A network regularized linear model to infer spatial expression pattern for single cell
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eLife Assessment
The study is useful for advancing spatial transcriptomics through its novel regression-based linear model (glmSMA) that integrates single-cell RNA-seq with spatial reference atlases, though its methodological framework remains incomplete regarding spatial communication applications and feature dependence. The approach demonstrates notable utility by enabling higher-resolution cell mapping across multiple biological systems and spatial platforms compared to existing tools.
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Abstract
Spatial transcriptomics, situated at the intersection of genomics and spatial biology, offers profound insights into the spatial organization of gene expression within tissues. However, its potential has been constrained by either limited resolution or throughput. While single-cell RNA-seq allows for in-depth profiling of cellular gene expression, the crucial spatial information is often sacrificed during sample collection. In a groundbreaking fusion of these two techniques, our research introduces the glmSMA computational algorithm. This innovative approach aims to predict cell locations by integrating scRNA-seq data with spatial-omics reference atlases. The essence of glmSMA lies in formulating cell mapping as a convex problem, strategically minimizing differences between cellular expression profiles and location expression profiles through L1 and Generalized L2 regularization. Our algorithm has undergone rigorous testing across diverse tissues, including mouse brain, drosophila embryo, and human PDAC samples. The compelling results validate glmSMA’s efficacy, demonstrating its capability to faithfully recapitulate spatial gene expression and anatomical structures. This marks a significant stride forward in overcoming the limitations of existing spatial transcriptomic techniques.
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eLife Assessment
The study is useful for advancing spatial transcriptomics through its novel regression-based linear model (glmSMA) that integrates single-cell RNA-seq with spatial reference atlases, though its methodological framework remains incomplete regarding spatial communication applications and feature dependence. The approach demonstrates notable utility by enabling higher-resolution cell mapping across multiple biological systems and spatial platforms compared to existing tools.
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Reviewer #1 (Public review):
Liu et al., present glmSMA, a network-regularized linear model that integrates single-cell RNA-seq data with spatial transcriptomics, enabling high-resolution mapping of cellular locations across diverse datasets. Its dual regularization framework (L1 for sparsity and generalized L2 via a graph Laplacian for spatial smoothness) demonstrates robust performance of their model and offers novel tools for spatial biology, despite some gaps in fully addressing spatial communication.
Overall, the manuscript is commendable for its comprehensive benchmarking across different spatial omics platforms and its novel application of regularized linear models for cell mapping. I think this manuscript can be improved by addressing method assumptions, expanding the discussion on feature dependence and cell type-specific …
Reviewer #1 (Public review):
Liu et al., present glmSMA, a network-regularized linear model that integrates single-cell RNA-seq data with spatial transcriptomics, enabling high-resolution mapping of cellular locations across diverse datasets. Its dual regularization framework (L1 for sparsity and generalized L2 via a graph Laplacian for spatial smoothness) demonstrates robust performance of their model and offers novel tools for spatial biology, despite some gaps in fully addressing spatial communication.
Overall, the manuscript is commendable for its comprehensive benchmarking across different spatial omics platforms and its novel application of regularized linear models for cell mapping. I think this manuscript can be improved by addressing method assumptions, expanding the discussion on feature dependence and cell type-specific biases, and clarifying the mechanism of spatial communication.
The conclusions of this paper are mostly well supported by data, but some aspects of model development and performance evaluation need to be clarified and extended.
(1) What were the assumptions made behind the model? One of them could be the linear relationship between cellular gene expression and spatial location. In complex biological tissues, non-linear relationships could be present, and this would also vary across organ systems and species. Similarly, with regularization parameters, they can be tuned to balance sparsity and smoothness adequately but may not hold uniformly across different tissue types or data quality levels. The model also seems to assume independent errors with normal distribution and linear additive effects - a simplification that may overlook overdispersion or heteroscedasticity commonly observed in RNA-seq data.
(2) The performance of glmSMA is likely sensitive to the number and quality of features used. With too few features, the model may struggle to anchor cells correctly due to insufficient discriminatory power, whereas too many features could lead to overfitting unless appropriately regularized. The manuscript briefly acknowledges this issue, but further systematic evaluation of how varying feature numbers affect mapping accuracy would strengthen the claims, particularly in settings where marker gene availability is limited. A simple way to show some of this would be testing on multiple spatial omics (imaging-based) platforms with varying panel sizes and organ systems. Related to this, based on the figures, it also seems like the performance varies by cell type. What are the factors that contribute to this? Variability in expression levels, RNA quantity/quality? Biases in the panel? Personally, I am also curious how this model can be used similarly/differently if we have a FISH-based, high-plex reference atlas. Additional explanation around these points would be helpful for the readers.
