Heritability and cross-species comparisons of human cortical functional organization asymmetry
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Evaluation Summary:
This is an interesting paper that tries to quantify brain asymmetry in connectivity, looks at the heritability of this asymmetry, and compares it between humans and monkeys. The approach taken here is to first project the connectivity information into a low dimensional sub-space and then to quantify brain asymmetry in this low dimensional representation. The benefit of this approach is that it simplifies the problem to looking at scalar indices rather than matrices, and that it allows comparisons between subjects and species in connectivity space. This work should be of interest to the field of brain asymmetry and evolution. However, there are fundamental issues with the method, as outlined in the review. The paper would also benefit from a stronger focus on the biological interpretation. At present, the main contribution of this work is providing interesting data.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Abstract
The human cerebral cortex is symmetrically organized along large-scale axes but also presents inter-hemispheric differences in structure and function. The quantified contralateral homologous difference, that is asymmetry, is a key feature of the human brain left-right axis supporting functional processes, such as language. Here, we assessed whether the asymmetry of cortical functional organization is heritable and phylogenetically conserved between humans and macaques. Our findings indicate asymmetric organization along an axis describing a functional trajectory from perceptual/action to abstract cognition. Whereas language network showed leftward asymmetric organization, frontoparietal network showed rightward asymmetric organization in humans. These asymmetries were heritable in humans and showed a similar spatial distribution with macaques, in the case of intra-hemispheric asymmetry of functional hierarchy. This suggests (phylo)genetic conservation. However, both language and frontoparietal networks showed a qualitatively larger asymmetry in humans relative to macaques. Overall, our findings suggest a genetic basis for asymmetry in intrinsic functional organization, linked to higher order cognitive functions uniquely developed in humans.
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Author Response
Reviewer #1 (Public Review):
The paper is very well written, the question is interesting, and the analyses are innovative. However, I do have concerns about the overall approach. My main concern is about looking at asymmetries in the low dimensional representation of connectivity. A secondary concern has to do with looking at the parcellated connectome. I explain these concerns in succession below.
We thank the Reviewer for the appreciation of our work and the insightful comments, which we have addressed below. The page numbers are corresponding to the clean version of the manuscript.
The first concern is to me quite a fundamental issue: looking at connectivity in a low dimensional space, that of the laplacian eigenvectors. There are two issues with this. The first one, which is less important than the second, is …
Author Response
Reviewer #1 (Public Review):
The paper is very well written, the question is interesting, and the analyses are innovative. However, I do have concerns about the overall approach. My main concern is about looking at asymmetries in the low dimensional representation of connectivity. A secondary concern has to do with looking at the parcellated connectome. I explain these concerns in succession below.
We thank the Reviewer for the appreciation of our work and the insightful comments, which we have addressed below. The page numbers are corresponding to the clean version of the manuscript.
The first concern is to me quite a fundamental issue: looking at connectivity in a low dimensional space, that of the laplacian eigenvectors. There are two issues with this. The first one, which is less important than the second, is that the authors have a reference embedding to which they align other embeddings using a procrustes method with no scaling. While the 3D embedding is still optimally representing the connectivity (because distances don't change under rotations), we can no longer look at one axis at a time, which is what the authors do when they look at G1. In this case, G1 is representative of the connectivity of the reference matrix (LL), but not the others.
But even if the authors only projected their matrices onto a single G1 dimension with no procrustes (and only sign flipping if necessary), there is still a major issue. One implicit assumption of this whole approach is that if there is a change in connectivity somewhere in the original matrix, the same "nodes" of the matrix will change in the embedding. This is not the case. Any change in the original matrix, even if it is a single edge, will affect the positions of all the nodes in the embedding. That is because the embedding optimises a global loss function, not a local one.
To make this point clear, consider the following toy example. Say we have 4 brain regions A,B,C,D. Let us say that we have the following connectivity:
In the Left Hemisphere: A-B-C-D
In the Right Hemisphere: A-B=C-D
So the connection between B and C is twice as strong in the right hemi, and everything else remains the same.
The low dimensional embedding of both will look like this:
Left: ... A ... B ....... C ... D ...
Right A... ... ... B ... C ... ... ... D
Note how B,C are closer to each other in the RIGHT, but also that A,D have moved away from each other because the eigenvector has to have norm 1.
