## Abstract

Psychoactive drugs can transiently perturb brain physiology while preserving brain structure. The role of physiological state in shaping neural function can therefore be investigated through neuroimaging of pharmacologically-induced effects. This paradigm has revealed that neural and experiential effects of lysergic acid diethylamide (LSD) are attributable to its agonist activity at the serotonin-2A receptor. Here, we integrate brainwide transcriptomics with biophysically-based large-scale circuit modeling to simulate acute neuromodulatory effects of LSD on human cortical dynamics. Our model captures the topographic effects of LSD-induced changes in cortical BOLD functional connectivity. These findings suggest that serotonin-2A-mediated modulation of pyramidal cell gain is the circuit mechanism through which LSD alters cortical functional topography. Individual-subject fitting reveals that the model captures patterns of individual neural differences in drug response that predict altered states of consciousness. This work establishes a framework for linking molecular-level manipulations to salient changes in brain function, with implications for precision medicine.

## Introduction

What are the respective roles of structure and physiology in shaping the spatiotemporal dynamics of networked neural systems? Areal differences in gene transcription, cellular architecture and long-range connectivity patterns have been linked to areal differences in specialization of cortical function (** Felleman and Van Essen, 1991; Hilgetag et al., 2016; Burt et al., 2018; Huntenburg et al., 2018; Demirtaş et al., 2019**). Yet it remains unclear how embedded neurophysiological changes impact functional network organization and structure-function relationships. Non-invasive neuroimaging of pharmacologically-induced changes in brain function permits selective, transient and

*in vivo*perturbation of physiology, while preserving brain structure. Pharmacological neuroimaging therefore provides a unique test bed for investigating the roles of neurophysiological properties in shaping patterns of large-scale brain function.

The central role of physiological state in shaping functional brain dynamics and influencing human consciousness and behavior is supported by neuroimaging studies of the acute functional disturbances induced by psychopharmacological compounds. Serotonergic hallucinogens, in particular, produce rapid and profound alterations of consciousness that are linked to widespread, stereotyped patterns of functional network disruption (** Tagliazucchi et al., 2014, 2016; Lord et al., 2018; Muthukumaraswamy et al., 2013; Atasoy et al., 2017; Preller et al., 2018, 2020**). Recently, our group has shown that LSD-induced disruptions of BOLD functional connectivity and concomitant changes in consciousness are extinguished by pre-treatment with ketanserin, a selective serotonin-2A (5-HT

_{2A}) receptor antagonist (

**). This result suggests that the 5-HT**

*Preller et al., 2018*_{2A}receptor plays a critical role in LSD’s mechanism of action (

**).**

*Vollenweider and Preller, 2020; Holze et al., 2020***) analyzed regional changes in mean BOLD functional connectivity, called global brain connectivity (GBC), which is a graph-theoretic measure of functional integration (**

*Preller et al. (2018***). We found that the regional topography of LSD-induced changes in GBC is aligned with the topography of regional expression levels of HTR2A, the gene which encodes the 5-HT**

*Cole et al., 2010; Anticevic et al., 2014b*_{2A}receptor (

**). However, the circuit mechanism through which LSD alters cortical GBC topography remains unclear.**

*Preller et al., 2018*One approach to bridge this mechanistic gap is to develop biophysically-based models of large-scale brain activity that incorporate key features of neuronal and synaptic dynamics. These models, which are grounded in human neurobiology, can be first calibrated to healthy-state data and then systematically perturbed through biophysically interpretable parameters. In doing so, selective manipulations at the synapse can be linked to their manifestations at empirically resolvable scales — for instance, at the length- and time-scales probed by functional magnetic resonance imaging (fMRI). Moreover, recent advances in high-throughput transcriptomics have led to rich genome-wide atlases of gene expression levels mapped across the human brain (** Hawrylycz et al., 2012, 2015**). Insofar as protein levels increase with the number of gene transcripts in a region (

**), gene expression maps provide a principled way to infer the spatial distribution of proteins of interest, e.g., drug targets. Gene expression maps therefore provide a means to simulate the regionally heterogeneous impacts of a drug on local circuit properties (**

*Liu et al., 2016***).**

*Murray et al., 2018*We employed this approach to generate mechanistic insight into the topography of LSD-induced GBC alterations (** Preller et al., 2018**). GBC is pharmacologically elevated in sensory cortex, especially in visual cortex, and reduced in association cortex (

**). Moreover, GBC changes correlate significantly with changes in subjects’ experience of consciousness, as determined by validated psychometric instruments (**

*Preller et al., 2018***). Here, we investigated the mechanism underlying this effect by extending a previously validated model of large-scale neural dynamics (**

*Studerus et al., 2010; Preller et al., 2018***). We found that our model accurately captures the spatial topography of LSD-induced GBC changes. Our findings suggest that the distribution of 5-HT**

*Wong and Wang, 2006; Deco et al., 2013, 2014*_{2A}receptors is critical for generating the topography of functional disruptions, and that neural gain is preferentially modulated on cortical pyramidal cells, consistent with known neurobiology. Fitting the model at the individual-subject level, we found that the model captures patterns of individual differences in drug response that predict altered states of consciousness. Our work therefore advances earlier pharmacological modeling studies that capture global effects at the group-level by capturing spatially heterogeneous effects in individuals. Broadly, this work establishes a flexible conceptual framework for linking mechanistic molecular hypotheses to human neuroimaging markers.

## Results

To investigate the circuit mechanism through which LSD alters cortical GBC topography, we extended a previously validated biophysically-based model of large-scale neural circuit dynamics (** Wong and Wang, 2006; Deco et al., 2013, 2014; Demirtaş et al., 2019**) (Fig. 1). The model is comprised of many local microcircuits, each consisting of coupled excitatory and inhibitory cell populations. Population dynamics are driven by recurrent synaptic interactions that are governed by neurophysiologically interpretable parameters. Our model consists of 180 interconnected nodes, each of which represents one left-hemispheric cortical parcel in the Human Connectome Project’s (HCP) MMP1.0 parcellation (

**). Note that we model only one cortical hemisphere, as the pharmacological fMRI data informing the model are approximately bilaterally symmetric (**

*Glasser et al., 2016***), and the gene expression data are sampled from the left hemisphere but confirmed to show bilateral correspondence (**

*Preller et al., 2018***). Nodes in the network interact through structured long-range excitatory projections. The relative strengths of these projections are informed by a diffusion MRI-derived, group-averaged (N=339) structural connectivity (SC) matrix (Fig. 1A) (**

*Hawrylycz et al., 2015***). To evaluate model outputs against fMRI-derived data, simulated synaptic activity in each node is transformed into an observable blood-oxygen level dependent (BOLD) signal using the Balloon-Windkessel model for the hemodynamic response (**