(3) Application 3 (spatial communication) in the graphical abstract appears relatively underdeveloped. While it is clear that the model infers spatial proximities, further explanation of how these mappings translate into insights into cell-cell communication networks would enhance the biological relevance of the findings.
(4) What is the final resolution of the model outputs? I am assuming this is dictated by the granularity of the reference atlas and the imposed sparsity via the L1 norm, but if there are clear examples that would be good. In figures (or maybe in practice too), cells seem to be assigned to small, contiguous patches rather than pinpoint single-cell locations, which is a pragmatic compromise given the inherent limitations of current spatial transcriptomics technologies. Clarification on the precise spatial scale (e.g., pixel or micrometer resolution) and any post-mapping refinement steps would be beneficial for the users to make informed decisions on the right bioinformatic tools to use.
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Reviewer #2 (Public review):
Summary:
The author proposes a novel method for mapping single-cell data to specific locations with higher resolution than several existing tools.
Strengths:
The spatial mapping tests were conducted on various tissues, including the mouse cortex, human PDAC, and intestinal villus.
Weaknesses:
(1) Although the researchers claim that glmSMA seamlessly accommodates both sequencing-based and image-based spatial transcriptomics (ST) data, their testing primarily focused on sequencing-based ST data, such as Visium and Slide-seq. To demonstrate its versatility for spatial analysis, the authors should extend their evaluation to imaging-based spatial data.
(2) The definition of "ground truth" for spatial distribution is unclear. A more detailed explanation is needed on how the "ground truth" was established for each …
Reviewer #2 (Public review):
Summary:
The author proposes a novel method for mapping single-cell data to specific locations with higher resolution than several existing tools.
Strengths:
The spatial mapping tests were conducted on various tissues, including the mouse cortex, human PDAC, and intestinal villus.
Weaknesses:
(1) Although the researchers claim that glmSMA seamlessly accommodates both sequencing-based and image-based spatial transcriptomics (ST) data, their testing primarily focused on sequencing-based ST data, such as Visium and Slide-seq. To demonstrate its versatility for spatial analysis, the authors should extend their evaluation to imaging-based spatial data.
(2) The definition of "ground truth" for spatial distribution is unclear. A more detailed explanation is needed on how the "ground truth" was established for each spatial dataset and how it was utilized for comparison with the predicted distribution generated by various spatial mapping tools.
(3) In the analysis of spatial mapping results using intestinal villus tissue, only Figure 3d supports their findings. The researchers should consider adding supplemental figures illustrating the spatial distribution of single cells in comparison to the ground truth distribution to enhance the clarity and robustness of their investigation.
(4) The spatial mapping tests were conducted on various tissues, including the mouse cortex, human PDAC, and intestinal villus. However, the original anatomical regions are not displayed, making it difficult to directly compare them with the predicted mapping results. Providing ground truth distributions for each tested tissue would enhance clarity and facilitate interpretation. For instance, in Figure 2a and Supplementary Figures 1 and 2, only the predicted mapping results are shown without the corresponding original spatial distribution of regions in the mouse cortex. Additionally, in Figure 3c, four anatomical regions are displayed, but it is unclear whether the figure represents the original spatial regions or those predicted by glmSMA. The authors are encouraged to clarify this by incorporating ground truth distributions for each tissue.
(5) The cell assignment results from the mouse hippocampus (Supplementary Figure 6) lack a corresponding ground truth distribution for comparison. DG and CA cells were evaluated solely based on the gene expression of specific marker genes. Additional analyses are needed to further validate the robustness of glmSMA's mapping performance on Slide-seq data from the mouse hippocampus.
(6) The tested spatial datasets primarily consist of highly structured tissues with well-defined anatomical regions, such as the brain and intestinal villus. It remains unclear whether glmSMA can be effectively applied to tissue types where anatomical regions are not distinctly separated, such as liver tissue. Further evaluation of such tissues would help determine the method's broader applicability.
