Hierarchy provides a unifying principle for the macroscale organization of anatomical and functional properties across primate cortex, yet microscale bases of specialization across human cortex are poorly understood. Anatomical hierarchy is conventionally informed by invasive tract-tracing measurements, creating a need for a principled proxy measure in humans. Moreover, cortex exhibits marked interareal variation in gene expression, yet organizing principles of cortical transcription remain unclear. We hypothesized that specialization of cortical microcircuitry involves hierarchical gradients of gene expression. We found that a noninvasive neuroimaging measure—MRI-derived T1-weighted/T2-weighted (T1w/T2w) mapping—reliably indexes anatomical hierarchy, and it captures the dominant pattern of transcriptional variation across human cortex. We found hierarchical gradients in expression profiles of genes related to microcircuit function, consistent with monkey microanatomy, and implicated in neuropsychiatric disorders. Our findings identify a hierarchical axis linking cortical transcription and anatomy, along which gradients of microscale properties may contribute to the macroscale specialization of cortical function.

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We thank B.D. Fulcher, X.-J. Wang, R. Chaudhuri, and D.C. Glahn for useful discussions. This research was supported by NIH grants R01MH112746 (J.D.M.), R01MH108590 (A.A.), and TL1TR000141 (J.D.M.), and by BlackThorn Therapeutics (J.D.M., A.A.).

Author information


  1. Department of Physics, Yale University, New Haven, CT, USA

    • Joshua B. Burt
    • , William J. Eckner
    •  & John D. Murray
  2. Department of Psychiatry, Yale University School of Medicine, New Haven, CT, USA

    • Murat Demirtaş
    • , Alan Anticevic
    •  & John D. Murray
  3. Neuroscience Program, Tulane University, New Orleans, LA, USA

    • Natasha M. Navejar
  4. Interdepartmental Neuroscience Program, Yale University, New Haven, CT, USA

    • Jie Lisa Ji
  5. BlackThorn Therapeutics, San Francisco, CA, USA

    • William J. Martin
  6. Department of Engineering, University of Cambridge, Cambridge, UK

    • Alberto Bernacchia


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J.B.B., W.J.M., A.B., A.A., and J.D.M. designed the research. J.B.B., M.D., W.J.E., N.M.N., and J.L.J. analyzed the data. J.D.M. supervised the project. J.B.B. and J.D.M. wrote the manuscript and prepared the figures. All authors contributed to editing the manuscript.

Competing interests

W.J.M. is an employee for BlackThorn Therapeutics. A.A. and J.D.M. are consultants for BlackThorn Therapeutics. W.J.M., A.A., and J.D.M. are co-inventors on a provisional patent application #62567087 related to using gene expression topography for predictive therapeutic applications.

Corresponding author

Correspondence to John D. Murray.

Integrated supplementary information

  1. Supplementary Figure 1 Group-averaged cortical T1w/T2w maps exhibit interspecies homology and interhemispheric symmetry.

    (a) Unparcellated group-averaged (N=339) T1w/T2w map in human cortex visualized bilaterally on an inflated cortical surface. (b) Unparcellated group-averaged (N=19) T1w/T2w map in monkey cortex visualized bilaterally on an inflated cortical surface. (c) Primary sensory (visual, V1; auditory, A1; somatosensory, S1) and primary motor (M1) homologues in human and monkey cortex, corresponding to the four bordered areas in panels a and b, exhibit high T1w/T2w map values relative to the average value computed across all higher-order sensory and association (Non-Primary) areas. Grey bars mark the standard error on the mean. The low T1w/T2w map value found in monkey area A1 (relative to human area A1) is likely driven by the size and lack of spatial specificity of the corresponding M132 parcel which extends deep down into temporal cortex. Note that human Brodmann area 3 is further subdivided into areas 3a and 3b in the HCP parcellation, the latter which was used for this analysis. (d) Functional networks derived from resting-state functional connectivity from the Human Connectome Project (HCP). Cortical areas are parcellated using the HCP multi-modal parcellation (MMP1.0). We assigned each region to a functional network using a community detection method applied to resting-state fMRI data from the HCP, and designated functional labels to networks, including three sensory and five association, that align with previously reported functional networks (with abbreviations labeled in Fig. 1b): Auditory (AUD), Visual (VIS), Somatomotor (SOM), Dorsal Attention (DAN), Frontoparietal (FPN), Ventral Attention (VAN), Default (DMN), and Cingulo-Opercular (CON).

