The natural axis of transmitter receptordistribution in the human cerebral cortexAlexandros Goulasa,1, Jean-Pierre Changeuxb, Konrad Wagstylc,d, Katrin Amuntse,f, Nicola Palomero-Gallaghere,g, and ClausC Hilgetaga,h

aInstitute of Computational Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg, Germany; bCollège de France and Institut Pasteur CNRS, Paris, France;cMcGill Centre for Integrative Neuroscience, Montréal Neurological Institute, Montréal, Canada; dDepartment of Psychiatry, University of Cambridge, Cambridge, UnitedKingdom, Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom; eInstitute of Neuroscience and Medicine (INM-1), Research CentreJülich, Jülich, Germany; fC. and O. Vogt Institute for Brain Research, University Hospital Düsseldorf, Heinrich Heine University Düsseldorf, Düsseldorf, Germany; gDepartmentof Psychiatry, Psychotherapy, and Psychosomatics, Medical Faculty, RWTH Aachen, and JARA-Translational Brain Medicine, Aachen, Germany; hHealth Sciences Department,Boston University, 635 Commonwealth Ave. Boston, MA 02215, USA

Transmitter receptors constitute a key component of the molecular machinery for inter-cellular communication in the brain. Recent effortshave mapped the density of diverse transmitter receptors across the human cerebral cortex with an unprecedented level of detail. Here, wedistil these observations into key organizational principles. We demonstrate that receptor densities form a natural axis in the human cerebralcortex, reflecting decreases in differentiation at the level of laminar organization, and a sensory-to-association axis at the functional level.Along this natural axis, key organizational principles are discerned: progressive molecular diversity (increase of the diversity of receptordensity), excitation/inhibition (increase of the ratio of excitatory-to-inhibitory receptor density) and mirrored, orderly changes of the densityof ionotropic and metabotropic receptors. The uncovered natural axis formed by the distribution of receptors aligns with the axis that isformed by other dimensions of cortical organization, such as the myelo- and cytoarchitectonic levels. Therefore, the uncovered natural axisconstitutes a unifying organizational feature linking multiple dimensions of the cerebral cortex, thus bringing order to the heterogeneity ofcortical organization.

cortical organization | unifying principles | molecular diversity

Ttransmitter receptors are essential for cellular communica-tion, since they are the molecular elements responsible for

the responsiveness of cells to distinct types of neurotransmit-ters. Such key role has naturally attracted concerted effortsthat aim to map and elucidate the role of receptors in aplethora of neurobiological phenomena, ranging from cellularto cognitive processes, with important ramifications for under-standing pathologies involving disturbances at the receptorlevel and drug design (1–7). Positron emission tomography ofthe human brain can offer a coarse mapping of the distributionof certain receptors, useful for modeling receptor dynamicsin the human brain (8) and understanding the pathogenesisof brain disorders at the molecular level (9). While densitiesfor some receptors can be measured in humans with positronemission tomography, for instance, for serotonin (10), thereare no suitable positron-emission tomography tracers that canmap a plethora of key receptors in living humans in a safeway (e.g., for NMDA). Furthermore, the number of differentreceptor types that can be examined in a single individualis very small. In vitro quantitative receptor autoradiographyof receptor densities has been used for a broad range of keytransmitter receptors and offers spatial resolution suitable foruncovering details pertaining to the laminar architecture ofthe cerebral cortex (7, 11, 12). Moreover, receptor autoradio-graphy reflects quantitative, neurobiologically interpretablemeasurements. Recent efforts have mapped the distributionof a broad range of transmitter receptors in multiple corticalareas across different laminar compartments (6, 7, 13). Theseadvancements also pose the challenge of compressing theseraw observations into a parsimonious set of comprehensible,key organizational principles.

Building on recent endeavors (7), here, we distill key orga-

nizational principles of the transmitter receptor distribution ofthe human cerebral cortex. We highlight an axis of maximumvariance of the receptor distribution across the cortex. Thisnatural axis ranges from sensory to association areas of thecerebral cortex. The arrangement of areas along this axisalso entails three organizational principles. First, progressivemolecular diversity is observed, that is, an increase of thediversity of receptor densities when proceeding from one endof the axis (sensory areas) to the other end of the axis (associ-ation areas). Second, progressive excitation/inhibition ratio,that is, the increase of the ratio of excitatory-to-inhibitory re-ceptor density, is also observed along the same direction alongthe natural axis. Third, progressive, mirrored changes of thedensity of ionotropic and metabotropic receptors are observed,that is, the density of metabotropic receptors increases whenproceeding from sensory to association areas, while the den-sity of ionotropic receptors is mirrored, thus, decreasing alongthis direction. The aforementioned principles manifest in alaminar-wise fashion, showcasing the importance of uncoveringorganizational principles at a fine spatial resolution. Moreover,the uncovered receptor-based natural axis aligns with the spa-tially ordered changes of the cerebral cortex at other levels ofarchitecture, such as the myelo- and cytoarchitectonic levels,in agreement with classic and more recent studies. Our resultsgenerate concrete testable predictions that are pertinent tocognitive, computational, and comparative neuroscience.