*Van Essen et al., 2013; Demirtaş et al., 2019***) (Fig. 1B). We henceforth refer to this hemodynamically-coupled neural circuit model as the “baseline” or “unperturbed” model.**

*Friston et al., 2003; Stephan et al., 2007; Demirtaş et al., 2019*To simulate the action of LSD in human cortex, we systematically perturb the baseline model. In earlier work, we found that LSD’s influence on brain function and on behavior is primarily mediated through its agonist activity at the 5-HT_{2A} receptor (** Preller et al., 2018**). Stimulation of 5-HT receptors alters the response properties and membrane excitability of mammalian cortical neurons, such that firing rates are selectively enhanced for strongly depolarizing currents — that is, such that neural gain is enhanced (

**). This 5-HT receptor-mediated enhancement or modulation of gain is thought to be mediated specifically by the 5-HT**

*Araneda and Andrade, 1991; Andrade, 2011; Zhang and Arsenault, 2005*_{2A}receptor (

**). We therefore simulate the action of LSD by manipulating neural gain equations in the model (Fig. 1C). Neural gain in the model is defined by a non-linear expression of the form**

*Zhang and Arsenault, 2005**r*=

*f*(

*aI*) (Equation 2), which relates pre-synaptic current

*I*to post-synaptic firing rate r by the non-linear function

*f*with scalar gain parameter

*a*. We mathematically express gain modulation as a fractional change in

*a*, i.e.,

*a*--- (1 +

*δ*)

*a*

_{0}, where

*a*

_{0}is the unperturbed parameter value.

To account for the heterogeneous spatial distribution of 5-HT_{2A} receptors in cortex, gain modulation in each node is scaled in proportion to the local expression level of HTR2A — the gene which encodes the 5-HT_{2A} receptor — using transcriptomic data from the Allen Human Brain Atlas (** Hawrylycz et al., 2012, 2015; Burt et al., 2018**). In mammalian cortex, 5-HT

_{2A}receptors are present on glutamatergic projection neurons and GABAergic interneurons (

**). We introduce an additional degree of freedom into the model to let gain modulation differentially impact the excitatory and inhibitory cell populations, thereby remaining agnostic as to the precise distribution of 5-HT**

*Mengod et al., 2010; Burnet et al., 1995; Santana et al., 2004*_{2A}receptors across cell types (Fig. 1C). Specifically, the gain parameter a of cell population p in brain region i is given by , where

*h*

_{i}is proportional to the expression level of gene HTR2A in the

*i*-th region. For brevity, in what follows we drop the subscript

*i*and superscript

*p*notation. Note that the scalar gain parameter

*a*depends linearly on

*δ*, and the gain function

*r*=

*f*(

*aI*) scales non-linearly with

*a*; thus, the gain functions scale non-linearly with

*δ*.

### Quantifying function organization with global brain connectivity (GBC) maps

Functional organization of cortical dynamics, in the model and in the data, can be operationalized by constructing cortical GBC maps. The change in GBC by LSD provides a topographic map across cortical regions of the mean effect on functional connectivity, which we have previously compared to the topography of the HTR2A gene expression map (** Preller et al., 2018**). The first step in computing a GBC map is to construct a functional connectivity (FC) matrix, defined as the matrix of Pearson correlation coefficients between pairs of brain regions’ BOLD signal time-traces. The off-diagonal elements of this matrix are Fisher Z-transformed such that values are approximately normally distributed. Off-diagonal elements of the resulting symmetric matrix are then averaged along either rows or columns, yielding a map of GBC which consists of a single scalar value for each region.

As reported in ** Preller et al. (2018**), GBC maps were constructed from resting-state BOLD fMRI scans for 24 study participants. Subjects served as their own controls. GBC maps were constructed for each subject in both drug conditions (placebo & LSD). The group-averaged contrast map of the change in GBC for LSD vs. placebo drug conditions — henceforth referred to as the ΔGBC map — specified the target model output (Fig. 1D). In other words, we sought to recapitulate in our model the pattern of functional reorganization indicated by changes in cortical GBC topography.

Empirically, the group-averaged ΔGBC map reveals widespread LSD-induced hyper-connectivity of sensory–somatomotor regions, and hypo-connectivity of association regions (** Preller et al., 2018**).

*In silico*, we generate a GBC map for both the unperturbed and neuromodulated models, corresponding to models for the placebo and LSD conditions, respectively (described in more detail below). From these maps, we compute a model ΔGBC map which is then quantitatively compared to the empirical ΔGBC map (Fig. 1D).

### Model captures the spatial topography of LSD-induced changes in cortical GBC

The operating point of the unperturbed model was first calibrated such that it optimally captured empirical FC in the placebo condition. This was achieved by performing a one-dimensional grid search over the value of a global conductance parameter, which uniformly scales the strengths of all long-range connections between nodes (** Deco et al., 2014**). We determined the value of this coupling parameter that yielded the greatest Spearman rank correlation between the off-diagonal elements of the simulated and empirical FC matrices. The coupling parameter was subsequently fixed at this value. The model FC matrix was then used to compute a baseline model GBC map — our computational analog of the empirical GBC map in the placebo condition.

Next we performed a two-dimensional grid search over the two free model parameters setting the strength of gain modulation on excitatory and inhibitory neurons (*δ*^{E} and *δ*^{I}), such that a modulation of gain by 1% corresponds to *δ* = 0.01 (Fig. 2A). For each combination of parameters (i.e., at each point on the grid), we updated the simulated gain functions and re-computed the system’s stable fixed point. This now-perturbed system is used to generate a new FC matrix, from which we again compute a model GBC map — this time, our computational analog of the empirical GBC map in the LSD condition. For each combination of free parameters, we then computed a model ΔGBC map by calculating the difference between the perturbed and unperturbed model GBC maps. To evaluate the quality of the model for each set of parameters, we evaluated the statistical similarity of each model ΔGBC map to the empirical ΔGBC map. We quantified similarity by computing the “loading” of the model ΔGBC map onto the empirical ΔGBC map, which we define as the Cartesian dot product between the two ΔGBC maps (expressed as vectors), divided by the squared norm of the empirical ΔGBC map (the natural length scale in the quantity). This metric was constructed specifically for its sensitivity to both the topography and magnitude of the model perturbation.

