The genetic architecture of structural left–right asymmetry of the human brain

Left–right hemispheric asymmetry is an important aspect of healthy brain organization for many functions including language, and it can be altered in cognitive and psychiatric disorders. No mechanism has yet been identified for establishing the human brain’s left–right axis. We performed multivariate genome-wide association scanning of cortical regional surface area and thickness asymmetries, and subcortical volume asymmetries, using data from 32,256 participants from the UK Biobank. There were 21 significant loci associated with different aspects of brain asymmetry, with functional enrichment involving microtubule-related genes and embryonic brain expression. These findings are consistent with a known role of the cytoskeleton in left–right axis determination in other organs of invertebrates and frogs. Genetic variants associated with brain asymmetry overlapped with those associated with autism, educational attainment and schizophrenia. Comparably large datasets will likely be required in future studies, to replicate and further clarify the associations of microtubule-related genes with variation in brain asymmetry, behavioural and psychiatric traits.

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Thank you for the opportunity to review your work. Please do not hesitate to contact me if you have any questions or would like to discuss the required revisions further. the human cortex by carrying out a genome-wide association study and subsequent follow-up analyses. They report 21 genomic loci that were significantly associated of which most were new findings. The carry these genomic loci forward into in silico follow-up analyses integrating different types of data. This is an interesting article that sheds new light on a brain phenotype that is associated with a wide variety of outcomes. Their provide consistent evidence of involvement of the cytoskeleton using gene-mapping and gene-set testing. I have several comments, questions and suggestions to improve the current version of the manuscript: -Overall, the main text should provide more emphasis why these results are relevant, based on prior evidence of involvement of abnormal lateralization processes in psychiatric disorders (as mentioned in the abstract), instead of summing up results from GWAS follow-up analyses, and how these results be used for further research.
-SNP heritabilities: the main text should mention what software was used to estimate the SNP heritabilities, also for the genetic correlations that follow, instead of only referring to the methods section.
-The estimated SNP heritabilities of the AI indices are in general quite low. It would be of interest to mention the estimated heritability from previous twin study literature for context. Could they also mention the areas with the highest and lowest heritabilities in the main text? -The authors did not correct for handedness. How much of the genetic signal can be attributed to brain asymmetry differences due to handedness, if this would have been corrected for? (i.e. number of loci, genetic correlation before and after correction) -Main text: in the result section, the authors provide quite a long list of chromosomal regions (why are these necessary?), lead SNP rs-ids and gene names. I do not see the use of writing out all the data that is also available in table format. Could the authors create some structure in these results (grouping of results) instead of providing a list with results? This would greatly improve the readability of the text.
-The gene-based association testing does not mention the software that was used, this should be stated.
-'Significant enrichment within various microtubule-related sets was also found …' is vague, please provide examples of the top associated sets.
- Figure 2: there is no reason to visualize Manhattan plots as circular plots other than aesthetic reasons. This makes it more difficult to compare heights along each chromosome.
- Figure 4: panel A shows the protein-protein interactions. The authors mention that both experimentally validated interactions are investigated. Is it possible that the authors make clear in the figure which ones are actually experimentally validated interactions and which ones are just based on expert opinion? - Figure 4: the authors mention that the set of genes show 117 (putative) associations in the STRING database. The authors mention that this is more than a random set in the proteome. I do not think these findings are that surprising, since any set of genes that is associated with a phenotype is likely to have more interactions that a random set (i.e. gene sets for brain volume, psychiatric disorders, personality, height, intelligence etc.) it would be a fair comparison to compare the set with a set of involved genes of other traits or brain phenotypes.
- Figure 4: the authors state that micro-tubule related genes are located more centrally in the network. Would it be possible to provide the reader with a more quantitative measure for network centrality than using a qualitative term? - Figure 4: would it be possible to make clear in the figure which protein-protein interactions are actually based on experimentally validated interactions in the STRING database? -Brain span analyses: the authors again do not mention how these analyses were carried out. Did you use the gene-to-func function embedded in FUMA? -FUMA has an integrated function of looking into enrichment on the neuronal level. Since the main text mentions associations of genes to neuronal cell-types, it would be interesting whether the authors would actually test this with readily available single-cell data in FUMA.
