This paper (2022) combines data of the brain’s resting state under the influence of LSD and cortical mapping of 5-HT2A receptors within the framework of network control theory to validate the central tenets of the REBUS model of psychedelics. In accordance with this model, LSD-induced flattening of the brain’s energy landscape, corresponding to greater flexibility for state transitions and more dwell time in brain states than encode bottom-up activity (e.g. salience network) and decreased persistence of states dominated by top-down (frontoparietal) activity.
Psychedelics including lysergic acid diethylamide (LSD) and psilocybin temporarily alter subjective experience through their neurochemical effects. Serotonin 2a (5-HT2a) receptor agonism by these compounds is associated with more diverse (entropic) brain activity. We postulate that this increase in entropy may arise in part from a flattening of the brain’s control energy landscape, which can be observed using network control theory to quantify the energy required to transition between recurrent brain states. Using brain states derived from existing functional magnetic resonance imaging (fMRI) datasets, we show that LSD and psilocybin reduce control energy required for brain state transitions compared to placebo. Furthermore, across individuals, reduction in control energy correlates with more frequent state transitions and increased entropy of brain state dynamics. Through network control analysis that incorporates the spatial distribution of 5-HT2a receptors (obtained from publicly available positron emission tomography (PET) data under non-drug conditions), we demonstrate an association between the 5-HT2a receptor and reduced control energy. Our findings provide evidence that 5-HT2a receptor agonist compounds allow for more facile state transitions and more temporally diverse brain activity. More broadly, we demonstrate that receptor-informed network control theory can model the impact of neuropharmacological manipulation on brain activity dynamics.
Serotonergic psychedelics such as LSD produce profound but transient changes in perception and subjective experience, and recent neuroimaging work has been synthesised in the RElaxed Beliefs Under Psychedelics (REBUS) model. REBUS frames the brain as a prediction engine and proposes that agonism at cortical 5-HT2a receptors relaxes top-down priors, allowing increased influence of bottom-up sensory input and greater temporal diversity (entropy) of brain activity. Formally, this relaxation is hypothesised to correspond to a reduction in the energy required for the brain to move between recurrent functional states — a “flattening” of the brain’s energy landscape — but this specific prediction had not been tested empirically. This study set out to test that prediction by combining resting-state fMRI with diffusion MRI-derived structural connectivity and PET-derived maps of serotonin receptor density, analysed with network control theory. The investigators tested whether LSD lowers the transition energy between empirically derived recurrent brain-states relative to placebo, whether such lowering is associated with increased state switching and entropy of brain dynamics, and whether the spatial distribution of 5-HT2a receptors can mechanistically account for energy reductions.
Papers cited by this study that are also in Blossom
Carhart-Harris, R. L., Friston, K. J. · Pharmacological Reviews (2019)
Carhart-Harris, R. L., Leech, R., Shanahan, M. et al. · Frontiers in Human Neuroscience (2014)
Luppi, A. I., Carhart-Harris, R. L., Roseman, L. et al. · NeuroImage (2021)
Deco, G., Cruzat, J., Cabral, J. et al. · Current Biology (2018)
The study used a within-subjects design in which 20 healthy volunteers underwent two scanning sessions at least 14 days apart: one after intravenous placebo and one after LSD (75 μg infused over two minutes, given 115 minutes before resting-state scanning). After exclusions for anxiety and excessive motion, 15 participants (four women; mean age 30.5 ± 8.0) remained for analysis. On each session three eyes-closed resting-state scans of 7:20 minutes were acquired; the music-containing middle scan was excluded and analyses used resting scans without external stimulation. Standard fMRI pre-processing steps were applied and regional time series were extracted for 462 grey-matter regions. Recurrent brain-states were identified by concatenating all subjects' fMRI time series (both conditions) and applying k-means clustering with Pearson correlation as the distance metric. Stability checks and an elbow criterion supported k = 4 clusters, which grouped into two anti-correlated meta-states (labelled SOM+/-, reflecting somatomotor/ventral attention dominance, and FPN+/-, reflecting frontoparietal dominance). Temporal metrics computed from the state time series included fractional occupancy, dwell time, appearance rate, and transition probabilities. Because diffusion MRI was not acquired in the LSD cohort, a population-average structural connectome derived from 1,021 Human Connectome Project subjects was used for network control theory analyses. PET-derived serotonin receptor density maps were taken from a high-resolution atlas (n = 210). Network control theory was applied with a linear time-invariant model x˙ = Ax + Bu(t) to compute the minimum input energy (transition energy, TE) required to move the system from one empirical state to another. The control input weight matrix B was set to the identity for uniform inputs, and, when incorporating receptor data, to a diagonal matrix whose entries were 1 plus the normalized receptor density (values therefore between 1 and 2). Entropy of brain-state sequences was quantified using normalised Lempel–Ziv compressibility after reducing the four-state series to a two-state meta-state sequence (because direct sub-state transitions were rare). Statistical comparisons included paired t-tests with Benjamini–Hochberg correction where indicated, and a permutation test (10,000 permutations) to assess whether the true spatial distribution of 5-HT2a produced lower transition energies than shuffled versions of the same weight set.
