302, p = 0.741) or Cowan’s K (F(2,64) = 0.141, p = 0.252) across diagnostic groups, but numerically lower values for patients. A full breakdown of this data can be found in the supplemental material. Given the similarity in results, and to maximize power, we collapsed across SCZ and BP for the rest of the analyses.

3.2. Theta-gamma PAC by condition, group, electrode cluster, and time window

The overall pattern in PLV is shown in Fig. 4, broken down by group (HC vs PSY), task (Active WM+, Active WM-, and Passive WM-), time window (600 ms time windows ranging from −900 to + 1800 from stimulus onset), electrode cluster (frontal or posterior), and gamma frequency band (25–35 Hz or 45–55 Hz).

We first asked the question of whether theta-gamma PAC differs by task condition. In a previous study, we found that theta-gamma PAC does not differ according to task (Papaioannou et al., 2022). Here, we performed a one-way repeated measures ANOVA comparing the mean PLV across the three tasks and found a trend level effect of task (F(2,132) = 3.04, p = 0.0504, HFe = 0.991). Post-hoc pairwise comparisons showed no significant differences between Active WM+ (M = 0.3057) and Active WM- (M = 0.3054; t₆₆ = 1.30, p = 0.199) nor between Active WM- and Passive WM- (M = 0.3050; t₆₆ = 1.24, p = 0.219). A small but significant difference between Active WM + and Passive WM- was found (t₆₆ = 2.36, p = 0.021). Taken together, PLV during Active WM + seems to be marginally larger than in the other tasks, but any effect is very small (see Fig. 5). Note that in order to best visualize the variability across tasks (rather than between-subject variability), Fig. 5 shows only within-subject variability. A detailed breakdown of the procedure can be found in the supplemental material.

Fig. 5.

Normalized mean PLV across the three tasks. The mean PLV value for each participant was centered to the grand average value (see supplemental material for details). Thus, the resulting boxplots only show within-subject variability, allowing for better comparison across the tasks. The thicker middle line represents the median value, and the filled circle the mean. The upper and lower box boundaries represent the 25% and 75% quartiles respectively. Unfilled circles are outlier values that fall more than 1.5 times the interquartile range from the median. AU refers to arbitrary units.

Importantly, for this study we were specifically interested in whether PSY exhibit lower theta-gamma PAC compared to HC, particularly in the Active WM + condition. Contrary to our expectations, we found that the PLV was very similar between the two groups (see Fig. 6A). A 2x2 task by group ANOVA found no significant main effect of group (F(1,65) = 2.12, p = 0.151), and no significant interaction between group and task (F(2,130) = 0.26, p = 0.770, HFe = 0.992), indicating that across all tasks, PSY and HC do not show significantly different levels of PAC.

Fig. 6.

Main effects on mean PLV, separated by diagnostic group (HC in green and PSY in blue). Shaded regions represent the group-level 95 % confidence interval (i.e. between-subject variance). Error bars represent the 95 % individual-level confidence interval (i.e. the within-subject variance). * represent an overall significant main effect at the p < 0.05 level, tested through the mixed effects ANOVA. # represents a significant difference between neighboring time windows, tested as pairwise paired t-tests within each group. AU refers to arbitrary units. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

We next sought to verify that there were no group differences in temporal, spatial, or spectral patterns in PAC. In line with previous work (Papaioannou et al., 2022), a 2x8 group by time ANOVA showed a main effect of time window (F(7,462) = 2.50, p = 0.021, HFe = 0.870; see Fig. 6B), but no significant interaction between group and time window (F(14,924) = 0.62, p = 0.851, HFe = 0.818). Similarly, a 2x2 group by electrode cluster ANOVA revealed that PLV was higher in the posterior electrode cluster than in the frontal electrode cluster (F(1,65) = 49.18, p < 0.001), but showed no significant interaction between electrode cluster and group (F(1,65) = 0.11, p = 0.741; Fig. 6C). Lastly, a 2x2 group by frequency ANOVA revealed a significant main effect of frequency band (F(1,65) = 492.35, p < 0.001), with PLV being higher for the 25–35 Hz band than for the 45–55 Hz band. However, once again, we found no significant interaction between group and frequency band (F(1,65) = 1.73, p = 0.193; Fig. 6D). Thus, the two groups showed similar patterns of theta-gamma PAC, both in terms of magnitude, and temporal, spatial, and spectral distribution.

