Causal roles of prefrontal cortex during spontaneous perceptual switching are determined by brain state dynamics

The prefrontal cortex (PFC) is thought to orchestrate cognitive dynamics. However, in tests of bistable visual perception, no direct evidence supporting such presumable causal roles of the PFC has been reported except for a recent work. Here, using a novel brain-state-dependent neural stimulation system, we identified causal effects on percept dynamics in three PFC activities—right frontal eye fields, dorsolateral PFC (DLPFC), and inferior frontal cortex (IFC). The causality is behaviourally detectable only when we track brain state dynamics and modulate the PFC activity in brain-state-/state-history-dependent manners. The behavioural effects are underpinned by transient neural changes in the brain state dynamics, and such neural effects are quantitatively explainable by structural transformations of the hypothetical energy landscapes. Moreover, these findings indicate distinct functions of the three PFC areas: in particular, the DLPFC enhances the integration of two PFC-active brain states, whereas IFC promotes the functional segregation between them. This work resolves the controversy over the PFC roles in spontaneous perceptual switching and underlines brain state dynamics in fine investigations of brain-behaviour causality.


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Dynamic and flexible changes are among fundamental key properties of human cognition and 2 perception. Bistable visual perception has been widely used to investigate such cognitive dynamics 1,2 , 3 and the prefrontal cortex (PFC)-in particular, right frontal eye fields (FEF) and anterior/posterior 4 dorsolateral PFC (a/pDLPFC)-has been thought to be involved in the spontaneous perceptual 5 switching [1][2][3][4][5][6][7][8][9][10] . Theoretical work also indicates that top-down signals from these PFC regions to the 6 visual cortex are essential to the perceptual inference 11,12 . These studies indicate that inhibitory neural 7 modulation of the PFC areas should induce behavioural changes in the bistable visual perception.

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However, no empirical human study has identified such behavioural causality of the PFC 2 . Instead, 9 research using transcranial magnetic stimulation (TMS) reported that neural suppression of a brain 10 area near the right aDLPFC did not affect bistable visual perception 13 , and other studies claimed that 11 the PFC activity is not essential to the emergence of multistable perception 14,15 but mere a 12 consequence of it [15][16][17][18] .

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Why is it so difficult to detect the prefrontal causal roles in the multistable perception paradigm?

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Here, given that the whole-brain neural activity during bistable perception is described as large-scale 15 brain state dynamics 19 , we hypothesise that causal roles of the PFC regions should also be 16 dynamically changing during the fluctuating visual awareness. That is, if the neural activity in the 17 multistable perception can be stated as dwelling in and transitions between a parsimonious number of 18 brain states 19 , the detectability of the prefrontal causal effects on the perceptual awareness should be 19 determined by the brain state in which the neural activity pattern is staying when the neural 20 stimulation is administered. If so, such state-dependent behavioural causality should be hardly 21 observed when we intervene in the PFC activity without tracking the large-scale brain state dynamics.

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To focus on neural mechanisms in the higher-order cortex, this study did not adopt a test of binocular 27 rivalry, which has been often explained by inter-hemispheric neural suppression in the lower-level 28 brain systems [31][32][33] ; instead, we used a test of bistable visual perception induced by a structure-from-29 motion (SFM) stimulus (Fig. 1a), in which the same visual stimulus is presented to both of the eyes of    Fig. 1c. We first conducted offline energy landscape analysis, whose results allowed us 7 to categorise brain activity patterns into either of the major brain states. By implementing 8 such classification information to an online EEG analysis, we tracked brain state 9 dynamics and administered inhibitory TMS in state-/state-history-dependent manners.

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These EEG observations are essentially the same as our previous fMRI findings 19 , which also 25 provides face validation to the locations of the EEG electrodes.  In the graph, a branch end represents a local minimum, and the lower energy values of 4 the local minima indicate the more stable brain states; the heights of the energy barriers 5 between the local minima are known to be inversely correlated with the transition 6 frequencies between the brain states.  neural activity pattern at each timepoint into either of the three major brain states. In Control

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Experiment II, we implemented such classification information into an online EEG analysis 29,30 (right 20 panel of Fig. 1c) and tracked the brain state dynamics with high accuracy (similarity to results based 21 on the offline analysis >82.3%; Fig. 1i). Then, by linking the online analysis to monophasic TMS, we 22 succussed in triggering a burst of inhibitory TMS only when the neural activity pattern was staying in 23 a specific major brain state (accuracy >84.8%, Fig. 1j; latency <0.8msec, Fig. 1k).

