Original: Learning Spatially-Aware Representations of Transcriptomic Data via Transfer Learning
Revised: Learning Spatially-Aware Representations of Transcriptomic Data via Transfer Learning

Original: Abstract
Revised: Abstract

Original: Computationally integrating spatial transcriptomics (ST) and single-cell transcriptomics (SC) greatly beneﬁts biomedical research such as cellular organization,embryogenesis and tumorigenesis, and could further facilitate therapeutic developments.
Revised: Computationally integrating spatial transcriptomics (ST) and single-cell transcriptomics (SC) greatly beneﬁts biomedical research such as cellular organization, embryogenesis and tumorigenesis, and could further facilitate therapeutic developments.

Original: We proposed a transfer learning model, STEM, to learn spatially-awareembeddings from gene expression for both ST and SC data.
Revised: We proposed a transfer learning model, STEM, to learn spatially-aware embeddings from gene expression for both ST and SC data.

Original: The embeddingssatisfy both the preservation of spatial information and the elimination of thedomain gap between SC and ST data.
Revised: The embeddings satisfy both the preservation of spatial information and the elimination of the domain gap between SC and ST data.

Original: We used these embeddings to infer the
Revised: We used these embeddings to infer the

Original: SC-ST mapping and the pseudo SC spatial adjacency, and adopted the attributionfunction to indicate which genes dominate the spatial information.
Revised: SC-ST mapping and the pseudo SC spatial adjacency, and adopted the attribution function to indicate which genes dominate the spatial information.

Original: We designeda comprehensive evaluation pipeline and conducted two simulation experiments,and STEM achieved the best performance compared with previous methods.
Revised: We designed a comprehensive evaluation pipeline and conducted two simulation experiments, and STEM achieved the best performance compared with previous methods.

Original: Weapplied STEM to human squamous cell carcinoma data and successfully uncoveredthe spatial localization of rare cell types.
Revised: We applied STEM to human squamous cell carcinoma data and successfully uncovered the spatial localization of rare cell types.

Original: STEM is a powerful tool for building single-cell level spatial landscapes and could provide mechanistic insights ofheterogeneity and microenvironments in tissues.
Revised: STEM is a powerful tool for building single-cell level spatial landscapes and could provide mechanistic insights of heterogeneity and microenvironments in tissues.

Original:  Introduction
Revised:  Introduction

Original: High-resolution single-cell gene expression data with spatial information is critical for revealingthe mechanisms of cellular organization, embryogenesis and tumorigenesis [1–5], and could furtherfacilitate therapeutic developments [6, 7].
Revised: High-resolution single-cell gene expression data with spatial information is critical for revealing the mechanisms of cellular organization, embryogenesis and tumorigenesis [1–5], and could further facilitate therapeutic developments [6, 7].

Original: Recently, many spatial transcriptomic (ST) proﬁlingprotocols have been developed [8–11].
Revised: Recently, many spatial transcriptomic (ST) proﬁling protocols have been developed [8–11].

Original: The most commonly-used ST protocols aggregate multiplecells into one spot and the provided data contain both spatial coordinates and in-situ gene expressionswith limited resolution and gene coverage [12].
Revised: The most commonly-used ST protocols aggregate multiple cells into one spot, and the provided data contain both spatial coordinates and in-situ gene expressions with limited resolution and gene coverage [12].

Original: On the contrary, single-cell RNA sequencing (SC)captures exact single-cell level transcripts with a higher throughput of gene species [13] but cannotdetect any spatial information.
Revised: On the contrary, single-cell RNA sequencing (SC) captures exact single-cell level transcripts with a higher throughput of gene species [13] but cannot detect any spatial information.

Original: Computationally integrating SC and ST data can build an informativesingle-cell level spatial landscape and beneﬁts studies of both sides [14].
Revised: Computationally integrating SC and ST data can build an informative single-cell level spatial landscape and beneﬁts studies of both sides [14].

Original: For example, inferring thepseudo spatial adjacency association of SC data helps identify spatial structures of cell types or niches[15, 16], and deconvoluting cell type proportions of spots in ST data by using annotated SC data canbeneﬁt the illustration of cell spatial niches and communication landscapes in microenvironments[17–20].
Revised: For example, inferring the pseudo spatial adjacency association of SC data helps identify spatial structures of cell types or niches [15, 16], and deconvoluting cell type proportions of spots in ST data by using annotated SC data can beneﬁt the illustration of cell spatial niches and communication landscapes in microenvironments [17–20].