-The authors used iSECA to estimate genetic overlap with previously associated traits. The merely provide P values for the statistical test, I am missing effect sizes of how much overlap / correlation these was with these traits. Also, how do these relate to more commonly used software to estimate genetic overlap, such as LD Score regression? -Did the authors estimate overlap with the 2020 Grasby et al. Science paper that carried out GWAS meta-analysis of cortical morphology? The authors mention distinct gene-sets, it would be of interest whether significant overlap with this meta-analysis is present.
-Any single-sample GWAS should provide some measure of external validation of their findings in another sample (i.e. the reproducibility of loci or explained variance by a polygenic score etc.) since the use of only UK Biobank data is prone to overfitting.
-For transparency and to allow other groups to make optimal use of the results, do the authors plan to make the GWAS summary statistics publicly available?
Reviewer #2: Remarks to the Author: The authors conducted a genome-wide association study (GWAS) of left-right asymmetry of various brain regions. The subjects were 32,256 participants in the UK Biobank. Despite the relatively small sample size by GWAS standards and the low GCTA heritabilities of the asymmetries, the authors were able to detect 21 genome-wide significant loci associated with different asymmetries. They employed MetaPhat, a new GWAS tool that implements canonical correlation analysis and uses a stepwise procedure to identify the components of the multivariate phenotype contributing to a significant canonical correlation. Using the enrichment tool MAGMA, they found that genes with low association p-value SNPs were unusually likely to be implicated in microtubule function. Despite what might have seemed a low statistical power to detect such enrichment, this finding seems statistically secure and is thus quite impressive and intriguing. Some readers may be skeptical of the canonical correlation analysis. This may seem like a way to get something out of nothing. Without studying the specific method more closely, I think it is warranted to be skeptical of whether a significant multivariate hit can be followed up to determine the contributing components with an overwhelming degree of confidence. But in most of the downstream analyses, only the multivariate results are used, and I think the resulting inferences can be trusted. Readers can inspect Supplementary Table 11 to see the univariate associations that seem to be driving each multivariate hit, and this provides some transparency.
I recommend the publication of this paper, upon a few minor revisions and clarifications.
p. 5, lines 103-104: "Seventy-two of the 112 genes have been reported to associate with educational attainment" The cited paper used two different gene-prioritization tools, DEPICT and MAGMA (the one used by these authors). The DEPICT genes were nearly a subset of the MAGMA genes. Nevertheless, it will helpful to state which of the two lists of prioritized genes in the cited paper were checked for overlap with the 112 asymmetry genes.
pp. 13-14, lines 328-334: There needs to be clarification of what qualifies a gene to "belong" to a particular stage. I.e., what makes a gene an "early prenatal" gene or a "late childhood" gene? Right now the authors say "differential mRNA expression (significantly higher gene expression)," but this is too vague.

Author responses to reviewer comments
Sha et al., The genetic architecture of structural left-right asymmetry of the human brain Authors: We thank the editor and reviewers for helpful comments on the manuscript.

