Inhibitory control in WM gate-opening: Insights from alpha desynchronization and norepinephrine activity under atDCS stimulation

Our everyday activities require the maintenance and continuous updating of information in working memory (WM). To control this dynamic, WM gating mechanisms have been suggested to be in place, but the neuro-physiological mechanisms behind these processes are far from being understood. This is especially the case when it comes to the role of oscillatory neural activity. In the current study we combined EEG recordings, and anodal transcranial direct current stimulation (atDCS) and pupil diameter recordings to triangulate neurophysiology, functional neuroanatomy and neurobiology. The results revealed that atDCS, compared to sham stimulation, affected the WM gate opening mechanism, but not the WM gate closing mechanism. The altered behavioral performance was associated with specific changes in alpha band activities (reflected by alpha desynchronization), indicating a role for inhibitory control during WM gate opening. Functionally, the left superior and inferior parietal cortices, were associated with these processes. The findings are the first to show a causal relevance of alpha desynchronization processes in WM gating processes. Notably, pupil diameter recordings as an indirect index of the norepinephrine (NE) system activity revealed that individuals with stronger inhibitory control (as indexed through alpha desynchronization) showed less pupil dilation, suggesting they needed less NE activity to support WM gate opening. However, when atDCS was applied, this connection disappeared. The study suggests a close link between inhibitory controlled WM gating in parietal cortices, alpha band dynamics and the NE system.


Introduction
Cognitive control heavily depends on the functions of working memory (WM).It is argued that there is a WM gating mechanism that regulates WM content (Kessler, 2017).That is, there is a gate that controls the two aspects of WM: keeping information in memory (maintenance) and making changes to it (updating).The gate can be imagined as a switch.When it is closed, WM focuses on maintaining the information, and when it is open, WM focuses on making changes to that information.In simpler terms, opening the gate switches WM from holding information to modifying/updating it, while closing the gate does the opposite.This concept has been well demonstrated using the reference-back paradigm (see methods) (Rac-Lubashevsky and Kessler, 2018Kessler, , 2015) ) on a behavioral level.When it comes to WM gate opening, higher levels of intentional control are required.This is due to the switch from the default state of merely maintaining information to the more demanding task of updating it.The reference-back task incorporates comparison trials that do not necessitate WM updating, thereby providing a baseline for comparison in contrast to the classic N-back task (Gevins and Cutillo, 1993).This allows the identification of gating processes and the calculation of the associated costs (Rac-Lubashevsky and Kessler, 2016).Given that the gate closed state is considered a default WM gating mode, the process of gate closing represents a transition from WM demanding state (updating) to a default state (maintenance).In contrast, gate opening signifies a shift from the WM default state (maintenance) to a demanding state (updating).The distinction between gate opening and closing has been highlighted in previous research (Konjusha et al., 2023;Rac-Lubashevsky and Kessler, 2016;Rempel et al., 2021;Yu et al., 2022c).It seems that this distinction depends on the nature of the tasks at hand.The switch cost is more pronounced when switching from a more difficult task to an easier one.However, it is not present when switching from an easier task to a more difficult one (Allport and Wylie, 1999;Gilbert and Shallice, 2002;Schneider and Anderson, 2010).The differences in gate opening and gate closing are linked mainly to two mechanisms related to task switching: reconfiguration (Rogers and Monsell, 1995) and interference control (Allport and Wylie, 1999).The preceding gate states remain primed involuntarily: gate-close (maintenance) for WM gate opening and gate-open (updating) for WM gate closing.In this case, a recollection of the previous gate state (irrelevant to the current task) is carried over to the present state and inhibiting this state consequently causes a switch cost.Hence, the increased control required to perform the difficult task has more carryover information than the control required for the easy task (Evans et al., 2015).Accordingly, closing the WM gate, i.e. switching from the demanding state (open) to the default state (close) of the WM gate (Nir-Cohen et al., 2020), requires more control, compared to opening the gate.Baddeley and colleagues argued that an important process in working memory is the inhibition of no longer relevant task sets (Baddeley et al., 1998).Indeed, inhibition is a key process underlying switch cost (Arbuthnott and Frank, 2000) and in working memory tasks, the switch costs are attributed to the inhibition processes (Arbuthnott, 2008).The switch costs can arise due to inhibitory input causing a decrease in the speed (Boag et al., 2021).Thus, it seems that inhibitory mechanisms also play a role and could trigger the relevant WM function to facilitate WM gate opening and gate closing.However, as of now, the neurophysiological processes underlying WM gating processes are insufficiently understood, because causal mechanistic insights are scarce.Providing further causal mechanistic insights into WM gating neurophysiology through non-invasive brain stimulation in combination with EEG recordings is the goal of the present work.At a neurophysiological level, aforementioned inhibitory control processes are linked to modulations in alpha frequency oscillations (Klimesch et al., 2007).Alpha oscillations increase with more working memory load (Jensen et al., 2002) and also are modulated by the degree of working memory interference (Wianda and Ross, 2019).Parietal alpha band activities have been linked to the suppression of distractors (Sauseng and Liesefeld, 2020) and alpha band activity likely serves WM maintenance (Bonnefond and Jensen, 2012;Jensen et al., 2002).
Consequently, decreases in alpha band activity has been identified as reflecting the ability to gate information by inhibiting task-irrelevant processes (Cooper et al., 2003;Jensen and Mazaheri, 2010;Klimesch et al., 2007;Konjusha et al., 2022;Van Diepen et al., 2019;Yu et al., 2021;Zhang et al., 2016bZhang et al., , 2016a)).Alpha desynchronization processes were shown during task performance (Klimesch, 1999), especially during the WM encoding phase (Wianda and Ross, 2019), suggesting that the desynchronization of alpha plays a role in information processing during WM.Yet, recent findings demonstrated different effects between the WM gate opening and closing, not only in alpha (Konjusha et al., 2023) but also in theta band activities (Yu et al., 2022b).Frontal theta band activity is often interpreted as a marker of cognitive control (Cavanagh and Frank, 2014) and plays an integrative role in controlling working memory processes such as encoding and retrieval (Hsieh and Ranganath, 2014;Sauseng et al., 2010).Moreover, theta oscillations seem to index goal-directed updating and task-set reconfiguration processes (Capizzi et al., 2020).Previous studies using the same task have highlighted the significance of theta frequency oscillations in gating mechanisms (Rempel et al., 2021;Yu et al., 2022b).The general functions of theta and alpha band activities seem to correspond to the two mechanisms of WM gating processes, as theta activity seems to reflect the reconfiguration of the WM gate state and alpha activity, particularly alpha desynchronization, seems to reflect the inhibition of previous gate state.Put together, it seems that the role of alpha desynchronization, indicating the capability of inhibitory control, is a central mechanism underlying the distinction between the WM gate opening and closing.It is therefore important to interfere with alpha band dynamics to provide causal mechanistic insights into the relevance of this for WM gating processes.Of note, GABAergic feedback is strongly implicated in generating the alpha rhythm (Jones et al., 2000;Lőrincz et al., 2009) and anodal transcranial direct current stimulation (atDCS) is thought to reduce GABA concentrations (Filmer et al., 2014;Krause et al., 2013;Nitsche and Paulus, 2011).Therefore, we hypothesize that atDCS may intervene in GABAergic transmission, ultimately resulting in the change of alpha desynchronization and consequently hindering WM gating processes.Therefore, the current study applies the atDCS to interfere with alpha band dynamics.As a target region for tDCS stimulation we used the left dorsolateral prefrontal cortex (dlPFC) because of (i) its critical role in WM maintenance (Barbey et al., 2013;Lin et al., 2022), (ii) WM gating processes (Badre, 2012;Hazy et al., 2007;Nir-Cohen et al., 2023, 2020), and (iii) a known association between WM processes and GABAergic concentrations in the dlPFC (Yoon et al., 2016).It has been reported that atDCS applied to the dlPFC improves WM performance such as retention and recognition (Berryhill and Jones, 2012;Boggio et al., 2006;Chua et al., 2017;Fregni et al., 2005;Jo et al., 2009;Ohn et al., 2008), but see other studies (Horvath et al., 2015).This fits to findings associating frontal and parietal regions with WM maintenance (Daume et al., 2017b;Owen et al., 2005;Roth et al., 2006) and frontal-parietal regions are associated with gate opening, but not gate closing (Nir-Cohen et al., 2020).To delineate how alpha band modulations induced by atDCS affect the processes in fronto-parietal structures, we apply source localization beamformer methods (Gross et al., 2001;Van Veen et al., 1997).Through this, the neurophysiological effects of atDCS become connected with the functional neuroanatomical level.From a conceptual perspective, the distinction between WM gate opening and closing is associated with different cognitive demands of switching from two WM gate states (open and close).Following our hypothesis, we also hypothesize that atDCS affects the alpha desynchronization differently between the WM gate opening and closing processes.If atDCS affects the WM gating processes by impeding the inhibition of the preceding gate state, it might be reflected by an increase in the demand to accomplish the WM gating process.This is likely to cause changes in the phasic norepinephrine (NE) dynamics, which is known to reflect the effort to achieve goals (Aston- Jones and Cohen, 2005).Evidence of atDCS modulating the NE system has been found in previous studies using pupil diameter recordings (Adelhöfer et al., 2019;Kuo et al., 2017).While previous studies have explored the cognitive demands associated with WM and the role of NE dynamics, there is a gap in understanding alpha desynchronization in individuals with varying levels of inhibitory control and how this relationship modulates the phasic NE release.This study could help clarify the mechanisms involved in WM gating and the role of NE dynamics by applying atDCS.To examine this, we record pupil diameter data during the experiment as an indirect indicator of norepinephrine activities (Aston- Jones and Cohen, 2005;Chmielewski et al., 2017;Gabay et al., 2011) that is also often used to measure the "effort" invested in a task (Aston- Jones and Cohen, 2005;da Silva Castanheira et al., 2021), and investigate its association with cortical activities (alpha desynchronization in particular) and behavioral performance.We hypothesize that more effort, indicated by a larger pupil diameter, is required for individuals with lower inhibitory control.This might be associated with lower alpha desynchronization.Moreover, we expect that atDCS application might lead to a general increase in phasic NE release to counteract its impairing effect.In addition, along with the atDCS-induced impairment of alpha desynchronization, its association with pupil dilation is also expected to vanish.