  2. Supplementary Figure 2 Anatomical cortical hierarchy derived from N = 1,243 laminar-specific interareal projections in monkey cortex.

    (a) Fraction of external labeled neurons (FLNe). Target area i is injected with a retrograde tracer that labels neurons in many source areas; the FLNe in source area j is then defined as the fraction of all external labeled neurons terminating in area i that originated in source area j. Each row of the FLN matrix is therefore normalized to 1. Measurements which yielded no labeled neurons are marked in grey. (b) Fraction of supragranular layer neurons (SLN), defined as the fraction of neurons in an interareal projection (to target area i from source area j) originating in supragranular layers. An SLN of 1 indicates that all labeled projection neurons were of supragranular origin, reflecting a pure feedforward connection; an SLN of 0 indicates that all projection neurons originated in deep infragranular layers, reflecting a pure feedback connection. Measurements which yielded no labeled neurons are marked in grey. (c) Model-estimated hierarchy levels for 89 cortical regions. The blue line indicates hierarchy levels estimated by the model after shifting and re-scaling them to lie on the unit interval. The red indicates hierarchy values passed through a logistic function to remove the nonlinearity introduced by the logit link function in the GLM fitting procedure. The monotonicity of this transformation preserves the order of the cortical regions and therefore does not affect the Spearman rank correlations reported in the main text. (d) Group-averaged T1w/T2w map values for 89 cortical areas in the monkey.

  3. Supplementary Figure 3 The strength of the correspondence between laminar projection profiles and T1w/T2w value is strongest in high-T1w/T2w areas.

    (a) 1243 retrograde tracer-labeled projections are separated by target area (i.e., by N=29 unique injection sites; see Supplementary Table 1). The laminar profile of a projection is quantified by the fraction of labeled supragranular layer neurons (SLN) in the source area. We found the Spearman rank correlation between SLN and the areal difference in T1w/T2w map values (ΔT1w/T2w; target minus source) is stronger for areas with higher T1w/T2w values (rs = −0.63; P = 2.9*10−4; Spearman rank correlation). This indicates that the relationship between laminar specificity and structural dissimilarity holds more strongly in sensory areas at lower levels of the anatomical hierarchy, which have high T1w/T2w values. (b) Hierarchically organized structure in the strength of the relationship between laminar specificity (SLN) and structural dissimilarity (ΔT1w/T2w) for the 29 unique target areas, visualized on the inflated monkey cortical surface.

  4. Supplementary Figure 4 Expression maps and TMCs for genes that encode markers of distinct inhibitory interneuron cell types, and for weighted profiles characteristic of distinct neuronal cell types derived from single-cell RNA-seq of human cortical neurons.

    (a) Markers for inhibitory interneuron cell types. (b) Weighted gene sets for excitatory neuronal cell types, derived from single-cell RNA sequencing. (c) Weighted gene sets for inhibitory neuronal cell types, derived from single-cell RNA sequencing. Expression map values are standardized (i.e., z-scored) and shown in units of standard deviations from the mean. Expression maps use the same colormap and scale as Fig. 1a. Statistical significance is calculated using a spatial autoregressive model to account for spatial autocorrelation, Bonferroni-corrected by the number of genes in each set (*, P < 0.05; **, P < 10−2; ***, P < 10−3). Grey lines mark the jackknife estimate of standard error.

  5. Supplementary Figure 5 Expression maps and TMCs for genes encoding synaptic receptor subunits and neuromodulator receptor subunits.