Original: The core of building a single-cell level spatial landscape is to establish SC-ST and SC-SC spatialassociations.
Revised: The core of building a single-cell level spatial landscape is to establish SC-ST and SC-SC spatial associations.

Original: The computational challenge is to recover the spatial information of SC data, whichrequires us to learn the relation between gene expression proﬁles and locations from ST data andtransfer it to SC data for spatial information inference.
Revised: The computational challenge is to recover the spatial information of SC data, which requires us to learn the relation between gene expression proﬁles and locations from ST data and transfer it to SC data for spatial information inference.

Original: In this study, we proposed a deep transfer learning model, STEM, to learn SpaTially-aware EMbeddings of ST and SC data.
Revised: In this study, we proposed a deep transfer learning model, STEM, to learn SpaTially-aware EMbeddings of ST and SC data.

Original: We designed a shared encoder for SC and ST data to get uniﬁedembeddings in one latent space, and optimized the embeddings to satisfy both the preservation of spatial information and the elimination of the domain gap between SC and ST data.
Revised: We designed a shared encoder for SC and ST data to get uniﬁed embeddings in one latent space, and optimized the embeddings to satisfy both the preservation of spatial information and the elimination of the domain gap between SC and ST data.

Original: We further usedthe embeddings to infer the SC-ST mapping and the pseudo SC spatial adjacency.
Revised: We further used the embeddings to infer the SC-ST mapping and the pseudo SC spatial adjacency.

Original: Compared with existing methods [15, 16, 21–23], STEM overcomes the domain gap between SCand ST data and explicitly extracts the spatial information from gene expression as spatially-awareembeddings.
Revised: Compared with existing methods [15, 16, 21–23], STEM overcomes the domain gap between SC and ST data and explicitly extracts the spatial information from gene expression as spatially-aware embeddings.

Original: Based on the embeddings, STEM provides a ﬂexible and accurate way to infer spatialassociations.
Revised: Based on the embeddings, STEM provides a ﬂexible and accurate way to infer spatial associations.

Original: Moreover, STEM identiﬁes spatially dominant genes (SDGs) that highly dominate theinferred spatial location of a cell, which could beneﬁt the understanding of underlying mechanismsrelated to cellular spatial organization or communication.
Revised: Moreover, STEM identiﬁes spatially dominant genes (SDGs) that highly dominate the inferred spatial location of a cell, which could beneﬁt the understanding of underlying mechanisms related to cellular spatial organization or communication.

Original: We designed a comprehensive pipeline at both single-cell and tissue levels for evaluation, includingexamining the correctness of the predicted SC-ST mapping matrix and the inferred SC spatialadjacency matrix.
Revised: We designed a comprehensive pipeline at both single-cell and tissue levels for evaluation, including examining the correctness of the predicted SC-ST mapping matrix and the inferred SC spatial adjacency matrix.

Original: We conducted two simulation experiments, and the results shown the superiority of
Revised: We conducted two simulation experiments, and the results shown the superiority of

Original: STEM in inferring spatial associations.
Revised: STEM in inferring spatial associations.

Original: We further used STEM to identify SDGs in mouse gastrulationdata [24] and locate enriched regions of rare cell types in human squamous cell carcinoma [19].
Revised: We further used STEM to identify SDGs in mouse gastrulation data [24] and locate enriched regions of rare cell types in human squamous cell carcinoma [19].

Original: These experiments highlight the power of representation learning for extracting spatial informationfrom gene expression, and demonstrate the feasibility of transfer learning models for integrating datain different modalities and constructing cross-domain associations.
Revised: These experiments highlight the power of representation learning for extracting spatial information from gene expression, and demonstrate the feasibility of transfer learning models for integrating data in different modalities and constructing cross-domain associations.