Results

We analyzed the previously collected data of transmitter re-ceptor densities across a wide range of areas of the humancerebral cortex (7). Density for multiple excitatory, inhibitory,

1

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

ionotropic and metabotropic receptors has been measured(AMPA, NMDA, kainate, GABAA, GABAA/BZ, GABAB ,M1, M2, M3, a4b2, a1, a2, 5-HT1A, 5-HT2, D1). Data wereacquired in a laminar-wise fashion summarized in densitiesfor granular, infra- and supragranular layers. For the receptorautoradiographical incubation protocols used and overall den-sitometric analytical procedure, see (7). An exemplary sectionis shown in Fig. 1 A.

Fig. 1. In vitro receptor autoradiography for estimation of transmitter receptor densities.A. Example of coronal sections through a human hemisphere, revealing the densityof cholinergic muscarinic M2 receptors (left) and the distribution of cell bodies (right)for multiple visual areas. B. Summary of cortical areas for which laminar transmitterreceptor measurements were carried out in (7, 11). Panel A adapted from (7, 11).SG=supragranular, G=granular, IG=infragranular.

Uncovering the natural axis of transmitter receptor density.As a first step, we assembled the receptor density profile ofeach cortical area, that is, the density measured in each areafor each of the aforementioned receptors in granular, infra- andsupragranular layers (hereafter G, IG and SG respectively).Note that due to the agranular character (lack of the granularlayer) of area 24, the only area with this feature in the setof the 44 cortical areas analyzed in (7) (Fig. 1 B), this areawas not included in the analysis to have a consistent profilewith IG, G, and SG measurements for all areas. Inclusionof area 24 and analysis based only on measurements on IGand SG layers led to qualitatively similar results. We aimedat uncovering the trajectory across which most variance ofreceptor density manifests. To this end, we applied PrincipalComponent Analysis (PCA) to the receptor density profile ofall cortical area. The arrangement of cortical areas in the spacespanned by PC1 while PC2 unveiled a sensory-to-associationaxis (PC1, accounting for 28% of the variance) and PC2 was

driven by the "outlier" character of areas 6 and 4, separatingthem from the rest of cortical areas (PC1, accounting for 22%of the variance) (Fig. 2). Note that here the terms "associ-ation" and "sensory" are not used to denote strict categoriesfor grouping cortical areas. Instead, the terms are used todenote the broad character of areas that span the two extremeends of the natural axis. In other words, the current resultsunderline the natural axis as a continuum (or gradient) of re-ceptor density variations and not as a discrete set of categories.The biplot simultaneously depicts the observations, that is,cortical areas (denoted with circles tagged with the names ofeach area), and the features, that is, laminar-wise receptordensities (arrows tagged with the names of each receptor andcorresponding laminar compartment), in the PCA space (Fig.2). Therefore, the biplot allows deciphering what receptordensity measurements drive the segregation of cortical areasacross the PCA space. Here, we will focus on PC1, whichexplains the largest amount of variance, and is, thus, referredto as the primary natural axis of receptor distribution.

Certain insights into the receptor signatures that segregatecortical areas along the primary natural axis can be discernedin the biplot (Fig. 2). First, receptor density of the IGlayers is more prominent in segregating association areas fromsensory areas along the natural axis (note the concentrationof loadings related to IG measurements with magenta colorin the left part of the biplot). Second, the biplot reveals astriking segregation along the natural axis with respect to theglutamate receptors AMPA and NMDA. NMDA is prominenton the sensory-related end of the natural axis, while AMPAis prominent in the association-related end. Third, the biplotreveals the distinctive receptor signatures of sensory areas, thatis, the prominent role the GABAA, a2, m2 and D1 receptorsin visual sensory areas from association areas (Fig. 2).

We subsequently aimed at distilling organizational princi-ples that are not readily discernable from the biplot. Specifi-cally, we estimated the diversity of receptor density of each cor-tical area as the Shannon entropy of the receptor profile of eacharea. Entropy was calculated as H = -sum(N.*log(N)/log(M),where N is the normalized receptor profile of the area with eachentry denoting each receptor density value as a proportion tothe overall receptor density of the area and M denoting thetotal number of features of the profile, that is, 45 (densitiesfor 15 receptors for G, IG and SG layers) and log is the nat-ural logarithm (hence, entropy was normalized to the [0 1]interval). We also estimated the excitation/inhibition ratiofor each cortical area by dividing the sum of the density of allthe excitatory receptors by the sum of the inhibitory recep-tors. Lastly, we estimated the changes of the receptor densityacross cortical areas for ionotropic and metabotropic receptorsseparately. For the assignment of receptors to the aforemen-tioned categories, that is, excitatory, inhibitory, ionotropicand metabotropic, see (7). The aforementioned metrics wereestimated on a laminar-wise basis. The insights provided bythese analyses are detailed in the sections below.