    (a) NMDA receptor subunits. (b) GABAA receptor subunits. (c) Muscarinic acetylcholine receptors (CHRM). (d) Nicotinic acetylcholine receptors (CHRN). (e) Norepinephrine receptors (ADR). (f) Dopamine receptors (DRD). (g) Serotonin receptors (HTR). Expression map values are standardized (i.e., z-scored) and shown in units of standard deviations from the mean. All maps use the same colormap and scale as Fig. 1a. Statistical significance is calculated using a spatial autoregressive model to account for spatial autocorrelation, Bonferroni-corrected by the number of genes in each set (*, P < 0.05; **, P < 10−2; ***, P < 10−3). Grey lines mark the jackknife estimate of standard error.

  6. Supplementary Figure 6 The dominant axis of gene expression variation is better captured by the group-averaged T1w/T2w map than by two alternative candidate proxies: cortical thickness and distance from primary visual cortex (V1).

    (a–e) For five categorical gene sets, the Spearman rank correlation between the first principal component (PC1) and the T1w/T2w map, the map of cortical thickness, and the map of geodesic distance from primary visual cortex. For each gene set, PC1 is more strongly correlated with the T1w/T2w map than with the two other candidate maps. (f–j) For five gene sets, the amount of gene expression variance captured, relative to PC1, for the three candidate maps. For each gene set, the T1w/T2w map captures more gene expression variance than do the other two maps. (k–o) Percentage of gene expression variance captured by the top 10 of 179 total PCs. For all five gene sets, PC1 captures between 21% and 27% of the variance, roughly two to three times the amount captured by PC2. (p–t) Distribution of T1w/T2w map correlations (TMCs) across genes in each gene set. Dashed lines mark the mean of the distribution. For all five gene sets, the distributions are broad, containing large fractions of strong positive and negative TMCs, and centered near zero, with a range of means (-0.05, +0.05). Statistical significance is calculated through permutation testing with surrogate maps that preserve the spatial autocorrelation structure of each map (*, P < 0.05; **, P < 10−2; ***, P < 10−3). Grey lines mark the bootstrap estimated 95% confidence interval.

  7. Supplementary Figure 7 Spatial autocorrelation structure in gene expression and group-averaged T1w/T2w maps.

    (a) Spatial autocorrelation in the parcellated cortical gene expression data is well-approximated by a decaying exponential function of distance. Gene co-expression is defined as the pairwise Spearman rank correlation between cortical parcels’ gene expression values, here for the 2413 brain-specific genes. Proximal cortical parcels exhibit more similar gene expression values compared to distal parcels. Pairs of parcel with geodesic separation distance less than 100 mm (8247 of 16,110 total pairs) were used to fit the characteristic scale of spatial autocorrelation, illustrated in red (i.e., exp(−d/d0)), where d is geodesic distance and d0 = 25 mm. Each data point corresponds to the co-expression of a pair of cortical parcels. Top: Mean co-expression value as a function of geodesic distance bin. (b) Gene co-expression values after correcting for spatial autocorrelation structure by subtraction of the fitted exponential in a. After correction, the mean co-expression value is near zero across all geodesic distance bins. (c) Example randomized surrogate maps with spatial autocorrelation structure matched to the empirical T1w/T2w map (see Methods). Autocorrelation structure-preserving surrogate maps are used for nonparametric calculation of statistical significance values for PCA results in Figs. 5 and 6, and Supplementary Figs. 6 and 10. (d) Distribution of pairwise Spearman rank correlations between 39,800 pairs of surrogate T1w/T2w maps.

  8. Supplementary Figure 8 PCA reveals that the dominant axis of gene expression variation (i.e., the first principal component, PC1) is conserved across five categorical gene sets.

    PC1, which aligns with the T1w/T2w map, combines sensory areas (e.g., primary visual, somatosensory, and auditory cortical areas), and separates sensory areas from association areas. In contrast, the secondary mode of gene expression tends to fractionate sensorimotor cortical areas by modality, separating early visual cortex from somatomotor cortex. Rows correspond to the first three PCs, respectively, across gene sets.

  9. Supplementary Figure 9 Evidence for spatial structure in residual gene expression variance not captured by the group-averaged T1w/T2w map.