Original:  Task Formulation
Revised:  Task Formulation

Original: ST data include two types of information: a gene expression matrix X ST ∈ R N × K and a spatialcoordinate matrix
Revised: ST data include two types of information: a gene expression matrix X ST ∈ R N × K and a spatial coordinate matrix

Original: Y ST ∈ R N × 2 , where N is the number of sequenced spots and K is the number ofgenes.
Revised: Y ST ∈ R N × 2 , where N is the number of sequenced spots and K is the number of genes.

Original: SC data only have the gene expression matrix X SC ∈ R M × K , where M is the number ofsequenced single cells.
Revised: SC data only have the gene expression matrix X SC ∈ R M × K , where M is the number of sequenced single cells.

Original: As SC and ST data are obtained by different techniques, distributions of geneexpressions within X ST and X SC such as the sparsity and maximum expression values are different.
Revised: As SC and ST data are obtained by different techniques, distributions of gene expressions within X ST and X SC such as the sparsity and maximum expression values are different.

Original: Three goals are needed for establishing SC and ST spatial associations.
Revised: Three goals are needed for establishing SC and ST spatial associations.

Original: The ﬁrst goal is to inferthe spatial information of SC data.
Revised: The ﬁrst goal is to infer the spatial information of SC data.

Original: It can be formulated as a SC adjacency matrix S c ∈ R M × M orthe estimated spatial coordinate ˜ Y SC ∈ R M × 2 .
Revised: It can be formulated as a SC adjacency matrix S c ∈ R M × M or the estimated spatial coordinate ˜ Y SC ∈ R M × 2 .

Original: The second goal is to learn the spatial associationsbetween SC and ST data, and it can be formulated as a SC-ST mapping matrix C ∈ R M × N .
Revised: The second goal is to learn the spatial associations between SC and ST data, and it can be formulated as a SC-ST mapping matrix C ∈ R M × N .

Original: Thethird goal is to know the contribution of genes to determining the spatial location of one single cell,i.e. a gene attribution vector.
Revised: The third goal is to know the contribution of genes to determining the spatial location of one single cell, i.e. a gene attribution vector.

Original: The attribution vector W of a single cell i is deﬁned as
Revised: The attribution vector W of a single cell i is deﬁned as

Original: [Equation]
Revised: [Equation]

Original: where F is an attribution function, the vector C i is the corresponding row in the mapping matrix C ,and a j is the contribution of gene j to the mapping result C i .
Revised: where F is an attribution function, the vector C i is the corresponding row in the mapping matrix C , and a j is the contribution of gene j to the mapping result C i .

Original: The vector W can be further used toidentify SDGs.
Revised: The vector W can be further used to identify SDGs.

Original:  Methodology
Revised:  Methodology

Original: STEM is in an encoder-predictor fashion (Fig. 1).
Revised: STEM is in an encoder-predictor fashion (Fig. 1).

Original: The encoder represents SC and ST gene expressionvectors as embeddings in a uniﬁed latent space.
Revised: The encoder represents SC and ST gene expression vectors as embeddings in a uniﬁed latent space.

Original: The embeddings are simultaneously optimizedby two modules of predictor: the spatial information extracting module and the domain alignmentmodule.
Revised: The embeddings are simultaneously optimized by two modules of predictor: the spatial information extracting module and the domain alignment module.

Original: These two modules predict the same ST spatial adjacency in different ways.
Revised: These two modules predict the same ST spatial adjacency in different ways.

Original: The spatialinformation extracting module only uses the ST embeddings and guarantees the learned embeddingscontain spatial information extracted from the gene expression.
Revised: The spatial information extracting module only uses the ST embeddings and guarantees the learned embeddings contain spatial information extracted from the gene expression.

Original: The domain alignment module uses
Revised: The domain alignment module uses

Original: SC and ST embeddings and eliminates the SC-ST domain gap by ﬁrst minimizing the Maximum
Revised: SC and ST embeddings and eliminates the SC-ST domain gap by ﬁrst minimizing the Maximum

Original: Mean Discrepancy (MMD) [25] of SC and ST embeddings and then constructing ST-SC-ST spatialassociations as ST adjacency to ﬁnd the optimal mapping matrix C .
Revised: Mean Discrepancy (MMD) [25] of SC and ST embeddings and then constructing ST-SC-ST spatial associations as ST adjacency to ﬁnd the optimal mapping matrix C .