So if we were to calculate an asymmetry index, we would say that:
A is higher on the LEFT
B is higher on the RIGHT
C is higher on the LEFT
D is higher on the RIGHT
So we have found asymmetry in all of our regions. But in fact the only thing that has changed is the connection between B and C.
This illustrates the danger of using a global optimisation procedure (like low-dim embedding) to analyse and interpret local changes. One has to be very careful.
We thank the Reviewer for the detailed description of the first concern. We agree that low-dimensional embeddings describe global embedding of local features, rather than local phenomena. Moreover, we indeed assume that the connectivity embedding of a given node gives us information about its position along ‘gradients’ relative to other nodes and their respective embedding. Thus, indeed, when a single node (node X) has a different connectivity profile in the right hemisphere relative to the left, this will also have some impact on the embeddings of all nodes showing a relevant (i.e., top 10%) connection to node X.
To evaluate whether asymmetry could be observed in average connectivity within functional networks, an alternative approach to measure asymmetry was taken by computing average connectivity within different functional networks. Following we compared the within-network connectivity between left and right. We have now added this conceptual analysis to our results robustness analysis section. In short, we observed that transmodal networks (DMN, FPN, and language network) showed higher connectivity in the left hemisphere but other networks showed higher connectivity in the right hemisphere. Thus, this indicates that observations made with respect to asymmetry of functional gradients are similar to those observed for within-network functional asymmetry between the left and right hemispheres. We have now detailed the outcome of this analysis in our Result section and Supplementary Materials.
Results, p.14.: “As low-dimensional embedding is a global approach to summarize functional connectivity we reiterated our analysis by evaluating asymmetry of within network functional connectivity in the current sample. Observations made with respect to asymmetry of functional gradients are similar to those observed for within-network functional asymmetry between the left and right hemispheres.”
“To further explore functional connectivity asymmetry between left and right hemispheres, we calculated the LL within network FC and RR within network FC (Figure 2-figure supplement 5). It showed that connections in the left hemisphere and right hemisphere were relatively equal in the global scale. However, for the local differences, networks showed significant subtle leftward or rightward asymmetry (vis1: t = -5.203, P < 0.001; vis2: t = -22.593, P < 0.001; SMN: t = -8.262, P < 0.001; CON: t = -32.715, P < 0.001; DAN: t = -11.272, P < 0.001; Lan.: t = 33.827, P < 0.001; FPN: t = 24.439, P < 0.001; Aud.: t = 0.191, P = 0.849; DMN: t = 11.303, P < 0.001; PMN: t = -35.719, P < 0.001; VMN: t = -11.056, P < 0.001; OAN: t = 0.311, P = 0.756).”
Irrespectively, we have further highlighted that such a global interpretation for asymmetry of areas is still meaningful, given that a node is always placed in a global context. We have now further explained that our metrics give insights in local embedding of global phenomena in the introduction, p. 3.
Introduction, p. 3: “These low-dimensional gradient embeddings describe global embedding of local features, rather than local phenomena. Thus, interpretation for asymmetry of areas is under a global context.”
My second concern is about interpreting the brain asymmetry as differences in connectivity, as opposed to differences in other things like regional size. The authors use a parcellated approach, where presumably the parcels are left-right symmetric. If one area is actually larger in one hemisphere than in the other, the will manifest itself in the connectivity values. To mitigate this, it may be necessary to align the two hemispheres to each other (maybe using spherical registration) using connectivity prior to applying the parcellation.
Thanks for this nice idea. We have now computed the differences of the mean rsfMRI connectome along the first gradient at the vertex level using 100 random subjects, as we have the data mapped to a symmetric template (fs_LR_32k), indicating that each vertex has a symmetric counterpart in the right hemisphere. Our results show left-right asymmetry as language/default mode-visual-frontoparietal vertices, which is consistent with the main results of the parcel-based approach. We have also added this response to the Supplementary materials.