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Fig. 1i-k. In Control Experiment II, the online EEG analysis could track brain state 1 dynamics as accurately as the offline analysis (panel i). Brain-state-dependent TMS 2 triggering system also achieved accurate neural tracking (panel j) with short delays 3 (panel k). Note that the accuracy in the TMS trigger (panel j) tended to be higher than 4 that in simple brain-state tracking (panel i) presumably because TMS was triggered only 5 when a specific brain state was expected to continue in a certain period (here, 150msec) 6 and such a criterion should work as temporal smoothing and improve the signal-to-noise 7 ratio. Each dot represents each participant. *** indicates PBonferroni < 0.001 in paired t-tests 8 (df = 64).

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By applying this state-dependent TMS over the three PFC regions (i.e., aDLPFC, pDLPFC and FEF;

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The neural inhibition of aDLPFC during F state prolonged the percept duration (t33=9.4,

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If some behavioural causalities are detectable when the whole-brain neural activity pattern is dwelling 12 in specific brain states, others may emerge when the neural activity pattern has finished travelling a 13 particular brain state trajectory. We then tested this hypothesis and found such state-history-dependent 14 causality (F5,33=85.6, P<10 -3 for the main effect in a two-way ANOVA; Fig. 2b). Here, we focused on 15 Int state because only the brain state had two incoming pathways (i.e., a path from F state and one 16 from V state; Fig. 1g).

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The

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These behavioural results imply that the neural mechanisms underlying this behavioural causality 13 should be also understood in terms of brain state dynamics. Therefore, we then sought for such 14 neurobiological accounts for these seemingly complicated behavioural observations by probing how 15 the TMS affected the brain state dynamics.

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First, we formulated working hypotheses on the neural effects by conducting numerical simulation on 17 how TMS would affect the structure of the energy landscape that underpinned the brain state 18 dynamics. In particular, we calculated changes in the heights of the energy barriers between the three 19 major brain states (Fig. 2d), because the barrier heights are associated with the dwelling time in the 20 brain states and inversely correlated with the transition frequency between them 19 .  As to aDLPFC (Fig. 2e), the numerical simulation showed that the TMS should increase the energy 2 barrier heights between F and Int state (F4,33=340.1, P<10 -3 for the main effect in a two-way 3 ANOVA; t33>15.2, PBonferroni<0.001 in post-hoc paired t-tests, d>2.6) and decrease the barrier height 4 from Int to V state (t33=38.0, PBonferroni<0.001, d=6.7). As a result, the ratio of the Int-to-F barrier to the 5 Int-to-V barrier should significantly increase (t33=27.1, PBonferroni<0.001, d=4.8).

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Regarding pDLPFC (Fig. 2f), the neural inhibition of the region should alleviate the energy barriers 7 between F and Int state (F4,33=89.10, P<10 -3 for the main effect in a two-way ANOVA; t33>11.6,

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PBonferroni<0.001, d>2.0) and that from Int to V state (t33=48.9, PBonferroni<0.001, d=8.6). The magnitude 9 of the decrease in the Int-to-F barrier height should become larger than that in the Int-to-V barrier,

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Effects on brain state dynamics

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These structural changes in the energy landscapes allowed us to infer the TMS-induced neural effects 26 on the brain state dynamics (Fig. 2h).
For example, the increase in the height of the F-to-Int energy barrier-which is supposed to be 1 induced by TMS over aDLPFC-should enhance the segregation between F and Int state, impede the 2 transition from F to Int state and prolong the dwelling in F state. Moreover, such longer F-state 3 dwelling should be observed in F-state-dependent TMS condition the most clearly.