3.3. Theta-gamma PAC and task performance

We next turned to the question of whether individual variation in average theta-gamma PAC is associated with task performance. To limit the number of comparisons and avoid unnecessary segmentation of the data, we applied nested linear regression models to determine whether adding specific factors (task, time window, electrode cluster, frequency band) increased the explanatory power of the models above and beyond a simple correlation between K and average theta-gamma PAC. We found that adding task as a factor did not significantly increase the explained variance (or, more accurately, significantly decrease the residual sum of squares) compared to the base model (F(4,199) = 0.05, p = 0.995). Similarly, neither time window (F(14,534) = 0.02, p = 1.00), nor electrode cluster (F(2,132) = 1.01, p = 0.368) significantly improved the model. However, adding frequency band as a factor did result in a more predictive model (F(2,32₎ = 9.39, p < 0.001), suggesting that separating the PLV by frequency band changes the association between PLV and K.

To further explore this effect, we conducted two separate correlation analyses between PLV and K (one for each frequency band). Across both PSY and HC, the mean PLV over the 45–55 Hz band had a significant negative correlation with K (r = -0.460, p < 0.001), whereas the mean PLV within the 25–35 Hz band exhibited a trend-level positive correlation with K (r = 0.230, p = 0.061; see Fig. 7A). Similarly, we compared the mean PLV across high-performing and low-performing participants (based on a median split) for each frequency band (see Fig. 7A). We found that PLV for the 45–55 Hz band was significantly lower in participants that performed better (t (65) = -3.04, p-value = 0.003). Conversely, PLV for the 25–35 Hz band was significantly higher in participants that performed better (t(65) = 2.27, p-value = 0.03). This matches the patterns seen in the correlations above, and highlights the differences between the two frequency bands.

Fig. 7.

(A) Relationship between the actual working memory capacity (K) for each participant and theta-gamma PAC at each frequency band, shown as a correlation (top) or as median-split boxplots (bottom). The thicker middle line represents the median value, and the filled circle the mean. The upper and lower box boundaries represent the 25 % and 75 % quartiles respectively. Unfilled circles are outlier values that fall more than 1.5 times the interquartile range from the median. AU refers to arbitrary units. (B) Correlation between actual working memory capacity and working memory capacity predicted by our linear regression model. The model takes into account each participant’s mean PLV at each frequency and across all three tasks to predict K. (C) shows the same model, but using only electrophysiological data from the Passive WM- condition. Note that in this condition, the participants are not expected to hold any information in working memory, or even attend to the colored squares at all, and yet we can still predict their behavioral performance from the Active WM+ condition.

To better capture the interplay between the two bands, we created one final model that included mean PLV within the 45–55 Hz band and mean PLV within the 25–35 Hz band as separate predictors of working memory capacity (K ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}). Fig. 7B shows the predicted K values from this model, plotted against the actual K values of said participants calculated from the behavioral responses during Active WM + . We observed that the expected and predicted values are very strongly correlated (r = 0.578, R² = 0.334, p < 0.001), with theta-gamma PAC explaining approximately 1/3 of the individual variability in working memory capacity.

Note that adding task as a factor to our model did not significantly change its predictive power. To further illustrate this null effect, we ran the above model again using theta-gamma PAC from only the Passive WM- condition. Even when measuring theta-gamma PAC in an entirely different task, with very little demand on attentional or working memory processes, we were able to significantly predict working memory capacity in the Active WM + task (r = 0.540, R² = 0.291, p < 0.001). The resulting correlation between predicted K and actual K from this model is shown in Fig. 7C. Model fits by task, group, and frequency band can be found in Table 2.