Original: After training, the embeddings of SC and ST are used to infer SC-ST mapping matrix and SC-SCspatial adjacency matrix.
Revised: After training, the embeddings of SC and ST are used to infer SC-ST mapping matrix and SC-SC spatial adjacency matrix.

Original: The SDGs are found by applying the integrated gradient [26] technique asan attribution function upon the trained model.
Revised: The SDGs are found by applying the integrated gradient [26] technique as an attribution function upon the trained model.

Original: Encoder We input SC and ST gene expression vectors (rows in X SC or X ST ) into one encoder.
Revised: Encoder We input SC and ST gene expression vectors (rows in X SC or X ST ) into one encoder.

Original: As one spot in ST data contains more than one cell in SC data, the number of expressed genes inone spot is usually more than that in one cell.
Revised: As one spot in ST data contains more than one cell in SC data, the number of expressed genes in one spot is usually more than that in one cell.

Original: To make our model robust to data sparsity, We add anadditional dropout layer [27] for ST data before the encoder.
Revised: To make our model robust to data sparsity, We add an additional dropout layer [27] for ST data before the encoder.

Original: The dropout rate d is deﬁned as follows:
Revised: The dropout rate d is deﬁned as follows:

Original: [Figure]

Original: [Equation]
Revised: [Equation]

Original: where n SC and n ST represent the number of expressed gene species in each cell or spot, respectively.
Revised: where n SC and n ST represent the number of expressed gene species in each cell or spot, respectively.

Original: We use a MLP encoder to embed the expression vectors into latent embeddings Z ST ∈ R h and
Revised: We use a MLP encoder to embed the expression vectors into latent embeddings Z ST ∈ R h and

Original: Z SC ∈ R h with the same dimension size h .
Revised: Z SC ∈ R h with the same dimension size h .

Original: Predictor part 1: spatial information extracting module We use the ST embeddings Z ST toconstruct the ST spatial adjacency matrix ˜ S and calculate the loss between it and the ground truth STspatial adjacency matrix S .
Revised: Predictor part 1: spatial information extracting module We use the ST embeddings Z ST to construct the ST spatial adjacency matrix ˜ S and calculate the loss between it and the ground truth ST spatial adjacency matrix S .

Original: The ground truth matrix S is created from the spatial coordinate labelsvia a spatial kernel function φ which could be Gaussian, Mahalanobis or others.
Revised: The ground truth matrix S is created from the spatial coordinate labels via a spatial kernel function φ which could be Gaussian, Mahalanobis or others.

Original: Here we use the
Revised: Here we use the

Original: Gaussian kernel (see Appendix 1 for details).
Revised: Gaussian kernel (see Appendix 1 for details).

Original: We apply the L1 normalization over columns in S tolet the sum of adjacency values of each spot be 1:
Revised: We apply the L1 normalization over columns in S to let the sum of adjacency values of each spot be 1:

Original: [Equation]
Revised: [Equation]

Original: Meanwhile, the predicted ˜ S matrix is measured by the inner product of two ST embedding vectorswith softmaxing over columns:
Revised: Meanwhile, the predicted ˜ S matrix is measured by the inner product of two ST embedding vectors with softmaxing over columns:

Original: [Equation]
Revised: [Equation]

Original: We use the cross entropy H to calculate the loss between ˜ S and S :
Revised: We use the cross entropy H to calculate the loss between ˜ S and S :

Original: [Equation]
Revised: [Equation]

Original: Predictor part 2: domain alignment module We reduce the mean distance between ST and
Revised: Predictor part 2: domain alignment module We reduce the mean distance between ST and

Original: SC embeddings, and use these embeddings to estimate the SC-ST and ST-SC mapping matrices.
Revised: SC embeddings, and use these embeddings to estimate the SC-ST and ST-SC mapping matrices.

Original: Then we exploit two mapping matrices to construct another two-step ST spatial adjacency matrixˆ S .
Revised: Then we exploit two mapping matrices to construct another two-step ST spatial adjacency matrix ˆ S .

Original: As ˆ S depends on the SC-ST cross-domain spatial relationship, we can indirectly ﬁnd the optimalcross-domain relationship by directly optimizing ˆ S .
Revised: As ˆ S depends on the SC-ST cross-domain spatial relationship, we can indirectly ﬁnd the optimal cross-domain relationship by directly optimizing ˆ S .