Though overall findings are consistent, spherical registration may also have new issues. Total anatomical spatial symmetry may not provide functional comparability at the vertex level between left and right hemisphere. For example, during language tasks in the current sample, the activated frontal region in the left hemisphere is larger than the activated contralateral region in the right hemisphere. In the current study, we aimed to evaluate asymmetry between functionally and structurally homologous regions, as described by the Glasser atlas. In case of the resting state fMRI data, we used the region-wise symmetric multimodal parcellation (Glasser et al., 2016). This parcellation ensures the functional contralateral regions in both hemispheres. A previous study (Williams et al., 2021) investigated the structural and functional asymmetry in newborn infants. They used spherical registration (make fs_LR symmetric) for structural asymmetry but not for functional asymmetry. As such spheric registration may hide functional information, we think spherical registration may be more suitable for structural studies.
To address the concern regarding the alignment of hemispheres, we used joint alignment for LL and RR to compare the results between this and the Procrustes alignment technique (Pearson r=0.930, P_spin<0.001), below is the figure of asymmetry along the principal gradient (upper: joint alignment, below: Procrustes alignment) indicating convergence between both approaches. We have reported this information in the Supplementary Materials.
Lastly, we do agree that parcel size might be an important issue influencing the asymmetry pattern. To test for such an effect, we performed the correlation between the rank of parcel size (left-right)/(left+right) and rank of asymmetry index. It suggests only a small insignificant correlation along G1 (Spearman r_intra=0.130, P_spin=0.105; Spearman r_inter=0.130, P_spin=0.084). Of note, there is a systematic difference in parcel size as a function of sensory-association hierarchy, indicating that the link between parcel-size and asymmetry may vary as a function of sensory vs associative regions.
Reviewer #2 (Public Review):
Using recently-developed functional gradient techniques, this study explored human brain hemispheric asymmetry. The functional gradient is a hot technique in recent years and has been applied to study brain asymmetries in two papers of 2021. Compared to previous studies, the current study further evaluated the degree of genetic control (heritability) and evolutionary conservation for such gradient asymmetries by using human twin data and monkey's fMRI data. These investigations are of value and do provide interesting data. However, it suffers from a lack of specific hypotheses/questions/motivations underlying all kinds of analyses, and the rich observational or correlational results seem not to offer significant improvement of theoretical understanding about brain asymmetries or functional gradient. In addition, given the limited number of twins in HCP project (for a heritability estimation), the limited number of monkeys (20 monkeys), and the relatively poor quality of monkeys' resting functional MRI data, the results and conclusion should be taken cautiously. Below are major concerns and suggestions.
We thank the Reviewer for the evaluation of our work and the helpful suggestions.
The gradient from resting-state functional connectome has been frequently used but mainly at the group level. The current study essentially applied the gradient comparison (i.e., gradient score) at the individual level. Biological interpretation for individual gradient score at the parcel level as well as its comparability between individuals and between hemispheres should be resolved. This is the fundamental rationale underlying the whole analyses.
We thank the Reviewer for this remark, and are happy to provide further rationale for using and comparing individual gradients scores to evaluate individual variation in asymmetry and associated heritability. Though gradients from resting-state functional connectivity have been frequently used at the group level, various studies have also studied individual differences. For example, using linear mixed models to compare gradient scores between left and right across subjects (Liang et al., 2021), applying the individual gradient scores to compare disease and controls (Dong et al., 2020, 2021; Hong et al., 2019; Park et al., 2021), and link individual hippocampal gradients to memory recollection (Przeździk et al., 2019). Together, these studies show individual variations of local gradients, indicating changes in node centrality and hubness (Hong et al., 2019), and connectivity profile distance (Y. Wang et al., 2021). Of note, low-dimensional embeddings describe global embedding of local features, rather than local phenomena. Thus, interpretation for asymmetry of areas is under a global context. The biological interpretation for individual gradients would be to what degree the system segregated and integrated has changed patterns of ongoing neural activity (Mckeown et al., 2020). It reflects that individuals have different functional boundaries between anatomical regions. Whereas, individual neurons are embedded under the global-local boundaries through a cortical wiring space consisting of intricate long- and short-range white matter fibers (Paquola et al., 2020).
Introduction, p. 4: “We applied the individual gradient scores to study the asymmetry, consistent with prior studies (Gonzalez Alam et al., 2021; Liang et al., 2021). Individual variation along the gradients reflects a global change across subjects in the functional connectome integration and segregation, and it is under genetic control (Valk et al., 2021). Moreover, to what degree the system segregated and integrated relates to patterns of ongoing neural activity (Mckeown et al., 2020), and different individuals have different functional boundaries between anatomical regions.”