Participants
A total of N = 66 healthy participants were recruited for this study.The inclusion criteria involved no history of neurological or psychological disorder, no cardiovascular disease, no pacemaker or defibrillator, no pregnancy or breastfeeding, nor any metal implantations in the body.All participants had normal or corrected-to-normal vision.A total of N = 19 participants was excluded from the study due to dropout (N = 2), low task performance (N = 10 participants with an accuracy lower than 60% for at least one trial condition), poor EEG signals (N= 1 participants with less than 20 valid trials remained after EEG artefact rejection), or incomplete pupil data (N = 3).Outliers with any WM gating parameters on the behavioral level (reaction time (RT) or accuracy) that were more than three scaled median absolute deviations away from the median were also excluded (N = 3).The final sample encompassed N = 47 participants (age 27.40 ± 5.31, N = 21 males).The sample is comparable to previously conducted studies using the same task (Konjusha et al., 2023;Rempel et al., 2021;Yu et al., 2022b).The participants were instructed to not drink coffee, energy drinks, or smoke before the experiment.The study was conducted adhering to the ethical guidelines and principles outlined by the Technische Universität Dresden and in accordance with the Declaration of Helsinki.Before participation, all participants provided written informed consent and were reimbursed 45 euros after the second appointment for their participation.

Study design
The current study used a sham-controlled cross-over design, with participants being kept unaware of the type of stimulation and the experimental procedure.The experiment was conducted in two sessions, with a minimum of one-week interval between the two appointments.One-half of the group received active atDCS stimulation at the first session and sham stimulation at the second session.Whereas the other half received sham stimulation at the first session and active atDCS at the second session.The order of stimulation conditions (atDCS first vs.sham first) was counterbalanced across all participants.