Table 2.

Association between PLV at each frequency and working memory performance (K), calculated across diagnostic groups (HC, PSY, or both combined) and using PLV from each task (Active WM+, Active WM-, Passive WM-, or the mean of all 3). In all cases, we are predicting model K as a function of PLV at each band. “β-low band” is the regression coefficient for PLV in the low frequency band; “β-high band” is the regression coefficient for PLV in the high frequency band. F statistics represent the nested model comparison between that model and a null model (where K is predicted by a single constant). Significance denotes if the association was significant after group-level FDR correction (* for significant, or n.s. for not significant). No group differences in correlation were significant.

Association between PLV per frequency band and K
		β-low band	β-high band	Adjusted R2	F	df	p value	Significance
Active WM +	HC	0.354	−0.542	0.249	6.64	(2,32)	0.004	*
	PSY	0.297	−0.497	0.251	5.92	(2,29)	0.007	*
	Combined	0.322	−0.518	0.269	13.15	(2,64)	<0.001	*
Active WM-	HC	0.357	−0.571	0.277	7.50	(2,32)	0.002	*
	PSY	0.401	−0.446	0.274	6.86	(2,29)	0.003	*
	Combined	0.375	−0.519	0.298	15.00	(2,64)	<0.001	*
Passive WM-	HC	0.283	−0.577	0.300	8.29	(2,32)	0.001	*
	PSY	0.346	−0.442	0.222	5.43	(2,29)	0.009	*
	Combined	0.313	−0.521	0.284	14.07	(2,64)	<0.001	*
All Tasks	HC	0.365	−0.597	0.310	6.76	(2,32)	< 0.001	*
	PSY	0.362	−0.485	0.271	8.64	(2,29)	0.003	*
	Combined	0.360	−0.546	0.313	16.05	(2,64)	<0.001	*

3.4. Correlations with clinical, cognitive, and functional outcome measures

Finally, we examined the associations between theta-gamma PAC and more global measures of cognitive functioning, as well as symptom severity and functional outcome. To do this, we ran separate multiple regression models (separately for each group) using the PLV at each frequency band to predict the score of 6 scales measuring different aspects of cognitive functioning (WTAR, WASI, MCCB; see Table 3 for a summary of results). Specifically, we ran models predicting three objective scales of cognitive function (WTAR ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}, WASI IQ ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}, and MCCB ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}), as well as a subjective scale of cognitive function (PRECIS ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}). Furthermore, for the PSY group only, we also tested for associations with symptom severity (BPRS ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}) and level of functioning (SLOF ∼ PLV_{45-55 Hz} + PLV_{25-35 Hz}). To account for multiple comparisons, we applied a group-level false discovery rate (FDR) correction (Benjamini and Yekutieli, 2001) to the final results. We observed that PLV at the two frequency bands was significantly associated with Attention and Working Memory subtests from the MCCB in HC but not PSY at the 0.05 level (Attention: (β_{25-35 Hz} = 0.279, β_{45-55 Hz} = -0.430, r² = 0.186, p = 0.045); Working Memory: (β_{25-35 Hz} = 0.239, β = -0.489, R² = 0.217, p = 0.025). However, these correlations were no longer significant following FDR correction. We found no significant associations between PLV and symptom severity (BPRS-Positive: F(2,29) = 1.57, p = 0.225; BPRS-Negative: F(2,29) = 0.376, p = 0.690; BPRS-Disorganized: F(2,29) = 0.411, p = 0.667) or levels of functioning (SLOF-Social: F(2,29) = 0.414, p = 0.665; SLOF-Occupational: F(2,29) = 1.36, p = 0.271). Thus, overall, there is no clear relationship between PLV and clinical scales in our sample. The heterogeneity of psychotic symptoms makes it harder to find consistent effects at these sample sizes, so we cannot rule out the possibility that a small or symptom-specific association exists but is not evident in our data.