Results, p. 5: “Next, individual gradients were computed for each subject and the four different FC modes and aligned to the template gradients with Procrustes rotation. It rotates a matrix to maximum similarity with a target matrix minimizing sum of squared differences. As noted, Procrustes matching was applied without a scaling factor so that the reference template only matters for matching the order and direction of the gradients. Therefore, it allows comparison between individuals and hemispheres. The individual mean gradients showed high correlation with the group gradients LL (all Pearson r > 0.97, P spin < 0.001).”
Only the first three gradients are used but why? What about the fourth gradient? Specific theoretical interpretation is needed. At the individual level, is it ensured that the first gradients of all individuals correspond to each other? In this study, it is unclear whether we should or should not care about the G2 and G3. The results of G2 and G3 showed up randomly to some degree.
In the current study we focused on the principal gradient in the main analysis, given its association with sensory-transmodal hierarchy, microstructure, and evolutionary alterations (Margulies et al., 2016; Paquola et al., 2019; Xu et al., 2020).
Conversely, gradient 2 reflects the dissociation between visual and sensory-motor networks and gradient 3 is linked to task-positive, control, versus ‘default’ and sensory-motor regions. We analyzed asymmetry and its heritability of the first three gradients (explaining respectively 23.3%, 18.1%, and 15.0% of the variance of the rsFC matrix). However, we extracted the first ten gradients to maximize the degree of fit (Margulies et al., 2016; Mckeown et al., 2020). We have now also shown G4-10 mean asymmetry results as a supplementary figure. To ensure correspondence of gradients across individuals, we aligned the individual gradients to the group level template with Procrustes rotation. Procrustes rotation rotates a matrix to maximum similarity with a target matrix minimizing sum of squared differences. The approach is typically used in comparison of ordination results and is particularly useful in comparing alternative solutions in multidimensional scaling. Figure S1 shows the mean gradients across subjects of each FC mode, which is close to the Figure 1D template gradient space.
Results, p. 5: “The current study analyzed asymmetry and its heritability of the first three gradients explaining most variance (Figure 1d). As they all have reasonably well described functional associations (G1: unimodal-transmodal gradient with 24.1%, G2: somatosensory-visual gradient with 18.4%, G3: multi-demand gradient with 15.1%). However, given we extracted ten gradients to maximize the degree of fit 26,52. We stated mean asymmetry of G4-10 in Figure 1-figure supplement 1.”
The intra-hemispheric gradient is institutive. However, it is hard to understand what the inter-hemispheric gradient means. From the data perspective, yes you can do such gradient comparison between the LR and RL connectome but what does this mean? Why should we care about such asymmetry? From the introduction to the discussion, the authors simply showed the data of inter-hemispheric gradients without useful explanation. This issue should be solved.
We are happy to further clarify. The LR and RL connectivity reflects cross-hemispheric functional signal interaction via corpus callosum, whose structural asymmetry is usually studied (Karolis et al., 2019). Such intra-hemispheric connections, compared to the inter-hemispheric connections, have been suggested to reflect the inhibition of corpus callosum, and underlie hemispheric specialization. Different information relies on hemispheric specialization (e.g., visual, motor, and crude information) and/or inter-hemispheric information transfer (e.g., language, reasoning, and attention) (Gazzaniga, 2000). To clarify and motivate the analysis of both intra- and inter-hemispheric asymmetry in functional gradients, we have now added further detail in the introduction, p. 5.
Here is text: Introduction, p. 4. “The full FC matrix contains both intra-hemispheric and inter-hemispheric connections. Intra-hemispheric connections, compared to the inter-hemispheric connections, have been suggested to reflect the inhibition of corpus callosum and may underlie hemispheric specializations involving language, reasoning, and attention. Conversely, inter-hemispheric connectivity may reflect information transfer between hemispheres, for example a wide range of modal and motor information, and crude information concerning spatial locations 48. Previous studies have reported intra-hemispheric FC to study gradient asymmetry 6,38. By having the callosum related to association white matter fibers, one hemisphere could develop for new functions while the other hemisphere could continue to perform the previous functions for both hemispheres 48. Therefore, in addition to the intra-hemispheric FC gradients, we depicted the inter-hemispheric FC, which is abnormal in patients with schizophrenia 23,49 and autism 24.”