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Reviewer #3 (Public review):
Summary:
The authors aim to develop glmSMA, a network-regularized linear model that accurately infers spatial gene expression patterns by integrating single-cell RNA sequencing data with spatial transcriptomics reference atlases. Their goal is to reconstruct the spatial organization of individual cells within tissues, overcoming the limitations of existing methods that either lack spatial resolution or sensitivity.
Strengths:
(1) Comprehensive Benchmarking:
Compared against CellTrek and Novosparc, glmSMA consistently achieved lower Kullback-Leibler divergence (KL divergence) scores, indicating better cell assignment accuracy.
Outperformed CellTrek in mouse cortex mapping (90% accuracy vs. CellTrek's 60%) and provided more spatially coherent distributions.
(2) Experimental Validation with Multiple Real-World …
Reviewer #3 (Public review):
Summary:
The authors aim to develop glmSMA, a network-regularized linear model that accurately infers spatial gene expression patterns by integrating single-cell RNA sequencing data with spatial transcriptomics reference atlases. Their goal is to reconstruct the spatial organization of individual cells within tissues, overcoming the limitations of existing methods that either lack spatial resolution or sensitivity.
Strengths:
(1) Comprehensive Benchmarking:
Compared against CellTrek and Novosparc, glmSMA consistently achieved lower Kullback-Leibler divergence (KL divergence) scores, indicating better cell assignment accuracy.
Outperformed CellTrek in mouse cortex mapping (90% accuracy vs. CellTrek's 60%) and provided more spatially coherent distributions.
(2) Experimental Validation with Multiple Real-World Datasets:
The study used multiple biological systems (mouse brain, Drosophila embryo, human PDAC, intestinal villus) to demonstrate generalizability.
Validation through correlation analyses, Pearson's coefficient, and KL divergence support the accuracy of glmSMA's predictions.
Weaknesses:
(1) The accuracy of glmSMA depends on the selection of marker genes, which might be limited by current FISH-based reference atlases.
(2) glmSMA operates under the assumption that cells with similar gene expression profiles are likely to be physically close to each other in space which not be true under various heterogeneous environments.
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Author response:
Reviewer #1 (Public review):
Summary:
Liu et al., present glmSMA, a network-regularized linear model that integrates single-cell RNA-seq data with spatial transcriptomics, enabling high-resolution mapping of cellular locations across diverse datasets. Its dual regularization framework (L1 for sparsity and generalized L2 via a graph Laplacian for spatial smoothness) demonstrates robust performance of their model and offers novel tools for spatial biology, despite some gaps in fully addressing spatial communication.
Overall, the manuscript is commendable for its comprehensive benchmarking across different spatial omics platforms and its novel application of regularized linear models for cell mapping. I think this manuscript can be improved by addressing method assumptions, expanding the discussion on feature dependence …
Author response:
Reviewer #1 (Public review):
Summary:
Liu et al., present glmSMA, a network-regularized linear model that integrates single-cell RNA-seq data with spatial transcriptomics, enabling high-resolution mapping of cellular locations across diverse datasets. Its dual regularization framework (L1 for sparsity and generalized L2 via a graph Laplacian for spatial smoothness) demonstrates robust performance of their model and offers novel tools for spatial biology, despite some gaps in fully addressing spatial communication.
Overall, the manuscript is commendable for its comprehensive benchmarking across different spatial omics platforms and its novel application of regularized linear models for cell mapping. I think this manuscript can be improved by addressing method assumptions, expanding the discussion on feature dependence and cell type-specific biases, and clarifying the mechanism of spatial communication.
The conclusions of this paper are mostly well supported by data, but some aspects of model development and performance evaluation need to be clarified and extended.
We thank the reviewer for their thoughtful comments. We will clarify the model assumptions and the feature selection process to make it more understandable. To clarify, the performance of glmSMA does not depend on cell type. For some rare cell types, the small number of cells can lead to a drop in performance. To better illustrate our results and reduce cell type-specific biases, we will shuffle and randomly sample the cell types.
(1) What were the assumptions made behind the model? One of them could be the linear relationship between cellular gene expression and spatial location. In complex biological tissues, non-linear relationships could be present, and this would also vary across organ systems and species. Similarly, with regularization parameters, they can be tuned to balance sparsity and smoothness adequately but may not hold uniformly across different tissue types or data quality levels. The model also seems to assume independent errors with normal distribution and linear additive effects - a simplification that may overlook overdispersion or heteroscedasticity commonly observed in RNA-seq data.
