Transcriptional Cartography Integrates Multiscale Biology of the Human Cortex

Reviewer #1 (Public Review):

The manuscript by Wagstyl et al. describes an extensive analysis of gene expression in the human cerebral cortex and the association with a large variety of maps capturing many of its microscopic and macroscopic properties. The core methodological contribution is the computation of continuous maps of gene expression for >20k genes, which are being shared with the community. The manuscript is a demonstration of several ways in which these maps can be used to relate gene expression with histological features of the human cortex, cytoarchitecture, folding, function, development and disease risk. The main scientific contribution is to provide data and tools to help substantiate the idea of the genetic regulation of multi-scale aspects of the organisation of the human brain. The manuscript is dense, but clearly written and beautifully illustrated.

# Main comments

The starting point for the manuscript is the construction of continuous maps of gene expression for most human genes. These maps are based on the microarray data from 6 left human brain hemispheres made available by the Allen Brain Institute. By technological necessity, the microarray data is very sparse: only 1304 samples to map all the cortex after all subjects were combined (a single individual's hemisphere has ~400 samples). Sampling is also inhomogeneous due to the coronal slicing of the tissue. To obtain continuous maps on a mesh, the authors filled the gaps using nearest-neighbour interpolation followed by strong smoothing. This may have two potentially important consequences that the authors may want to discuss further: (a) the intrinsic geometry of the mesh used for smoothing will introduce structure in the expression map, and (b) strong smoothing will produce substantial, spatially heterogeneous, autocorrelations in the signal, which are known to lead to a significant increase in the false positive rate (FPR) in the spin tests they used.

## a. Structured smoothing

A brain surface has intrinsic curvature (Gaussian curvature, which cannot be flattened away without tearing). The size of the neighbourhood around each surface vertex will be determined by this curvature. During surface smoothing, this will make that the weight of each vertex will be also modulated by the local curvature, i.e., by large geometric structures such as poles, fissures and folds. The article by Ciantar et al (2022, https://doi.org/10.1007/s00429-022-02536-4) provides a clear illustration of this effect: even the mapping of a volume of *pure noise* into a brain mesh will produce a pattern over the surface strikingly similar to that obtained by mapping resting state functional data or functional data related to a motor task.

1. It may be important to make the readers aware of this possible limitation, which is in large part a consequence of the sparsity of the microarray sampling and the necessity to map that to a mesh. This may confound the assessments of reproducibility (results, p4). Reproducibility was assessed by comparing pairs of subgroups split from the total 6. But if the mesh is introducing structure into the data, and if the same mesh was used for both groups, then what's being reproduced could be a combination of signal from the expression data and signal induced by the mesh structure.
2. It's also possible that mesh-induced structure is responsible in part for the "signal boost" observed when comparing raw expression data and interpolated data (fig S1a). How do you explain the signal boost of the smooth data compared with the raw data otherwise?
3. How do you explain that despite the difference in absolute value the combined expression maps of genes with and without cortical expression look similar? (fig S1e: in both cases there's high values in the dorsal part of the central sulcus, in the occipital pole, in the temporal pole, and low values in the precuneus and close to the angular gyrus). Could this also reflect mesh-smoothing-induced structure?
4. Could you provide more information about the way in which the nearest-neighbours were identified (results p4). Were they nearest in Euclidean space? Geodesic? If geodesic, geodesic over the native brain surface? over the spherically deformed brain? (Methods cite Moresi & Mather's Stripy toolbox, which seems to be meant to be used on spheres). If the distance was geodesic over the sphere, could the distortions introduced by mapping (due to brain anatomy) influence the geometry of the expression maps?
5. Could you provide more information about the smoothing algorithm? Volumetric, geodesic over the native mesh, geodesic over the sphere, averaging of values in neighbouring vertices, cotangent-weighted laplacian smoothing, something else?
6. Could you provide more information about the method used for computing the gradient of the expression maps (p6)? The gradient and the laplacian operator are related (the laplacian is the divergence of the gradient), which could also be responsible in part for the relationships observed between expression transitions and brain geometry.

