LSD flattens the brain′s energy landscape: evidence from receptor-informed network control theory

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.”

Authors: S. Parker Singleton, Andrea I. Luppi, Robin L. Carhart-Harris, Josephine Cruzat, Leor Roseman, David J. Nutt, Gustavo Deco, Morten L. Kringelbach, Emmanuel A. Stamatakis & Amy Kuceyeski


Psychedelics like LSD alter subjective experience by temporarily altering the brain’s neurochemical effects. Network control theory shows that LSD reduces the energy required to transition between different brain states, and that this reduction correlates with more frequent state transitions and increased entropy of brain-state dynamics.

We present a multi-modal framework for quantifying the effects of psychedelic drugs on brain dynamics. We demonstrate that serotonin 2a receptors are key for generating these effects and that this approach could be used to understand how drugs act on different receptors in the brain.

Recent neuroimaging studies of psychedelics have culminated in a model of psychedelic action that integrates previous accounts of psychedelic action with the view of the brain as a prediction engine. This model predicts that psychedelics alter cognitive functioning by serotonergic action at 5-HT2a receptors in higher-order cortical regions.

Neurobiologically informed whole-brain computational models have shown that serotonergic psychedelics influence brain activity through action at 5HT2a receptors, and that 5-HT2a receptor agonism increases the temporal diversity of brain activity.

A computational approach to modelling brain dynamics is network control theory, which quantifies and controls how a dynamical system moves through its state space. This approach has been used to reveal neurobiologically and cognitively relevant brain activity dynamics.

Here, we combine functional MRI data with structural MRI and PET data to examine how LSD affects the brain. We found that 5-HT2a receptors flatten the energy landscape more than any other receptor.

We investigated the effect of LSD on the human brain using functional MRI data, and found that the effect was due to 5HT2A receptor agonism.

We identified four recurrent states of brain activity using the k-means clustering algorithm. These four states can be divided into two meta-states, each composed of two sub-states that represent opposing activation patterns.

To identify the effects of LSD on brain-state dynamics, fMRI data were characterised in terms of the four identified brain-states. The brain most frequently occupies the SOM+/-state, and 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+/-.

The empirical transition probabilities calculated independently for each individual and each condition supported the hypothesis that the brain should transition more frequently to states dominated by bottom-up somatomotor/salience activity under the effects of LSD.

We used network control theory to quantify the ease of state transitions in a dynamical system, and found that LSD lowered the energy requirement to transition between different states in all possible combinations of initial and final brain-states.

Network control theory requires a specification of a set of control points, and the regional distribution of serotonin 2a (5-HT2a) receptors in the brain may correspond to especially suitable control points for inducing a reduction in transition energy.

To test the hypothesis that serotonin receptors’ spatial distribution across brain regions is critical for inducing low-energy state transitions, 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.

We found that the 5-HT2a receptor was the most effective at lowering the energy to transition between empirically defined brain-states, and that the average TE reduction by LSD was significantly correlated with the empirically observed changes in state dwell times and appearance rates.

We hypothesized that a flattened energy landscape, where lower barriers between brain-states results in increased frequency of state transitions and shorter state dwell times, would also predict a more intense subjective experience, but we did not find any significant correlations.

We asked whether energy reduction induced by LSD would correlate with more complex (entropic) brain-state time series. We found that the more a subject’s energy landscape was flattened, the more entropic their brain-state time series became, supporting the central hypothesis of REBUS 2.

Here, we combined fMRI, PET and diffusion MRI with network control theory to test the claim that serotonergic psychedelics like LSD induce a flattening of the energy landscape in the human brain. Our results support the claim that psychedelics promote bottom-up activity and reduce energy required for state transitions.

LSD increased the relative prevalence of FPN-dominated vs SOM-dominated states in the brain compared to placebo. Additionally, LSD lowers the transition energy between all states.

We found that the spatial distribution of 5-HT2a receptors across the human cortex reduced the transition energies, mirroring the effects of LSD. Further, the original 5-HT2a distribution consistently resulted in lower energies than randomly shuffled maps.

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. We found that increased LSD-induced transition energy reductions correlated with more dynamic brain activity.

This study combines network control theory with specific information about neurobiology to provide powerful insights into brain function and how pharmacology may modulate it. The study also provides empirical support for key theoretical predictions of the REBUS model.

Different notions of energy can be employed in neuroscience: the variational free-energy of the REBUS model is used here, and it should not be confused with metabolic energy of ATP molecules.