Thank you for this comment. We acknowledge that the non-linear relationships can be present in complex tissues and may not be fully captured by a linear model.
Our choice of a linear model was guided by an investigation of the relationship in the current datasets, which include intestinal villus, mouse brain, and fly embryo.
There is a linear correlation between expression distance and physical distance [Nitzan et al]. Within a given anatomical structure, cells in closer proximity exhibit more similar expression patterns. In tissues where non-linear relationships are more prevalent—such as the human PDAC sample—our mapping results remain robust. We acknowledge that we have not yet tested our algorithm in highly heterogeneous regions like the liver, and we plan to include such analyses in future work if necessary. Regarding the regularization parameters, we agree that the balance between sparsity and smoothness is sensitive to tissue-specific variation and data quality. In our current implementation, we explored a range of values to find robust defaults.
(2) The performance of glmSMA is likely sensitive to the number and quality of features used. With too few features, the model may struggle to anchor cells correctly due to insufficient discriminatory power, whereas too many features could lead to overfitting unless appropriately regularized. The manuscript briefly acknowledges this issue, but further systematic evaluation of how varying feature numbers affect mapping accuracy would strengthen the claims, particularly in settings where marker gene availability is limited. A simple way to show some of this would be testing on multiple spatial omics (imaging-based) platforms with varying panel sizes and organ systems. Related to this, based on the figures, it also seems like the performance varies by cell type. What are the factors that contribute to this? Variability in expression levels, RNA quantity/quality? Biases in the panel? Personally, I am also curious how this model can be used similarly/differently if we have a FISH-based, high-plex reference atlas. Additional explanation around these points would be helpful for the readers.
Thank you for this thoughtful comment. The performance of our method is indeed sensitive to the number and quality of selected features. To optimize feature selection, we employed multiple strategies, including Moran’s I statistic, identification of highly variable genes, and the Seurat pipeline to detect anchor genes linking the spatial transcriptomics data with the reference atlas. The number of selected markers depends on the quality of the data. For high-quality datasets, fewer than 100 markers are typically sufficient for accurate prediction. To address this more clearly, we will revise the manuscript to include detailed descriptions of our feature selection process and demonstrate how varying the number of selected features impacts performance.
We evaluated our method across diverse tissue types and platforms—including Slide-seq, 10x Visium, and Virtual-FISH—which represent both sequencing-based and imaging-based spatial transcriptomics technologies. Our model consistently achieved strong performance across these settings. It's worth noting that the performance of other methods, such as CellTrek [Wei et al] and novoSpaRc [Nitzan et al], also depends heavily on feature selection. In particular, performance degrades substantially when fewer features are used.
We do not believe that the observed performance is directly influenced by cell type composition. Major cell types are typically well-defined, and rare cell types comprise only a small fraction of the dataset. For these rare populations, a single misclassification can disproportionately impact metrics like KL divergence due to small sample size. However, this does not necessarily indicate a systematic cell type–specific bias in the mapping. To mitigate this issue, we will implement shuffling and sampling procedures to reduce potential bias introduced by rare cell types.
(3) Application 3 (spatial communication) in the graphical abstract appears relatively underdeveloped. While it is clear that the model infers spatial proximities, further explanation of how these mappings translate into insights into cell-cell communication networks would enhance the biological relevance of the findings.
Thank you for this valuable feedback. We agree that further elaboration on the connection between spatial proximity and cell–cell communication would enhance the biological interpretation of our results. While our current model focuses on inferring spatial relationships, we may provide some cell-cell communications in the future.
(4) What is the final resolution of the model outputs? I am assuming this is dictated by the granularity of the reference atlas and the imposed sparsity via the L1 norm, but if there are clear examples that would be good. In figures (or maybe in practice too), cells seem to be assigned to small, contiguous patches rather than pinpoint single-cell locations, which is a pragmatic compromise given the inherent limitations of current spatial transcriptomics technologies. Clarification on the precise spatial scale (e.g., pixel or micrometer resolution) and any post-mapping refinement steps would be beneficial for the users to make informed decisions on the right bioinformatic tools to use.