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By the same logic, the relatively lower Int-to-V barrier, which is expected to occur in the aDLPFC 5 TMS condition, should increase the Int-to-V transitions. Regarding the TMS over pDLPFC, the lower 6 F-to-Int energy barrier should shorten the F-state dwelling, whereas the relatively lower barrier from 7 Int to F state should increase the Int-to-F transitions. In the FEF TMS condition, the lower F-to-Int 8 barrier should reduce the F-state dwelling.

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We tested and confirmed these hypotheses by measuring the dwelling time of the three major brain 17 states and transition frequencies between them in all the state-dependent TMS conditions.

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In the experiments administering TMS over aDLPFC, the increase in the F-to-Int energy barrier was 19 correlated with the longer F-state dwelling seen in the F-state-dependent aDLPFC TMS (t33=11.6, 20 PBonferroni<0.001, d=2.0; r33=0.59, P<0.001; Fig. 3a). Also, the relatively larger Int-to-F energy barrier 21 was associated with more frequent Int-to-V transitions that was seen in the Int-state-dependent TMS

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In the sessions administering TMS over pDLPFC, the lower F-to-I energy barrier was correlated with 24 the shorter F-state dwelling that was measured in the F-state-dependent neural suppression (t33=6.9,

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These results clarify TMS-induced effects on the brain state dynamics during the bistable visual 6 perception and demonstrate that such neural effects are underpinned by the structural changes in the 7 hypothetical energy landscapes.

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We investigated this question by tracking the magnitudes of the correlations between the neural 22 effects and the energy barrier changes (Figs. 3a-e) when we were sliding the time window that was used to quantify the neural effects (the upper panel of Fig. 3f). This analysis detected that all the 1 correlations began to weaken after an approximately 1.5-sec mild decline (the lower graph in Fig. 3f).

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This result indicates that the current TMS-induced neural effects started to decay within ~1.5sec after 3 the stimulation; thus, the brain state dynamics and corresponding energy landscapes began to return to 4 the original forms in such a time scale.

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As to the state-dependent behavioural changes, the longer percept duration seen after the F-state-19 dependent TMS over aDLPFC was largely due to the prolonged F-state dwelling, which was induced 20 by the higher energy barrier from F state to Int state (Fig. 4a). In contrast, the de-stabilised visual 21 perception induced by the F-state-dependent TMS over pDLPFC/FEF was attributable to the shorter 22 F-state dwelling time, which was caused by the lower F-to-Int energy barrier (Figs. 4b and 4c).

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If we admit that the percept duration is closely linked with the length of the F-Int-V travel (Fig. 1h), 24 the state-history-dependent behavioural causality could also be seen as a consequence of the transient 25 changes in the brain state dynamics.

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In the mediation analysis, the shorter percept duration observed after the Post-F Int-state-dependent 27 TMS over aDLPFC was caused by the increase in the Int-to-V transitions, which was induced by the larger gap between the Int-to-F barrier and Int-to-V barrier (Fig. 4d). This statistical result is 1 reasonable because the relatively lower Int-to-V energy barrier would facilitate the Int-to-V 2 transitions transiently, accelerate the completion of the F-Int-V travel and shorten the percept 3 duration.

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Conversely, the longer percept duration yielded by the Post-V Int-state-dependent TMS over aDLPFC 5 is interpretable as a result of the relatively higher Int-to-F energy barrier's impeding the Int-to-F 6 transitions, accelerating the backward moves to V state and slowing down the completion of the F-Int-7 V travel (Fig. 4e).

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The mediation analysis showed that the state-history-dependent causal roles of pDLFPC were also 9 explainable by the same logic. The longer percept duration yielded by the pDLPFC TMS during Post-10 F Int state could be regarded as a behavioural manifestation of the temporary slowdown of the F-Int-V 11 travel due to the more frequent backward Int-to-F transitions, which was originated from the 12 relatively lower Int-to-F energy barrier (Fig. 4f). In contrast, the shorter percept duration induced by 13 the pDLPFC TMS during Post-V Int state can be seen as results of the acceleration of the F-Int-V 14 travel due to the more frequent forward moves from Int to F state, which was induced by the lower

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This study has identified state-/state-history-dependent causal behavioural roles of the three PFC Intermediate state, whereas pDLPFC activity supports the functional diversity between the two PFC-4 active brain states; the FEF activation plays a critical role in the stabilisation of Frontal-area-dominant 5 state.