We hypothesized that the transition energy modifications by LSD would correlate with our participants’ subjective experience, but there may be numerous factors limiting our ability to model these effects, such as prior psychedelic use, individual differences in pharmacological dose response, and unique structural connectome and 5-HT2a receptor distribution.

We used network control theory to model brain activity and used a simpler linear model than other recent computational investigations using e.g. whole-brain simulation through dynamic mean-field modelling of brain activity.

We used fMRI, diffusion MRI, PET and network control theory to understand how LSD influences human brain function. Our results support the REBUS hypothesis of LSD effects.

Twenty healthy volunteers underwent two MRI scanning sessions, one with placebo and the other with LSD. After an infusion of doxycycline, subjects had a brief acclamation period in a mock fMRI scanner. Three eyes-closed resting-state scans were acquired at 3T with TR/TE = 2000/35ms, FoV = 220mm, 64 x 64 acquisition matrix, parallel acceleration factor = 2, 90 flip angle, and 35 oblique axial slices were acquired.

Structural Connectivity Network Construction

Since diffusion MRI was not acquired as part of the LSD study, a population-average structural connectome was constructed from data from the Human Connectome Project. Multishell diffusion MRI was acquired using b-values of 1000, 2000, 3000 s/mm 2 , with 90 directions and 1.25 mm iso-voxel resolution. Deterministic tractography was performed using DSI Studio’s modified FACT algorithm, and the structural connectome was constructed using the number of streamlines connecting every pair of regions.

PET data were acquired on a Siemens HRRT scanner operating in 3D acquisition mode with an approximate in-plane resolution of 2mm. MRI data were processed to coregister the data to a common atlas.

We concatenated all subjects’ fMRI time series for both conditions and applied k-means clustering to identify clusters of brain activation patterns, or states. We chose k = 4 for its straightforward and symmetric interpretation, however the main findings are replicated with k = 5 in the Supplemental Information.

Characterization of brain states and their hierarchy

Each cluster centroid was characterized by the cosine similarity between it and binary representations of seven a priori defined RSNs. The centroid pairs were grouped together based on their Pearson correlation values.

We can extract group-average centroids, condition-average centroids, and individual condition-specific centroids from fMRI data. These centroids are highly correlated with one another, and are also very similar to the group-average centroids shown here.

We calculated the temporal dynamics of brain-states after administration of LSD 29 and calculated the fractional occupancy, dwell time, appearance rate, and transition probability values for each state.

We constructed a structural connectome of the human brain using deterministic tractography and employed a linear time-invariant model to analyze the relationships between brain activation patterns and 5-HT2a receptor distribution.

The transition energy was computed as the minimum energy required to transition between all pairs of the substates for each individual’s LSD and placebo centroids separately, for each individual’s placebo centroids while varying the control input weights B , and for each random permutation of B .

Lempel-Ziv Complexity

We used the Lempel-Ziv algorithm to quantify the entropy of each subject’s brain-state time series, and converted them to binary sequences that returned 0 or 1 for each time point. This allowed 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 receptor energy matrix was calculated 10,000 times and compared to a randomly shuffled distribution. P-values were calculated as the fraction of times the randomized distribution resulted in a lower energy than the true distribution.

Ethics and Approval

The original study 32 was approved by the National Research Ethics Service committee London-West London and conducted under a Home Office license.

Citation and Gender Diversity Statement

Recent work in neuroscience and other fields has identified a bias in citation practices that under-cites papers from women and other minorities. We sought to proactively consider choosing references that reflect the diversity of the field.

Acknowledgements :

SPS is supported by the National Science Foundation, AIL is supported by the Gates Cambridge Trust, RLC-H is supported by the Alex Mosley Charitable Trust, GD is supported by the Spanish Ministry of Science and Innovation, MLK is supported by the Center for Music in the Brain.

Shulgin AT, Shulgin A, Carhart-Harris RL, Friston KJ, Luppi AI, Cruzat J, Cabral J, et al., The Continuation of Tihkal, The Anarchic Brain, The Entropic Brain, and the Free-Energy Principle: Toward a Unified Model of the Brain Action of Psychedelics. We explore the network dynamics underlying brain activity during rest using whole-brain computational connectomics and show that functional connectivity dynamically evolves on multiple time-scales over a static structural connectome.