## b. Potentially inflated FPR for spin tests on autocorrelated data

Spin tests are extensively used in this work and it would be useful to make the readers aware of their limitations, which may confound some of the results presented. Spin tests aim at establishing if two brain maps are similar by comparing a measure of their similarity over a spherical deformation of the brains against a distribution of similarities obtained by randomly spinning one of the spheres. It is not clear which specific variety of spin test was used, but the original spin test has well known limitations, such as the violation of the assumption of spatial stationarity of the covariance structure (not all positions of the spinning sphere are equivalent, some are contracted, some are expanded), or the treatment of the medial wall (a big hole with no data is introduced when hemispheres are isolated).

Another important limitation results from the comparison of maps showing autocorrelation. This problem has been extensively described by Markello & Misic (2021). The strong smoothing used to make a continuous map out of just ~1300 samples introduces large, geometry dependent autocorrelations. Indeed, the expression maps presented in the manuscript look similar to those with the highest degree of autocorrelation studied by Markello & Misic (alpha=3). In this case, naive permutations should lead to a false positive rate ~46% when comparing pairs of random maps, and even most sophisticated methods have FPR>10%.

7. There's currently several researchers working on testing spatial similarity, and the readers would benefit from being made aware of the problem of the spin test and potential solutions. There's also packages providing alternative implementations of spin tests, such as BrainSMASH and BrainSpace (Weinstein et al 2020, https://doi.org/10.1101/2020.09.10.285049), which could be mentioned.
8. Could it be possible to measure the degree of spatial autocorrelation?
9. Could you clarify which version of the spin test was used? Does the implementation come from a package or was it coded from scratch?
10. Cortex and non-cortex vertex-level gene rank predictability maps (fig S1e) are strikingly similar. Would the spin test come up statistically significant? What would be the meaning of that, if the cortical map of genes not expressed in the cortex appeared to be statistically significantly similar to that of genes expressed in the cortex?

Reviewer #2 (Public Review):

The authors convert the AHBA dataset into a dense cortical map and conduct an impressively large number of analyses demonstrating the value of having such data.

I only have comments on the methodology. First, the authors create dense maps by simply using nearest neighbour interpolation followed by smoothing. Since one of the main points of the paper is the use of a dense map, I find it quite light in assessing the validity of this dense map. The reproducibility values they calculate by taking subsets of subjects are hugely under-powered, given that there are only 6 brains, and they don't inform on local, vertex-wise uncertainties). I wonder if the authors would consider using Gaussian process interpolation. It is really tailored to this kind of problem and can give local estimates of uncertainty in the interpolated values. For hyperparameter tuning, they could use leave-one-brain-out for that.

I know it is a lot to ask to change the base method, as that means re-doing all the analyses. But I think it would strengthen the paper if the authors put as much effort in the dense mapping as they did in their downstream analyses of the data.

It is nice that the authors share some code and a notebook, but I think it is rather light. It would be good if the code was better documented, and if the user could have access to the non-smoothed data, in case they was to produce their own dense maps. I was only wondering why the authors didn't share the code that reproduces the many analyses/results in the paper.

Author Response

The authors would like to thank the reviewers and editors for this thorough and constructive assessment of our paper. We look forward to addressing their suggestions for improvement of our work in a revised manuscript. In particular: (i) Reviewer 1 raises interesting questions regarding the potential impact of intrinsic cortical and mesh morphology on interpolation, smoothing and the resultant patterns of gene expression. We will test these ideas by developing a null model framework. (ii) Reviewer 2 suggests re-creating dense expression maps using an alternative Gaussian Processes for interpolation. We will implement this suggestion and compare the resulting maps with those generated by the current interpolation method. Notwithstanding these helpful lines of further enquiry, we believe our study provides a meaningful step forwards in multiscale analysis of the human brain by generating. validating, describing and annotating dense gene expression maps which can accelerate translation between neuroimaging and genomic analysis of the human cortical sheet.