The model ΔGBC map loaded most strongly onto the empirical ΔGBC map across a quasidegenerate range of parameter values (Fig. 2A, off-diagonal yellow band). The location of this regime suggests that neural gain is preferentially modulated on excitatory pyramidal cells. To investigate this further, we next characterized the relationship between changes in model E/I balance and model-empirical loading. For each combination of gain modulation parameters (i.e., at each location on the two-dimensional grid in parameter space), we computed the the model’s excitatory-to-inhibitory (E/I) firing-rate ratio, relative to its unperturbed value, where we define E/I ratio as the ratio of the mean excitatory firing rate (computed across nodes) to the mean inhibitory firing rate. We find that model-empirical loadings, when plotted as a function of fractional change in E/I ratio, collapse to form an approximately one-dimensional curve which peaks at positive shifts in E/I ratio (Fig. 2B). One-dimensional collapse suggests that gain modulation-induced changes in E/I balance are the primary mechanism through which GBC topography is altered under LSD. Moreover, the fact that the peak occurs for positive shifts in E/I balance suggests that LSD has a net-excitatory effect on cortical activity.

The model generates a strong functional perturbation that is aligned with the data, but does it also capture fine-grained functional network-specific and parcel-level effects? Empirically, LSD exhibits bidirectional effects across sensory and association brain networks, inducing hyper-connectivity of constituent brain regions in sensory and somatomotor networks, while inducing hypo-connectivity of regions in associative networks (** Preller et al., 2018**). To investigate network effects in the model, we set the gain modulation parameters to the values that yielded the greatest model-empirical loading (indicated by the black star in Fig. 2A). We then characterized the distribution of model ΔGBC values across parcels within each functional network defined in the Cole-Anticevic Brain Network parcellation (CAB-NP) (Fig. 2C) (

**). We found that empirical network specificity of GBC changes was recapitulated in the model (Fig. 2D-E). This finding indicates that the strong model-empirical loading is not driven by select functional networks or by a small subset of all cortical parcels. In fact, at the level of parcels we find a remarkably strong spatial correspondence between ΔGBC topographies in the model and data (**

*Ji et al., 2018**r*

_{s}= 0.73;

*p*< 10

^{−5}; Spearman rank correlation) (Fig. 2F). Note that brain map values, here and in subsequent figures, are plotted on a flattened (i.e., unfolded) representation of the cortical surface, to better illustrate maps’ contiguous spatial topographies. This statistical association was significantly stronger than the association between the HTR2A gene expression map and the empirical ΔGBC map (

*p*= 0.011; test for difference between dependent correlations) (Fig. 2H). Heterogeneous physiological responses to LSD thereby play a critical role in shaping the cortical topography of LSD-induced GBC changes.

Global signal regression (GSR) remains a debated pre-processing step that is frequently included in fMRI analyses (** Murphy and Fox, 2017**).

**) reported statistically significant brain-behavior relationships between the neural and experiential effects of LSD when — and only when — GSR was performed. Moreover, GSR was found to substantially alter the topography of the empirical ΔGBC map: when GSR was not used, the spatial correspondence of the ΔGBC map with the HTR2A expression map is dramatically attenuated (**

*Preller et al. (2018***). Here, we find that when GSR is not performed, maximal model-empirical loading and Spearman rank correlation between the model and empirical ΔGBC maps are both reduced significantly (Supplementary Fig. 1). This finding further supports the notion that GSR attenuates non-neuronal components or artifacts which otherwise obscure meaningful neuronal effects in pharmacological fMRI signals.**

*Preller et al., 2018*### Receptor topography plays a critical role in shaping large-scale functional effects

In addition to stimulating 5-HT_{2A} receptors, LSD exerts predominately agonistic activity at (5-HT)-2C, -1A/B, -6, and -7 receptors, as well as dopamine D1 and D2 receptors (** Nichols, 2004; Passie et al., 2008**). Molecular signaling across these disparate receptor subtypes will certainly impact physiology differently; however, these neuromodulatory systems are known to be important regulators of cortical gain (

**). We therefore asked whether modulation of gain via these other receptor subtypes also explains the spatial topography of cortical GBC changes. To test this, we repeated our grid-search over model parameters, except that instead of modulating gain in proportion to HTR2A expression levels, we modulated gain in proportion to the expression level of, in turn: serotonergic genes HTR1A, HTR2C, and HTR7, and dopaminergic genes DRD1 and DRD2 (excluding 5-HT**

*Thurley et al., 2008; Ferguson and Cardin, 2020*_{1B}and 5-HT

_{6}encoding genes for lack of reliable transcriptomic data in the Allen Human Brain Atlas). The result of this process is illustrated in Figure 3A. Of the receptor-encoding genes that we tested, using the HTR2A map in the model yields the maximal model-empirical loading and Spearman rank correlation between empirical and simulated ΔGBC maps (Fig. 3B). These findings highlight the importance of the spatial distribution of drug targets in mediating their large-scale functional effects.

We examined whether a strong model-empirical loading could be simply explained by general statistical properties of the HTR2A map, rather than its specific topographic pattern. To quantify the significance of the HTR2A map’s topography, we sought to establish statistical expectations for model-empirical loading under an appropriate null hypothesis. A widely-adopted approach to quantifying significance for a complex, model-generated statistic (such as model-empirical loading) is to perform a non-parametric permutation test: by randomly permuting the brain map and re-generating a quantity of interest, one can construct a null distribution of expected outcomes due to random chance. When permutation tests of this type are applied to brain maps, the implicit null hypothesis is that any brain map with the same distribution of values but with a random topography is statistically likely to have produced a comparable or more extreme effect.

One problem with this approach is that spatial autocorrelation — a characteristic statistical property of brain maps — is necessarily destroyed by random spatial permutations. Spatial auto-correlation is fundamentally important for two reasons: i) it violates the assumption that samples are independent or exchangeable, an assumption which underlies many common statistical tests (including the permutation test); and ii), this violation dramatically inflates p-values in studies of brain maps (** Burt et al., 2020**). In light of this limitation, here we leverage a recent method to generate autocorrelation-preserving surrogate brain maps (

**). By construction, these surrogate brain maps have randomized topographies but a fixed spatial autocorrelation (Fig. 3C). Building a null distribution from these autocorrelation-preserving brain maps facilitates a test that controls for this important property.**

*Burt et al., 2020*To perform such a test, we repeatedly redefined gain functions in the model, each time by modulating gain in proportion to regional values of a random SA-preserving surrogate brain map. Each surrogate map was constructed to have the same spatial autocorrelation structure as the HTR2A map. For each surrogate map, we regenerated a model ΔGBC map, from which we computed a model-empirical loading. The resulting null distribution of model-empirical loadings was then used to evaluate the significance of the HTR2A map’s specific topography (Fig. 3D). We found that modulating gain in proportion to HTR2A expression levels produces a statistically significant loading (*p* = 0.012). The null distribution further reveals that none of the alternative gene expression maps reach significance. These findings further implicate the 5-HT_{2A} receptor in LSD’s mechanism of action, while simultaneously acting as a statistical control for the model complexity.