Table 3.

Association between PLV at each frequency and various scales, separated by diagnostic group. Significance denotes if the association was significant after group-level FDR correction (* for significant, or n.s. for not significant, −- if the test was not possible). In all cases, we are predicting the scale scores as a function of PLV at each band. “β-low band” is the regression coefficient for PLV in the low frequency band; “β-high band” is the regression coefficient for PLV in the high frequency band. F statistics represent the nested model comparison between that model and a null model (where the scale score is predicted by a single constant). A breakdown of the specific scales used and their acronyms is given in the methods.

Association between PLV per frequency band and Scale Scores
		β-low band	β-high band	Adjusted R2	F	df	p value	Significance
WTAR	HC	0.289	−0.177	0.082	1.43	(2,32)	0.253	n.s.
	PSY	0.199	−0.057	0.040	0.60	(2,29)	0.554	n.s.
WASI − Full IQ	HC	0.131	−0.285	0.075	1.18	(2,29)	0.321	n.s.
	PSY	0.159	−0.307	0.109	1.71	(2,28)	0.199	n.s.
MCCB − Processing Speed	HC	0.007	−0.223	0.045	0.71	(2,30)	0.498	n.s.
	PSY	0.107	−0.284	0.086	1.33	(2,28)	0.282	n.s.
MCCB − Attention	HC	0.279	−0.430	0.186	3.44	(2,30)	0.045	n.s.
	PSY	0.114	−0.138	0.029	0.41	(2,28)	0.665	n.s.
MCCB − Working Memory	HC	0.239	−0.489	0.217	4.17	(2,30)	0.025	n.s.
	PSY	−0.003	−0.180	0.033	0.49	(2,28)	0.621	n.s.
MCCB − Composite	HC	0.198	−0.339	0.111	1.87	(2,30)	0.172	n.s.
	PSY	0.102	−0.302	0.096	1.49	(2,28)	0.242	n.s.
SLOF − Social	HC	NA	NA	NA	NA	NA	NA	−-
	PSY	0.000	0.167	0.028	0.41	(2,29)	0.665	n.s.
SLOF − Occupational	HC	NA	NA	NA	NA	NA	NA	−-
	PSY	0.294	−0.005	0.086	1.36	(2,29)	0.271	n.s.
PRECIS	HC	−0.063	−0.029	0.006	0.09	(2,29)	0.910	n.s.
	PSY	−0.047	−0.117	0.017	0.26	(2,29)	0.774	n.s.
BPRS − Positive	HC	NA	NA	NA	NA	NA	NA	−-
	PSY	0.224	0.189	0.098	1.57	(2,29)	0.225	n.s.
BPRS − Negative	HC	NA	NA	NA	NA	NA	NA	−-
	PSY	−0.159	0.000	0.025	0.38	(2,29)	0.690	n.s.
BPRS − Disorganization	HC	NA	NA	NA	NA	NA	NA	−-
	PSY	−0.154	−0.045	0.028	0.41	(2,29)	0.667	n.s.

4. Discussion

In this study, we set out to determine a) the specificity of cortical theta-gamma PAC as a working memory marker, b) the degree to which theta-gamma PAC is associated with behavioral measures of working memory, and c) the degree to which differences in theta-gamma PAC dynamics can account for working memory deficits in PSY. Consistent with previous work (Papaioannou et al., 2022), we observed that theta-gamma PAC was not impacted by task instruction, nor did it appear to change as a function of time, for either group. However, the magnitude of theta-gamma PAC did appear to be strongly associated with working memory capacity in both groups, irrespective of the task in which theta-gamma PAC was measured. From this pattern, we can conclude that the processes related to cortical theta-gamma PAC are not necessarily specific to working memory maintenance; however, there does seem to be an association between the magnitude of this nonspecific coupling process and working memory capacity in both clinical and non-clinical populations.