AtDCS protocol
A battery-operated atDCS device, specifically the DC-Stimulator Plus (NeuroConn, Illmenau, Germany), was utilized in the study.This device delivered a current of 2 mA through two rubber electrodes (5 × 5 cm 2 ; NeuroConn, Illmenau, Germany), which were applied to the skin using Ten20 conductive paste, ensuring a paste thickness of 5 mm between the electrode surface and the skin.This procedure adheres to safety guidelines for atDCS (Antal et al., 2017).The same size of electrodes was used for both the active and reference electrodes to prevent potential skin sensations that could affect blinding in the cross-over study design (Fertonani et al., 2015).The electrode impedance was below 5 kΩ.According to our hypothesis (see Introduction), the experiment aimed to stimulate the left dlPFC.Therefore, the anodal electrode was positioned at the left prefrontal side of the head, centred at EEG recording electrode F3 and surrounded by electrodes AF3, F5, FC3, and F1 according to previous studies stimulating the same brain region (Dubreuil-Vall et al., 2019;El-Hagrassy et al., 2021).The reference electrode was fixed on the right deltoid muscle.The participants underwent 20 minutes of current flowing during the real atDCS appointment.During this stimulation, the current gradually ramped up over 15 seconds, reaching its maximum, which was maintained for the full 20 minutes, and then slowly ramped down for 15 seconds after stimulation.On the other appointment, participants received sham stimulation where the maximum current was only applied with 30 seconds ramping-up following 30 seconds ramping-down while the equipment remained on participants for another 20 minutes to mimic real atDCS.Participants were naïve of the stimulation condition and had no prior experience with atDCS.

Tasks and procedures
For the current study, we used the reference-back task paradigm (Konjusha et al., 2023;Rac-Lubashevsky and Kessler, 2016;Rempel et al., 2021;Yu et al., 2022bYu et al., , 2022c)).This is a wellvalidated task that has been used frequently in measuring the mechanism of WM gating processes (Rempel et al., 2021;Yu et al., 2022bYu et al., , 2022c) ) and also concerning brain modulation techniques (Konjusha et al., 2023).In each trial, there was a centrally presented capital letter ("X" or "O") framed by a coloured square (blue or red).Participants were asked to determine whether the presented letter matched the previously displayed red-framed letter.Response buttons were assigned accordingly, with the right "Ctrl" button pressed for identical letters and the left "Ctrl" button pressed for non-identical letters.This task requires the participants to maintain the previously seen red-framed letter in WM and update it upon the appearance of a new red-framed letter.The trials featuring red-framed letters served as reference trials, while those with blue-framed letters served as comparison trials, used solely for comparing with the preceding red-framed letter.Trials with the same color frame as the previous trial were categorized as nonswitch trials, whereas those with a different color frame were categorized as switch trials.Additionally, the required response distinguished trials as either match (identical) or mismatch (non-identical).A schematic representation of this task can be seen in Figure 1.Each trial commenced with the presentation of a fixation cross for a random duration between 600 and 1000 ms, followed by the presentation of the stimulus which lasted for 1500 ms or until the participant responded.After the stimulus, the screen remained blank for 1000 ms.Before the actual experiment, participants were familiarized with the task and completed a practice session consisting of 30 trials.The main experiment comprised a total of 800 trials evenly divided into 4 blocks.10-second breaks were placed between blocks to allow participants to relax their figures and eyes.The entire experiment lasted approximately 35 minutes.Among these trials, 30 % were switch trials.The frame colour and the required response for each trial were assigned in a random but balanced manner.Additionally, the order of stimulus presentation was randomized but was the same across all participants.Every block commenced with a reference trial that did not require any response.

Computing indices of WM gating processes
The total number of trials was evenly distributed across both sessions, with each participant completing 800 trials per session.Within each session, the trials were classified into eight conditions based on three features: reference/comparison, switch/nonswitch, and match/mismatch.Following the methodology outlined in the study by Rac-Lubashevsky and Kessler (2016), gate opening and gate closing indices were computed for each session using only the trials with correct responses.These indices were calculated using these formulas: Formula 1: Formula 2: As demonstrated by the aforementioned formulas, the WM gate opening refers to the cost associated with switching in reference trials.Whilst, gate closing pertains to the cost of switching in comparison trials.In reference trials, participants were required to update the reference letter, whereas, in comparison trials, participants had to maintain the previous reference.Therefore, the processes of switching in WM were defined in terms of updating and maintenance.Switch reference trials reflect a transition from a closed to an open WM gate state, while nonswitch reference trials reflect a consistent open WM gate state and can be considered as a baseline for the updating process.Consequently, the contrast between switch reference trials and nonswitch reference trials represents the WM gate-opening action that terminates the WM maintenance and activates the WM updating process.Likewise, the contrast between switch comparison trials and nonswitch comparison trials illustrates the WM gate closing action, which reverts the active reference updating process to the default WM state of maintenance.Of note, WM gating is a cognitive process instead of a process of response selection or motor reaction.Therefore, gating parameters regarding time and accuracy likely deviate from normal RT and accuracy in trials.In other words, the accuracy and time of WM gating should be comparable to 0 instead of a general RT (e.g., 500 ms) and accuracy (e.g., 85%) as they represent a cost.It should also be noted that the "match/mismatch" feature does not contribute to the construction of WM gating processes.However, including this feature is crucial when defining trials instead of concatenating trials from these two levels, as the possible unequal number of correct trials can result in data skewness.The potential influence is reduced when averaging across trials for each level.To enhance data visualization, we displayed the data by disregarding the "match/mismatch" feature and instead presenting the mean of variables that were averaged across trials from both levels during certain analyses.In other words, data from eight conditions were merged into four conditions: switch reference, nonswitch reference, switch comparison, and nonswitch comparison.