Editor
... one of the requirements at Nature Human Behaviour for GWAS studies is the need to provide external validation of findings in at least one replication sample. We would ask you therefore to either conduct an analysis in a replication sample, or to explain why this cannot be done (for example, if you believe there are no suitable replication samples available, please explain why UK Biobank is the only suitable sample.) Authors: We have added additional results in the "Validation of lead SNPs associated with brain asymmetry" section (page 8): "To achieve a reasonable level of genetic homogeneity in our mvGWAS, we had excluded any individuals not annotated as having 'white British ancestry' (through a combination of self-report and clustering based on principal components that capture major axes of genotypic diversity 94 (Methods)). The UK Biobank includes additional participants who self-identify as being 'white', but who did not self-identify as British, or did not cluster genetically with the bulk of the 'white British' ancestry participants (Methods). After applying the same quality control criteria to these additional participants as in our discovery mvGWAS (except with respect to ancestry), and imposing the extra criterion that relatedness kinship coefficients should not be greater than 0.0442 with any participants from the discovery mvGWAS, data were available from 3,600 participants for an independent replication set. We tested each of the 27 lead SNPs from the mvGWAS in the replication set, using the same approach as the mvGWAS analysis, except that 40 genetic principle components were used as covariates to control for the greater degree of ancestral diversity in the replication set. Table 19). The combined p value of the remaining 17 lead SNPs was p=3.3×10 -4 in the replication set (calculated by Stouffer's method), which we confirmed by permutation with respect to 10,000 repeat random samplings of 17 SNPs from the whole genome in the replication set (permutation-based p=4×10 -4 ). This indicates that the limited sample size of the replication set, compared to the discovery set, did not provide adequate power to replicate at the level of some individual SNPs, but that in combination there was evidence for replication. Moreover, among the 17 SNPs that showed p>0.05 in multivariate testing in the replication set, some showed association p<0.05 in univariate testing of the specific central traits identified for those SNPs in the discovery mvGWAS (Supplementary Table 19). It is also worth noting that four of these 17 SNPs (or SNPs in high linkage disequilibrium with them) have been reported to associate with left-handedness at a genome-wide significant level 42 (see above for details), which is an additional form of validation with respect to a phenotype related to brain asymmetry. As also mentioned above, the high degree of functional clustering of genes identified through gene-based association testing is another form of support for the association results in the mvGWAS."

Ten of the 27 independent lead SNPs from the discovery mvGWAS showed association p values < 0.05 in multivariate testing in the replication set (Supplementary
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Reviewer #1: In this study, the authors investigated genetic factors underlying thickness and volume symmetry of the human cortex by carrying out a genome-wide association study and subsequent follow-up analyses. They report 21 genomic loci that were significantly associated of which most were new findings. The carry these genomic loci forward into in silico follow-up analyses integrating different types of data. This is an interesting article that sheds new light on a brain phenotype that is associated with a wide variety of outcomes. Their provide consistent evidence of involvement of the cytoskeleton using gene-mapping and gene-set testing. I have several comments, questions and suggestions to improve the current version of the manuscript: Authors: We thank the reviewer for these valuable comments and suggestions.
-Overall, the main text should provide more emphasis why these results are relevant, based on prior evidence of involvement of abnormal lateralization processes in psychiatric disorders (as mentioned in the abstract), instead of summing up results from GWAS follow-up analyses, and how these results be used for further research.
Authors: The main inference from our results on genetic overlap is that genes affecting brain asymmetry are also involved in susceptibility to autism and schizophrenia. We discuss this observation with reference to previous literature and causal versus correlational models, and how these might be distinguished in the future. However, we have not reduced the emphasis in the main text on the other major aspect of this research, i.e. that brain laterality is particularly affected by microtubule and embryonicallyexpressed genes, which is highly relevant to understanding the genetic and developmental foundations of brain laterality, regardless of any connection to disorders. The discussion section on the genetic overlap with psychiatric disorders now reads like this (page 11): "We found significant genetic overlaps of brain asymmetry with autism, schizophrenia and educational attainment, which indicates that genes affecting brain asymmetry also influence these traits. This is in line with literature that has shown phenotypic associations between altered brain asymmetry and these traits (see Introduction), and indicates that such phenotypic associations are contributed to an extent by genetic factors. As we found that brain asymmetry-related genes tend to be especially highly expressed in the embryonic brain, then it seems likely that the genetic overlap of brain asymmetry and disorders reflects a genetic susceptibility to alterations of early neurodevelopment away from the typical trajectory. However, brain asymmetry continues to develop throughout the lifespan 105,106 , and the UK Biobank consists of middle to older age adults, so that our mvGWAS may have also identified genetic factors that affect brain asymmetrical changes later in life. Further research, for example using Mendelian Randomization 107 , will be needed to understand whether brain asymmetries mediate gene-disorder associations in a causal sense, or whether altered brain asymmetry and disorder susceptibility are two distinct consequences arising from a partly overlapping genetic basis. It will also be important to map, on a brain-regional basis, which aspects of asymmetry show the strongest genetic overlaps with disorder susceptibility. Larger imaging-genetic datasets may be needed to support causal mediation and mapping studies with respect to disorders, as the present genetic association analysis was based on brain-wide asymmetry (albeit in a multivariate context)." -SNP heritabilities: the main text should mention what software was used to estimate the SNP heritabilities, also for the genetic correlations that follow, instead of only referring to the methods section.