Progressive molecular diversity. We associated the entropyof the areas, that is, their receptor diversity, to the primarynatural axis. This association was performed on a laminar-wise basis. The analysis reveals that the entropy of areas, isaligned with the natural axis. Specifically, for the IG layersthe progression from sensory to association areas along theprimary natural axis marked an increase of the entropy, and

2 Goulas et al.

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

Fig. 2. The natural axis of transmitter receptor density distribution. A. PC1 reveals thedistribution of the areas along an axis explaining most of the receptor density varianceacross cortical areas. The axis stretches from sensory to association areas. We referto this axis (PC1) as the primary natural axis of transmitter receptor density distribution.Note that here, the terms "association" and "sensory" denote the broad character ofareas that span the two extreme ends of the natural axis. In this context, "association"refers to non-sensory areas. Note that different receptor densities across differentlaminar compartments, depicted as the PCA coefficients, have a more prominent rolein the arrangement of different area constellations along the natural axis. For instance,receptor density of the IG layers is more prominent in association areas and NMDA inthe primary areas, while AMPA is prominent in association areas. Lastly, a distinctiveprofile for primary areas is highlighted, that is, prominence of density of the GABAA,a2, M2 and D1 receptors. B. The natural axis rendered in a surface map of the humancortex. Colours correspond to the PC1 values. Note the "association" to "sensory"arrangement of areas along the natural axis.

thus, diversity of receptors (rho=-0.79, p<0.01). This relationwas less pronounced for the G layers (rho=-0.42, p<0.01) andstatistically absent for the SG layers (rho=-0.13, p>0.1) (Fig.3 A). A laminar-wise rank ordering of cortical areas basedon their receptor entropy is provided in SI Appendix Fig.S1. These results indicate that the transition from sensory toassociation areas along the natural axis is accompanied by anincrease of the diversity of the receptor profile that an areaexhibits. This relation was more prominent in IG layers. Wedenote this phenomenon as progressive molecular diversityacross the primary natural axis of the cerebral cortex. Wealso summarized the entropy of the receptor density acrossall areas on a laminar-wise basis. The highest entropy wasobserved for the IG layers, followed by the entropy in the G

and SG layers. Statistically significant differences concernedthe entropy of the IG receptors when compared to the entropyof the G and SG layers (two-sample Kolmogorov-Smirnov test,0.45, 0.50, respectively, p<0.01) (Fig. 3 C).

Progressive molecular excitation/inhibition. We associatedthe excitation/inhibition of cortical areas to the primary nat-ural axis. This association was performed on a laminar-wisebasis. For all layers, the ratio of excitatory to inhibitoryreceptor density increased along the natural axis when transi-tioning from sensory to association areas (rho=-0.49, p<0.05,rho=-0.68, -0.71, p<0.01, for the IG, G and SG layers respec-tively) (Fig. 3 B). A laminar-wise rank ordering of corticalareas based on their excitation/inhibition ratio is providedin SI Appendix Fig. S2. Therefore, the transition from pri-mary to association areas across the natural axis is accom-panied by a progressive increase of the excitability of corti-cal areas. This progressive excitability was more prominentin SG layers. We denote this phenomenon as progressivemolecular excitation/inhibition across the primary naturalaxis of the cerebral cortex. We also summarized the ratio ofexcitation/inhibition across all areas on a laminar-wise basis.The highest excitation/inhibition ratio was observed for the IGlayers, followed by the excitation/inhibition ratio in the G andSG layers. Statistically significant differences concerned theexcitation/inhibition ratio of the IG layers when compared tothe entropy of the G and SG layers (two-sample Kolmogorov-Smirnov test, 0.58, 0.78, respectively, p<0.01), as well as theexcitation/inhibition ratio of the G layers when compared tothe entropy of the SG layers (two-sample Kolmogorov-Smirnovtest, 0.34, p<0.05) (Fig.3 D).

Mirrored density changes of ionotropic and metabotropictransmitter receptors. We next examined the relation of thedensity of ionotropic and metabotropic receptors to the pri-mary natural axis. This analysis revealed mirrored changesof the density of the ionotropic and metabotropic receptorsalong the natural axis. Specifically, ionotropic receptor densityincreased when transitioning from association to sensory areaswith the more prominent, statistically significant increase ob-served for the SG layers (rho=0.67, p<0.001). Contrary to theG and SG layers, the density of metabotropic receptors in IGdecreased along the natural axis (rho=-0.49, p<0.001) (Fig. 4A). The mirrored pattern was observed for the metabotropicreceptors for all layers along the natural axis. Specifically,metabotropic receptor density decreased when transitioningfrom association to sensory areas, with the more prominentdecrease observed for the IG layers (rho=-0.82, rho=-0.65,p<0.001, rho=-0.44, p<0.05, for the IG, G and SG layers re-spectively) (Fig. 4 B). A laminar-wise rank ordering of corticalareas based on the density of ionotropic and metabotropic re-ceptors is provided in SI Appendix Fig. S3. In sum, the densityof ionotropic receptors, on average, increases when transition-ing from association to sensory areas, while the density ofmetabotropic receptors, on average, decreases. We denote thisphenomenon as mirrored density changes of ionotropic andmetabotropic receptors along the primary natural axis of thecerebral cortex.