Clustering of concatenated fMRI data produced four recurrent substates that pair into two anti-correlated meta-states: Meta-State 1 (SOM+/-) characterised by opposition between somatomotor/ventral attention and default-mode network (DMN) activity, and Meta-State 2 (FPN+/-) characterised by opposition between frontoparietal and DMN/visual/somatomotor networks. Across conditions the SOM+ substate had the highest fractional occupancy and the longest dwell times. Comparing LSD with placebo, LSD increased occupancy of SOM-dominated (bottom-up) meta-states and decreased dwell times of FPN-dominated (top-down) states; group-level appearance rates of individual sub-states did not differ between conditions. Empirical transition probabilities showed increased switching towards the SOM meta-states under LSD. Network control theory analyses revealed that LSD reduced the transition energy between every pair of empirically derived brain-states: the minimum energy required to induce transitions (or to persist in a given state) was lower for LSD-derived centroids than for placebo-derived centroids when inputs were uniformly weighted. To test a mechanistic role for serotonin receptors, the investigators reweighted control inputs for placebo centroids according to cortical 5-HT2a density from PET. These 5-HT2a-weighted inputs produced lower transition energies than uniform inputs across virtually all transitions. A permutation test (10,000 shuffles of the receptor map) showed that the true spatial distribution of 5-HT2a yielded significantly lower energies than shuffled maps, indicating spatial specificity. When comparing other serotonergic targets (5-HT1a, 5-HT1b, 5-HT4, and the serotonin transporter 5-HTT), 5-HT2a weighting was most effective at lowering mean transition energy. At the individual level (n = 15), the relative reduction in average transition energy induced by LSD correlated with empirically observed decreases in dwell time and increases in appearance rate (p < 0.05, uncorrected). Energy reduction also correlated with increased entropy of the meta-state sequence as measured by normalised Lempel–Ziv complexity. No significant correlations were found between energy flattening and subjective experience ratings. The extracted text also notes that the structural connectome and PET receptor maps used were population averages rather than individual-specific.
Parker Singleton and colleagues interpret their findings as empirical support for central aspects of the REBUS model. They report four converging observations: increased engagement of bottom-up (somatomotor/salience) states under LSD; a reduction in the transition energy between recurrent brain-states consistent with a flattened energy landscape; a positive relationship between energy flattening and increased temporal diversity (entropy) of brain-state sequences; and a mechanistic account in which the empirical spatial distribution of 5-HT2a receptors is especially well-suited to produce energy reductions. The authors situate these results within existing theory, noting that the observed link between energy landscape flattening and increased entropy provides an empirical bridge between the Entropic Brain Hypothesis and the free-energy principle that underpin REBUS. They further suggest that combining network control theory with receptor maps can yield mechanistic insight into how pharmacological agents modulate brain dynamics, pointing to potential future applications in clinical populations (for example, depression or schizophrenia). Several limitations acknowledged by the investigators temper interpretation. The sample size is small (15 analysed), and the dataset has been the subject of prior analyses, so replication in independent and larger cohorts is needed. The term "energy" here is a modelling proxy for variational free energy and should not be conflated with metabolic energy or other energy notions used in neuroscience. Individual differences in subjective reports may be influenced by prior psychedelic exposure, dose–response variability, and individual structural connectomes or receptor distributions; notably, the structural connectome and PET maps in these analyses were representative population averages rather than subject-specific measures. Finally, the network control approach uses a linear model to compute minimum input energies, which differs from non-linear whole-brain mean-field models that capture other aspects of 5-HT2a neuromodulation; the authors suggest combining approaches in future work to capitalise on the strengths of each.
The investigators introduce a receptor-informed network control theory framework and present convergent evidence that LSD flattens the brain’s energy landscape, facilitating more frequent state transitions and increased temporal diversity of brain activity. They further show that the cortical spatial distribution of 5-HT2a receptors can account for this flattening, providing a plausible mechanistic link between LSD’s neurochemical action and altered brain dynamics in support of the REBUS hypothesis.