as well as Discussion, p. 16 “Conversely, the transmodal frontoparietal network was located at the apex of rightward preference, possibly suggesting a right-ward lateralization of cortical regions associated with attention and control and ‘default’ internal cognition 62,63. The observed dissociation between language and control networks is also in line with previous work suggesting an inverse pattern of language and attention between hemispheres 3,64. Such patterns may be linked to inhibition of corpus callosum 65, promoting hemispheric specialization. It has been suggested that such inter-hemispheric connections set the stage for intra-hemispheric patterns related to association fibers 48. Future research may relate functional asymmetry directly to asymmetry in underlying structure to uncover how different white-matter tracts contribute to asymmetry of functional organization.”
and Discussion, p.18 “Though overall intra- and inter-hemispheric connectivity showed a strong spatial overlap in humans, we also observed marked differences between both metrics across our analysis. For example, although we found both intra- and inter-hemispheric differences in gradient organization to be heritable, only for intra-hemispheric asymmetry we found a correspondence between degree of asymmetry and degree of heritability. Similarly comparing asymmetry observed in human data to functional gradient asymmetry in macaques, we only observed spatial patterning of asymmetry was conserved for intra-hemispheric connections. Whereas intra-hemispheric asymmetry relates to association fibers, commissural fibers underlie inter-hemispheric connections 77 It has been suggested that there is a trade-off within and across mammals of inter- and intra-hemispheric connectivity patterns to conserve the balance between grey and white-matter 76. Consequently, differences in asymmetry of both ipsi- and contralateral functional connections may be reflective of adjustments in this balance within and across species. Secondly, previous research studying intra- and inter-hemispheric connectivity and associated asymmetry has indicated a developmental trajectory from inter- to intra-hemispheric organization of brain functional connectivity, varying from unimodal to transmodal areas 78,79. It is thus possible that a reduced correspondence of asymmetry and heritability in humans, as well as lack of spatial similarities between humans and macaques for inter-hemispheric connectivity may be due to the age of both samples (young adults in humans, adolescents in macaques). Further research may study inter- and intra-hemispheric asymmetry in functional organization as a function of development in both species to further disentangle heritability and cross-species conservation and adaptation.”
When aligning intra-hemispheric gradient, choosing averaged LL mode as the reference may introduce systematic bias towards left hemisphere. Such an issue also applies to LR-RL gradient alignment as well as cross-species gradient alignment. This methodological issue should be solved.
We thank the Reviewer for raising this point. Indeed, we also used RR as reference, the results were virtually identical. We have stated this in the Results, p. 13. Regarding the cross-species alignment, we averaged the left and right hemispheres to reduce the systematic bias. It showed that the correlation and comparison results remained robust. Now we have updated the method and corresponding results (p.10). Here is the text:
Results (p.15): “We also set the RR FC gradients as reference, the first three of which explained 22.8%, 18.8%, and 15.9% of total variance. We aligned each individual to this reference. It suggested all results were virtually identical (Pearson r > 0.9, P spin < 0.001).”
Results (p.10): “To reduce a possible systematic hemispheric bias during the cross-species alignment, we averaged the left and right hemisphere. We found that the macaque and macaque-aligned human AI maps of G1 were correlated positively for intra-hemispheric patterns (Pearson r = 0.345, P spin = 0.030). For inter-hemispheric patterns, we didn’t observe a significant association (Pearson r = -0.029, P spin = 0.858)”
The sample size of monkey (i.e., 20) is far less than human subjects (> 1000). Such limitation raises severe concern on the validity of the currently observed gradient asymmetry pattern in the monkey group, as well as the similarity results with human gradient asymmetry pattern. Despite the marginal significance of G1 inter-hemisphere gradient between humans and monkeys, I feel overall there is no convincingly meaningful similarity between these two species. However, the authors' discussion and conclusion are largely based on strong inter-species similarity in such asymmetry. The conclusion of evolutionary conservation for gradient asymmetry, therefore, is not well supported by the results.
We agree with your comments. Although it is a small sample compared to humans, in NHP studies, it is a relatively decent sample size (most of the studies have N<10). Of note, recent work suggested that the individual variation pattern can be captured using 4 subjects in both human and macaques (Ren et al., 2021).