We also estimated the overall density for ionotropic andmetabotropic receptors across cortical areas on a laminar-wisebasis. Ionotropic receptors form transmembrane ligand-gatedion channels. Metabotropic receptors do not form channels,

Goulas et al. 3

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

DB

IGG

SG

Exc/Inh

ratio o

f

recepto

r density

Natural axis (PC1)

rho=-0.43** rho=-0.68* rho=-0.71*

*p<0.01

**p<0.05

KS=0.58* KS=0.79*

0.35

0.45

0.55

0.65

KS=0.34**

Exc/Inh

ratio o

f

recepto

r density

Fig. 3. The principle of progressive molecular diversity and excitatory/inhibitory receptors ratio along the natural axis. A. Diversity of receptor profiles varies along the naturalaxis for each laminar compartment (IG, G, SG). Progressive molecular diversity refers to the increase of the entropy, thus diversity, of the receptor profile of areas whentransitioning from sensory to association areas, especially prominent in IG layers. Bottom, surface maps depict the entropy values across the cerebral cortex. Note thesensory-to-association increase of entropy. B. Same as in (A), but for the excitatory/inhibitory receptors ratio. the ratio of excitatory/inhibitory receptors increases whentransitioning from sensory to association areas, more prominently in SG layers. Note the sensory-to-association increase of the excitatory/inhibitory receptors ratio. C. Entropyof receptor profiles summarized for each laminar compartment (IG, G, SG) for all cortical areas. D. Same as in (C) but for the excitatory/inhibitory receptors ratio. Note that boththe overall entropy and excitatory/inhibitory receptors ratio, summarized across all areas, is decreasing across IG, G, SG layers (panels C and D).

and their impact on the channels that a cell exhibits relies onsignal transduction, that is, a cascade of intracellular events.Hence, on average, the effect of ionotropic receptors on thechannels of the cell that they inhabit is faster when comparedto the effect of metabotropic receptors. For both metabotropicand ionotropic receptors, an increase in the density was ob-served across IG, G and SG. These laminar-wise differenceswere statistically significant (two-sample Kolmogorov-Smirnovtest Ionotropic: 0.81, 0.95, 0.51, Metabotropic: 0.41, 0.83, 0.76,for IG versus G, IG versus SG and G versus SG, respectively,p<0.001) (Fig. 4 C, D).

Discussion

The natural axis of transmitter receptor distribution. Numer-ous classic (14–18) and more recent studies (19–26) dictatethat the heterogeneity of the cerebral cortex of mammals in

general, and humans in particular, is not spatially random,but instead manifests as spatially ordered changes (gradationprinciple in (15)). These changes have a characteristic spatialtrajectory with sensory areas at one end and association areasat the other end (14, 17, 27). This sensory to associationaxis also entails more to less laminar differentiation, that is,distinguishability and prominence of the layers of the cerebralcortex, for instance, in terms of cell packing density and/orsize of cell bodies (14, 22, 26). Our results highlight that thedistribution of transmitter receptor density also follows thisspatial trajectory, and thus, forms a natural axis of variationat the molecular level. Therefore, this spatial trajectory at themolecular level is tightly linked with the spatial trajectory thatpertains to the myeloarchitectonic (19), cytoarchitectonic (22)and functional (25) dimensions of cortical organization. Theseassociations are yet another manifestation of the principle of

4 Goulas et al.

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

CA

IGG

SG

Density o

f

ionotropic

recep

tors

rho=-0.49* rho=0.22 rho=0.67*

*p<0.001

**p<0.01

KS=0.51*

KS=0.95*

600

800

1000

1200

1600 KS=0.81*

Fig. 4. Mirrored density changes of ionotropic versus metabotropic transmitter receptors along the natural axis. A. Density of ionotropic receptors increases in the SG layerswhen transitioning from sensory to association areas. B. Same for (A) but for the metabotropic receptors. Note that the metabotropic receptor density exhibits a mirrored patternalong the natural axis when compared to the density of the ionotropic receptors (with the exception of IG layers). Note that there is an increase of metabotropic receptor densitywhen transitioning from sensory to association areas, more prominently in IG layers, whereas there is a decrease of ionotropic receptor density when transitioning from sensoryto association areas, more prominently in SG layers. C. Density of ionotropic receptors across all areas summarized for each laminar compartment (IG, G, SG). D. Same as in(C) but for the metabotropic receptors.

concurrent change that pertains to the cerebral cortex, that is,variations of features across the cortical sheet are concurrentand involve multiple dimensions of cortical organization (27).