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These findings may not be directly applicable to other types of multistable visual perception, such as 7 binocular rivalry, which is often explained by neural responses in lower-level brain architectures 8 including the visual cortex 31,32 and lateral geniculate nucleus 33 . Instead, for the SFM-induced bistable 9 perception, the current behavioural observations were robust. All these behavioural findings were 10 replicated in a small but independent cohort (N=14; t13>2.9, P<0.01 in one-sample t-tests; Fig. 5a).

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The error bars show the s.e.m.

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The current observations re-highlight the fact that brain-behaviour causality is changing so 26 dynamically even during a simple cognitive task that we often cannot behaviourally detect it in 27 conventional neurostimulation experiments that do not consider the temporal changes of the brain 28 states 21,38 . Previous work has addressed this issue by controlling, inferring or monitoring the brain state: some studies controlled the brain state using external stimuli and applied the TMS when a 1 specific sensory stimulus was presented to the participants 39-41 ; a clinical research adopted emotional 2 states as indicators of the neural activity and determined the timing of the deep brain stimulation 3 based on such inference 42 ; neurophysiological studies monitored neural activity and determined the 4 timing of brain stimulation based on the frequency, phase or power of the neural signal 28-30,43,44 .

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The current TMS method is categorised into the last group and could be seen as advancement of such 6 direct-neural-monitoring-based brain stimulation. Differently from the previous work monitoring a 7 single neural activity 28-30,43,44 , the TMS system used here can track the brain state using neural 8 activity patterns recorded from multiple remote brain regions. Given the multi-regional brain state 9 dynamics underpin complex cognitive activities 19,23,45 , such a multivariate monitoring approach could 10 be regarded as a more effective manner to investigate more physiological brain-behaviour causality.

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Moreover, the combination of EEG-triggered TMS and energy landscape analysis may become 12 foundation of a novel tool to control seemingly unstable behaviours. In fact, two-month longitudinal 13 experiments (N=63) revealed accumulative effects of this closed-loop neural modulation system.

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To interpret the current observations in psychological contexts such as predictive coding 2,11 , more 11 model-based neuroimaging studies and theoretical work would be necessary. However, this study has 12 resolved the long-lasting controversy over prefrontal causal roles in multistable perception 2 and 13 revealed distinct functions of the PFC in the brain state dynamics that underpin spontaneous 14 perceptual inference. Furthermore, the combination of the brain-state tracking method and neural-15 activity-dependent brain stimulation system may re-ignite neurobiological investigation on state-16 dependent dynamic causality 20 in human cognition and become another foundation of more effective 17 neural perturbation tools to intervene in neuropsychiatric conditions.  Fig. 1).

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First, 65 healthy adult individuals underwent two control experiments, in which we recorded their 4 EEG signals while they were experiencing bistable visual perception induced by a structure-from-5 motion (SFM) stimulus (Fig. 1a). In the Control Experiment I, The EEG data were used to (i) identify 6 individual brain dynamics during bistable visual perception and (ii) verify the locations of EEG 7 electrodes and TMS stimulation site. In the Control Experiment II, we examined the accuracy of the 8 brain-state tracking and state-dependent TMS system.

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This study was approved by Institutional Ethics Committees in RIKEN and The University of Tokyo.

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The TMS protocols used here complied with the guideline issued by the Japanese Society for Clinical  The test design of bistable visual perception paradigm in this study is essentially the same as that used 20 in our previous work 19,46 . The participants were presented with a structure-from-motion (SFM) 21 stimulus (Fig. 1a)

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In each run, the participants were instructed to see the SFM stimulus for 90 sec with their chins put on    14 Using a stereoscopic neuro-navigation system (Brainsight Neuronavigation, Rogue Research, UK) 15 and structural MRI brain images, we located the TMS-compatible EEG electrodes right above on 16 these seven ROIs. Also, for the following calculation of Hjorth signals 53 (see Section 3.2.1), we put 17 three other EEG electrodes around each ROI electrode (i.e., four electrodes were used for one ROI;