Original: The similar idea is proposed in the Haeusser’swork [28, 29].
Revised: The similar idea is proposed in the Haeusser’s work [28, 29].

Original: In our work, we extend its applicability from classiﬁcation to relation construction andfully utilize the cross domain association matrix as the SC-ST mapping matrix.
Revised: In our work, we extend its applicability from classiﬁcation to relation construction and fully utilize the cross domain association matrix as the SC-ST mapping matrix.

Original: We introduce the MMD loss on SC embeddings Z SC and ST embeddings Z ST in a mini-batch toreduce the mean distance between them (Appendix 2):
Revised: We introduce the MMD loss on SC embeddings Z SC and ST embeddings Z ST in a mini-batch to reduce the mean distance between them (Appendix 2):

Original: [Equation]
Revised: [Equation]

Original: We get the similarity between ST and SC embeddings as B ij := < Z SCi , Z STj > .
Revised: We get the similarity between ST and SC embeddings as B ij := < Z SCi , Z STj > .

Original: We deﬁne themapping matrix C ∈ R M × N from SC to ST by softmaxing B over columns: 
Revised: We deﬁne the mapping matrix C ∈ R M × N from SC to ST by softmaxing B over columns: [Equation] ij

Original: [Equation]
Revised: [Equation]

Original: We also deﬁne the mapping matrix from ST to SC ˆ C ∈ R N × M by replacing B with B T .
Revised: We also deﬁne the mapping matrix from ST to SC ˆ C ∈ R N × M by replacing B with B T .

Original: We can getthe two-step spatial adjacency matrix ˆ S ∈ R N × N from ST to ST as:
Revised: We can get the two-step spatial adjacency matrix ˆ S ∈ R N × N from ST to ST as:

Original: [Equation]
Revised: [Equation]

Original: where
Revised: where

Original: [Equation]
Revised: [Equation]

Original: We calculate the cross entropy loss between ˆ S and the ground truth spatial adjacency matrix S :
Revised: We calculate the cross entropy loss between ˆ S and the ground truth spatial adjacency matrix S :

Original: [Equation]
Revised: [Equation]

Original: The total loss of our model consists of three parts (Equation 5, 6 and 9):
Revised: The total loss of our model consists of three parts (Equation 5, 6 and 9):

Original: [Equation]
Revised: [Equation]

Original: We set the hyper parameter α = 0 .
Revised: We set the hyper parameter α = 0 .

Original: 2 and gradually increase β from 0 to 1 during training, whichenforces the model ﬁrst to rebuild the spatial adjacency in ST and then learn the spatial mappingbetween ST and SC.
Revised: 2 and gradually increase β from 0 to 1 during training, which enforces the model ﬁrst to rebuild the spatial adjacency in ST and then learn the spatial mapping between ST and SC.

Original: Attribution function The integrated gradient (IG) requires three parts for computing attributions:the input and output of the deep learning model, and a baseline input (Appendix 3).
Revised: Attribution function The integrated gradient (IG) requires three parts for computing attributions: the input and output of the deep learning model, and a baseline input (Appendix 3).

Original: For cell i in SCdata, we set the input as the corresponding SC gene expression vector X SCi , the baseline as a zerovector, and the output as the maximum value in the corresponding row in the mapping matrix C i · :
Revised: For cell i in SC data, we set the input as the corresponding SC gene expression vector X SCi , the baseline as a zero vector, and the output as the maximum value in the corresponding row in the mapping matrix C i · :

Original: [Equation]
Revised: [Equation]

Original: As the maximum value of C i · indicates that this cell has the maximum probability located aroundsome ST spot, the attribution vector shows the contribution of genes for determining this spatiallocation.
Revised: As the maximum value of C i · indicates that this cell has the maximum probability located around some ST spot, the attribution vector shows the contribution of genes for determining this spatial location.

Original: We use the attribution function to get the gene attribution vector of each cell in SC data andgroup all attribution vectors by cell annotation (e.g. cell type or spatial regions).
Revised: We use the attribution function to get the gene attribution vector of each cell in SC data and group all attribution vectors by cell annotation (e.g. cell type or spatial regions).