In particular, our analysis unveils the prominent receptorsthat drive the segregation of cortical areas along the naturalaxis. Specifically, glutamate receptors AMPA and NMDAexhibit opposed preferences: NMDA is prominent in the sen-sory, highly differentiated cortical areas, while AMPA is moreprominent in less differentiated cortical areas. Moreover, theseopposed preferences manifest in a layer-wise fashion. Whilethe more pronounced NMDA preference towards highly dif-ferentiated sensory cortical areas involves the SG layers, themore pronounced AMPA preference towards less differenti-ated association cortical areas involves the IG layers. In otherwords, the laminar-wise relative preferences of AMPA andNMDA receptors reflect the shifts of the laminar-wise rela-tive preference of termination of inter-areal connections, as

empirical observations in the monkey and cross-species wiringprinciples dictate (20, 29–31) (Fig. 5 B). Such organizationalprinciples substantiate prior suggestions in the context of themodeling of the global neuronal workspace hypothesis (32).These suggestions postulate that top-down connections (as-sociation to sensory) are more related to the propensity ofNMDA receptors, whereas bottom-up connections (sensoryto association) are more related to the propensity of AMPAreceptors (32). Moreover, our results highlight the prominenceof the GABAA, a2, M2 and D1 receptors for the highly differ-entiated sensory cortical areas. In sum, we reveal the naturalaxis of transmitter receptor distribution in the human cerebralcortex and the associated contributions of specific receptortypes to the segregation of cortical areas along this axis.

Progressive molecular complexification, excitability and mir-rored ionotropic/metabotropic changes along the natural

Goulas et al. 5

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

Low

differentiation

High

differentiationB

Orig

inTe

rminat

ion

High

differentiation

Low

differentiationOrigin

Termination

High differentiation

(sensory) area

Pronounced ionotropic

receptors and inhibition

Low entropy (high specificity)In

com

ing

conn

ectio

ns

from

low d

iffer

entia

tion

(ass

ocia

tion)

are

as

Low differentiation

(association) area

Pronounced metabotropic

receptors and excitation

High entropy (low specificity)

Inco

min

g co

nnec

tions

from

hig

h di

ffere

ntia

tion

(sen

sory

) are

as

CIonotropic density

Exc/Inh

Entropy

Metabotropic density

Exc/Inh

Entropy

SG G IG

Fig. 5. Organizational principles of receptor distribution and the inter-areal cortical projection system. A. Summary of organizational principles of receptor distribution along theprimary natural axis. Note that this is a schematic representation denoting the overall changes across the sensory to association axis. For detailed results, see (Fig. 2, 3, 4). B.Wiring principles dictating the predominant origin and termination of cortico-cortical connections in the monkey. Less differentiated areas elicit connections predominantly fromdeep laminar compartments (IG layers) and when targeting more differentiated areas they terminate predominantly in upper layers (SG layers). The reverse pattern of originand termination of connections is observed for efferents from more to less differentiated areas. The differentiation of areas is the most consistent explanatory model of the shiftsof the laminar connectional patterns (28–30) and can be used for monkey to human extrapolations (20, 29). C. Receptor principles across layers for more and less differentiatedareas. In more differentiated areas, towards the sensory end of the natural axis, the density of ionotropic receptors increases from deep (IG) to upper (SG) layers. Moreover,entropy and excitatory/inhibitory receptors ratio decreases, thus, a high specificity and an inhibitory nature prevails. These graded changes at the receptor level are alignedwith the predominant terminations of connections from less differentiated areas to upper layers, as predicted by the monkey-based model in panel (B). In less differentiatedareas, towards the association-related end of the natural axis, the density of metabotropic receptors increases from upper (SG) to lower (IG) layers. Moreover, entropy andexcitatory/inhibitory receptors ratio increases, thus, a high molecular diversity and an excitatory nature prevails. These graded changes at the receptor level are aligned with thepredominant terminations of connections from more differentiated areas to deep layers, as predicted by the monkey-based model in panel (B). Thus, the uncovered receptorprinciples distil insights that can be combined with predictions pertaining to the connectional level to unveil a molecular-connectional synergy in the human cerebral cortex.