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First, seven electrodes were located right above on the seven ROIs using a stereoscopic 28 neuro-navigation system. Then, for each ROI, three additional electrodes were placed right around the electrodes for the following Hjorth signal calculation. The yellow circles 1 schematically represent the electrodes put above the ROIs, whereas the blue ones 2 indicate the neighbouring electrodes.  14 In addition, to obtain sufficient length of clean EEG data for the following brain-state tracking, we put

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The MEPs of the right FDI were recorded using a pair of 9mm-diameter Ag/AgCl surface cup 25 electrodes that were placed over the muscle belly and the metacarpophalangeal joint of the index 26 finger 56 . Before offline analyses, the MEP signals underwent a temporal filter (100Hz-3kHz). The 27 optimal place for the single-pulse TMS for the right FDI muscle was determined as the area over 28 which the simulation induced the largest MEP.

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The mean AMT across the entire participant cohort in the three types of the current TMS experiment  In this study, we analysed the EEG data in both offline and online manners. We described the details 1 of the two types of EEG analysis in the following sections. The offline EEG analysis was applied to data obtained in the control experiment. We conducted the 5 following conventional preprocessing 57 to the EEG data using MATLAB (MathWorks, US) and 6 EEGLAB 58 .

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First, the EEG data were referenced to the average across all the electrodes, down-sampled to 300Hz 8 and underwent a temporal filter (1-80Hz). Then, we conducted an independent component analysis to 9 remove cardio-ballistic artefacts and other artefacts induced by eye blinks, eye movements and 10 muscle activity. Next, we marked epochs whose mean global field power was too large (> 5SD of 11 mean power across entire recording) and excluded those time periods in all the following main 12 analysis. We then filtered the data to delta (1-4Hz), theta (4-8Hz), alpha (8-13Hz), beta (13-30Hz) 13 and gamma (30-80Hz) bands and estimated a Hilbert envelope amplitude for the gamma-band signal 14 57,59 .

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We used the Hilbert envelope amplitude for the gamma band as a neural signal for each electrode, 16 because the aim of the current EEG recording was to trace the brain state dynamics that was seen in 17 our previous fMRI study 19 and the gamma-band signal dynamics were correlated with fMRI signals

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First, as in our previous fMRI work on the brain dynamics during bistable perception, we binarised 27 each ROI time-series data using the temporal average of the signals as the thresholds. We then fitted a  Next, we built an energy landscape and searched for major brain states. The energy landscape was 18 defined as a network of brain activity patterns Vk (k = 1, 2, …, 2 N ) with their energy E(Vk), in which two 19 activity patterns were regarded as adjacent if and only if they took the opposite binary activity at a 20 single ROI. We then searched for local energy minima, whose energy values were smaller than those 21 of all the N adjacent patterns.

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We then examined hierarchal structures between the local minima by building disconnectivity graphs 23 as follows 19,23 : (i) first, we prepared a so-called hypercube graph, in which each node representing a 24 brain activity pattern was adjacent to the N neighbouring nodes. (ii) Next, we set a threshold energy

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Based on the obtained results, we built a hierarchical tree whose leaves (i.e., terminal nodes down in 32 Based on this dysconnectivity graph, we then estimated basin sizes of the local minima as follows. We 3 first chose a node i from the 2 N nodes. If any of its neighbour nodes had a smaller energy value than the 4 node i, we moved to the neighbour node with the smallest energy value. Otherwise, we did not move,

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indicating that the node was a local min. We repeated this protocol until we reached a local min. The 6 initial node i was then assigned to the basin of the local min that was finally reached. This classification 7 procedure was repeated for all the 2 N nodes. The basin size was defined as the fraction of the number 8 of the nodes belonging to the basin.

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The energy barrier between local minima ℓ and m was defined based on the procedure of building the 10 disconnectivity graph. When we built the disconnectivity graph by lowering the threshold energy level

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Through this coarse-graining procedure, we defined the three major brain states (i.e., Frontal,

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Intermediate and Visual states) and calculated structural indices of the energy landscapes (i.e., the 24 height of the energy barrier). In addition, this summarisation allowed us to classify all the nodes (i.e., 25 brain activity patterns) on the energy landscape-except for nodes on the saddles-into any of the three 26 major brain states for each participant. The vectors that were not classified into any of the three major 27 brain states were labelled as "other state". This classification information would be used in the following 28 EEG-triggered state-dependent TMS experiment.