Behavioral statistics
Behavioral data were analyzed using IBM SPSS Statistics version 28.0.The gating parameters employed in the analysis included the average time cost and accuracy of the selected participants computed from Formulas 1 and 2. Only trials with accurate responses were considered for the computation.Only responses with an RT within a distance of 3 standard deviations from the mean among all trials were considered accurate responses.To investigate the impact of atDCS on the WM gating performance, repeated measures analysis of variance (ANOVA) was applied.This analysis included within-subject factors of "stimulation" (active atDCS vs. sham stimulation) and "WM gating" (opening vs. closing).Then, to understand which factors underlie the potential distinction of atDCS effects between WM gate opening and closing processes, we calculated the differences of RT and accuracy between atDCS and sham as the atDCS effect for each trial condition regardless of the "match/mismatch" dimension (see above).Subsequently, separate ANOVAs were carried out with RTs and accuracy as dependent variables.They were applied to atDCS effects using within-subject factors "switch/nonswitch" and "reference/comparison".When necessary, Greenhouse-Geisser and Bonferroni-corrections were applied.Further, paired-sample t-tests were applied to behavioral parameters separately for each condition to compare the performance under the atDCS and sham stimulation.This aimed to provide a general view of behavioral performance.Descriptive statistics are reported as mean values along with the standard error of the mean (SEM).

EEG recording and preprocessing
The EEG signals were recorded using a set of 60 equidistantly positioned Ag/AgCl electrodes while the participants performed the task.The signal amplification was carried out by a BrainAmp amplifier (Brain Products GmbH).The ground and reference electrodes were placed at coordinates theta=58, phi=78 and theta=90, phi=90, respectively.The BrainVision Recorder software package (Brain Products, Inc.) was utilized to simultaneously capture EEG and pupil data, with a sampling rate of 500 Hz.Subsequently, the raw EEG recorded data underwent preprocessing procedures through the following steps.Initially, the recorded data were downsampled to 256 Hz.Afterwards, infinite impulse response filters were applied, encompassing a frequency range of 0.5 to 20Hz with a slope of 48 dB/oct.Noisy or defective electrode channels were removed and the remaining channels were re-referenced to a common average reference.Moreover, artefacts such as eye blinks, saccades or pulse artefacts were removed utilizing independent component analysis.Other artifacts such as technical noise and offsets in the signal were manually inspected and removed from the raw data.For the previously discarded channels, neighboring electrodes were used to perform topographical interpolation using spherical spines.
After the EEG data preprocessing, the data was epoched into the different experimental conditions (i.e., trial types) and locked onto the stimulus.Only trials with correct responses within a specified response time window between 100 and 1500 ms were considered for analysis.Each epoch, spanning 4000 ms in length, commenced 2000 ms before the stimulus and continued until 2000 ms after the stimulus onset.The total count of trials in each session, meeting the criteria of correct responses and lacking artefacts, were classified into the eight conditions outlined in the task section (see above).Participants with less than 20 trials in any of the eight trial conditions were excluded from the data.This was done to maintain a reasonable signal-to-noise ratio for the subsequent analysis.

Time-frequency decomposition
Following the pre-processing and segmentation of EEG signals, the time-frequency analysis was conducted within a frequency range from 1 to 20 Hz (step size of 0.5 Hz).We used a Morlet wavelet transformation using the FieldTrip toolbox (Oostenveld et al., 2010).The Morlet wavelet parameters were set to a width of 5.5 and a length of 3. To optimize computational efficiency, a padding method called "nextpow2" was implemented.Subsequently, the timefrequency power estimates were normalized to capture task-induced activities by employing a decibel conversion.This normalization process involved utilizing baseline activities observed between -200 and 0 ms relative to the onset of the stimulus.The formula used for the decibel conversion was dB = 10 × log10(P / P0), where dB represents the value in decibels, P and P0 denote the power to be normalized and of baseline, respectively.Next, the normalized timefrequency representations were averaged across trials.Parameters associated with WM gate opening and closing processes were calculated based on the averaged powers corresponding to the respective trial conditions, utilizing Formula 1 for each participant within each stimulation setting (i.e., atDCS and sham).In light of the hypothesized significance of theta and alpha oscillations, frequency bands ranging from 4 to 7 Hz, and from 8 to 12 Hz were specifically selected and averaged across respective frequencies to represent theta and alpha bands.

Cluster-based permutation tests
We aimed to examine the effects of atDCS on WM gating processes at the sensor level, specifically identifying the time points and electrodes that exhibited discrepancies between the atDCS and sham conditions.To achieve this, we employed cluster-based permutation tests to compare frequency band powers between the atDCS and sham stimulation.This was done for theta and alpha band activities and for the WM gate opening and closing processes separately.
For each frequency band and for each gating process, the permutation test was conducted in two stages: In the first stage, we conducted within-subject t-tests to compare the frequency powers at each electrode and time.Subsequently, clusters were formed by grouping time points and electrodes with an alpha value of ≤.05.A cluster required at least one electrode or time point.To establish a reference distribution, we applied a permutation test with 1,000 random draws using the Monte Carlo method on the identified clusters.At the cluster level, the resulting t-values were obtained by summing all t-values within the electrodes and time points of each cluster.We selected the time window that exhibited significant differences between the atDCS and sham conditions and averaged the corresponding frequency powers across the selected time window.The selected time window began from the first time point showing a significant atDCS effect (i.e., 170 ms after stimulus onset, see Results) with a length of 500 ms to satisfy sufficient cycles (N = 4) for the lowest alpha band frequency (i.e., 8 Hz) and to cover the average time duration till a response was made (around 450 ~ 630 ms average, see Results).These averaged frequency powers were used as input for the second stage to identify the specific electrodes that showed the atDCS effect.The cluster-based permutation tests in the second stage followed the same settings as the first stage, aiming to determine the electrodes that demonstrated the atDCS effect for WM gate opening and closing processes.