axis. We have highlighted three key organizational principles ofthe molecular composition of the cerebral cortex that manifestalong the natural axis (Fig. 5 A). The principle of progressivemolecular diversity illustrates that the diversity of receptordensities in each area increases when we transition from moredifferentiated, sensory areas to the less differentiated, associ-ation areas. This increase is more pronounced in IG layers.In other words, the entropy of the receptor profiles of eacharea increases along the natural axis. This principle indicatesthat association areas may exhibit their characteristic diversefunctional profile, that is, their engagement in diverse tasks(33, 34), due to their broad tuning at the molecular level thatallows them to be modulated by multiple neurotransmittersystems. Therefore, this principle offers cognitive neuroscienceinsights at the molecular level and generates a concrete predic-tion, that is, entropy of receptor profiles of cortical areas willbe predictive of their functional diversity, above and beyondfactors such as connectomic properties of areas (34). More-over, combining insights from invasive tract-tracing studiesin the monkey, cross-species wiring principles (20, 29–31) wecan also predict that the predominant laminar termination ofinter-areal structural connections will involve the IG layers ofthe human cerebral cortex and the current principle of molec-ular diversity (Fig. 5 C). This termination preference mirrorsthe increased entropy of the molecular profile of IG layers inassociation areas (Fig. 5 C). Therefore, we have a synergy

between the connectional and receptor levels of organizationthat bestow the IG layers of association areas with a prominentrole in accommodating incoming signals from areas that lietowards the other end of the natural axis. On the contrary, thepreferential termination in more differentiated, sensory areasinvolves the SG layers (Fig. 5 B). SG layers of these areasexhibit low entropy, thus, their molecular profile is specializedand not broad (Fig. 5 C). In sum, the principle of progressivemolecular diversity unifies receptor and connectional featuresand provides insights into the functional profile of corticalareas at the molecular level.

The principle of progressive excitation/inhibition ratio de-notes that the excitation/inhibition ratio of receptor densitiesincreases when we transition from more differentiated, sensoryareas to the less differentiated, association areas. Observa-tions in human and non-human primates indicate that thespine density of pyramidal cells increases in the transitionfrom sensory to association areas (35). This feature bestowsassociation areas with higher degrees of excitability that maycontribute to their integrative functional capacity, as empiricaland computational studies indicate (36–38). The principleof progressive increase in the excitatory/inhibitory receptorsratio extends these observations by offering a receptor-basedexplanation for the pronounced excitability of the neuronalpopulations inhabiting association areas. Such a principle canbe instantiated in computational models embodying regional

6 Goulas et al.

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

heterogeneity (36, 39, 40), thus offering enhanced neurobiologi-cal interpretability. Notably, the highest excitatory/inhibitoryreceptors ratio is observed in IG layers (Fig. 5 C). In mon-keys, the predominant termination of inter-areal connectionsin association areas involves the IG layers (30) (Fig. 5 B).Inter-areal connections, especially connections spanning longdistances are very weak in terms of the number of axons thatthey involve (31). Therefore, the highest excitability of IG mayconstitute a molecular signature that facilitates these weak,long-range connections to excite their downstream targets inthe human cerebral cortex. Advancements in the in vivo map-ping of long-range connections in humans may confirm suchconnectional-molecular synergy in the human cerebral cor-tex. Further predictions based on the principle of progressivemolecular excitation/inhibition pertain to the functional con-nectivity properties of cortical areas. In monkeys and humans,prior studies involving a small set of cortical areas highlighta relation between the excitation/inhibition ratio and thefunctional connectivity strength of areas (41, 42). Thus, theprinciple of progressive excitation/inhibition ratio constitutesa template for predicting such functional connectivity prop-erties of areas at a global whole-cortex level. From a clinicalstandpoint, the principle of progressive excitation/inhibitionratio across the cortical sheet may offer explanations and pre-dictions with respect to pathology. For instance, areas withhigh excitation/inhibition ratio, such as areas 6 and 38, may besituated close to an excitability threshold above which patho-logical neuronal activity may arise, as is the case in epilepsy.In sum, the principle of progressive excitatory/inhibitory ratiocan be instantiated in computational models to offer enhancedneurobiological interpretability and may predict and explaindeviant neurophysiological profiles in a clinical context.

Lastly, the mirrored ionotropic/metabotropic changes alongthe natural axis dictate that the density of ionotropic recep-tors increases when we transition from association-to-sensoryareas, while density of metabotropic receptors exhibits themirrored pattern, that is, increases when we transition fromsensory-to-association areas. Primary areas operate on fasttemporal scales and the predominant density of ionotropictransmitter receptors may bestow them with this functionalproperty, since the very nature of ionotropic receptors is thepresence of ion channels with fast, immediate effects on thecell that they inhabit. On the contrary, association areasare characterized by high density of metabotropic transmitterreceptors that have a slower, indirect impact on the cells thatthey inhabit. This property may bestow these areas with afunctional repertoire that operates at slow temporal scales(such as learning processes) possibly accounting for their in-tegrative and coordinating role. Such suggestion is furthersupported by empirical studies reporting higher concentrationsof the enzyme calcium calmodulin-dependent protein kinase IIin association areas of the monkey cortex (43). Notably, theincrease of metabotropic receptor density towards the end ofthe natural axis occupied by association areas is more promi-nent in the IG layers, while the increase of ionotropic receptordensity towards the other end of the natural axis occupied bysensory areas is more prominent in the SG layers (Fig. 5 A,C).Based on observations in the monkey and cross- species wiringprinciples (20, 29), for primary and association areas, thesechanges at the molecular level are centered around the mostprominent laminar terminations, and thus, incoming signals,

of inter-areal cortical connections (Fig. 5).