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3.2.5. Offline EEG analysis: simulation of brain state dynamics

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In the final part of the energy landscape analysis, we depicted and quantified the brain state dynamics 32 by a random-walk simulation in the energy landscape 19,23 . We simulated movement of the brain activity 33 patterns using a Markov chain Monte Carlo method with the Metropolis-Hastings algorithm 62, 63 . Any brain activity pattern Vi could move only to a neighbouring pattern Vj with probability 1 . For each individual, we repeated this random walk 10 5 steps with a randomly 2 chosen initial pattern, which depicted the trajectory of activity patterns as a series of staying in and 3 transitions between the three major brain states. The first 100 steps were discarded to minimise the 4 influence of the initial condition.

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Our previous work demonstrated a strong correlation between the percept duration and the length of 6 return travel between Frontal state and Visual state via Intermediate state 19 . Given this, we compared 7 the behaviourally observed percept duration to the length of the Frontal-Intermediate-Visual travel that 8 was calculated in the above random-walk simulation. 9 10 3.2.6. Offline EEG analysis: temporal smoothing

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In parallel with the random-walk simulation, we examined empirical brain state dynamics probing the 12 binary neural vectors with seven elements, ! . For this purpose, we first categorised all ! into either 13 of the three major brain states based on the classification information that was obtained in the above 14 "Offline EEG analysis: structure of energy landscape" section. The vectors that were not classified 15 into any of the three major brain states were labelled as "Other state".

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To reduce the effects of signal fluctuation, we then applied the following temporal smoothing to the 17 time-series of the brain states. First, in a sliding window manner (window length = 10 msec), we 18 calculated the appearance frequency for each brain state in the time window ( Supplementary Fig. 3a),

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which was assigned to each centre time point in the window as the representative appearance 20 frequency for each brain state ( Supplementary Fig. 3b). Next, a Gaussian smoothing filter (FWHM = 21 10msec) was applied to the representative appearance frequency curves ( Supplementary Fig. 3c).

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Based on the resultant appearance frequency values, we chose the most frequent brain state and 23 assigned it as the brain state at the time point ( Supplementary Fig. 3d). Note that this temporal 24 smoothing eliminated the "other state".

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This empirical brain state dynamics would be used to evaluate the accuracy of the following online 26 EEG analysis.

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28 Fig. 3. To reduce the effects of noise-oriented fluctuation in bran state 1 dynamics, we applied two temporal smoothing procedures to the original brain state 2 dynamics data. First, in a sliding window manner, we calculated three appearance 3 frequency values for the three brain states (panels a and b). Then, Gaussian temporal 4 smoothing was applied to the three appearance frequency curves (panel c). By 5 comparing the smoothed curves, we identified which brain state was the most dominant   Fig. 4c).

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Using the remaining 800msec of the neural signals, we then conducted an autoregressive forward inhibitory TMS in this study took 150msec, (ii) the temporal smoothing required 5msec more data 33 points for its sliding-window-based calculations (see Section 3.2.6), and (iii) we prepared 25-msec buffer for the following signal processing to realise a nearly simultaneous EEG-triggered TMS system 1 64 .

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We obtained such 280-msec time-series signal for each ROI and used them in the following analysis. the binary neural vectors into either of the three major brain states based on the classification information that was obtained in the offline energy landscape analysis in the control experiment. The 1 binary neural vectors that were not categorised into any of the three major brain states were labelled 2 as "Other state".

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Next, to reduce the effects of signal fluctuation, we applied the same temporal smoothing protocol to 4 the resultant brain state vector as that used in the "Offline EEG analysis: temporal smoothing". As a 5 result of these analyses and smoothing procedures, we obtained a series of representative brain states 6 in a period between T = -95msec and T = 175msec. Note that this temporal smoothing eliminated the 7 "Other state".