Serotonergic psychedelics like lysergic acid diethylamide (LSD) induce a profound but temporary alteration of perception and subjective experience. Combined with non-invasive neuroimaging such as functional MRI, these drugs offer a unique window into the function of the human mind and brain, making it possible to relate mental phenomena to their neural underpinnings. The insight provided by neuroimaging studies of psychedelics over the last decade has culminated in a recent model of psychedelic action, known as RElaxed Beliefs Under Psychedelics (REBUS). This model integrates previous accounts of psychedelic action with the view of the brain as a prediction engine, whereby perception and belief are shaped by both prior knowledge and incoming information. The REBUS model postulates that psychedelics alter cognitive functioning by serotonergic action at 5-HT2a receptors in higher-order cortical regions. Dysregulation of these regions' activity results in a weaker effect of prior beliefs and expectations in shaping the interpretation of bottom-up information, ultimately allowing the brain to explore its dynamic landscape more readily -as suggested by more diverse (entropic) brain activity. In accordance with the REBUS model, recent work has also provided indirect evidence of relaxed priors as the decreased coupling of structural and functional connectivity networks under LSD -thereby facilitating access to physiological states less constrained by anatomical connections. Formally, relaxed priors are theorized to correspond to a reduction in the energy required to transition between different brain-states, i.e., a "flattening of the energy landscape". However, this hypothesis remains thus far untested. One avenue to understand how psychedelics influence brain activity is through neurobiologically informed whole-brain computational models. Through these types of approaches, recent work has shown that the effects of serotonergic psychedelics on the dynamics of human brain activity are critically dependent on their action at 5HT2a receptors. Whole-brain neural-mass models have implicated the 5-HT2a receptor distribution across the cortex in shaping brain dynamics under the effects of LSD and psilocybin, as well as demonstrating a role for 5-HT2a receptor agonism in increasing the temporal diversity (entropy) of brain activity in a way that is consistent with empirical observations. An alternative computational approach to modelling brain dynamics is network control theory, which focuses on quantifying and controlling how a dynamical system moves through its state space. It is well-known that even at rest the brain is not static, but rather it dynamically alternates between a number of recurrent states. Such recurrent brain-states may be relevant for cognitionand even consciousness, and have been shown to undergo prominent reorganization during the psychedelic state induced by LSDand psilocybin. Crucially, network control theory approaches enable mapping of the brain's energy landscape by quantifying the energy required to transition between these recurrent states (Figure). Recent work utilized these tools to demonstrate that although the resting human brain has a spontaneous tendency to prefer certain brain-state transitions over others, cognitive demands can overcome this tendency in a way that is associated with age and cognitive performance. This work demonstrates that network control theory approaches can reveal neurobiologically and cognitively relevant brain activity dynamics., we calculated the minimum energy required to transition between states (or maintain the same state) using each individual's brain-states derived from the LSD and placebo conditions separately. Our calculations reveal an energy landscape that is flattened by LSD. (c) Weighting the energy calculations of the placebo brain-states with inputs from PET-derived receptor density maps of the serotonin 2a receptor also resulted in a flattened energy landscape, providing a mechanistic explanation for LSD's flattening effect. Here, we leverage recent advances in network control theory to probe a leading model for the action of psychedelics on the brain: we combine functional MRI data from 15 healthy volunteers under the effects of LSD or placebo, with structural (white-matter) connectivity networks obtained from diffusion MRI (dMRI), and receptor density maps from positron emission tomography (PET). In accordance with the REBUS model, we hypothesized that the energy required to transition between brain states would decrease under LSD compared to placebo. Further, we tested the mechanistic hypothesis that LSD's action at 5-HT2a receptors is responsible for this reduction in transition energy by demonstrating that the specific spatial pattern of 5-HT2a receptor expression flattens the energy landscape more than any other receptor distribution tested (Figure).
We investigated functional MRI data acquired from 15 volunteers over two sessions, either under the influence of the psychedelic LSD or a placebo, to address the central tenet of the leading REBUS model 2 of psychedelic action on the human brain and mind. Namely, does LSD induce a "flattening" of the brain's energy landscape, and, furthermore, is this effect a result of 5HT2A receptor agonism? Our first step was to identify recurrent states of brain activity. One commonly used approach to identifying recurrent brain-states is through the k-means clustering algorithm, whereby brain activation patterns from each individuals' scans are grouped into a pre-specified number of clusters k . Here, data-driven clustering of regional activity patterns identified k =4 stable clusters that achieved optimal division of the data (see Materials and Methods: Extraction of Brain-states for choice of k ). The four clusters can be divided into two meta-states (Meta-State 1 and Meta-State 2, Figure), each composed of two sub-states that represent opposing activation patterns (SOM+/-and FPN+/-, Figure). Dichotomy of the brain's dynamic states has previously been observedand is consistent with hierarchical organization. For each brain-state, we separately calculated the cosine similarity of its high-amplitude (supra-mean) activity and low-amplitude (sub-mean) activity to a priori resting-state networks 37 (RSNs); resulting similarity measures are represented via radial plots. Meta-State 1 (MS-1) is characterized by the contraposition of the somatomotor and ventral attention/salience networks with the default-mode network, whereas the Meta-State 2 (MS-2) is characterized by the contraposition of the default-mode, somatomotor and visual networks with the frontoparietal network. We therefore label them as SOM+/-(for MS-1) and FPN+/-(for MS-2) to indicate the main RSN that has the highest amount of overlap (defined as maximum cosine-similarity) with the brain-state and its amplitude. The dichotomy of these states can be observed visually in the radial plots and on the rendered brain volumes, and is confirmed via their negative, significant Pearson correlation (SI Figure, ii).