Authors: Done (page 4)
-The estimated SNP heritabilities of the AI indices are in general quite low. It would be of interest to mention the estimated heritability from previous twin study literature for context. Could they also mention the areas with the highest and lowest heritabilities in the main text?
Authors: We have added the information about highest and lowest heritabilites to the main text (page 4), and made an overall comparison with previous twin studies in the Discussion (page 11), together with some explanation of why twin-based heritabilities are often slightly higher than SNP-based heritabilities (SNP-based heritability is based on only one class of genomic variation, while twin studies can overestimate heritability when certain assumptions are not met).
In the "Heritabilities and genetic correlations of brain regional asymmetry measures" section of Results (page 4): "Forty-two AIs showed significant SNP-based heritabilities (FDR-corrected p<0.05), i.e. 28 of the surface area AIs, 8 cortical thickness AIs, and 6 subcortical volume AIs (Fig. 1A,  Supplementary Table 3), ranging from 2.2% for the AI of entorhinal cortical thickness, to 9.4% for the AI of superior temporal surface area. The overall pattern was consistent with previous twin-based heritability analyses 5,6 ." In the Discussion (page 11): "Many of the brain asymmetries were strong and directional at the population level, but their heritabilities were generally low, ranging up to 10%. This suggests that developmental mechanisms for brain asymmetry are tightly constrained and largely genetically invariant in the population, and that environmental factors and/or developmental randomness are responsible for most variability 43,108-110 . A cytoskeletonbased origin of brain asymmetry would fit this scenario, as the cytoskeleton is essential for various fundamental functions in cellular biology, beyond axis formation 111,112 . Previous twin-and family-based analyses 5,6 have reported heritabilities up to roughly 25% for some of the same asymmetry measures that we analyzed in the present study, with an overall similar regional pattern, i.e. higher heritabilities particularly for regions important in the language system (e.g. superior temporal cortex) and limbic system (e.g. medial temporal and cingulate cortex). Twin-based heritability is often measured to be higher than SNPbased heritability, which may be expected because SNPs are just one class of genetic variation, and also because twin studies can overestimate heritability when certain assumptions are not fully met 113 . As twin studies have not indicated effects of shared environment on brain aymmetries 5,6 , then early developmental randomness is likely to cause most variation 114 ." -The authors did not correct for handedness. How much of the genetic signal can be attributed to brain asymmetry differences due to handedness, if this would have been corrected for? (i.e. number of loci, genetic correlation before and after correction) Authors: It is generally not advisable in genetic analysis to correct for covariates which are themselves partly heritable (such as handedness), as collider bias can induce biased or spurious genetic effects on the target trait (in this case brain asymmetry). Handedness cannot therefore be treated safely as a confound variable when analyzing brain asymmetry. We are interested in any genetic effects on brain asymmetry, regardless of whether they might also be shared with other traits such as handedness. Having identified genetic effects on brain asymmetry, we then report post hoc whether they have been reported as significant in previous GWAS of handedness in over 1 million people (five of our identified variants associated with brain asymmetry were reported to associate with handedness by Partida et al. (biorxiv preprint)). As reported in the paper, apart from this small number of individual loci, we did not find a significant genome-wide genetic overlap between brain asymmetry and handedness.