### Model captures experientially-relevant modes of neural variation

Our model captures cortical GBC alterations at the group level, but is it expressive enough to capture individual differences? To characterize individual variation — first, in the empirical data — we performed a principal components analysis (PCA) on subjects’ individual ΔGBC maps. We focused on the leading principal component (PC1) of ΔGBC variation (Fig. 4A). By definition, PC1 corresponds to the spatial map that (linearly) captures maximal variance in ΔGBC across subjects. We found that PC1 correlates strongly with the group-averaged ΔGBC map (*r*_{s} = 0.72; *p* < 10^{−5}; Spearman rank correlation). This indicates that individual differences are primarily driven by the strength with which subjects exhibit the group-averaged pattern.

To explore individual variation in the model, for each subject we repeated the two-dimensional grid search over the two gain-modulating parameters. Model-empirical loading for each subject was computed using that subject’s ΔGBC map as the target model output. For each subject, we selected the combination of gain modulation parameters that maximized model-empirical loading. We then used those parameters to construct subjects’ model ΔGBC maps (Supplementary Fig. 1). We performed PCA on these subject-specific maps to derive PC1 of ΔGBC variance in the model (Fig. 4B). We found that, as in the empirical data, PC1 is topographically aligned with the group-level ΔGBC map (*r*_{s} = 0.87; *p* < 10^{−5}; Spearman rank correlation). Moreover, model PC1 and empirical PC1 exhibited similar spatial topographies (*r*_{s} = 0.63; *p* < 10^{−5}; Spearman rank correlation). These findings reveal a convergence between the dominant modes of neural variation in the data and in the model.

The PC variance spectra show that variation across subjects’ simulated ΔGBC maps is almost entirely captured by the two leading model PCs (Fig. 4C). We also find topographic alignment between model PC2 and empirical PC2 (*r*_{s} = 0.51; *p* < 10^{−5}; Spearman rank correlation) (Fig. 4D). However, the empirical PC variance spectrum reveals that the data exhibit approximately five significant modes of variation (Fig. 4C). The data therefore exhibit three more modes than the model. That model variation lies within a two-dimensional subspace is expected due to our fitting of two free parameters to *δ*GBC. However, a linear subspace analysis revealed that 67% of model variance fell within the subspace defined by the data’s leading five PCs (see Methods and Materials). In other words, we found that the majority of model variation lies within a low-dimensional sub-space defined by the principal axes of empirical variation.

With only two significant modes of variation, is the model expressive enough to capture individual differences in LSD-induced alterations of consciousness? Changes in conscious experience were determined psychometrically using the five-dimensional altered states of consciousness (5D-ASC) questionnaire (** Dittrich et al., 2010**), which was administered to study participants 180 minutes after drug infusion (

**). The short version of the 5D-ASC questionnaire quantifies changes in conscious experience along five distinct experiential dimensions: experiences of disembodiment, elemental imagery, changed meaning of percepts, blissful state, and spiritual experience — each of which is profoundly altered under LSD (Fig. 4E). We performed a neurobehavioral linear regression analysis to find patterns of altered GBC that were predictive of experiential effects. For each (parcel, experiential dimension) pair, we performed a linear regression across subjects, such that each sample in the regression between ΔGBC in parcel**

*Preller et al., 2018**i*(the predictor variable) and change along experiential dimension

*j*(the target variable) corresponds to a (ΔGBC

_{i}, Δ Score

_{j}) pair for one subject.

For each experiential dimension, we performed one regression per parcel, and aggregated the linear regression coefficients across all parcels to create a spatial brain map (Fig. 4F). We hence-forth refer to these maps as “experiential regression maps.” By construction, experiential regression maps reflect ΔGBC patterns that predict individuals’ change in experience. For instance: if a subject’s ΔGBC map strongly resembles the Meaning regression map (Fig. 4F), then we expect that subject to have reported a relatively strong change in the meaning of percepts. How consistent are these experiential regression maps across experiential dimensions? We found evidence for a single dominant experiential regression map pattern (Fig. 4G).

Returning to our original question — do modes of model variation have experiential relevance? — we compared PC1 maps (which characterize neural variation) to experiential regression maps (which are defined by their experiential relevance) (Fig. 4G). We find notably strong correlations of model PC1 with the meaning (*r*_{s} = 0.38; *p* < 10^{−5}; Spearman rank correlation) and disembodiment (*r*_{s} = 0.61; *p* < 10^{−5}; Spearman rank correlation) experiential regression maps. Most strikingly, however, we find that the model PC1 map strongly resembles the dominant experiential regression map pattern (*r*_{s} = 0.65; *p* < 10^{−5}; Spearman rank correlation). This indicates that the model flexibly captures patterns of functional variation that are predictive of pharmacologically-induced changes in experience.

## Discussion

In this study we integrated transcriptomic mapping into a biophysically-based model of large-scale cortical dynamics to investigate the circuit mechanisms underlying LSD-induced changes in cortical GBC topography. Recently, our group has shown that LSD induces experientially-relevant changes in GBC through its agonist activity at the 5-HT_{2A} receptor (** Preller et al., 2018**). Here, we found that the ΔGBC topography was captured

*in silico*when LSD’s effect on molecular signaling was modeled as a modulation of neuronal gain, mediated by 5-HT

_{2A}receptor agonism, with preferential impact on pyramidal neurons. Moreover, our findings were specifically attributable to the topography of the HTR2A expression map — our transcriptomic proxy measure of the spatial distribution of 5-HT

_{2A}receptors. Finally, we showed that the model has enough expressivity to fit individual subjects and exhibits patterns of variation that predict drug-induced alterations of consciousness. This work establishes a framework for linking molecular-level manipulations to salient changes in brain function by integrating transcriptomics, biophysical modeling, and pharmacological neuroimaging.

Our findings complement a recent modeling study which showed that a gain-modulatory mechanism captures changes in global spatiotemporal properties of group-level neural dynamics under LSD (** Deco et al., 2018**), but did not examine cortical topographic effects. The authors of that study characterized changes in the distribution of pairwise correlations between sliding-window dynamic functional connectivity matrices, or functional connectivity dynamics (FCD) (

**). FCD and other global statistical metrics have revealed interesting dynamical consequences of gain modulation in simulated neural systems (**

*Hansen et al., 2015***). However, changes in global metrics may be driven by spatially non-specific effects and non-neuronal components or artifacts, particularly in imaging studies of serotonergic psychedelics (**

*Shine et al., 2018; Deco et al., 2018; Li et al., 2019; Pfeffer et al., 2020***). Our findings here demonstrate that gain modulation is a molecular mechanism that explains the specific spatial topography of LSD’s functionally disruptive effects. This key result illustrates how our proposed modeling framework could be used in future studies to inform the development of therapeutics that precisely target pathological brain circuits while minimizing off-target effects.**