Beamforming analysis
A statistically significant atDCS effect was observed on alpha band activities during the WM gate opening process at the sensor level, specifically between 170 and 670 ms after stimulus onset (see Results section).To identify the anatomical sources underlying this effect, we employed dynamic imaging of coherent sources (DICS) beamforming analysis (Gross et al., 2001).The analysis was conducted at the single-subject level.At first, the frequency powers and cross-spectral density matrix were transformed using a single Hanning taper within the time window of interest and the corresponding baseline time window (-500 ~ 0 ms relative to stimulus onset).This transformation was performed separately for each condition related to the WM gate opening process for each stimulation type.Furthermore, all activities within the above time window and from the above conditions and stimulation settings were concatenated.A cross-spectral density matrix of the concatenated signals was generated using the same Hanning taper, and a spatial filter with a regularization parameter of 5% was constructed.This spatial filter was then applied to the previously calculated frequency powers of individual conditions to estimate the sources for each condition.The resulting sources within the time window of interest were converted into decibels following the same procedure as at the sensor level.The source activity for the WM gate opening process was computed using the baseline-corrected source activities of each condition, averaged across participants, following Formula 1, for atDCS and sham stimulation separately.
To represent the atDCS effect at the source level, a contrast between the source alpha powers under atDCS and sham stimulation was calculated.This contrast was then projected onto a FieldTrip (Oostenveld et al., 2010) head model template ("standard_mri").Based on the atDCSinduced increase of the alpha activation observed in the WM gate opening process at the sensor level, we selected the top 1% of voxels with positive values of the atDCS-sham contrast to form neuroanatomical clusters indicating enhanced alpha activation after atDCS, employing the DBSCAN method (Ester et al., 1996).To investigate the temporal interaction between pupil activities and cortical activities, we reconstructed the alpha band time series in conditions related to WM gate opening from anatomical voxels displaying a high atDCS effect, as identified in the previous DBSCAN step.This reconstruction was accomplished using a linearly constrained minimum variance (LCMV) beamformer (Van Veen et al., 1997) for each participant.Specifically, for all conditions related to the WM gate opening process under all stimulation types, a covariance matrix was generated using the concatenated EEG single trials from the abovementioned conditions and stimulations to construct a common spatial filter for reconstructing the time series of each selected voxel.This common filter was then applied to the trials of each condition and stimulation type separately to construct the corresponding time series at the source level.The reconstructed time series for each condition and stimulation type were subsequently averaged across voxels and transformed into time-frequency representations of alpha band activities, following the same method employed for the sensor-level timefrequency decomposition.Similarly, the reconstructed alpha band powers for the WM gate opening processes were computed using the same steps as at the sensor level, separately for atDCS and sham stimulation.Paired-sample t-tests were then applied to the source-level alpha band activities at all time points separately to examine the atDCS effect.

Pupil diameter analysis and statistics
The integration of the pupil diameter data and EEG data followed established protocols (Adelhöfer et al., 2019;Giller et al., 2020;Mückschel et al., 2017).Pupil diameter data were acquired through the RED 500 eye tracker program, utilizing iView X software (SensoMotoric Instruments GmbH) at a sampling rate of 256 Hz.The eye tracker was positioned below the monitor at an approximate distance of 60 cm from the participants.Following the data recording, the raw pupil diameter data were synchronized with the EEG data obtained from the participants.This synchronization was achieved by aligning the start and end markers in both datasets, carried out through the EYE-EEG extension of EEGLAB.Afterwards, a low-pass filter of 20 Hz was applied to remove high-frequency activities.Additionally, a median filter was used to discard pupil spikes.To account for artefacts such as eye movements, a linear interpolation technique was implemented.This interpolation procedure was carried out using an open-source toolbox developed by Kret and Sjak-Shie (2019).Following pre-processing, the pupil diameter data from both eyes of each participant were averaged.All trials with correct responses in each session were categorized into eight conditions as mentioned in the computation of gating indices section above.For each trial condition and session, the task-related pupil diameter was averaged across all corresponding trials.Additionally, these values were baseline-normalized by applying the averaged pupil diameter between -200 and 0 ms relative to stimulus onset.

Correlations among alpha band activities, pupil dilations, and RTs
To explore the relationship among NE activities, cortical neural activities, and behavioral performance, during the WM gate-opening process and how they are modulated by atDCS, we conducted correlation analyses among them in pairs.To represent phasic NE activities, we utilized the pupil sizes obtained from the WM gate opening calculations described previously.
For cortical activities, we used the reconstructed time series of alpha band activities obtained from the previous LCMV beamforming step.RT was selected as a behavioral parameter due to the selective atDCS effect on it.Before conducting the correlation analysis between sourcelevel alpha and pupil dilations, the source-level alpha band activities of the WM gate opening process were averaged across voxels, frequencies (8 ~ 12 Hz), and trials.This averaging resulted in a one-dimensional vector that represented the time series of alpha band activities for each participant.This format closely resembled the variable format of the pupil sizes.After that, the alpha power and pupil diameter at each of their respective time point were correlated with the RT of the WM gate opening process using Pearson correlation.Subsequently, the two time series, namely the averaged alpha band activities and pupil sizes, were correlated for each time point.The above correlation analyses were performed across all participants, separately for atDCS and sham stimulation.

Behavioral performance
Figure 2 shows the behavioral performance in aspects of accuracy and time.Focus of the current study was the tDCS effect on WM gating.Therefore, the calculated behavioral indices for WM gate opening and gate closing were focused in the statistical analysis.
The repeated measures ANOVA revealed a main effect of WM gating (F(1,46) = 9.47, ηp 2 = .17,p = .004):The accuracy cost of the WM gate opening process (5%) was significantly higher than the closing process (0.7%).However, no atDCS effect or interaction effect between stimulation and WM gating processes was observed for the accuracy cost (all F(1,46) < .13,ηp 2 < .003,p > .72).Regarding time cost, a main effect of WM gating was observed (F(1,46) = 19.90, ηp 2 = .30,p < .001) that the time cost of the WM gate opening process (58.83 ms) was significantly lower than the closing process (118.95ms).Importantly, an interaction effect between stimulation and WM gating processes was also found (F(1,46) = 6.01, ηp 2 = .12,p = .018).The post-hoc pairwise comparisons showed that the interaction was driven by an increased time cost after atDCS in the WM gate opening (46.28 ms for sham and 71.38 ms for atDCS, p = .008)while time cost remained at a similar level in the WM gate closing process (121.77ms for sham and 116.12 ms for atDCS, p = .57).According to Figure 2D, the application of atDCS generally resulted in an increase in RTs across all trial conditions.However, the notable increase in RTs was observed specifically in switch reference trials (19.59 ms), while the other conditions, especially nonswitch reference trials (7.04 ms), did not exhibit such a significant increase.Hence, the particular atDCS effect (as increased time cost) on the WM gate-opening process was likely driven by the exclusive effect on switch reference trials.The overall task performance, accuracies and RTs for individual conditions are presented in Table 1.Please note that these behavioral indices are not the focus of the present study and only reflect constitutent behavioral parameters necessary to calculate the gating opening and gate closing index which is the focus of the current study.The accuracies ranged from 87.9% to 93.8% across all trial conditions and stimulation settings.A atDCS effect on accuracies was observed only in the nonswitch comparison mismatch condition (t( 46