To identify the effects of LSD on brain-state dynamics, each subject's fMRI data were characterised in terms of the four identified brain-states. From each subject's temporal sequence of brain-states (Figure) we obtained a systematic characterization of the temporal dynamics of the 4 states, namely, their (i) fractional occupancies, or the probability of occurrence of each state (Figure, i), (ii) dwell times, or the mean duration that a given state was maintained, in seconds (Figure, ii), (iii) appearance rates, or how often each state appeared per minute (Figure, iii), and (iv) transition probabilities, or the probability of switching from each state to every other state (Figure). We found that for both LSD and placebo conditions, the brain most frequently occupies the SOM+/state (higher fractional occupancy) whose constituent sub-states are also visited for the longest periods of time (highest dwell times) (Figure). LSD modifies the fractional occupancy of these states by decreasing the dwell times of FPN+/-and further increasing dwell times of the already dominant SOM+/-(Figure). No differences in appearance rate for the 4 sub-states was found when comparing the LSD and placebo conditions. Empirical transition probabilities were calculated independently for each individual and each condition (Figure). Since the SOM+/-meta-states are characterized by prominent engagement of the bottom-up somatomotor and ventral attention/salience networks, we hypothesised that under LSD the brain should transition more frequently to these states, since the REBUS model predicts a shift in favour of bottom-up processing under the effects of psychedelics. Our analysis of transition probabilities supported this hypothesis (Figure, i, diagonal). The increased persistence of states (SOM-) dominated by somatomotor/salience (bottom-up) activity and correspondingly, the decreased persistence of states (FPN+) dominated by frontoparietal (top-down) activity seen under LSD fits with a flattening of the functional hierarchy proposed by REBUS.
However, we sought to provide a more direct test of the REBUS model's hypothesis about LSD's decreased energy requirement to transition between different states. To this end, we turned to network control theory, which offers a framework to quantify the ease of state transitions in a dynamical system. Specifically, we calculated the transition energy (TE), which is the minimum amount of energy that would need to be injected into a network (here, the structural connectome) to induce transitions between the possible states of its functional dynamics (note that the transition energy from a given state to itself is the energy required to remain in that state, sometimes referred to as "persistence energy"). For each subject and condition, we calculated the energy needed to transition between each pair of brain-states. Comparing the two conditions, we found that LSD lowered the TE (Figure, ii) between all possible combinations of initial and final brain-states. Importantly, network control theory requires a specification of a set of "control points" where energy is injected into the system to induce the desired transition. For the previous analysis, we chose uniform inputs over all brain regions. However, one can also ask whether this effect may be driven by a specific set of regions. This is relevant because the changes in brain function under investigation in the present study arise from the administration of LSD. The serotonin 2a (5-HT2a) receptor is well established as the site responsible for the subjectiveand neuraleffects of LSD and other classic serotonergic psychedelics, and this receptor is not uniformly distributed across the brain. Therefore, we sought to determine if the specific regional distribution of 5HT2a receptors in the brain could correspond to especially suitable control points for inducing a reduction in transition energy. To test this hypothesis, we utilized a high resolution in vivo atlas of the serotonin receptor 5HT2a derived from PET imaging to extract biologically relevant weights for our model. First, we recalculated the energy matrices for the placebo condition, this time weighting the energy injected into every region in proportion to its amount of 5-HT2a expression. In every possible transition, we observed that the 5-HT2a-weighted inputs provided lower TE than the uniform inputs (Figure, iii). However, it could be argued that giving additional control to some regions will result in a lower control energy, regardless of the choice of regions. To demonstrate that our results are specific to 5-HT2a receptors' spatial distribution across brain regions, we compared the TEs obtained from the true 5-HT2a distribution, versus 10,000 permutations obtained by randomly reshuffling the spatial positions of the same weights -thereby preserving the set of weights but not the regions they correspond to. The true distribution of 5-HT2a resulted in significantly lower energies (Figure, iv), demonstrating the critical role of the specific regional distribution of 5HT2a receptors for inducing low-energy state transitions such as those empirically observed under the effects of LSD. In a final demonstration of the specific importance of the 5-HT2a receptor, we investigated the shift in TEs provided by three additional serotonin receptors (5-HT1a, 5-HT1b, 5-HT4) and the serotonin transporter, 5-HTT, all obtained from the same high-resolution PET atlas. We compared the overall mean of the energy matrix for each individual's 2a-weighted calculations versus all others and found that 5-HT2a was the most effective at lowering the overall energy to transition between empirically defined brain-states (Figure). This is especially noteworthy because serotonin 2a receptor agonism plays a prominent role in how LSD and other classic psychedelics influence neural activityand subjective experience. Together, these results demonstrate that the 5-HT2a receptor is neurobiologically and spatially well-suited for energy landscape flattening -a key tenet of psychedelic action according to the REBUS model.) Comparison of the empirically observed transition probabilities between states, derived from the brain-state time series, e.g. Figure. (a, ii) Comparison of the transition energies calculated from placebo brain-states versus those calculated from LSD brain-states using uniformly-weighted whole-brain inputs. LSD brain-states had significantly lower energy required for every transition. (a, iii) Weighting with the 5-HT2a receptor density mapresults in significantly lower energies for the placebo brain-states compared to uniformly-weighted inputs. (c, iv) To probe the spatial specificity of part (iii), we repeated the calculations using 10,000 random receptor maps, created by permuting the original 5-HT2a receptor map. We found that the true 5-HT2a receptor map had significantly lower energy required for nearly every transition compared to the shuffled receptor maps. (b) Additionally, we weighted our model with expression maps of other serotonin receptors (5-HT1a, 5-HT1b, and 5-HT4), and the serotonin transporter (5-HTT), and found that 5-HT2a resulted in significantly lower transition energy (averaged across all pairs of states) than all others. ( See SI for choice of the time-span T over which the transition energy was computed ). *significant before multiple comparisons correction, ** significant after multiple comparisons correction.