*Lewis et al., 2017; Preller et al., 2018, 2020; Vollenweider and Preller, 2020*Whereas prior modeling work explored the effects of modulating neural gain uniformly across cell types (** Deco et al., 2018**), our study investigated the cell-type specificity of LSD’s effects. Our finding that the best model fits are associated with positive shifts in E/I balance and gain modulation that is biased towards excitatory populations suggests that LSD preferentially targets pyramidal cells. This finding converges with multiple lines of experimental evidence in humans (

**), monkeys (**

*Pazos et al., 1987; Hall et al., 2000***), and in rats (**

*Jakab and Goldman-Rakic, 1998***), which show that 5-HT**

*Willins et al., 1997; Santana et al., 2004*_{2A}receptors are preferentially found on apical dendrites of cortical pyramidal cells. Moreover, 5-HT

_{2A}receptor agonists have been shown to induce substantial increases in cortical pyramidal cell firing rates (

**). State-of-the-art single-cell RNA sequencing data across multiple cortical areas in humans also reveals that HTR2A expression is significantly elevated in excitatory cell types, relative to inhibitory cell types (Supplementary Fig. 1D). Intriguingly, the localization of 5-HT**

*Martín-Ruiz et al., 2001; Puig et al., 2003; Lladó-Pelfort et al., 2018*_{2A}receptors on apical dendrites of cortical pyramidal cells may help explain why serotonergic psychedelics induce such profound alterations of somatosensory perception and consciousness (

**).**

*Aru et al., 2019; Manita et al., 2015; Phillips et al., 2016*Most prior models of psychedelics’ pharmacological effects in humans have been fitted to group-level statistical measures (** Deco et al., 2018; Preller et al., 2019; Kringelbach et al., 2020; Herzog et al., 2020; Pfeffer et al., 2020**). Here we have shown that by fitting our model to individual subjects, the model can capture experientially-relevant modes of neural variation. Our model fit the majority of subjects well (Supplementary Fig. 1). However, this study was not statistically well powered for individual differences analyses, and several subjects were too idiosyncratic in their neural responses for us to accurately predict individuals’ experiential responses to LSD. Pharmacological modeling studies informed by other imaging modalities and powered by larger sample sizes are needed to fully characterize the predictive power and limitations of this approach.

LSD primarily mediates its effects on the human brain through 5-HT_{2A} receptors (** Preller et al., 2018; Holze et al., 2020**), but LSD also acts as an agonist at other serotonergic and dopaminergic receptor sites (

**). In particular, LSD exhibits high affnity for 5-HT**

*Nichols, 2004; Passie et al., 2008*_{1A}receptor subtypes, which function as inhibitory autoreceptors in the raphe nuclei and induce post-synaptic membrane hyperpolarization in limbic areas (

**). Thus, 5-HT**

*Filip and Bader, 2009*_{2A}and 5-HT

_{1A}receptors mediate opposing influences on membrane excitability. Interestingly, this bidirectionality appears consistent with the “anti-psychedelic” properties of partial 5-HT

_{1A}receptor agonists in humans (

**). In addition, 5-HT**

*Pokorny et al., 2016*_{2A}receptors are found in all cortical laminae but appear predominately in agranular medial layers (

**), often colocalized with 5-HT**

*Jakab and Goldman-Rakic, 1998; Burnet et al., 1995*_{1A}receptors on pyramidal cells (

**). 5-HT**

*Araneda and Andrade, 1991; Amargós-Bosch et al., 2004*_{2A}receptors are also found on GABAergic interneurons, though relatively infrequently (

**).**

*Willins et al., 1997; Santana et al., 2004*Functional neuroimaging-derived measures including GBC are sensitive to the global signal (GS), which represents shared variation across brain regions and may partially reflect non-neuronal physiological, movement- and scanner-related artifacts (** Murphy et al., 2013**). In particular, GS artifacts exhibit dramatic differences in clinical populations and following pharmacological manipulations (

**). The decision to include or forego GSR therefore has a significant bearing on findings in studies of psychedelics (**

*Driesen et al., 2013; Yang et al., 2014; Power et al., 2017; Yang et al., 2017; Lewis et al., 2017***): it has been shown that results do not replicate across samples when GSR is not performed (**

*Preller et al., 2018, 2020***), while studies that use GSR have reported replicable findings (**

*Tagliazucchi et al., 2016; Preller et al., 2018; Müller et al., 2017; Preller et al., 2020***). Here, we found that multiple measures of model-empirical similarity were significantly improved when GSR was performed (Supplementary Fig. 1), providing further support for its use. However, use of GSR remains debated (**

*Preller et al., 2018, 2020***), and in general there is no single “right” way to process resting-state data (**

*Fox et al., 2009; Saad et al., 2012***). In principle, it may be possible to circumvent some complications introduced by GSR by using a combination of spatial and temporal ICA-based de-noising (**

*Murphy and Fox, 2017***), but this has not yet been tested in pharmacological studies.**

*Glasser et al., 2018*In this study we leveraged recent advances in generative null modeling to establish statistical benchmarks while controlling for the confounding influence of spatial autocorrelation in analyses of brain maps (** Burt et al., 2020**). Spatial autocorrelation occurs ubiquitously in empirical brain maps and can dramatically inflate

*p*-values in analyses of both cortical and subcortical brain maps (

**). Importantly, however, maps of brain features often exhibit the most marked differences across (as opposed to within) neuroanatomical structures. For instance, although gene expression profiles exhibit characteristic hierarchical patterns of intra-cortical variation (**

*Burt et al., 2020***), cortico-cortical gene expression variance is small relative to cortico-subcortical variance (**

*Burt et al., 2018***). In addition to spatial autocorrelation within brain structures, these sharp distinctions between brain structures introduce additional bias into spatially-naive permutation tests performed at the whole-brain level (e.g., as used by**

*Hawrylycz et al., 2015***).**

*Deco et al., 2018*We used gene expression maps, derived from the Allen Human Brain Atlas, as proxy correlates of receptor densiities (** Hawrylycz et al., 2012, 2015; Burt et al., 2018**).

**) found that variation in gene expression levels across human brain regions generally well captured regional variation in protein expression levels. Positron emission tomography (PET) is a neuroimaging modality which can measure regional variation in receptor availability**

*Carlyle et al. (2017**in vivo*.