Conclusions

We uncovered organizational principles that pertain to the dis-tribution of the density of transmitter receptors in the humancerebral cortex. We demonstrate that receptor densities areorganized along a natural axis in the cerebral cortex, rangingfrom sensory to association areas. The constellation of areasalong this axis is characterized by organizational changes thatare regulated by the principles of progressive molecular diver-sity, excitation/inhibition and mirrored changes of the densityof ionotropic and metabotropic receptors. Our results show-case the importance and feasibility of taming the complexity ofthe cerebral cortex by distilling key organizational principlesthat bring order to the heterogeneity of cortical organization.

Materials and Methods

Receptor autoradiography data that were used for this study werecollected as described in (7). For analyses and metrics used, see SIAppendix SI Text. Python code used for the analysis and figures isavailable at: https://github.com/AlGoulas/receptor_principles

ACKNOWLEDGMENTS. Funding from the European Union’sHorizon 2020 Research and Innovation Programme, grant agreementno. 604102 (HBP, SGA1) (KA), No. 785907 (HBP SGA2) (KA,CCH, JPC) and No. 945539 (HBP SGA3) (KA), as well as fundingfrom the Deutsche Forschungsgemeinschaft (SFB 936/A1; TRR169/A2; SPP 2041/HI 1286/7-1, HI 1286/6-1) (CCH) is gratefullyacknowledged.

1. MR Bennett, The concept of transmitter receptors: 100 years on. Neuropharmacology 39,523 – 546 (2000).

2. FK Bedford, et al., Gabaa receptor cell surface number and subunit stability are regulated bythe ubiquitin-like protein plic-1. Nat. Neurosci. 4, 908–916 (2001).

3. A Nieoullon, Dopamine and the regulation of cognition and attention. Prog. Neurobiol. 67, 53– 83 (2002).

4. JP Changeux, Allosteric receptors: From electric organ to cognition. Annu. Rev. Pharmacol.Toxicol. 50, 1–38 (2010) PMID: 20055696.

5. I Shimada, T Ueda, Y Kofuku, MT Eddy, K Wüthrich, Gpcr drug discovery: integrating solutionnmr data with crystal and cryo-em structures. Nat. Rev. Drug Discov. 18, 59–82 (2019).

6. K Zilles, K Amunts, Receptor mapping: architecture of the human cerebral cortex. CurrentOpinion in Neurology 22, 331–339 (2009).

7. K Zilles, N Palomero-Gallagher, Multiple transmitter receptors in regions and layers of thehuman cerebral cortex. Front. Neuroanat. 11, 78 (2017).

8. ML Kringelbach, et al., Dynamic coupling of whole-brain neuronal and neurotransmitter sys-tems. Proc. Natl. Acad. Sci. 117, 9566–9576 (2020).

9. J Ceccarini, H Liu, K Van Laere, ED Morris, CY Sander, Methods for quantifying neurotrans-mitter dynamics in the living brain with pet imaging. Front. Physiol. 11, 792 (2020).

10. V Beliveau, et al., A high-resolution in vivo atlas of the human brain’s serotonin system. J.Neurosci. 37, 120–128 (2017).

11. R Corte´s, A Probst, HJ Tobler, J Palacios, Muscarinic cholinergic receptor subtypes in thehuman brain. ii. quantitative autoradiographic studies. Brain Res. 362, 239 – 253 (1986).

12. K Amunts, et al., Broca’s region: Novel organizational principles and multiple receptor map-ping. PLOS Biol. 8, 1–16 (2010).

13. N Palomero-Gallagher, K Zilles, Cortical layers: Cyto-, myelo-, receptor- and synaptic archi-tecture in human cortical areas. NeuroImage 197, 716 – 741 (2019).

14. CF von Economo, GN Koskinas, Die Cytoarchitektonik der Hirnrinde des erwachsenen Men-schen. (Julius Springer Verlag, Vienna, Berlin), (1925).

15. F Sanides, Die Architectonik des menschlichen Stirnhirns. (Berlin-Heidelberg: Springer-Verlag), (1962).

16. AA Abbie, Cortical lamination in the monotremata. J. Comp. Neurol. 72, 429–467 (1940).17. DN Pandya, EH Yeterian, Association and Auditory Cortices, eds. A Peters, EG Jones.

(Springer US, Boston, MA), pp. 3–61 (1985).18. R Nieuwenhuys, The myeloarchitectonic studies on the human cerebral cortex of the vogt-

vogt school, and their significance for the interpretation of functional neuroimaging data. BrainStruct. Funct. 218, 303–352 (2013).