We have now explained in the revised Discussion (page 12): "We did not correct for handedness as a covariate in our genetic analyses, as it is generally not advisable to correct for covariates which are themselves partly heritable. This is because biased genetic effects can arise with respect to the target trait 115 (in this case brain asymmetry). Handedness cannot therefore be treated safely as a confound variable when analyzing brain asymmetry. We were interested in any genetic effects on brain asymmetry, regardless of whether they might also be shared with other traits such as handedness.
Having identified genetic effects on brain asymmetry, we then queried post hoc whether they have been reported as significant in previous GWAS of handedness in over 1 million people 42 . We did not observe a significant genetic overlap between structural brain asymmetry and handedness at the genome-wide level, which again may be due to the relatively low SNP-based heritabilities of these traits, in combination with limited statistical power in the present sample size for this kind of analysis. However, five individual SNPs affecting brain asymmetry and handedness were identified, which suggests that a significant genome-wide overlap might be detected when using a larger dataset in the future." -Main text: in the result section, the authors provide quite a long list of chromosomal regions (why are these necessary?), lead SNP rs-ids and gene names. I do not see the use of writing out all the data that is also available in table format. Could the authors create some structure in these results (grouping of results) instead of providing a list with results? This would greatly improve the readability of the text.

Authors:
We have re-organized into three distinct paragraphs, the first for summarizing the significant variants and associated brain traits in mvGWAS analysis, the second about loci that implicate microtubule-related genes specifically, and the third about all other loci associated with neural and brain development (page 5). It is important to retain this information in text form locus-by-locus, because it distills a selection of particularly notable biological annotations for each of the 27 independent lead SNPs that are associated with brain asymmetry, whereas the supplementary tables and figures have more detailed information of different types and are not necessarily organized by loci. These paragraphs also cite many primary references in which relevant information is reported for each locus. Inserting citations may not work in table form.
-The gene-based association testing does not mention the software that was used, this should be stated.
Authors: MAGMA v1.08 was used to perform gene-based association analysis. We have clarified this in the Methods (page 18).
-'Significant enrichment within various microtubule-related sets was also found …' is vague, please provide examples of the top associated sets.

to the 27 lead SNPs (Supplementary
- Figure 2: there is no reason to visualize Manhattan plots as circular plots other than aesthetic reasons. This makes it more difficult to compare heights along each chromosome.

Authors: This figure is generated by the STRING software. Edges between nodes represent different types of protein-protein associations provided in the STRING database. We have added details to the figure legend on the color coding of the different types of interaction (page 36): "Edges between nodes represent different types of protein-protein interactions according to the STRING database (Methods), including known interactions (turquoise and dark purple represent interactions identified by curated databases and biological experiments, respectively), predicted interactions (green, red and blue represent interactions predicted by gene neighborhood, gene fusions and gene co-occurrence, respectively) and others (yellow, black and light purple represent interactions determined by textmining, coexpression and protein homology, respectively)."
- Figure 4: the authors mention that the set of genes show 117 (putative) associations in the STRING database. The authors mention that this is more than a random set in the proteome. I do not think these findings are that surprising, since any set of genes that is associated with a phenotype is likely to have more interactions that a random set (i.e. gene sets for brain volume, psychiatric disorders, personality, height, intelligence etc.) it would be a fair comparison to compare the set with a set of involved genes of other traits or brain phenotypes.
Authors: This analysis primarily provides a validation of our genetic association data, as the clustering of genes implicated by genetic association analysis into an interacting set, at a level far exceeding chance, is a strong indicator that the genetic association data themselves are not merely random noise. In addition, the protein-protein interaction analysis helps to increase biological understanding of the genetic contributions to brain asymmetry.

We do not know the extent to which it is a general principle that any set of genes associated with a phenotype is likely to have more protein-protein interactions than a random set. This is an empirical question that would require gathering GWAS summary statistics from many traits (certainly an interesting idea and study, but not the goal of ours). The comparison with our data might only be meaningful for traits with similar numbers of associated genes, in which case the particular genetic architecture of those traits would likely determine the outcome of the comparison, rather than any general principal of complex trait genetic architecture.