Thank you for the comment. For each cell, our algorithm generates a probability vector that indicates its likely spatial assignment along with coordinate information. We will include the resolution and the number of cells assigned to each spot in future versions. In our framework, each cell is mapped to one or more spatial locations with associated probabilities. Depending on the amount of regularization through L1 and L2 norms, a cell may be localized to a small patch or distributed over a broader domain. For the 10x Visium data, we applied a repelling algorithm to enhance visualization [Wei et al]. If a cell’s original location is already occupied, it is reassigned to a nearby neighborhood to avoid overlap. The users can also see the entire regularization path by varying the penalty terms.
Nitzan M, Karaiskos N, Friedman N, Rajewsky N. Gene expression cartography. Nature. 2019;576(7785):132-137. doi:10.1038/s41586-019-1773-3
Wei, R. et al. (2022) ‘Spatial charting of single-cell transcriptomes in tissues’, Nature Biotechnology, 40(8), pp. 1190–1199. doi:10.1038/s41587-022-01233-1.
Reviewer #2 (Public review):
Summary:
The author proposes a novel method for mapping single-cell data to specific locations with higher resolution than several existing tools.
Thank you for recognizing our contribution. Our goal was to develop a method that achieves higher spatial resolution in mapping single-cell data compared to existing tools. We are encouraged by the results and will continue to refine the approach to improve accuracy and generalizability across platforms and tissue types.
Strengths:
The spatial mapping tests were conducted on various tissues, including the mouse cortex, human PDAC, and intestinal villus.
Thank you for this comment. We believe that evaluating our method across diverse tissue types—such as the mouse cortex, human PDAC, and intestinal villus—demonstrates its robustness and broad applicability. We plan to continue expanding these evaluations to additional tissue contexts and species to further validate the method’s generalizability.
Weakness:
(1) Although the researchers claim that glmSMA seamlessly accommodates both sequencing-based and image-based spatial transcriptomics (ST) data, their testing primarily focused on sequencing-based ST data, such as Visium and Slide-seq. To demonstrate its versatility for spatial analysis, the authors should extend their evaluation to imaging-based spatial data.
Thank you for the comment. We have tested our algorithm on the virtual FISH dataset from the fly embryo, which serves as an example of image-based spatial omics data. However, such datasets often contain a limited number of available genes. To address this, we will conduct additional testing on image-based data if needed. The Allen Brain Atlas provides high-quality ISH data, and we can select specific brain regions from this resource to further evaluate our algorithm if necessary [Lein et al]. Currently, we plan to focus more on the 10x Visium platform, as it supports whole-transcriptome profiling and offers a wide range of tissue samples for analysis.
(2) The definition of "ground truth" for spatial distribution is unclear. A more detailed explanation is needed on how the "ground truth" was established for each spatial dataset and how it was utilized for comparison with the predicted distribution generated by various spatial mapping tools.
Thank you for the comment. To clarify how ground truth is defined across different tissues, we provide the following details. Direct ground truth for cell locations is often unavailable in scRNA-seq data due to experimental constraints. To address this, we adopted alternative strategies for estimating ground truth in each dataset:
- 10x Visium Data: We used the cell type distribution derived from spatial transcriptomics (ST) data as a proxy for ground truth. We then computed the KL divergence between this distribution and our model's predictions for performance assessment.
- Slide-seq Data: We validated predictions by comparing the expression of marker genes between the reconstructed and original spatial data.
- Fly Embryo Data: We used predicted cell locations from novoSpaRc as a reference for evaluating our algorithm.
These strategies allowed us to evaluate model performance even in the absence of direct cell location data. In addition, we can apply multiple evaluation strategies within a single dataset.
(3) In the analysis of spatial mapping results using intestinal villus tissue, only Figure 3d supports their findings. The researchers should consider adding supplemental figures illustrating the spatial distribution of single cells in comparison to the ground truth distribution to enhance the clarity and robustness of their investigation.
Thank you for the comment. We will include additional details for this dataset in the supplementary figures. As the intestinal villus is a relatively simple tissue, most existing algorithms performed well on it. For this reason, we did not initially provide extensive details in the main text.