**) directly compared PET maps for serotonin receptors and found good alignment with gene expression levels from the Allen Human Brain Atlas. A key limitation of using PET-derived maps for model simulations of pharmacology is that for many receptors of interest, PET mapping is not yet possible due to lack of developed radioligands (**

*Beliveau et al. (2016***). Our study demonstrates proof of concept that transcriptomic mapping can inform large-scale models of pharmacological neuroimaging.**

*Pike, 2016*Our parsimonious model of LSD’s effects in cortex treats excitatory and inhibitory cells as statistical ensembles, providing a description of neural dynamics at a level of resolution and complexity appropriate for proof-of-concept comparisons with BOLD neuroimaging data. However, future work which expands, constrains, and tests biophysical models of pharmacology will be critical to address a number of open questions that remain. Neuromodulatory and disease processes may predominately influence spatiotemporal properties within rather than across areas, suggesting the need for multi-scale models that go beyond descriptions of brain areas in aggregate. Cell-type specific pharmacological effects can be further investigated by more fine-grained, multi-compartment models or models which include multiple interneuron subtypes. Cell-type specific effects could be introduced into such models by integrating bulk transcriptomics with single-cell RNA-sequencing to inform the joint distribution of pharmacological targets across distinct areas and cell types, respectively (** Lake et al., 2016; Burt et al., 2018**). Moreover, while 5-HT

_{2A}receptors are predominately found in cortex (Supplementary Fig. 1A-C), future work can incorporate the 5-HT

_{2A}receptorrich claustrum (

**), which may play a role in mediating the effects of serotonergic psychedelics (**

*Hall et al., 2000***). Comparing pharmacological models to data from multiple imaging modalities may also generate new and complementary insights: for instance, the mechanisms underlying LSD-induced changes in broadband oscillatory power (**

*Barrett et al., 2020***) and increased neural signal diversity (**

*Muthukumaraswamy et al., 2013; Carhart-Harris et al., 2016***) remain unclear.**

*Schartner et al., 2017*Recent years have experienced a resurgence of clinical interest in the use of psychedelics as therapeutics for the treatment of mood disorders, alcohol and substance abuse, and end-of-life distress in terminally-ill patients (** Carhart-Harris and Goodwin, 2017; Nichols et al., 2017; Vollenweider and Preller, 2020**). The common therapeutic mechanism of serotonergic psychedelic drugs remains unclear, although multiple lines of evidence now point to 5-HT

_{2A}receptor-mediated glutamate release (

**). Spatial gradients in drug targets, e.g. serotonergic receptor subtypes, can be approximated using the topography of gene transcripts — particularly in the case of receptors which lack suitable PET radioligands. Studies that leverage transcriptomic mapping (**

*Vollenweider and Kometer, 2010; Mason et al., 2020; Vollenweider and Preller, 2020***) and regionally heterogeneous modeling (**

*Grandjean et al., 2020***) will further elucidate the mechanisms underlying the complex functional signatures of pharmacologically-induced neuromodulatory effects (**

*Demirtaş et al., 2019***).**

*Pfeffer et al., 2020; Alamia et al., 2020*## Code Availability

Custom analysis routines and a computational implementation of the model are available from the corresponding author upon request.

## Methods and Materials

### Structural neuroimaging data

Group-averaged left-hemispheric structural connectivity (SC) matrices were constructed from diffusion MRI data using probabilistic tractography for 339 unrelated subjects from the Human Connectome Project (HCP) 900-subject data release ** Van Essen et al. (2013**). SC matrices were parcellated into 180 areas using the HCP’s Multi-Modal Parcellation (MMP1.0) (

**). In simulations, diagonal elements of the SC matrix were set identically to zero, and the SC matrix was row-wise normalized such that the total long-range inputs to each node were normalized. The Cole-Anticevic Brain Network Parcellation (CAB-NP) was used to determine parcels’ functional network assignments (**

*Glasser et al., 2016***). Pairwise inter-parcel geodesic distance matrices, which were used for constructing SA-preserving surrogate maps (**

*Ji et al., 2019***), were computed by averaging over surface-based distances between grayordinate vertices in each pair of parcels i and j, where surface-based distances were computed across the left-hemisphere midthickness surface in the HCP atlas.**

*Burt et al., 2020*### Pharmacological fMRI data

A complete description of data collection and pre-processing procedures was reported in ** Preller et al. (2018**). Briefly, fMRI data derived from a double-blind, placebo-controlled, and within-subject study design, ensuring that each subject served as their own control. 24 healthy human participants received either (i) placebo or (ii) LSD (100 µg po). Resting-state scans were collected 75 minutes following drug administration. Functional MRI data were obtained and processed following HCP-compliant acquisition standards (

**). Behavioral measures were derived from the short version of the 5-Dimensional Altered States of Consciousness (5D-ASC) questionnaire (**

*Glasser et al., 2013***), which includes 45 items that comprise five different scales: spiritual experience, blissful state, disembodiment, elementary imagery, and changed meaning of percepts. The 5D-ASC questionnaire was administered 180 minutes following drug infusion.**

*Dittrich et al., 2010*### Transcriptomic data

The Allen Human Brain Atlas (AHBA) is a publicly available transcriptional atlas of microarray data containing samples from hundreds of neuroanatomical structures in six normal post-mortem human brains. Microarray expression data and all accompanying metadata were downloaded from the AHBA (http://human.brain-map.org) ** Hawrylycz et al. (2012**, 2015). An exhaustive description of our pre-processing procedure was reported in

**). Briefly, cortical microarray data in volumetric space were mapped onto subjects’ native 2D cortical surfaces by minimizing 3D Euclidean distance between microarray samples and grayordinate vertex coordinates. For parcels that were not directly sampled, we performed a surface-based interpolation of sample expression values using a Voronoi diagram approach to create a dense gene expression map (at the level of grayordinates); this interpolated map was then parcellated by averaging across grayordinate vertices in each parcel. One representative microarray probe was selected for each unique gene, and gene expression profiles for selected gene probes were z-scored. Finally, group-averaged expression profiles were computed for genes whose expression profiles were reliable in at least four of the six subjects. These steps yielded group-averaged gene expression values across 180 left-hemispheric cortical areas.**

*Burt et al. (2018*Single-nucleus transcriptomic data that quantify the expression of HTR2A across distinct cell types in human cortex was obtained from the Allen Brain Institute’s Human Multiple Cortical Areas SMART-seq database (https://portal.brain-map.org/atlases-and-data/rnaseq/human-multiple-cortical-areas-smart-seq). We downloaded the CSV file containing “Gene expression by cluster, trimmed means” and aggregated columns that included either “Exc” or “Inh”.