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The state-dependent TMS was performed based on the brain states that were predicted to appear in the 9 forthcoming period between T = 25msec and T = 175msec. The TMS was administered only when the 10 target brain state was dominant in the period (>90% of the brain states). For example, for the Frontal- 14 This 21msec buffer for the online EEG analysis was chosen because the EEG data took ~3msec to 15 reach the analysis machine and the TTL signal from the analysis machine took ~1msec to trigger the 16 TMS. Given these latencies, the TMS was supposed to start almost 25msec after the EEG recording 17 (T = 25msec; Supplementary Fig. 5).

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In addition, the 21msec buffer was sufficiently long for the online EEG analysis. By connecting the

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TTL signal back to the DAQ board of the real-time analysis machine, we evaluated the signal 20 processing delay using the EEG data collected in the Control experiment I and confirmed that the 21 TTL signal reached back to the analysis machine 21.3±0.02msec (mean±s.d., 21.1msec-21.5msec)

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after the EEG signals were input into the machine.

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For the neural-history-specific TMS, we looked into both the forthcoming period (T = 25msec to T = 8 175msec) and the preceding period (T = -95msec to T = 25msec). The TMS was administered only 9 when both the two periods dominantly showed the target brain states. That is, for example, Post-

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Frontal Intermediate-specific TMS was administered only when Intermediate state was dominant in 11 the forthcoming period (>90% of the brain states) and Frontal state was dominant in the neighbouring 12 time window.

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Note that, for both the brain-state-/history-specific stimulation, once a TMS was administered, we did 14 not conduct the next stimulation until at least 9 sec passed. Such an interval gave the current brain-15 state-dependent TMS system a sufficient length of clean EEG data before the next TMS.

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In the Control Experiment I, we collected EEG signals while the participants were conducting the test 31 of bistable visual perception (1.5min/run × 10 runs). The participants started this EEG recording 32 sessions after sufficient training of the test.
For the aim (i), we applied the offline energy landscape analysis to the EEG data and examined whether 1 the brain dynamics seen in our previous fMRI study 19 were qualitatively reproduced in the current EEG 2 experiment. This analysis was conducted for the aim (ii) as well: if we successfully confirmed the 3 reproducibility, such observations would provide face validation to the locations of the EEG electrodes.

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The details of this offline energy landscape were stated above (see "Offline EEG analysis" sections). In the Control Experiment II, the participants underwent test of bistable visual perception (1.5min/run 8 × 11 runs) with the brain-state-dependent TMS system, which was almost the same as stated in the 9 sections (see "Device setup: TMS" and "Online EEG analysis") except for the locations of the TMS 10 coil and an EEG electrode. We placed one of the 32 TMS-compatible Ag/AgCl ring electrodes-which 11 was located on A1 in the original setting-on a wooden table that was set remotely from the participants.

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The TMS coil was placed over the electrode. Using the signal from this electrode, we measured when 13 each TMS stimulation was conducted without causing significant artefacts on the EEG data from the 14 participants.

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The scalp EEG data in the first run were used to calculate the threshold value for binarisation. Therefore,

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we did not apply TMS in the run. In the rest ten runs, the TMS was performed in the following five

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Intermediate-state-dependent conditions. Each temporal condition was tested in two runs.

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In the analysis, we performed both the offline and online analyses using the same EEG data. As stated 20 above, the online EEG analysis required (i) the classification information to determine which major 21 brain state would be assigned to each neural activity pattern and (ii) the threshold to binarise the neural 22 signals. The requirement (i) was met by employing the results of the first half of the control experiment.

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For the requirement (ii), the data during in the first run were used: we conducted the preprocessing part

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Using the classification information and binarisation threshold, we performed the online analysis with 27 the EEG data recorded during the rest of the runs (10 runs). This online EEG analysis was the same as 28 that described above "Online EEG analysis" sections, and we obtained a time-series vector representing 29 brain state dynamics.

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For the sake of comparison, the offline analysis also used the EEG data recorded in the 2 nd -11 th run and 31 estimated the brain-state dynamics. We applied all the above-mentioned "Offline EEG analysis" 32 procedures to the data except for the last random-walk simulation part. This offline analysis provided 33 us with information about which major brain state should be assigned to each neural activity pattern.
Based on the classification information, we then labelled the preprocessed EEG time-series data, which 1 resulted in a time-series vector of brain state dynamics.