Original: For a cell group ofinterest, we perform the one-versus-others Wilcoxon test [25] and deﬁne genes that have signiﬁcantlyhigher values in that group as SDGs.
Revised: For a cell group of interest, we perform the one-versus-others Wilcoxon test [25] and deﬁne genes that have signiﬁcantly higher values in that group as SDGs.

Original:  Experimental design 
Revised:  Experimental design 4.1 Evaluation pipeline

Original: 4.1 Evaluation pipeline

Original: We design a comprehensive evaluation pipeline which includes three processes: simulation datageneration, output uniﬁcation, and performance evaluation (Fig. 2).
Revised: We design a comprehensive evaluation pipeline which includes three processes: simulation data generation, output uniﬁcation, and performance evaluation (Fig. 2).

Original: Simulation data generation Transcriptomic data with spatial information at the single-cell resolution is required for evaluating the methods’ ability of inferring spatial associations.
Revised: Simulation data generation Transcriptomic data with spatial information at the single-cell resolution is required for evaluating the methods’ ability of inferring spatial associations.

Original: Currently, suchdata can only be provided by some less popular spatial sequencing technologies [8, 30–32] which arelow-throughput and require complicated operations.
Revised: Currently, such data can only be provided by some less popular spatial sequencing technologies [8, 30–32] which are low-throughput and require complicated operations.

Original: We take these experimental single-cell resolutionspatial transcriptomic data as SC data with the ground-truth spatial information, and simulate pseudo
Revised: We take these experimental single-cell resolution spatial transcriptomic data as SC data with the ground-truth spatial information, and simulate pseudo

Original: ST data by creating a spatial grid on the spatial space of these data.
Revised: ST data by creating a spatial grid on the spatial space of these data.

Original: The detailed simulation processcan be found in Appendix 4.
Revised: The detailed simulation process can be found in Appendix 4.

Original: Each spot in the simulated pseudo ST data has the information of geneexpression, spatial coordinate and cell type proportion.
Revised: Each spot in the simulated pseudo ST data has the information of gene expression, spatial coordinate and cell type proportion.

Original: Output uniﬁcation To make the results comparable, we unify the outputs of different methodsinto three parts: the SC spatial adjacency matrix, the reconstructed SC spatial coordinates and the
Revised: Output uniﬁcation To make the results comparable, we unify the outputs of different methods into three parts: the SC spatial adjacency matrix, the reconstructed SC spatial coordinates and the

Original: SC-ST mapping matrix.
Revised: SC-ST mapping matrix.

Original: For methods that predict SC coordinates, the SC-ST mapping matrix and
Revised: For methods that predict SC coordinates, the SC-ST mapping matrix and

Original: SC adjacency matrix are obtained by calculating the spatial distance between or within single cellsand spots.
Revised: SC adjacency matrix are obtained by calculating the spatial distance between or within single cells and spots.

Original: The closer the spatial distance between the cells or spots, the higher the weight in thematrix.
Revised: The closer the spatial distance between the cells or spots, the higher the weight in the matrix.

Original: For other methods that provide the SC-ST mapping matrix, the SC coordinates are obtainedby averaging the coordinates of spots according to the mapping weights.
Revised: For other methods that provide the SC-ST mapping matrix, the SC coordinates are obtained by averaging the coordinates of spots according to the mapping weights.

Original: Performance evaluation For the ﬁrst and second goals, we validate the model performance at thesingle-cell level and tissue level, respectively.
Revised: Performance evaluation For the ﬁrst and second goals, we validate the model performance at the single-cell level and tissue level, respectively.

Original: For the third goal, it is worth emphasizing that ourmodel STEM is the only one that could achieve it, and thus we validate the detected SDGs by knownknowledge.
Revised: For the third goal, it is worth emphasizing that our model STEM is the only one that could achieve it, and thus we validate the detected SDGs by known knowledge.

Original: At the single-cell level, we focus on whether the spatial association within single cellscan be inferred.
Revised: At the single-cell level, we focus on whether the spatial association within single cells can be inferred.

Original: We use the mean squared error (MSE) as the error metric between the predicted andtrue spatial coordinates.
Revised: We use the mean squared error (MSE) as the error metric between the predicted and true spatial coordinates.