Crucially, the results demonstrating the specific role of 5HT2a receptors in flattening the energy landscape were based exclusively on calculations using placebo data. Therefore, we next sought to test how the average TE reduction by LSD (Figure, ii) may affect empirical transition energies and corresponding brain dynamics. Specifically, we show that, across the 15 individuals, the relative change in energy induced by LSD was significantly correlated with the empirically observed changes in state dwell times (Figure, i) and appearance rates (Figure, ii), p<0.05, uncorrected. Our results show that the more LSD lowered the average transition energy of a given subject, the more the empirically observed dwell times decreased and the more the empirically observed appearance rates increased. The latter is particularly interesting, as there were no group-level differences in appearance rates of individual states between the two conditions. Both findings are consistent with our hypothesis of a flattened energy landscape, where lower barriers between brain-states results in increased frequency of state transitions and shorter state dwell times. Ratings of the drug's subjective effects were also obtained from each individual ( see SI for details ) and we hypothesized that transition energy reduction by LSD would also predict a more intense subjective experience. We did not find any significant correlations between energy flattening and subjective ratings; extending the present modelling framework to subjective measures may be a fruitful avenue for future research. Lastly, we asked whether energy reduction induced by LSD would correlate with more complex (entropic) brain-state time series. This experiment aimed to test the theoretical link between a flatter energy landscape and more entropic brain activity postulated by REBUS. One could imagine a scenario where shorter dwell times and larger appearance rates results in a sequence that is highly predictable (i.e. [1 2 1 2 1 2]). We wanted to test the hypothesis that the true scenario would be the opposite -namely, that a flatter energy landscape would in fact correspond to an increase in the diversity of brain dynamics. Numerous studies have linked changes in the entropy of neuroimaging signals to the psychedelic stateand the ability for these compounds to increase neural entropy via 5-HT2a agonism is thought to be a key process in the breakdown of the functional hierarchy of the brain and a central component of REBUS. To test this hypothesis, we used Lempel-Ziv compressibility to compute the entropy rate of the temporal sequence of brain meta-states (SOM and FPN). Supporting our hypothesis, we found that the more a subject's energy landscape was flattened, the more entropic their brain-state time series became (Figure, iii). This result directly and quantitatively links the energy of the landscape with empirical changes in entropy rate for the first time and serves as a validation of REBUS' central hypothesis.