It is hard to know if this theta-gamma PAC reflects a specific process that happens to be relevant to all tasks, or if it is a more general feature of efficient brain dynamics. For example, it is possible that theta-gamma PAC is somehow related to visual processing, or preparatory processes associated with it. The fact that PLV was higher for the posterior cluster is consistent with this theory, as is the slight increase in PLV during the first 300–600 ms from stimulus onset. However, PLV remains high well before and well after stimulus presentation, so it is unlikely that visual processing is the sole source of the coupling. Similarly, it could reflect attentional processes, such as attentional monitoring, or continuous sustained attention. Both the Active WM+ and Active WM- tasks relied heavily on attention. The Passive WM- tasks did not require active attentional engagement, though we cannot be certain that participants did not pay any attention at all. In fact, the presentation of salient stimuli, even if they are task-irrelevant, is almost certainly capturing spatial attention to some degree. However, the persistent presence of theta-gamma PAC even before the stimulus presentation steers us towards a more consistently activated process than attentional capture. Perhaps future studies looking at longer-term attentional effects, or incidental attentional lapses can shed more light on the relationship between theta-gamma PAC and attention.

Another possibility is that theta-gamma PAC reflects some ubiquitous feature of brain dynamics, such as the efficiency of neural communication or the capacity for information processing. Coupling might increase slightly when more information is being processed, such as immediately after a visual stimulus is presented, or when comparing a difficult working memory task to passive viewing, but our results suggest that such an effect is rather small compared to the overall amount of coupling. Thus, it is more likely that PAC reflects the potential for information processing rather than the current amount of information stored.

Nevertheless, the robust correlation with working memory capacity suggests that theta-gamma PAC reflects a meaningful signal, not just neural noise. Specifically, it seems that high-capacity participants (in both PSY and HC) show less PAC in the higher frequencies (45–55 Hz), but more PAC in the lower frequencies (25–35 Hz) − perhaps suggesting that favoring lower frequency coupling leads to more efficient information processing, or a higher capacity for active maintenance of information. The strong negative correlation between high-frequency coupling and working memory capacity also demonstrates that more coupling is not always better – in fact, the participants with higher capacity tend to have lower high-frequency PAC overall. It seems that you need some balance between cross-frequency communication and within-frequency variability for efficient cognition.

Interestingly, PSY did not significantly differ from HC with respect to theta-gamma PAC; they did not exhibit abnormal elevations or reductions in overall PAC, nor was there an interaction effect between group and condition, time, frequency band, or electrode cluster. Although it may be tempting to conclude that theta-gamma PAC is normal among PSY, it is important to note that we also did not find the expected deficit in working memory capacity among this group of PSY. As such, it is possible that this particular sample is unusual in some respect − our HC sample has a slightly lower K than typically reported, and our PSY sample has a slightly higher K than typically reported (Gold et al., 2019). This could be due to differences in demographic matching, or due to random variability in sample composition.

Furthermore, other measures of coupling that can index subcortical-cortical connections or functional connections across different brain regions may yet reveal relevant differences in coupling between PSY and HC that lie beyond the scope of this experiment. Nevertheless, our results suggest that theta-gamma PAC is a cognitively meaningful measure at the individual level in our clinical group. Although not directly evident in our results, it is possible that the measure also has clinical relevance, given the established relationship between reduced working memory capacity and quality of life (Savilla et al., 2008).