    (a) Map of the brain-specific PC1 residual, defined as the magnitude of the vertical distance between an area’s brain-specific PC1 weight and the best-fit Theil-Sen estimator of linear slope for the PC1 vs. T1w/T2w relationship (i.e., absolute vertical distance between scatter points and best-fit line in Fig. 5c). (b) Map of the local T1w/T2w gradient, defined as the mean absolute difference between an area’s T1w/T2w map value and the values of all neighboring areas, i.e. \(x_i = \frac{1}{N}\mathop {\sum }\limits_{n \in \{ N_i\} } \left| {T_i - T_n} \right|\), where Ti is the T1w/T2w value for area i, and {Ni} is the set of all areas bordering area i. (c) The brain-specific PC1 residual is highly correlated with the magnitude of the local T1w/T2w gradient (rp = 0.70; P < 10−5; Pearson correlation). This relationship shows that areas with the strongest T1w/T2w gradient tend to be those that drive the discrepancy between the brain-specific gene PC1 and T1w/T2w map topographies. This is consistent with the reported correspondence shown in Fig. 5c being limited by the relatively poor spatial resolution of gene expression sampling in the AHBA.

  10. Supplementary Figure 10 Validation of key results in human cortex using the group-averaged (N = 69) Conte69 T1w/T2w map.

    (a) The parcellated T1w/T2w map. (b) Human T1w/T2w map values are significantly lower in functionally defined association networks than in sensory networks (P < 10−5; two-sided Wilcoxon signed-rank test on N=6608 paired differences). Box plots mark the median and inner quartile ranges for areas in each network, and whiskers indicate the 95% confidence interval. (c) The average expression map of 5 genes preferentially expressed in human granular layer 4 (L4) is positively correlated with the T1w/T2w map (rs = 0.73; P < 10−5; Spearman rank correlation). (d) Average expression maps of laminar-specific genes show significant T1w/T2w map correlations (TMCs). L1-3: supragranular layers 1-3 (rs = −0.49; P < 10−5); L5/6: infragranular layers 5 and 6 (rs = −0.44; P < 10−5) (e) Genes coding for calretinin (CALB2; rs = −0.55; P < 10−5) and parvalbumin (PVALB; rs = 0.78; P < 10−5) exhibit homologous hierarchical gradients in human cortex. (f) TMCs of genes coding for markers of specific inhibitory interneuron cell types. (g) The gene coding for the NMDA receptor subunit NR2B (GRIN2B) exhibits a negative TMC (rs = −0.69; P < 10−5). (h, i) TMCs of genes coding for distinct subunits of NMDA & GABAA receptors. (j) PC1 for the brain-specific gene set is highly correlated with the T1w/T2w map (rs = 0.88; P < 10−5). (k) Across all five gene sets, PC1 exhibits a highly similar areal topography to the T1w/T2w map (TMC range: 0.86–0.88; P < 10−5 for each). (l) Gene expression variance captured by the T1w/T2w map (\(_{{\mathrm{T}}1{\mathrm{w}}/{\mathrm{T}}2{\mathrm{w}}}^2\)) relative to PC1 (\(_{{\mathrm{PC}}1}^2\)). Statistical significance in panels d, f, h, and i is calculated with a spatial autoregressive model to account for spatial autocorrelation, and in panels k and l, through permutation testing with surrogate maps that preserve spatial autocorrelation structure, Bonferroni-corrected by the number of genes in each set (*, P < 0.05; **, P < 10−2; ***, P < 10−3). Grey lines in panels d, f, h, and i mark the jackknife estimate of standard error, and in panels k and l, the bootstrap estimated 95% confidence interval. Expression in panels c, e, and g is plotted in units of standard deviations (s.d.; σ) from the mean.

Supplementary information

  1. Supplementary Text and Figures

    Supplementary Figures 1–10

  2. Reporting Summary

  3. Supplementary Table 1

    Compiled monkey microanatomical data for cytoarchitectural type, Spearman rank correlations for projections terminating in each target area, inhibitory interneuron proportions, and pyramidal neuron dendritic spine counts (Figs. 4a,d,g; Supplementary Fig. 3).

  4. Supplementary Table 2

    T1w/T2w map correlation (TMC) values and cortical differential stability (DSc) for all genes we analyzed, and sets of brain-, neuron-, oligodendrocyte-, synaptome-, and layer-specific genes.

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