We have clarified the issue in the revised Results section "Functional annotations of genomic loci associated with brain asymmetry" (page 7): "For the proteins encoded by the 57 genes, there were 80 known or putative pairwise interactions in the STRING database 66 , compared to 8 interactions expected for a random set of this size from the whole proteome (p<1×10 -16 ). This observation supports the validity of our mvGWAS association findings, as random noise would not lead to such functional clustering, - Figure 4: the authors state that micro-tubule related genes are located more centrally in the network. Would it be possible to provide the reader with a more quantitative measure for network centrality than using a qualitative term?

"Edges between nodes represent different types of protein-protein interactions according to the STRING database (Methods), including known interactions (turquoise and dark purple represent interactions identified by curated databases and biological experiments, respectively), predicted interactions (green, red and blue represent interactions predicted by gene neighborhood, gene fusions and gene co-occurrence, respectively) and others (yellow, black and light purple represent interactions determined by textmining, coexpression and protein homology, respectively)."
-Brain span analyses: the authors again do not mention how these analyses were carried out. Did you use the gene-to-func function embedded in FUMA?
Authors: Yes, we used the embedded function in FUMA. We have made sure to note this in the Methods (page 19).
-FUMA has an integrated function of looking into enrichment on the neuronal level. Since the main text mentions associations of genes to neuronal cell-types, it would be interesting whether the authors would actually test this with readily available single-cell data in FUMA.
Authors: There was no significant genome-level enrichment of association signals with respect to cell-types. In the Results, we describe that some of the individual genes at the 21 associated genomic loci have shown particularly high expression in the context of certain tissues, cell types or subcellular structures, but this does not necessarily imply significant enrichment at the whole-genome level. Thus the genome-wide testing does not impact on the validity of observations made with respect to the top loci from the GWAS. We have added the relevant methods and results in the revised manuscript: In the "Functional annotations of genomic loci associated with brain asymmetry" section of Results (page 7): "We observed no statistically significant relation of our gene-based association p values with differential expression across cell types (Methods)." In the "Gene-set enrichment analysis" of Methods (page 19): "Finally, we used the CELL TYPE function (as implemented within FUMA) to test whether lower gene-based association p values for brain asymmetry were associated with differential expression levels across cell types, using Bonferroni correction within each separate analysis with respect to each cell-type expression dataset included in FUMA." -The authors used iSECA to estimate genetic overlap with previously associated traits. The merely provide P values for the statistical test, I am missing effect sizes of how much overlap / correlation these was with these traits. Also, how do these relate to more commonly used software to estimate genetic overlap, such as LD Score regression?
Authors: We used multivariate GWAS analysis to achieve data reduction and increase statistical power, for exploiting genetic covariance between 42 brain asymmetry measures. In this framework we perform one association test for each genetic variant simultaneously across all 42 asymmetry measures, rather than performing 42 separate tests per genetic variant. This approach has the advantage that we can then perform downstream analyses, such as functional enrichment and genetic overlap with disorders, using the results from one multivariate GWAS rather than separately for 42 GWAS of regional asymmetry measures. The latter approach would be cumbersome and difficult to interpret and/or underpowered with respect to correction for multiple testing. A consequence of our multivariate approach is that it does not yield association effect sizes across different traits, and therefore the results cannot be used for standard genetic correlation analyses, such as performed with LD score regression. This is why we refer to genetic overlap rather than genetic correlation, and is why we chose iSECA to investigate this, based only on P values and not univariate effect sizes. We have explained in more detail in the revised version: In the "Multivariate genome-wide association analysis (mvGWAS)" section of Results (page 5): "A multivariate approach had the dual advantages of achieving data reduction and increasing statistical power compared to running 42 separate univariate GWAS." In the Discussion (page 10): "In this study we identified genetic loci that are associated with 42 heritable aspects of brain asymmetry through a multivariate, brain-wide approach. A multivariate approach can boost statistical power while achieving data reduction, compared to separate univariate analyses of individual brain traits 37 . A single set of genome-wide association results, pertaining simultaneously to multiple aspects of brain asymmetry, was then taken forward into functional annotation and downstream analyses, such as testing for genetic overlaps with other traits. The multivariate approach therefore helped to detect and interpret key aspects of the genetic architecture of brain asymmetry, without the noise inherent in repeat univariate testing. An important challenge remained to identify the particular brain traits that drove the multivariate associations at each locus, which was achieved in MetaPhat 37 by

decomposing associations into sets of 'central' traits based on the Bayesian Information Criterion and univariate p-value statistics.