Here, we combined fMRI, PET and diffusion MRI with network control theory to test a central tenet of the REBUS model of psychedelic action: namely, that serotonergic psychedelics like LSD induce a "flattening" of the energy landscape in the human brain. A flatter energy landscape corresponds to lower barriers to transition between different states of brain activity. This is theorized to correspond to a flattening of the functional hierarchy as well, i.e. a relaxation of the weighting that high-level priors exert on inputs from lower-level (sensory) regions -thought to be a pivotal component of psychedelics' therapeutic mechanism of action as well as characteristic subjective effects of ego dissolution and visual/auditory distortions 2 . The present results support four central claims of the REBUS model of psychedelic action: (a) more engagement of bottom-up activity, here quantified in terms of increased occurrence of states dominated by SOM and VAT/salience networks, which primarily deal with bottom-up information-processing, (b) a flattening of the brain's energy landscape, indicated by lower energy being required to transition between brain states, and (c) a correlation between flattening of the energy landscape (reduced energy required for state transitions) and more diverse (entropic) sequences of brain activity. Combining fMRI with diffusion MRI and PET information, we were further able to provide computational evidence that (d) the serotonin 2a receptor is especially well-positioned to bring about this flattening of the energy landscape, over and above other 5HT receptors -once again in accordance with theoretical predictions of the REBUS model. Compared with placebo, subjects in the LSD condition spent a larger fraction of time occupying states characterized by the contraposition of the DMN with bottom-up sensorimotor and salience networks, and less time in states dominated by the contraposition between DMN and top-down fronto-parietal control network (Figure). Since our analysis was carried out on resting-state data, it is not surprising that the DMN was prominent across all four brain-states. However, our results indicating a change in the relative prevalence of FPN-dominated vs SOM-dominated states are in line with the prediction of the REBUS model of increased bottom-up activity under the effects of psychedelics. Additionally, our quantification of the brain's energy landscape through network control theory revealed that LSD lowers the transition energy between all states (Figure, ii). Given the well-known involvement of 5-HT2a receptors with the neurobiological and subjective effects of LSD, we next sought to determine if the spatial distribution of 5-HT2a receptors across the human cortex could provide a mechanistic explanation for our results. Weighting the model in proportion to the empirical regional density of 5-HT2a receptors obtained from in vivo PET imaging, we found that the resulting transition energies were greatly reduced, mirroring those of the LSD condition (Figure, iii). Further, to demonstrate the importance of this receptor's spatial distribution, we randomly shuffled the 5-HT2a distribution and found that the original map consistently resulted in lower energies than the shuffled maps (Figure, iv). The calculations were also repeated with other subsets of the 5-HT receptor class, and 5-HT2a was the most effective at reducing energy (Figure), consistent with the known specificity of LSD for this receptor. The Entropic Brain Hypothesis (EBH)proposes that increased neural entropy brought forth by psychedelics is reflected in the subjective experience as an increase in the richness of conscious content -viewing the brain and mind as two sides of the same coin. We found that at an individual subject level, increased LSD-induced transition energy reductions correlated with more dynamic brain activity (Figure, i,ii), thereby relating the theoretical interpretation of transition energy with its role in the empirical de-stabilization of brain-state dynamics. Remarkably, we also found that the entropy rate of an individual's sequence of meta-states increased in proportion to the LSD-induced energy reduction (Figure, iii), thereby relating the energy landscape of the brain to its entropy. This is especially noteworthy as it provides empirical evidence linking the EBH with the free-energy principle-the two theories that sit at the foundation of REBUS. More broadly, these results demonstrate that the combination of network control theory and specific information about neurobiology (here exemplified by receptor distributions from PET) can offer powerful insights about brain function and how pharmacology may modulate it -opening the avenue for analogous studies on the effects of pharmacological interventions in clinical populations (e.g. depression, schizophrenia). While other recent computational approaches have successfully modeled the effects of serotonergic compounds on dynamic brain statesand the entropy of spontaneous neural activity, the present approach is the first to do both while also quantitatively evaluating the energy landscape of the psychedelic state -thereby enabling us to provide empirical support for key theoretical predictions of the REBUS model.
Although small sample size is common in neuroimaging studies of psychedelics and other states of altered consciousness due to the inherent difficulties of collecting such data, future replications with larger samples would be appropriate. We also acknowledge that this specific dataset has been studied extensively beforeand replications in different datasets will be warranted to ensure the generalizability of these results. It is also important to note that different notions of energy can be employed in neuroscience: the term "energy" used here is a proxy for the variational free-energy of the REBUS model. It should not be confused with metabolic energy of ATP molecules, nor with the energy quantified through connectome harmonic decomposition, which has also been investigated in the context of this same datasetand other states of altered consciousness. As employed here, "energy" is to be interpreted as the magnitude of the input that needs to be injected into the system (the brain's structural connectome) in order to obtain the desired state transition. Additionally, we had hypothesized that the transition energy modifications by LSD would correlate with our participants' subjective experience as captured by intra-scanner visual analog scale ratings, and the 11-factor states of consciousness (ASC) questionnairetaken at the end of the day. There may be numerous factors that limit our ability to model these effects. For instance, both subjective experience ratings and the relative energy landscape (baseline or LSD) may be impacted by each individual's prior psychedelic use, individual differences in pharmacological dose response, as well as their own unique structural connectome and 5-HT2a receptor distribution. Indeed, the structural connectome and the PET data used in our analysis were representative examples obtained from population averages, rather than unique data derived from each individual in our study. Although these measures are thought to be less variable across individuals than brain activity dynamics, future work could explore how individual differences in the structural connectome or receptor maps influence the energy landscape -and possibly subjective experiences. Finally, our approach is based on network control theory, which differs from other recent computational investigations using e.g. whole-brain simulation through dynamic mean-field modelling of brain activity. These latter approaches employ a neurobiologically realistic model of brain activity based on mean-field reduction of spiking neurons into excitatory and inhibitory populations, and have been used to account for non-linear effects of 5HT2a neuromodulation induced by LSD and other psychedelics. In contrast, network control theory relies on a simpler linear model, which we employed due to its ability to address REBUS's specific prediction about the brain's energy landscape. Additionally, recent evidence suggests that most of the fMRI signal may be treated as linear. Combining both approaches to capitalize on the strengths of each will be a fruitful avenue for future work.