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In sum, these two types of EEG analysis gave us two time-series vectors representing the brain state 3 dynamics for each participant. We then compared the two vectors and estimated how accurately the 4 online analysis-based time-series vector predicted one that was based on the offline analysis.

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Technically, we counted timepoints whose brain states in the online analysis-based vector were the 6 same as those in the offline analysis-based vector. We repeated such counting for each of the three 7 major brain states in each participant and evaluated the accuracy.

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In parallel, we examined the temporal accuracy of the TMS. The brain-state-dependent TMS system 9 was designed to administer a TMS train 25msec after a specific brain state was detected in the EEG

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These experiments were conducted on four different days with more than one-week intervals. In each 24 day, the participants received TMS over the same brain sites in the five different brain-state

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This simulation was conducted based on the " and "# that were obtained in the offline energy 24 landscape analysis using the EEG data recorded during the control experiment. If ROIi was the target site of the inhibitory TMS, we removed all the binary neural vectors ! whose element i, " , was set 1 at +1 (i.e., active). Then, using the same " and "# , we built the disconnectivity graph (see "Offline 2 EEG analysis: disconnectivity graph in energy landscape analysis") and estimated the structural 3 properties of the energy landscape (see "Offline EEG analysis: structure of energy landscape"). When 4 the local minimum that represented any of the major brain states was removed in this simulation, we 5 alternatively used the brain state that included the neighbouring neural vector as the major brain state.

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The neighbouring neural vector was defined as a vector that was different from the vector for the local 7 minimum only in one element. In such numerical simulation, all the three major brain states were 8 preserved whichever PFC site was inhibited.

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In this experiment, we adopted the inhibitory QPS protocols that were used in our previous studies 35,36 .

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This TMS consisted of 360 consecutive bursts with 5-sec intervals (i.e., 30min), and each burst 6 comprised four monophasic 20Hz TMS whose intensity was set at 90% of AMT. We conducted this 7 QPS over either of the three PFC regions using the same TMS device as used in the main experiment.

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In addition, we performed a sham condition; thus, the participants came to the lab four times with more-9 than-one-week interval. The order of the TMS conditions was randomised and balanced across the 10 participants.

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In each day, the participants first completed the six control runs of bistable visual perception tests and

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Like the replication and validation experiments, we focused on the seven TMS conditions that 22 induced the significant behavioural changes. In addition, we added three sham conditions, in which 23 the TMS was administered over one of the three PFC regions at random timings. In total, the ten 24 conditions were examined.

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The 63 participants were randomly assigned to two of the ten conditions: each non-sham condition 26 had 13 individuals, whereas two sham condition had 12 participants and the other sham condition was 27 examined with 11 individuals.

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The accumulative effect of each TMS/sham condition was evaluated over nine weeks. In the first 29 eight weeks, the participants underwent weekly TMS/sham experiments. In each day, the participants 30 underwent a TMS session (six runs of bistable visual perception tests) and two control session (three 31 runs) before and after the TMS session. The details of the TMS protocol were the same as those for 32 the main experiment. The brain site for the sham condition was randomly chosen from the three PFC 33 areas for each participant for each session. The target brain sites were not changed during one period.
1 calculating proportional changes in the median percept durations within each day. We also tracked the 2 behavioural effects over the two-month experiment and examined whether the magnitude of the 3 behavioural response at each day was significantly different from the first day (week 0).

4
In the last week (week 9), the participants underwent the control sessions only. Such baseline 5 responses were used to evaluate whether the two-month weekly TMS affected the baseline perceptual 6 stability.     Fig. 1c. We first conducted offline energy landscape analysis, whose results allowed us to categorise 8 brain activity patterns into either of the major brain states. By implementing such classification 9 information to an online EEG analysis, we tracked brain state dynamics and administered inhibitory 10 TMS in state-/state-history-dependent manners.

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The intensity of the current TMS was set at 70% AMT.         The statistical significance of the α⨉β and the insignificance of the γ' support the conclusions.    conditions that induced significant behavioural effects ( Fig. 2a and 2b). In parallel, we also examined 6 behavioural changes in three sham conditions in which TMS was applied over either of the three PFC 7 regions with random intervals. In all the TMS conditions, the participants became more responsive to