A consequence of the multivariate approach is that it does not yield univariate association effect sizes, and therefore mvGWAS results cannot be used for standard genetic correlation analyses, such as is performed with LD score regression 104 . Therefore, we used iSECA 72 to explore the genetic overlap of brain asymmetry with neurodevelopmental disorders, behavioral and psychological traits." -Did the authors estimate overlap with the 2020 Grasby et al. Science paper that carried out GWAS meta-analysis of cortical morphology? The authors mention distinct gene-sets, it would be of interest whether significant overlap with this meta-analysis is present.
Authors: Grasby et al. worked with bilateral structural measures that were generally more heritable than the asymmetry measures that we have analyzed. They chose to perform mass univariate GWAS analyses in their study. In our study, we performed multivariate GWAS analysis to identify genetic loci that are associated with different aspects of brain asymmetry. We are unsure whether it would be informative to test for genetic overlaps between our multivariate results for brain asymmetry and each of Grasby's univariate sets of results for separate regional measures. We have included a test for genetic overlap with a previous ENIGMA consortium GWAS for overall brain size, which seems appropriate with respect to our multivariate approach that captures brain-wide asymmetry in a single genetic analysis. The results showed no significant genetic overlap of brain size with brain asymmetry, which indicates that the genetic architecture of brain asymmetry is distinct from brain size. Moreover, enrichment in microtubule-related sets was not reported in Grasby's GWAS of bilaterally averaged cortical surface area and thickness measures, suggesting a particular involvement in hemispheric asymmetry rather than bilateral measures.
-Any single-sample GWAS should provide some measure of external validation of their findings in another sample (i.e. the reproducibility of loci or explained variance by a polygenic score etc.) since the use of only UK Biobank data is prone to overfitting.
Authors: Please see above where we have addressed this point in a response to the Editor (we added a new analysis in an independent sample, and drew attention to various other aspects that help to validate the results).
-For transparency and to allow other groups to make optimal use of the results, do the authors plan to make the GWAS summary statistics publicly available?
Authors: We have noted in the revised Data Availability Statement that the GWAS statistics are made available online within the GWAS catalog https://www.ebi.ac.uk/gwas/ (this database publishes the statistics shortly after formal journal publication of the corresponding paper).

Reviewer #2:
Remarks to the Author: The authors conducted a genome-wide association study (GWAS) of left-right asymmetry of various brain regions. The subjects were 32,256 participants in the UK Biobank. Despite the relatively small sample size by GWAS standards and the low GCTA heritabilities of the asymmetries, the authors were able to detect 21 genome-wide significant loci associated with different asymmetries. They employed MetaPhat, a new GWAS tool that implements canonical correlation analysis and uses a stepwise procedure to identify the components of the multivariate phenotype contributing to a significant canonical correlation. Using the enrichment tool MAGMA, they found that genes with low association p-value SNPs were unusually likely to be implicated in microtubule function. Despite what might have seemed a low statistical power to detect such enrichment, this finding seems statistically secure and is thus quite impressive and intriguing. Some readers may be skeptical of the canonical correlation analysis. This may seem like a way to get something out of nothing. Without studying the specific method more closely, I think it is warranted to be skeptical of whether a significant multivariate hit can be followed up to determine the contributing components with an overwhelming degree of confidence. But in most of the downstream analyses, only the multivariate results are used, and I think the resulting inferences can be trusted. Readers can inspect Supplementary Table 11 to see the univariate associations that seem to be driving each multivariate hit, and this provides some transparency. I recommend the publication of this paper, upon a few minor revisions and clarifications.