### Modeling large-scale neural dynamics

We adapted the biophysically-based large-scale computational model described in ** Deco et al. (2014**). This model reduces the complexity and the number of local microcircuit parameters in a spiking neural network model using a dynamical mean-field approach (

**). By lever-aging a statistical description of ensemble neural activity and exploiting the long time-constants of NMDA receptors, the model reduces a high-dimensional spiking neural network to a computationally tractable two-dimensional dynamical system. Each node in the model comprises recurrently coupled excitatory (E) and inhibitory (I) populations, the dynamics of which are described via coupled non-linear stochastic differential equations. Time-varying activity of the excitatory and inhibitory synaptic currents in brain region**

*Wong and Wang, 2006**i*, denoted respectively by and , is defined as where

*I*

_{b}is constant background input current;

*S*is the synaptic gating variable, i.e., the fraction of open channels;

*G*is a global conductance parameter which scales the strengths of long-range connections;

*J*is the effective NMDA conductance;

*C*is the structural connectivity matrix; and remaining parameters are constants. Synaptic current

*I*

^{p}for population

*p*∈ {

*E, I*} is transformed into firing rate

*r*

^{p}via the transfer function where

*a, b*, and

*d*are cell-type specific parameters governing the form of the input-output relation. In particular, note that parameter

*a*, which regulates the slope of the transfer function, corresponds to the neural gain parameter. Finally, the time-evolution for synaptic gating variable

*S*is given by where

*τ*is a synaptic time constant,

*γ*is a kinetic parameter, and

*σ*is the standard deviation of the stochastic Gaussian input noise

*v*(

**). Following**

*Wong and Wang, 2006; Deco et al., 2014***), simulated synaptic covariance matrices were approximated analytically by linearizing Equations 1 to 3 around the dynamical system’s stable fixed point.**

*Deco et al. (2014*Neural gain modulation was implemented in the model by introducing a parametric rescaling of gain parameter *a* for each cell-type, in proportion to regional gene expression levels of HTR2A:
where *h*_{i} denotes the expression level of HTR2A in brain region *i, δ*^{E} and *δ*^{I} regulate the strength of the perturbation applied to excitatory and inhibitory cell populations, respectively. Thus, two-dimensional parameter sweeps reported in this study, for instance in Figure 2A, correspond to sweeps over free parameters *δ*^{E} and *δ*^{I}. Where brain maps (gene expression maps as well as surrogate maps) were used to modulate gain, they were first linearized using the error function (following ** Demirtaş et al. (2019**)).

Following ** Deco et al. (2014**), we implemented feedback inhibition control (FIC) in the model such that the firing rates were constrained to be 3 Hz

*prior to*neural gain modulation. This is accomplished by tuning the weight

*w*

^{EI}, which regulates the strength of local inhibitory-to-excitatory feedback, within each simulated brain region. Crucially, we note that FIC was calculated prior to but not following gain modulation, under the assumption that FIC represents neurobiological self-regulatory processes which balance neural activity in the brain on timescales much longer than the characteristic timescales of transient pharmacological manipulations.

### Modeling the hemodynamic response

To facilitate model comparisons with empirical fMRI data, excitatory synaptic activity within each brain region (given by *S*^{E} in Equation 3) was transformed to a blood-oxygen-level dependent (BOLD) signal using the Balloon-Windkessel model ** Friston et al. (2003**). In this model, the hemodynamic response obeys the following coupled system of equations:
where

*x*denotes the vasodilatory signal,

*f*the blood inflow,

*υ*the blood volume, and

*q*the deoxyhemoglobin content; and parameters

*p, τ*,,

*κ, γ*, and

*α*are the resting oxygen extraction fraction, hemodynamic transit time, rate of signal decay, rate of flow-dependent elimination, and the Grubb’s exponent, respectively (

**). In turn, the corresponding BOLD signal**

*Friston et al., 2003**y*is calculated as where

*V*

_{0}is the resting blood volume fraction. The three dimensionless magnetic field strength-dependent parameter values

*k*

_{1},

*k*

_{2}, and

*k*

_{3}were derived for a magnetic field strength of 3T using Appendix A of

**); all other hemodynamic parameter values were taken from**

*Heinzle et al. (2016***). Simulated BOLD covariance matrices were derived by linearizing these equations and then algebraically transforming the linearized synaptic covariance matrix, using a procedure which we previously reported in**

*Obata et al. (2004***).**

*Demirtaş et al. (2019*Values for all static parameters in the model are provided in Table 1.

### Modeling fitting

Tuning the model parameters consisted of two key sequential steps. First, the dynamical operating point of the model was calibrated such that (prior to gain modulation) the model optimally captured empirical functional connectivity derived from the placebo-condition fMRI scan. To this end, we performed a one-dimensional grid search over the global coupling parameter *G*, which linearly scales all long-range interactions between nodes (Equation 1). The grid search was over the range [0.01, 0.85] with a step size of 0.01. For each value, we solved for the stable fixed point of the system and then computed the linearized BOLD covariance matrix around that point. From the BOLD covariance matrix, we computed the FC matrix using the transformation from covariance to Pearson correlation coefficient. We computed the Spearman rank correlation between the *N* = 180(180-1)/2 upper-triangular elements of the model FC matrix and the placebo-condition empirical FC matrix. At the group level (i.e., using the group-averaged empirical FC), this step yielded an optimal global coupling value of *G* = 0.85, which resulted in a Spearman rank correlation of *r*_{s} = 0.45. This value of *G* was used for all group-averaged analyses in this study. We note that if the upper end of the range was extended beyond *G* = 0.85, the maximal fit to the group-level data occurred at *G* = 0.89. However, at this value the fit increases only marginally (*δ r*_{s} < 10^{−3}), while the system is then positioned so close to a critical bifurcation that even modest modulations of gain will dynamically destabilize the system. This class of computational models is known to produce optimal fits near the edge of stability (see, e.g., ** Deco et al. (2013**)).

After calibrating the system, next we performed a two-dimensional grid search over model parameters *δE* and *δI*, which determine the strength of excitatory and inhibitory gain modulation, respectively. For each combination of parameters, we updated the neural gain equations (Equation 5) in the model. We solved for the new fixed point and computed the linearized BOLD covariance matrix around that point. FC and GBC were then computed as described above. The difference between model GBC maps (expressed as Fisher Z-values) — perturbed minus baseline — yielded a model ΔGBC map. We then computed the model-empirical loading between the model ΔGBC map and the empirical ΔGBC map (LSD minus placebo). As illustrated in the heatmaps, the grid search for the gain modulation parameters was over the range [0, 0.03] with a step size of 0.003. Gain parameters that maximized model-empirical loading were then used for all analyses involving a model ΔGBC map, either at the group-or subject-level.