19. JB Burt, et al., Hierarchy of transcriptomic specialization across human cortex captured bystructural neuroimaging topography. Nat. Neurosci. 21, 1251–1259 (2018).

20. A Goulas, K Zilles, CC Hilgetag, Cortical gradients and laminar projections in mammals.Trends Neurosci. 41, 775 – 788 (2018).

21. BD Fulcher, JD Murray, V Zerbi, XJ Wang, Multimodal gradients across mouse cortex. Proc.Natl. Acad. Sci. 116, 4689–4695 (2019).

22. C Paquola, et al., Microstructural and functional gradients are increasingly dissociated intransmodal cortices. PLOS Biol. 17, 1–28 (2019).

Goulas et al. 7

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint

23. B Zikopoulos, MA Garcia-Cabezas, H Barbas, Parallel trends in cortical gray and white matterarchitecture and connections in primates allow fine study of pathways in humans and revealnetwork disruptions in autism. PLOS Biol. 16, 1–43 (2018).

24. JM Huntenburg, PL Bazin, DS Margulies, Large-scale gradients in human cortical organiza-tion. Trends Cogn. Sci. 22, 21–31 (2018).

25. DS Margulies, et al., Situating the default-mode network along a principal gradient ofmacroscale cortical organization. Proc. Natl. Acad. Sci. 113, 12574–12579 (2016).

26. K Wagstyl, et al., Bigbrain 3d atlas of cortical layers: Cortical and laminar thickness gradientsdiverge in sensory and motor cortices. PLOS Biol. 18, 1–21 (2020).

27. CC Hilgetag, SF Beul, SJ van Albada, A Goulas, An architectonic type principle integratesmacroscopic cortico-cortical connections with intrinsic cortical circuits of the primate brain.Netw. Neurosci. 3, 905–923 (2019).

28. SF Beul, CC Hilgetag, Neuron density fundamentally relates to architecture and connectivityof the primate cerebral cortex. NeuroImage 189, 777 – 792 (2019).

29. A Goulas, P Majka, MGP Rosa, CC Hilgetag, A blueprint of mammalian cortical connectomes.PLOS Biol. 17, 1–30 (2019).

30. H Barbas, N Rempel-Clower, Cortical structure predicts the pattern of corticocortical connec-tions. Cereb. Cortex 7, 635–646 (1997).

31. NT Markov, et al., Anatomy of hierarchy: Feedforward and feedback pathways in macaquevisual cortex. J. Comp. Neurol. 522, 225–259 (2014).

32. S Dehaene, JP Changeux, Experimental and theoretical approaches to conscious processing.Neuron 70, 200 – 227 (2011).

33. BTT Yeo, et al., Functional Specialization and Flexibility in Human Association Cortex. Cereb.Cortex 25, 3654–3672 (2014).

34. M Najafi, BW McMenamin, JZ Simon, L Pessoa, Overlapping communities reveal rich struc-ture in large-scale brain networks during rest and task conditions. NeuroImage 135, 92 – 106(2016).

35. GN Elston, I Fujita, Pyramidal cell development: postnatal spinogenesis, dendritic growth,axon growth, and electrophysiology. Front. Neuroanat. 8, 78 (2014).

36. R Chaudhuri, K Knoblauch, MA Gariel, H Kennedy, XJ Wang, A large-scale circuit mechanismfor hierarchical dynamical processing in the primate cortex. Neuron 88, 419 – 431 (2015).

37. C Honey, et al., Slow cortical dynamics and the accumulation of information over longtimescales. Neuron 76, 423 – 434 (2012).

38. U Hasson, E Yang, I Vallines, DJ Heeger, N Rubin, A hierarchy of temporal receptive windowsin human cortex. J. Neurosci. 28, 2539–2550 (2008).

39. M Demirtas, et al., Hierarchical heterogeneity across human cortex shapes large-scale neuraldynamics. Neuron 101, 1181–1194.e13 (2019).

40. G Deco, et al., Whole-brain multimodal neuroimaging model using serotonin receptor mapsexplains non-linear functional effects of lsd. Curr. Biol. 28, 3065 – 3074.e6 (2018).

41. E Turk, LH Scholtens, MP van den Heuvel, Cortical chemoarchitecture shapes macroscaleeffective functional connectivity patterns in macaque cerebral cortex. Hum. Brain Mapp. 37,1856–1865 (2016).

42. MP van den Heuvel, et al., Multimodal analysis of cortical chemoarchitecture and macroscalefmri resting-state functional connectivity. Hum. brain mapping 37, 3103–3113 (2016)27207489[pmid].

43. Marcía-Cabezas, MKP Joyce, YJ John, B Zikopoulos, H Barbas, Mirror trends of plasticityand stability indicators in primate prefrontal cortex. Eur. J. Neurosci. 46, 2392–2405 (2017).

8 Goulas et al.

(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted September 29, 2020. ; https://doi.org/10.1101/2020.09.28.316646doi: bioRxiv preprint