Neurophysiological activities of WM gating processes
At the sensor level, the cluster-based permutation tests revealed discernible atDCS effects only on the alpha band activities instead of the theta band activities and only in the WM gate opening process but not the closing process.Thus, only the results of the alpha band activities in the WM gate-opening process are presented.This effect became evident 170 ms after the onset of the stimulus on specific electrodes (refer to Figure 3A).In general, increased alpha band activity was observed across all time intervals following the atDCS application before a response was made (≤ 640 ms according to the behavioral result), and the enhancement of alpha band power predominantly occurred in the left parietal region (Figure 3B and 3C).As the current study focuses on the prior-response time window where the essential cognitive processes have been completed, only the alpha activities from 170 ms to 670 ms (around the average response time) were employed for further analysis.The interval was in particular 500 ms to obtain sufficient (N = 4) and complete cycles for the lowest alpha band (8 Hz).
At the source level, the results obtained from DBSCAN (Figure 3D) revealed that the elevated alpha activation, induced by atDCS, primarily originated from the left-lateralized parietal cortex, particularly the superior parietal gyrus (BA 7), postcentral gyrus (BA 1~3, 5), inferior parietal gyri (BA 40), and angular gyrus (BA39).This effect slightly extended to the paracentral lobule (BA 4) and precuneus (BA 7) during the period from 170 to 670 ms following stimulus presentation.The time series reconstructed from the above sources using LCMV demonstrated suppressed alpha band activity during the WM gate opening process under sham stimulation.The application of atDCS, however, mitigated this suppression (Figure 3E).The mitigation was significant from 355 to 523 ms, and also from 629 onwards (till 670 ms, the end of the time window of our interest).By deconstructing the atDCS-induced augmentation of the alpha power in the WM gate opening process, it was found that alpha band activities were generally suppressed, known as alpha desynchronization, after the stimulus presentation, particularly in switch reference trails (Figure 3E).However, the alpha desynchronization was significantly less pronounced after atDCS was administrated.In addition, significant correlation between time cost and the alpha power was only observed under the sham stimulation between 379 and 469 ms (mean r = 0.31, p = 0.037, Figure 3F), as well as from 652 ms onwards (till 670ms, the end of the time window of our interest, mean r = 0.30, p = 0.042).Pupil dilations and its correlations with alpha power and time cost in WM gate opening Task-induced pupil dilation took place around 1000 to 2000 ms after stimulus onset (Figure 4A).However, the t-tests comparing the sham and atDCS conditions did not reveal significant differences between them after stimulus onset.However, a significant correlation between time cost and pupil dilation was found only under the real stimulation.That is, time cost was positively correlated with the task-related pupil sizes after atDCS application from 1558 to 2440 ms (mean r =0.36, p = 0.018), while the pupil was dilating (Figure 4B).We also examined the associations between cortical activities and phasic NE activities as indirectly indexed using pupil diameter.During the period between 170 and 670 ms, when alpha desynchronization was diminished during the WM gate opening, a cluster of positive correlations was found in the sham condition between 400 and 650 ms after the stimulus for alpha activities, and around 600 to 2000 ms for pupil dilation (Figure 4C).This cluster consisted of 37555 data points (r = 0.34, p = 0.021).Of note, this positive cluster indicates an inverse correlation between the strength of alpha desynchronization and the degree of pupil dilation because alpha desynchronization was presented in negative values.No significant correlations between alpha desynchronization and pupil dilation were observed after atDCS application within the time of interest.The remaining clusters of significant correlations were not interpretable as they fell outside the range of pupil dilation.