To overcome potential overinterpretation of our findings, we have now changed the title to a more descriptive format: “Heritability and cross-species comparisons of asymmetry of human cortical functional organization”
And further detailed findings already in the Abstract; “These asymmetries were heritable in humans and, for intra-hemispheric asymmetry of functional connectivity, showed similar spatial distributions in humans and macaques, suggesting phylogenetic conservation.”
We have pointed out the small sample size in the limitation. Please find the text below: Discussion, p. 18: “Due to the small sample size of macaques, it is important to be careful when interpreting our observations regarding asymmetry in macaques, and its relation to asymmetry patterning observed in humans. Therefore, further study is needed to evaluate the asymmetry patterns in macaques using large datasets 53,79”
And nuanced the conclusion, p.19: “This asymmetry was heritable and, in the case of organization of intra-hemispheric connectivity, showed spatial correspondence between humans and macaques. At the same time, functional asymmetry was more pronounced in language networks in humans relative to macaques, suggesting adaptation.”
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Evaluation Summary:
This is an interesting paper that tries to quantify brain asymmetry in connectivity, looks at the heritability of this asymmetry, and compares it between humans and monkeys. The approach taken here is to first project the connectivity information into a low dimensional sub-space and then to quantify brain asymmetry in this low dimensional representation. The benefit of this approach is that it simplifies the problem to looking at scalar indices rather than matrices, and that it allows comparisons between subjects and species in connectivity space. This work should be of interest to the field of brain asymmetry and evolution. However, there are fundamental issues with the method, as outlined in the review. The paper would also benefit from a stronger focus on the biological interpretation. At present, the main …
Evaluation Summary:
This is an interesting paper that tries to quantify brain asymmetry in connectivity, looks at the heritability of this asymmetry, and compares it between humans and monkeys. The approach taken here is to first project the connectivity information into a low dimensional sub-space and then to quantify brain asymmetry in this low dimensional representation. The benefit of this approach is that it simplifies the problem to looking at scalar indices rather than matrices, and that it allows comparisons between subjects and species in connectivity space. This work should be of interest to the field of brain asymmetry and evolution. However, there are fundamental issues with the method, as outlined in the review. The paper would also benefit from a stronger focus on the biological interpretation. At present, the main contribution of this work is providing interesting data.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
The paper is very well written, the question is interesting, and the analyses are innovative. However, I do have concerns about the overall approach. My main concern is about looking at asymmetries in the low dimensional representation of connectivity. A secondary concern has to do with looking at the parcellated connectome. I explain these concerns in succession below.
The first concern is to me quite a fundamental issue: looking at connectivity in a low dimensional space, that of the laplacian eigenvectors. There are two issues with this. The first one, which is less important than the second, is that the authors have a reference embedding to which they align other embeddings using a procrustes method with no scaling. While the 3D embedding is still optimally representing the connectivity (because …
Reviewer #1 (Public Review):
The paper is very well written, the question is interesting, and the analyses are innovative. However, I do have concerns about the overall approach. My main concern is about looking at asymmetries in the low dimensional representation of connectivity. A secondary concern has to do with looking at the parcellated connectome. I explain these concerns in succession below.
The first concern is to me quite a fundamental issue: looking at connectivity in a low dimensional space, that of the laplacian eigenvectors. There are two issues with this. The first one, which is less important than the second, is that the authors have a reference embedding to which they align other embeddings using a procrustes method with no scaling. While the 3D embedding is still optimally representing the connectivity (because distances don't change under rotations), we can no longer look at one axis at a time, which is what the authors do when they look at G1. In this case, G1 is representative of the connectivity of the reference matrix (LL), but not the others.
But even if the authors only projected their matrices onto a single G1 dimension with no procrustes (and only sign flipping if necessary), there is still a major issue. One implicit assumption of this whole approach is that if there is a change in connectivity somewhere in the original matrix, the same "nodes" of the matrix will change in the embedding. This is not the case. Any change in the original matrix, even if it is a single edge, will affect the positions of all the nodes in the embedding. That is because the embedding optimises a global loss function, not a local one.
To make this point clear, consider the following toy example. Say we have 4 brain regions A,B,C,D. Let us say that we have the following connectivity:
In the Left Hemisphere: A-B-C-D
In the Right Hemisphere: A-B=C-DSo the connection between B and C is twice as strong in the right hemi, and everything else remains the same.