(4) The spatial mapping tests were conducted on various tissues, including the mouse cortex, human PDAC, and intestinal villus. However, the original anatomical regions are not displayed, making it difficult to directly compare them with the predicted mapping results. Providing ground truth distributions for each tested tissue would enhance clarity and facilitate interpretation. For instance, in Figure 2a and Supplementary Figures 1 and 2, only the predicted mapping results are shown without the corresponding original spatial distribution of regions in the mouse cortex. Additionally, in Figure 3c, four anatomical regions are displayed, but it is unclear whether the figure represents the original spatial regions or those predicted by glmSMA. The authors are encouraged to clarify this by incorporating ground truth distributions for each tissue.
Thank you for the comment. To improve visualization, we will include anatomical structures alongside the mapping results in the next version, wherever such structures are available (e.g., mouse brain cortex, human PDAC sample, etc.). Regions will be color-coded to enhance clarity and make the spatial organization easier to interpret.
(5) The cell assignment results from the mouse hippocampus (Supplementary Figure 6) lack a corresponding ground truth distribution for comparison. DG and CA cells were evaluated solely based on the gene expression of specific marker genes. Additional analyses are needed to further validate the robustness of glmSMA's mapping performance on Slide-seq data from the mouse hippocampus.
Thank you for the comment. The ground truth for DG and CA cells was not available. To better evaluate the model's performance, we will compute the KL divergence between the original and predicted cell type distributions, following the same approach used for the 10x Visium dataset.
(6) The tested spatial datasets primarily consist of highly structured tissues with well-defined anatomical regions, such as the brain and intestinal villus. Anatomical regions are not distinctly separated, such as liver tissue. Further evaluation of such tissues would help determine the method's broader applicability.
Thank you for the comment. We have already tested our algorithm on the fly embryo, where anatomical structures are not well defined or clearly separated. If needed, we can further apply glmSMA to more complex tissues such as the liver. To clarify the role of anatomical structures in our model: glmSMA does not require anatomical information as input. Instead, it leverages a distance matrix between cells to apply L2 norm regularization. Despite the absence of anatomical information, the model still demonstrates strong performance. We will include results to illustrate its effectiveness without anatomical input. Additionally, we plan to evaluate the model on tissues where anatomical regions are not clearly delineated.
Lein, E., Hawrylycz, M., Ao, N. et al. Genome-wide atlas of gene expression in the adult mouse brain. Nature 445, 168–176 (2007). https://doi.org/10.1038/nature05453
Reviewer #3 (Public review):
Summary:
The authors aim to develop glmSMA, a network-regularized linear model that accurately infers spatial gene expression patterns by integrating single-cell RNA sequencing data with spatial transcriptomics reference atlases. Their goal is to reconstruct the spatial organization of individual cells within tissues, overcoming the limitations of existing methods that either lack spatial resolution or sensitivity.
Strengths:
(1) Comprehensive Benchmarking:
Compared against CellTrek and Novosparc, glmSMA consistently achieved lower Kullback-Leibler divergence (KL divergence) scores, indicating better cell assignment accuracy.
Outperformed CellTrek in mouse cortex mapping (90% accuracy vs. CellTrek's 60%) and provided more spatially coherent distributions.
(2) Experimental Validation with Multiple Real-World Datasets:
The study used multiple biological systems (mouse brain, Drosophila embryo, human PDAC, intestinal villus) to demonstrate generalizability.
Validation through correlation analyses, Pearson's coefficient, and KL divergence support the accuracy of glmSMA's predictions.
We thank reviewer #3 for their positive feedback and thoughtful recommendations.
Weaknesses:
(1) The accuracy of glmSMA depends on the selection of marker genes, which might be limited by current FISH-based reference atlases.
We agree that the accuracy of glmSMA is influenced by the selection of marker genes, and that current FISH-based reference atlases may offer a limited gene set. To address this, we incorporate multiple feature selection strategies, including highly variable genes and spatially informative genes (e.g., via Moran’s I), to optimize performance within the available gene space. As more comprehensive reference atlases become available, we expect the model’s accuracy to improve further.
(2) glmSMA operates under the assumption that cells with similar gene expression profiles are likely to be physically close to each other in space which not be true under various heterogeneous environments.
While this assumption effectively captures spatial continuity in many cases, we acknowledge that it may not hold across all biological contexts. To address this, we plan to refine our regularization strategy and evaluate the model's performance in heterogeneous tissue regions.
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