Discussion
In the present study, we aimed to unravel the distinction between WM gate opening and closing mechanisms with a specific focus on the causal roles of inhibitory control on the preceding gate state and reconfiguring the new gate.To achieve this, we applied atDCS to modulate neurophysiological activities associated with the WM gating processes and we investigated the impact of atDCS on theta and alpha band activities.To further elucidate the functional neuroanatomical correlates of atDCS-induced modulations during WM gating processes, we applied an EEG beamforming approach.
The behavioral data showed that atDCS vs. sham modulated the response speed but not the response accuracy.Performance differences between the two conditions were only evident for the WM gate opening mechanism and not gate closing.The performance was compromised (i.e., higher time cost) when participants were atDCS stimulated compared to receiving sham stimulation.This was the case for almost all trial types; however, it was especially higher for the switch reference trials and it was lowest in nonswitch reference trials.The observed increase in time cost during the WM gate opening process after the atDCS application aligns with changes in cortical activities, where the atDCS effect was specifically found to influence the WM gate opening process rather than the gate closing process.During the sham stimulation condition, alpha band activities in both switch and nonswitch reference trials exhibited a significant decrease after stimulus onset, indicating more alpha desynchronization (Klimesch et al., 1997).The strength of desynchronization differed between switch reference and nonswitch reference trials (stronger in switch trials), resulting in the observed alpha desynchronization during the WM gate opening process (Figure 3E).This finding further shows that inhibitory control is seemingly an essential component of the WM gate opening mechanism and is reflected by alpha desynchronization.Alpha oscillations reflect a mechanism of inhibition that governs the neural system's state of excitability, this consequently affects information processing, which is essential for goal-directed behavior (Mathewson et al., 2011).This inhibition is believed to be achieved through the activation of inhibitory interneurons mediated by GABA (Iemi et al., 2022).Interestingly, atDCS has been found to reduce GABA concentrations (Filmer et al., 2014).Thereby the alterations in behavior linked to alpha oscillations might be driven by the modulation of neuronal excitability influenced also by atDCS.Notably, the desynchronization of the alpha band is linked with active processing (Klimesch, 1999) and is particularly sensitive to attentional demands (Klimesch et al., 2000).It is suggested that when alpha brainwaves are desynchronized, excitability increases (Pfurtscheller, 2001), resulting in improved performance (Mathewson et al., 2011).Conversely, reduced alpha desynchronization leads to lower excitability and poorer performance.Thus, this might explain our finding that during atDCS stimulation, alpha desynchronization was decreased and GABA was modulated, leading to compromised performance.Remarkably, the effects of atDCS, encompassing a discernible rise in time cost and a reduction in alpha desynchronization, are selectively observed during the WM gate opening rather than closing, despite both involving the inhibition of the preceding gate state.This accentuates the disparity in switch costs between WM gate opening and closing.Theoretically, inhibiting the preceding gate state (i.e., updating as gate-open) to close the WM gate proves more demanding than inhibiting the preceding gate (i.e., maintenance as gate-close) of the gate opening due to gateclose serving as the default WM state (Nir-Cohen et al., 2020).Hence, it is plausible that gate closing necessitates more robust inhibitory control compared to gate opening, aligning with the longer time cost, as observed frequently (Konjusha et al., 2023;Rac-Lubashevsky and Kessler, 2016;Rempel et al., 2021;Yu et al., 2022b), including in the present study.In light of this rationale, the absence of atDCS effects on WM gate closing may be ascribed to the potential ceiling effect of atDCS that when the demand of closing the WM gate is high enough to counteract with, hindering the inhibitory control by atDCS might not lead to noticeable impairment.However, this assumption requires validation through future investigations.
To clarify the selective impairment of atDCS on the WM gate opening, we conducted further analyses.There was a strong correlation between the strength of alpha desynchronization and the time cost during WM gate opening in the sham condition (as depicted in Figure 3F).A stronger alpha desynchronization corresponded to a reduced time cost, indicating that stronger inhibitory control over the preceding task set significantly decreased processing time.This finding approves Kessler's (2017) assumption on WM gating processes, emphasizing that gating mechanisms aim to protect from competing task sets rather than irrelevant perceptual information.The correlation between alpha desynchronization and RT disappeared after the atDCS application.This change coincided with higher RTs and diminished alpha desynchronization in both switch and nonswitch reference trials.Remarkably, the reduction in alpha desynchronization was comparable in both trial conditions, resulting in the disappearance of alpha desynchronization during the gate opening.This indicates that atDCS induced a generalized reduction in alpha desynchronization, independently of the trial type.Instead, it was the difference in alpha desynchronization between switch and nonswitch trials during typical task performance (i.e., sham) that contributed to the atDCS effect during the WM gateopening process.Consequently, atDCS hindered the inhibition of the previous gate state, thereby requiring longer processing time.
On a functional neuroanatomical level, alpha modulations were evident in the left-lateralized parietal cortex, as revealed by the beamforming analysis.Interestingly, the atDCS effects were not revealed in the dlPFC, rather mostly in the superior and inferior parietal regions.It has been shown that atDCS modulates not only the targeted stimulation sites but also interconnected regions of the brain (Weber et al., 2014).Earlier research has demonstrated a connection between the frontal and parietal regions in relation to the quantity of information effectively retained in WM (Daume et al., 2017a).Furthermore, efficient WM relies on intact frontoparietal circuits (Crone et al., 2006).According to the frontoparietal network theory, frontal and parietal regions are crucial areas for working memory functions (Marek and Dosenbach, 2018), which has also been demonstrated in research studies (Gazzaley et al., 2004;Palva et al., 2011;Sauseng et al., 2005).Therefore, stimulation of the dlPFC via atDCS might modulate the activity in this network, influencing the parietal lobe's engagement in the WM subprocesses.Furthermore, fMRI studies have found connections between dlPFC and widely distributed brain regions such as the parietal lobe (Courtney et al., 1998;Kim et al., 2003).This suggests, that WM correlates might not rely on a single regionally specific physiology, but rather occur as a result of interactions between brain regions.Previous research has highlighted the role of frontoparietal connections as important for sustaining WM functions (Daume et al., 2017a;Jensen et al., 2002;Pessoa et al., 2002) and that effective WM functions rely on intact frontoparietal networks (Crone et al., 2006).Palva et al., (2010) found enhanced inter-regional synchrony in MEG with increasing memory load among fronto-parietal regions in alpha frequency band, thereby revealing that alpha rhythms are closely linked with task demands in those regions.Overall, this supports the complexity of the neural networks involved in working memory, highlighting the importance of interactions between brain regions in sustaining effective working memory functions.Alpha desynchronization in the parietal lobe is specifically observed in these regions: the superior parietal gyrus (BA 7), postcentral gyrus (BA 1~3, 5), inferior parietal gyri (BA 40), and angular gyrus (BA39).These effects slightly extended to the paracentral lobule (BA 4) and precuneus (BA 7).The left inferior parietal cortices are likely essential for the updating of internal representations of the environmental context using incoming information (Geng and Vossel, 2013) and also act as an information buffer of WM (Koshino et al., 2005).Increased activation in the posterior and medial parts of the parietal cortex including the precuneus has been revealed during the process of gate opening (Nir-Cohen et al., 2020).Both the superior and inferior parietal cortex are involved in the updating mode of WM (Murty et al., 2011).More importantly, the superior parietal region is considered an area that supports the creation of adaptive links between perception and action-related feature codes (Gottlieb, 2007).In light of this, it appears that the alpha band signals, indicative of perception-action integration, are predominantly located in (superior) parietal regions.As posited in a recent framework (Beste et al., 2023), alpha band activity likely represents an interplay of top-down and bottom-up attention, steering binding and retrieval processes of mental representations from memory buffers.This framework aligns harmoniously with the well-established notion of alpha band activity's role in exerting inhibitory gating, which is relevant for suppressing irrelevant features (Beste et al., 2023).Interestingly, parietal alpha band activities have been linked with the suppression of distractors (Sauseng and Liesefeld, 2020).Others have reported, alpha desynchronization in the parietal regions during WM maintenance (Medendorp et al., 2007).Moreover, alpha band activity appears to have a key function, especially when there is a need for certain objects or features to be specifically ignored or selected against (Foxe and Snyder, 2011), also supported by causal evidence (Riddle et al., 2020).This function plays a vital role in WM updating, which relies on WM gate opening.When the gate is opened, distracting/irrelevant information is prevented from entering and is discarded.Therefore, considering also the behavioral data, the atDCS-induced decreased alpha desynchronization in the parietal region might reflect this important role.This aligns also with a framework presented by van Ede (2018), which emphasizes the significance of regionally specific alpha desynchronization when item specific information needs to prioritized in working-memory tasks.
Prior investigations have identified a correlation between augmented cortical activity and decreased pupil dilation (Yu et al., 2022a(Yu et al., , 2022b)), suggesting a coupling of cortical network and phasic NE dynamics.The correlation between pupil dilation and alpha power in sham stimulation corroborates this pattern.It signifies that individuals endowed with stronger inhibitory control capability as indicated by higher levels of alpha desynchronization necessitate less phasic NE activities as indicated by reduced pupil dilation (Aston- Jones and Cohen, 2005;Beatty, 1982;Gilzenrat et al., 2010) to open the gate.Phasic NE activity hints the task engagement and mental effort (Aston- Jones and Cohen, 2005;da Silva Castanheira et al., 2021;van der Wel and van Steenbergen, 2018).Thus, this correlation suggests that inhibitory control as a critical element involved in the WM gate-opening process is intricately linked to mental effort.Precisely, the greater the capacity of inhibitory control, the lower the amount of effort is required.Yet following the application of atDCS, this correlation became indiscernible, concomitant with the decline in alpha desynchronization whilst pupil dilation remained at the same level as in sham stimulation.It is not surprising that the variance of individual alpha powers might be intervened by atDCS and hence the correlation vanished.Nevertheless, a significant correlation between pupil activity and time cost emerged that increased pupil dilation aligned with prolonged time cost -an effect absent in the sham condition.When considering these facets collectively, it becomes evident that while WM gate opening remained demanding yet atDCS application impaired inhibitory control, longer time was requisite for individuals that perceived higher cognitive demand and invested more effort.Intriguingly, longer time cost was not associated with higher cognitive demand (evidenced by noncorrelation with pupil dilation) but with lower capability of inhibitory control in sham conditions when inhibitory control stayed sufficient.It is likely that when inhibitory control efficiently counteracts the demand of opening the WM gate, the speed of opening the gate is predominantly contingent upon the strength of inhibitory control instead of the gating demand.
In summary, the present study the role of inhibitory control processes in WM gating using a neurophysiological and brain stimulation approach with an emphasis on distinguishing between WM gate opening and closing mechanisms.We combined EEG recordings, atDCS, and pupil diameter recordings to triangulate neurophysiology, functional neuroanatomy and neurobiology.The results revealed that atDCS, compared to sham stimulation, affected the WM gate opening mechanism, but not the WM gate closing mechanism.The altered behavioral performance was associated with specific changes in alpha band activities (reflected by alpha desynchronization), indicating a role for inhibitory control during WM gate opening.Functionally, the left superior and inferior parietal cortex, were associated with these processes.The findings are the first to show a causal relevance of alpha desynchronization processes in WM gating processes.Notably, pupil diameter recordings as an indirect index of the NE system activity revealed that individuals with stronger inhibitory control (as indexed through alpha band desychronization) showed less pupil dilation, suggesting they needed less NE activity to support WM gate opening.The study suggests a close link between inhibitory controlled WM gating in parietal cortices, alpha band dynamics and the NE system.