The low dimensional embedding of both will look like this:
Left:
... A ... B ....... C ... D ...
Right
A... ... ... B ... C ... ... ... DNote how B,C are closer to each other in the RIGHT, but also that A,D have moved away from each other because the eigenvector has to have norm 1.
So if we were to calculate an asymmetry index, we would say that:
A is higher on the LEFT
B is higher on the RIGHT
C is higher on the LEFT
D is higher on the RIGHTSo we have found asymmetry in all of our regions. But in fact the only thing that has changed is the connection between B and C.
This illustrates the danger of using a global optimisation procedure (like low-dim embedding) to analyse and interpret local changes. One has to be very careful.
My second concern is about interpreting the brain asymmetry as differences in connectivity, as opposed to differences in other things like regional size. The authors use a parcellated approach, where presumably the parcels are left-right symmetric. If one area is actually larger in one hemisphere than in the other, the will manifest itself in the connectivity values. To mitigate this, it may be necessary to align the two hemispheres to each other (maybe using spherical registration) using connectivity prior to applying the parcellation.
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Reviewer #2 (Public Review):
Using recently-developed functional gradient techniques, this study explored human brain hemispheric asymmetry. The functional gradient is a hot technique in recent years and has been applied to study brain asymmetries in two papers of 2021. Compared to previous studies, the current study further evaluated the degree of genetic control (heritability) and evolutionary conservation for such gradient asymmetries by using human twin data and monkey's fMRI data. These investigations are of value and do provide interesting data. However, it suffers from a lack of specific hypotheses/questions/motivations underlying all kinds of analyses, and the rich observational or correlational results seem not to offer significant improvement of theoretical understanding about brain asymmetries or functional gradient. In …
Reviewer #2 (Public Review):
Using recently-developed functional gradient techniques, this study explored human brain hemispheric asymmetry. The functional gradient is a hot technique in recent years and has been applied to study brain asymmetries in two papers of 2021. Compared to previous studies, the current study further evaluated the degree of genetic control (heritability) and evolutionary conservation for such gradient asymmetries by using human twin data and monkey's fMRI data. These investigations are of value and do provide interesting data. However, it suffers from a lack of specific hypotheses/questions/motivations underlying all kinds of analyses, and the rich observational or correlational results seem not to offer significant improvement of theoretical understanding about brain asymmetries or functional gradient. In addition, given the limited number of twins in HCP project (for a heritability estimation), the limited number of monkeys (20 monkeys), and the relatively poor quality of monkeys' resting functional MRI data, the results and conclusion should be taken cautiously. Below are major concerns and suggestions.
The gradient from resting-state functional connectome has been frequently used but mainly at the group level. The current study essentially applied the gradient comparison (i.e., gradient score) at the individual level. Biological interpretation for individual gradient score at the parcel level as well as its comparability between individuals and between hemispheres should be resolved. This is the fundamental rationale underlying the whole analyses.
Only the first three gradients are used but why? What about the fourth gradient? Specific theoretical interpretation is needed. At the individual level, is it ensured that the first gradients of all individuals correspond to each other? In this study, it is unclear whether we should or should not care about the G2 and G3. The results of G2 and G3 showed up randomly to some degree.
The intra-hemispheric gradient is institutive. However, it is hard to understand what the inter-hemispheric gradient means. From the data perspective, yes you can do such gradient comparison between the LR and RL connectome but what does this mean? Why should we care about such asymmetry? From the introduction to the discussion, the authors simply showed the data of inter-hemispheric gradients without useful explanation. This issue should be solved.
When aligning intra-hemispheric gradient, choosing averaged LL mode as the reference may introduce systematic bias towards left hemisphere. Such an issue also applies to LR-RL gradient alignment as well as cross-species gradient alignment. This methodological issue should be solved.
The sample size of monkey (i.e., 20) is far less than human subjects (> 1000). Such limitation raises severe concern on the validity of the currently observed gradient asymmetry pattern in the monkey group, as well as the similarity results with human gradient asymmetry pattern. Despite the marginal significance of G1 inter-hemisphere gradient between humans and monkeys, I feel overall there is no convincingly meaningful similarity between these two species. However, the authors' discussion and conclusion are largely based on strong inter-species similarity in such asymmetry. The conclusion of evolutionary conservation for gradient asymmetry, therefore, is not well supported by the results.
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