### Global brain connectivity

Empirical GBC was computed using in-house Matlab tools for all grayordinates in the brain using an HCP-harmonized version of the FreeSurfer software (** Fischl et al., 2002; Cole et al., 2011; Anticevic et al., 2013, 2014a**), as reported in

**). Briefly, for each subject we computed the fMRI time-series correlation between pairs of grayordinates, thereby constructing an FC matrix. Off-diagonal FC matrix elements were Fisher Z-transformed and then averaged across rows to compute GBC values. Maps were then parcellated using the HCP MMP1.0 parcellation (**

*Preller et al. (2018***). This yielded a parcellated GBC map for each subject where each parcel’s value represents the mean FC of that region to all other regions. Parcellated GBC maps were averaged across subjects to construct the group-averaged GBC map. Similarly, to compute model GBC maps, we used the model to generate a parcellated BOLD FC matrix. Off-diagonal FC matrix elements were Fisher Z-transformed and then averaged across rows to compute GBC values. All illustrated GBC map values (empirical and simulated) are Fisher Z-values.**

*Glasser et al., 2016*### Global signal regression

Global signal regression (GSR) was performed on empirical fMRI-derived time-series data using widely adopted approaches (** Anticevic et al., 2013; Cole et al., 2011**), as described in

**). In the model, we performed GSR directly on the analytically approximated BOLD covariance matrices using the following approach. Let**

*Preller et al. (2018**y*

_{i}be the BOLD signal in brain region

*i*, and let

*x*be the global signal — i.e., the mean gray-matter BOLD signal across regions. Note that

*x*and

*y*are both implicit functions of time. We construct a linear regression model of the form where the residual signal following GSR is given by What we seek is an expression for the covariance between GS-regressed BOLD signal residuals in regions

*i*and

*j*, i.e., where denotes the temporal average of

*ϵ*. Substituting Equations 10 and 11, this expression can be rewritten as By manipulating Equation 10,

*β*can be expressed in terms of covariances: Substituting this expression into Equation 13 and simplifying, we obtain From the definition of global signal

*x*= Σ

_{i}

*y*

_{i}, Equation 15 can be rewritten as Collecting the summations and noting that we obtain Equation 18 analytically relates the covariance matrix of the raw BOLD signal (right-hand side) to the covariance matrix of GS-regressed residuals (left-hand side). We used this expression to perform GSR on model BOLD covariance matrices. FC matrices (i.e., Pearson correlation matrices) were then computed from GS-regressed BOLD covariance matrices.

### Generative modeling of surrogate brain maps

Spatial autocorrelation-preserving surrogate maps were constructed following ** Burt et al. (2020**) using the python-based BrainSMASH toolbox (https://brainsmash.readthedocs.io/). This approach operationalizes spatial autocorrelation in a brain map by computing a variogram, which quantifies variance in the brain map as a function of pairwise distance between areas. To construct each surrogate map, the empirical brain map is iteratively shuffled (to randomize topography), smoothed (to reintroduce spatial autocorrelation), and rescaled (to recover empirical spatial autocorrelation). After performing this procedure, we resampled our surrogate map values from the empirical brain map such that the distribution of values does not change: each surrogate map can then be conceptualized as one random realization of an (approximately) spatial autocorrelation-preserving permutation of the original brain map.

For each surrogate map , the surrogate map values {*h*_{i}} were substituted into Equations 5 such that the modulation of gain in each region was scaled in proportion to the values of the surrogate map, rather than the empirical HTR2A map. This “surrogate model” was then used to re-compute the statistic under consideration. Repeating for and aggregating across all surrogate maps yields a null distribution for the expected value of the statistic under the null hypothesis that the outcome of the statistical test is an artifact of spatial autocorrelation, and therefore not unique to a specific spatial topography. Specifically, where we report p-values that derive from a spatial autocorrelation-preserving surrogate map test, we are reporting the proportion of samples in the null distribution which were more extreme than the test statistic.

### Beta maps

To identify characteristic patterns of changes in GBC that predict subject-level changes in 5D-ASC scores, we constructed spatial brain maps of linear regression coefficients (i.e., beta coefficient maps or simply “beta maps”). To calculate the beta map value in the *i*-th cortical parcel for experiential dimension *d*, we solved for in the linear regression defined by:
where *δs*^{d} is the change in score *δs* along experiential dimension *d*; *α* and *β* are constant and linear regression coefficients, respectively; and ΔGBC_{i} is the change in GBC for parcel *i*; and vectors include 24 elements (one per subject).

### Linear decomposition

To define low-dimensional linear subspaces within the 180-dimensional neural state space, we used principal components analysis (PCA) to determine the dominant spatial modes of variation across different collections of brain maps. We let **X** be the *M*×*N* matrix comprised of *M* brain maps, each represented as an *N*-dimensional vector, where columns of **X** have been mean-subtracted. The spatial covariance matrix is then given by the *N* × *N* symmetric matrix **C**, where
The symmetric matrix **C** can in general be decomposed according to
where **P** is an *N* × *N* orthogonal matrix whose i-th column is an eigenvector of **C**, and **Λ** is an *N* ×*N* diagonal matrix whose *i*-th diagonal element *λ*_{i} is the eigenvalue associated with eigenvector *p*_{i}. Eigenvector is a principal component (PC) of **X**, and the normalized eigenvalue *λ*_{i}/Tr(**Λ**) is the fraction of total variance in **X** that occurs along . We will assume without loss of generality that eigenvectors are ordered such that *λ*_{i+1} < *λ*_{i}. In other words, we assume that eigenvectors are arranged such that eigenvalues are placed in descending order. Finally, note that if *M* < *N*, then *N* − *M* + 1 eigenvalues are identically zero (i.e., **C** will not be full rank).

To determine which PCs were statistically significant, we performed simple permutation testing. Each row in **X** (that is, each brain map) was randomly permuted to obtain a new matrix **X**′. The procedure described above was then performed on **X**′ and the fraction of variance captured per PC (ie., ) was recorded. To construct the gray dashed lines in Figure 4, we performed this procedure *N* = 1000 times and then computed the 5th percentile of the resulting null distribution (for each individual PC).

To investigate shared dimensions of variability in the model and in the data, we first performed PCA on both the model and empirical subject-specific ΔGBC maps. Permutation testing revealed that the leading two model PCs and the leading five empirical PCs were statistically significant. We then derived the covariance matrix **C** for the 24 × 180 data matrix **X**, comprised of subjects’ model ΔGBC maps, per Equation 20. Total model variance *V* was determined by computing the trace of **C**. Let **P** denote the 180 × 5 matrix whose columns correspond to the leading five empirical PCs; then we performed a linear transformation of **C** into the five-dimensional subspace defined by the columns of **P** according to
Finally, we determined the total variance *V*′contained in the subspace by computing the trace of **C**′. Then the fraction of model variance that falls within the data’s five-dimensional subspace (67%) is given by *V* ′/*V*.

## Acknowledgments

This research was supported by grants from the NIH (R01MH112746, JDM; DP5OD012109, AA; R01MH108590, AA), the Swiss National Science Foundation (P2ZHP1_161626, KHP), the Swiss Neuromatrix Foundation (2015-0103, FXV), the Usona Institute (2015-2056, FXV), the NIAA (P50AA012870-16, AA & JHK), the NARSAD Independent Investigator Grant (AA), and the Yale CTSA grant (UL1TR000142 Pilot Award, AA). The funding sources had no involvement in the study design; nor in the collection, analysis, and interpretation of data; nor in the writing of the manuscript; nor in the decision to submit the manuscript for publication.