We introduced a framework for receptor-informed network control theory to understand how the serotonergic psychedelic LSD influences human brain function. Combining fMRI, diffusion MRI, PET and network control theory, we presented evidence supporting the hypothesis that LSD flattens the brain's energy landscape and, furthermore, provided a mechanistic explanation for this observed energy reduction by demonstrating that the empirical spatial distribution of 5-HT2a receptor expression is particularly well-suited to flatten the brain activity landscape. This work highlights the potential of receptor-informed network control theory to allow insights into pharmacological modulation of brain function and, importantly, provides evidence to support the REBUS hypothesis of LSD effects.
Data acquisition is described in detail previously. In brief, twenty healthy volunteers underwent two MRI scanning sessions at least 14 days apart. On one day, participants were given placebo (10 mL saline), and on the other day they received LSD (75 μg in 10 mL saline), infused over two minutes, 115 minutes before resting-state scanning. Post-infusion, subjects had a brief acclamation period in a mock fMRI scanner. On each scanning day, three 7:20 minute eyes-closed resting-state scans were acquired. The first and third scan had no stimulation, while the second scan involved listening to music; this scan was not used in this analysis as we were interested in dynamics in the absence of external stimulation. BOLD fMRI was acquired at 3T with TR/TE = 2000/35ms, FoV = 220mm, 64 × 64 acquisition matrix, parallel acceleration factor = 2, 90 flip angle. Thirty-five oblique axial slices were acquired in an interleaved fashion, each 3.4mm thick with zero slice gap (3.4mm isotropic voxels). One subject was excluded due to anxiety, and 4 due to excessive head motion (> 15% of volumes with mean frame-wise displacement > 0.5), leaving 15 subjects (four women; mean age, 30.5 ± 8.0) for analysis. Data pre-processing utilized AFNI, Freesurfer, FSL and in-house code. Steps included 1) removal of first three volumes; 2) de-spiking; 3) slice time correction; 4) motion correction; 5) brain extraction; 6) rigid body registration to anatomical scans; 7) non-linear registration to 2mm MNI space; 8) scrubbing; 9) spatial smoothing; 10) band-pass filtering (0.01 to 0.08 Hz); 11) de-trending; 12) regression out of 6 motion-related and 3 anatomical-related nuisance regressors. Lastly, time series for 462 gray matter regionswere extracted (Lasuanne scale 4, sans brain-stem).
Since diffusion MRI was not acquired as part of the LSD study, the structural connectome used for network control theory analysis was identical to the one used in prior work. Namely, we relied on diffusion data from the Human Connectome Project (HCP,), specifically from 1021 subjects in the 1200-subject release. A population-average structural connectome was constructed and made publicly available by Yeh and colleagues in the following way. Multishell diffusion MRI was acquired using b-values of 1000, 2000, 3000 s/mm 2 , each with 90 directions and 1.25 mm iso-voxel resolution Following previous work, we used the QSDR algorithmimplemented in DSI Studio () to coregister the diffusion data to MNI space, using previously adopted parameters. Deterministic tractography with DSI Studio's modified FACT algorithmthen generated 1,000,000 streamlines, using the same parameters as in prior work, specifically, angular cutoff of 55•, step size of 1.0 mm, minimum length of 10 mm, maximum length of 400mm, spin density function smoothing of 0.0, and a QA threshold determined by DWI signal in the CSF. Each of the streamlines generated was screened for its termination location using an automatically generated white matter mask, to eliminate streamlines with premature termination in the white matter. Entries in the structural connectome A ij were constructed by counting the number of streamlines connecting every pair of regions i and j in the Lausanne-463and augmented Schaefer-232 atlasas done previously.
Details for obtaining the serotonin receptor density distribution have been previously described, however we provide a brief summary here. PET data for 210 participants were acquired on a Siemens HRRT scanner operating in 3D acquisition mode with an approximate in-plane resolution of 2mm (1.4 mm in the center of the field of view and 2.4 mm in cortex). Scan time and frame length were designed according to the radiotracer characteristics. For details on MRI acquisition parameters, which were used to coregister the data to a common atlas, see Knudsen et al. For details on MRI and PET data processing, see the original reference.
Following Cornblath et al., all subjects' fMRI time series for both conditions were concatenated in time and k -means clustering was applied to identify clusters of brain activation patterns, or states. Pearson correlation was used as the distance metric and clustering was repeated 50 times with different random initializations before choosing the solution with the best separation of the data. To further assess the stability of clustering and ensure our partitions were reliable, we independently repeated this process 10 times and compared the adjusted mutual information (AMI)between each of the 10 resulting partitions. The partition which shared the greatest total AMI with all other partitions was selected for further analysis. In general, we found that the mutual information shared between partitions was quite high, suggesting consistent clustering across independent runs ( see SI: Assessing the stability of clustering ). We chose the number of clusters k via the elbow criterion, i.e. by plotting the variance explained by clustering for k =2 through 14 and identifying the "elbow" of the plot, which was between 4-6 across the various partitions. In addition, increasing k beyond k =5 resulted in a gain of less than 1% of variance explained by clustering, a threshold used previously for determining k ( see SI: Choosing k ). We chose k =4 for its straightforward and symmetric interpretation, however the main findings are replicated with k =5 in the Supplemental Information.