Figure 1
Figure 1 Illustration of the reference back paradigm.The arrow indicates the order of stimulus presentation as an example.

Figure 2 .
Figure 2. Behavioral performance.Plots A and B respectively reveal switch accuracies and time costs during the WM gating processes under atDCS and sham stimulation.Plots C and D show the atDCS effects (i.e. the difference between atDCS and sham stimulation) on different conditions without distinguishing match and mismatch trials.Colored bars denote the mean across participants and error bars represent the standard errors.Each dot represents a participant.

Figure 3
Figure3Neurophysiological activities of the WM gate opening processes.Plot A shows the electrodes and time windows of significant atDCS effect at the sensor level.The time window of interest (170 ~ 670 ms) is bounded in red.Data points without significant atDCS effect are transparentized.Plot B reveals the topographies of atDCS effects (atDCSsham) in the time window of interest (170 ~ 670 ms).Bold red marks the electrodes revealing a significant atDCS effect (p≤.05).Warm colours in topographies denote higher alpha band activities under atDCS than under sham stimulation and the cold colours represent the opposite.Plot C presents the timefrequency representations of the averaged alpha band across the electrodes marked in Plot B for atDCS and sham conditions, respectively.Red rectangles mark the time window and frequency range of the interest.Only alpha band activities of the WM gate opening process are presented due to the lack of significant atDCS effect in neither WM gate closing processes nor theta band activities.In Plot D, orthogonal views display the anatomical sources of atDCS effects during the WM gate-opening processes.Coloured clusters represent the top 1% highest differences in alpha band activities between atDCS and sham stimulation at the source level.Plot E illustrates the reconstructed alpha band time series derived from the selected sources in the WM gate opening process and relevant trial conditions.The red line indicates the time points that exhibit a significant difference between atDCS and sham stimulation.Plot F shows correlations between the alpha powerand time cost during the WM gate opening.The significant correlations are marked in red.

Figure 4 .
Figure 4. Changes of pupil size and their correlations with time costs and source-level alpha powers in the WM gate opening process.Plot A illustrate the pupil size in the WM gate opening process.No significant difference between atDCS and sham stimulations (p≤.05) were observed.Plot B reveals the correlations between pupil size changes and time costs.Time points showing significant correlations (p≤.05) are marked in red.Plot C shows the correlations between source-level alpha powers and pupil changes.Only clusters formed with more than 1000 data points showing significant correlations (p≤.05) are marked by red boundaries.

Table 1 :
Behavioral performance in individual conditions