The present findings are somewhat at odds with previous work showing abnormal PAC in PSY. However, there are several methodological and experimental differences between the various studies that might explain the inconsistency. For one, there are a number of methods for calculating PAC, such as the phase locking value (PLV) (Sauseng et al., 2009, Papaioannou et al., 2022) or the modulation index (MI) (Barr et al., 2017). These different measures are not always equivalent and may be sensitive to different aspects of theta-gamma PAC (Tort et al., 2010). The different measures also employ different preprocessing steps; for example, before calculating PLV, it is customary to convert the data to current source density (CSD) rather than raw EEG. That does not seem to be the case for calculating the modulation index (Tort et al., 2010). CSD data have the advantage of being reference-independent, and “sharpen” the spatial and temporal distributions of the data (Kayser and Tenke, 2015) which may change the sensitivity of the resulting measure of PAC.

Even when using the same PAC measure, there are several aspects of the experimental design that affect coupling estimates, such as the time windows used, the specific frequencies investigated, or the different methods for preprocessing the EEG signal. For example, Barr and colleagues (who found lower PAC in patients during an n-back task) measured PAC during a long window that included motor responses (Barr et al., 2017), while Grove and colleagues (who found lower PAC in patients during a gaze discrimination task) examined the difference in PAC in a shorter time window right after stimulus presentation and before any motor response (Grove et al., 2021). On a related note, it is unclear to what extent the length of the time windows used in PLV analysis change the resulting values (Tort et al., 2010). One of the reasons we chose to use windows of equal length is to minimize any computational differences in PLV across our time windows. Given that across experiments (or sometimes even within an experiment), different time window lengths are used, there might be simple computational biases that contribute to the inconsistency of PAC results.

Another possible reason for the inconsistency of the results across studies is the different approaches in task and stimulus design. Even for experiments that focus on working memory, there are crucial differences in stimuli and tasks which might affect the pattern of the measured PAC. For example, Sauseng et al. used a lateralized change detection task, with participants attending to only one side of the screen (Sauseng et al., 2009). In contrast, both in previous experiments (Papaioannou et al., 2022) and for this experiment, we used centrally presented stimuli, where attention was not directed at any specific part of the screen. This might constitute a meaningful difference, as spatial attention and lateralized stimuli might lead to a different pattern of PAC across the scalp. Barr et al. used a different working memory task altogether (Barr et al., 2017), specifically an n-back paradigm rather than a change detection task. Although both kinds of tasks aim to measure working memory, change detection focuses more heavily on storing multiple items at once, while n-back tasks require continuous updating of the contents of working memory. Thus, it is possible that cortical PAC reacts differently to the demands of an n-back task compared to a relatively simpler change detection task. Further research is necessary to identify the limits and response patterns of PAC across stimulus types and working memory tasks.

Finally, one critical caveat for understanding the mechanisms behind PAC is that we are unable to verify that the signals extracted from the gamma range represent true sinusoidal oscillations. As detailed elsewhere (Donoghue et al., 2020), it has been argued that signals that appear to be manifestations of PAC at the EEG sensor level can instead be caused by non-oscillatory activity bursts. For example, Cole and colleagues used invasive electrocorticography to demonstrate that what appears to be abnormal beta-gamma phase-amplitude coupling in patients with Parkinson’s disease is in fact cause by non-sinusoidal beta bursts of activity (Cole et al., 2017). Thus, we cannot say for certain that what we measured as PAC is in fact reflective of true coupling between theta and gamma oscillations. Distinguishing between true oscillations and non-cyclical burst activity can be very difficult, especially without the use of invasive techniques. However, even though the exact nature of the observed coupling remains unknown, the strong correlation between PAC and cognition suggests that it is a behaviorally meaningful signal that should be examined in future studies.

CRediT authorship contribution statement

Orestis Papaioannou: Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Formal analysis, Data curation, Conceptualization. Kailey Clark: Investigation, Data curation. Nicole N Ogbuagu: Investigation, Data curation. Steven M Silverstein: Writing – review & editing, Conceptualization. Judy L Thompson: Writing – review & editing, Conceptualization. Molly A Erickson: Writing – review & editing, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the Supplementary data to this article:

Data availability

Data will be made available on request.