Each cluster centroid was characterized by the cosine similarity between it and binary representations of seven a priori defined RSNsas shown in the radial plots of Figure. Because the mean signal from each scan's regional time series was removed during bandpass filtering, positive values in the centroid reflect activation above the mean (high-amplitude) and negative values reflect activation below the mean (low-amplitude). To quantify the hierarchical relationship between centroids observed in the radial plots, we calculated the Pearson correlation values between all centroids (SI Figure) and grouped the anti-correlated pairs together, and refer to each individual centroid as a sub-state and the pair collectively as a meta-state. We can extract 1) group-average centroids by taking the mean of all TR's assigned to each cluster (all subjects, all conditions), 2) condition-average centroids by taking the mean of all TR's assigned to each cluster separately for each condition, and 3) individual condition-specific centroids by taking the mean of all TRs assigned to each cluster for a single subject and condition. When taking condition-average centroids (LSD and PL), we find that these two sets of centroids are highly correlated with one another (SI Figure), and thus are also very similar to the group-average centroids shown here. The differences that do exist (quantified here in terms of condition-average differences in cosine-similarity to RSNs) are consistent with prior observations and a break-down of the brain's functional hierarchy(SI Figure)
We then analyzed the temporal dynamics of these brain-states to observe how they change after administration of LSD. The fractional occupancy of each state was determined by the number of TRs assigned to each cluster divided by the total number of TRs. Dwell time was calculated by averaging the length of time spent in a cluster once transitioning to it. Appearance rate was calculated as the total number of times a state was transitioned into per minute. Transition probability values were obtained by calculating the probability that any given state i was followed by state j .
Network control theory allows us to probe the constraints of white-matter connectivity on dynamic brain activity, and to calculate the minimum energy required for the brain to transition from one activation pattern to another. Here, we utilized network control theory to understand the structural and energetic relationships between these states and the 5-HT2a receptor distribution. While this procedure has been detailed elsewhere, we summarize briefly here and in the Supplemental Information. We obtained a representative NxN structural connectome A obtained as described above using deterministic tractography from HCP subjects ( see Methods and Materials; Structural Connectivity Network Construction ), where N is the number of regions in our atlas. We then employ a linear time-invariant model: x(t) Bu(t) x ˙= A + where x is a vector of length N containing the regional activity at time t . B is an NxN matrix that contains the control input weights. B is the identity matrix for uniform inputs and contains the regional receptor density information in the diagonal when incorporating the 5-HT receptor maps. For the latter case, the diagonal of B was set to 1 plus the normalized regional receptor density value, resulting in a diagonal matrix whose non-zero entries were between 1 and 2. This computational approach allows us to compute the transition energy as the minimum energy required to transition between all pairs of the substates. The energy calculations in Figure(ii) consisted of separate calculations for each individual's LSD and placebo centroids separately, (iii) utilized each individual's placebo centroids while varying the control input weights B , and (iv) used the group average placebo centroids, and B was varied for each random permutation. Figureagain used each individual's placebo centroids, while varying control input weights B .
In order to quantify the entropy of each subject's brain-state time series, we chose the widely used Lempel-Ziv algorithm; this algorithm assesses the complexity of a binary sequence in terms of the number of unique patterns it contains. A sequence that contains a larger number of unique patterns is more diverse, making it less predictable and therefore more entropic. The normalised Lempel-Ziv complexity (also known as Lempel-Ziv compressibility) is then the number of patterns found in the sequence, divided by the total length of the sequence. In order to apply this algorithm to our brain-state time series, we first had to convert them to binary sequences that returned 0 or 1 for each time point. To do so, we considered the natural grouping of our 4 brain-states into two meta-states (Meta-State 1 and Meta-State 2). We consider this simplification to be justified by the fact that direct transitions between sub-states (e.g. SOM-to SOM+) were extremely rare (SI Figure), thereby allowing us to reduce the 4-state time series to a 2-state time series while losing very little information regarding transitions.
The 5-HT 2a -weighted inputs from the true receptor distribution were compared to the randomly shuffled distributions via a permutation test where the true receptor distribution was randomly reshuffled and the energy matrix re-calculated 10,000 times. P-values were calculated as the fraction of times that the randomized distribution resulted in a lower energy than the true distribution. All other metric comparisons were achieved using a paired t-test of group means and were corrected for multiple comparisons with Benjamini-Hochberg where correction is indicated.
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