The dynamic functional connectivity of the brain is described in several papers, including Kringelbach ML, Deco G, Hutchison RM, Womelsdorf T, Allen EA, et al. A study of healthy older adults found that spontaneous switching between states of functional connectivity during rest relates to cognitive performance. Human consciousness is supported by dynamic complex patterns of brain signal coordination, and consciousness-specific dynamic interactions of brain integration and functional diversity. Brain network integration dynamics are associated with loss and recovery of consciousness induced by sevoflurane, psilocybin, and cognitive demands, and are explained by network control theory, modulated by dopamine D1/D2 receptor function, and diminished in schizophrenia.

Multimodal neuroimaging reveals that the human brain is hierarchically organized in time, and that spontaneous fMRI network dynamics are governed by infraslow state fluctuations. The controllability of structural brain networks is also revealed, and a practical guide to methodological considerations is provided. LSD increases primary process thinking via serotonin 2A receptor activation, and serotonin 2A receptor activation is associated with increased self- and other-initiated social interaction in LSD-induced altered states. The entropic brain: revisited, a high-resolution in vivo atlas of the human brain’s serotonin system, and increased spontaneous MEG signal diversity for psychoactive doses of ketamine, LSD and psilocybin.

LSD-induced entropic brain activity predicts subsequent personality change, and psilocybin-induced entropic brain activity increases the fractal dimension of cortical brain activity. The brain’s default mode network is an important part of the brain’s anatomy and physiology. A number of studies have shown that the brain’s default mode network is where the idiosyncratic self meets the shared social world, and that the brain’s frequency-specific energy changes and repertoire expansion revealed using connectome-harmonic decomposition are common neural signatures of psychedelics. Nozari, Stiso, Caciagli, et al. asked if the brain was macroscopically linear. Schulz, M-A, Yeo, BTT, Vogelstein, JT, et al. asked if linear models and deep learning were different in UKBiobank brain images versus machine-learning datasets. The WU-Minn human connectome project combines network topology and information theory to construct representative brain networks.

The topographic organization of the human subcortex is unveiled with functional connectivity gradients, according to Tian Y, Margulies DS, Breakspear M, Zalesky A. The Center for Integrated Molecular Brain Imaging (Cimbi) database contains data on spatial resolution of the HRRT PET scanner using 3D-OSEM PSF reconstruction, the Adjusted Mutual Information, the Complexity of Finite Sequences, and the Gender Citation Gap in International Relations.


A great explanation of this paper was given by Parker Singleton on Twitter. The paper is also covered in Psychedelic Science Review. Interesting Engineering also covered the paper.

This paper may also pair well with Girn et al (2021).

The data from the 15 participants on 75ug of LSD (but not the new computer/brain-simulation models) come from Carhart-Harris et al (2017).

There are many different ways of peering inside our brains. We can do this with (repeated) fMRI studies that can take multiple snapshots of a brain. Another technique is called PET which can show changes in a system over time. Combining these techniques, and a few others, this paper provides more evidence for the leading theory of our brain on psychedelics.

This paper builds on earlier work that argues psychedelics relax our prior beliefs (REBUS). This framework argues that old beliefs are let go more easily and be replaced by new ideas, connections, or observations. This can explain how psychedelics allow a person to process emotions. Or how creative ideas are given space to flourish.

What makes this paper so special?

  • It calculated the influence of the serotonin 2a receptor and found it to be very well positioned to the flattening of the hierarchy
  • The paper combined fMRI, dMRI, PET, and NCT to show the flattening of the hierarchy from multiple angles
  • The easier information flow (in a flatter hierarchy) can both explain the synaesthesia experiences as well as the letting go of old beliefs. In other words, it has great explanatory power

Our brains not only become ‘flatter’ but also show a higher level of disorder (entropy). One way to interpret this is to say that there are more options available whilst under the influence of psychedelics.

Although the paper is quite technical, the graphs do help make sense of this exciting new research. The next steps could include the same analyses with different psychedelics, at different dosages (now 75μg LSD), and to find a relationship with the subjective experience (now no significant relationship was found).

Study details

Compounds studied

Topics studied

Study characteristics
Theory Building Bio/Neuro

14 Humans


Authors associated with this publication with profiles on Blossom

Leor Roseman
Leor Roseman is a researcher at the Centre for Psychedelic Research, Imperial College London. His work focussed on psilocybin for depression, but is now related to peace-building through psychedelics.

Robin Carhart-Harris
Dr. Robin Carhart-Harris is the Founding Director of the Neuroscape Psychedelics Division at UCSF. Previously he led the Psychedelic group at Imperial College London.

David Nutt
David John Nutt is a great advocate for looking at drugs and their harm objectively and scientifically. This got him dismissed as ACMD (Advisory Council on the Misuse of Drugs) chairman.

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