Authors: Thank you very much for these observations. As noted above in response to Reviewer 1, we have added more explanation for the multivariate approach, which has advantages in terms of data reduction and statistical power in the context of 42 regional asymmetry measures with relatively low but significant heritabilities. Indeed the univariate associations with each of the 'central' traits behind the multivariate associations can be found in the Supplementary Table 11, which are helpful to understand how each SNP relates to a subset of regional asymmetries.
p. 5, lines 103-104: "Seventy-two of the 112 genes have been reported to associate with educational attainment" The cited paper used two different gene-prioritization tools, DEPICT and MAGMA (the one used by these authors). The DEPICT genes were nearly a subset of the MAGMA genes. Nevertheless, it will helpful to state which of the two lists of prioritized genes in the cited paper were checked for overlap with the 112 asymmetry genes.
Authors: We used the MAGMA list from that paper because we used MAGMA for our own study. We have clarified this in the header of Supplementary Table 14. Please note that a preprint appeared in recent weeks https://www.biorxiv.org/content/10.1101/2020.08.20.260224v1 which found a problem with the 'SNP-wise mean model' implemented in MAGMA. The authors of MAGMA quickly fixed the problem, and we have updated all of our gene-based association testing and downstream analysis accordingly for this revision. In the updated results, there were 57 significant genes at Bonferroni-corrected p<0.05. Forty-three of the 57 genes have been reported to associate with educational attainment.
pp. 13-14, lines 328-334: There needs to be clarification of what qualifies a gene to "belong" to a particular stage. I.e., what makes a gene an "early prenatal" gene or a "late childhood" gene? Right now the authors say "differential mRNA expression (significantly higher gene expression)," but this is too vague.
Authors: Based on the gene-based association p-values for all 20,146 genes genome-wide, we used MAGMA (default settings as implemented in FUMA) to examine whether lower gene-based P values tended to be found for genes showing relatively higher expression in BrainSpan gene expression data from any particular ages compared to all other ages, separately for 29 different age groups ranging from 8 postconceptional weeks to 40 years old, and 11 defined developmental stages from early prenatal to middle adulthood. We corrected for multiple testing through a FDR of 0.05 (separately for the two analyses). Thus this is a quantitative analysis and does not require assigning genes categorically as e.g. 'early prenatal' etc., rather it just reflects that some genes tend to be expressed relatively more highly at some developmental stages.
We have now stated more clearly how this analysis works in the "Developmental stage analysis" section of Methods (page 19): "Using the gene-based association p-values for all 20,146 genes genome-wide, we used MAGMA (default settings as implemented in FUMA) to examine whether lower genebased p values tended to be found for genes showing relatively higher expression in BrainSpan 69 gene expression data from any particular ages compared to all other ages, separately for 29 different age groups ranging from 8 postconceptional weeks to 40 years old, and 11 defined developmental stages from early prenatal to middle adulthood. We corrected for multiple testing through a FDR of 0.05 (separately for the two analyses)." Authors: We have removed Supplementary Figure 10 as we agree it was not helpful. We used the 0.6 threshold because it is the default in FUMA, and there is merit in sticking to default parameters to avoid making arbitrary decisions for SNP annotations and gene mapping. FUMA uses the same parameter also for clumping the associated SNPs into distinct genomic loci, so that altering this single parameter would affect both the inclusivity of candidate SNP labelling and the process of clumping. We therefore prefer to leave this at the default setting 0.6, with respect to sensible clumping. The issue does not affect our conclusions, as all of the notable functional annotations referred to in the text for the top loci remain if the threshold is increased to 0.8.

Supplementary
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