Original: As the number of reference spots ( K ref ) may affect the predicted coordinateresults, we calculate MSEs under different K ref .
Revised: As the number of reference spots ( K ref ) may affect the predicted coordinate results, we calculate MSEs under different K ref .

Original: To measure the models’ ability of constructing thespatial relationship among cells, we use the SC spatial adjacency matrix to calculate the hit numberwhich is deﬁned as the number of one cell’s K-nearest neighbors that are successfully predicted.
Revised: To measure the models’ ability of constructing the spatial relationship among cells, we use the SC spatial adjacency matrix to calculate the hit number which is deﬁned as the number of one cell’s K-nearest neighbors that are successfully predicted.

Original: Atthe tissue level, we focus on whether the cell type information can be correctly mapped from singlecells to spots through the SC-ST mapping matrix.
Revised: At the tissue level, we focus on whether the cell type information can be correctly mapped from single cells to spots through the SC-ST mapping matrix.

Original: We calculate the Pearson correlation coefﬁcient(PCC) between the predicted and true cell type spatial distribution.
Revised: We calculate the Pearson correlation coefﬁcient (PCC) between the predicted and true cell type spatial distribution.

Original: 4.2 Simulation experiments
Revised: 4.2 Simulation experiments

Original: We conducted simulation experiments on two datasets with the evaluation pipeline.
Revised: We conducted simulation experiments on two datasets with the evaluation pipeline.

Original: The ﬁrst datasetis single-cell resolution mouse gastrulation data generated by seqFISH [30].
Revised: The ﬁrst dataset is single-cell resolution mouse gastrulation data generated by seqFISH [30].

Original: The second dataset ismouse hippocampus data generated by Slide-seq V2 [8] with a spatial resolution of 10 µm whichis comparable to the size of a cell.
Revised: The second dataset is mouse hippocampus data generated by Slide-seq V2 [8] with a spatial resolution of 10 µm which is comparable to the size of a cell.

Original: Both of the datasets consist of gene expression proﬁles, spatialcoordinates and cell type information, and we treated them as SC data with true spatial coordinates.
Revised: Both of the datasets consist of gene expression proﬁles, spatial coordinates and cell type information, and we treated them as SC data with true spatial coordinates.

Original: We compared STEM with ﬁve methods, including Seurat [21], Tangram [22], SpaOTsc [23], Celltrek[16] and scSpace [15].
Revised: We compared STEM with ﬁve methods, including Seurat [21], Tangram [22], SpaOTsc [23], Celltrek [16] and scSpace [15].

Original: Seurat integrates SC and ST data by performing canonical correlation analysison gene expression data.
Revised: Seurat integrates SC and ST data by performing canonical correlation analysis on gene expression data.

Original: Tangram optimizes the mapping matrix between SC and ST data byminimizing the cosine distance between predicted and true gene expression.
Revised: Tangram optimizes the mapping matrix between SC and ST data by minimizing the cosine distance between predicted and true gene expression.

Original: SpaOTsc introducesstructured and unbalanced optimal transport to integrate SC and ST data.
Revised: SpaOTsc introduces structured and unbalanced optimal transport to integrate SC and ST data.

Original: Celltrek builds a graphcontaining both SC and ST nodes based on the random forest distance and estimates the spatialcoordinates of SC data.
Revised: Celltrek builds a graph containing both SC and ST nodes based on the random forest distance and estimates the spatial coordinates of SC data.

Original: scSpace uses transfer component analysis to directly estimate the spatialcoordinates.
Revised: scSpace uses transfer component analysis to directly estimate the spatial coordinates.

Original: The original outputs of these approaches are summarized in Table 1.
Revised: The original outputs of these approaches are summarized in Table 1.

Original: We ran all thesemethods with default parameters and uniﬁed the outputs.
Revised: We ran all these methods with default parameters and uniﬁed the outputs.

Original: The embedding-based calculation makes
Revised: The embedding-based calculation makes

Original: STEM the only one that satisﬁes both goal without any additional result transformation.
Revised: STEM the only one that satisﬁes both goal without any additional result transformation.

Original: [Table]

Original: 4.3 Real data application
Revised: 4.3 Real data application

Original: We applied STEM to human squamous cell carcinoma (hSCC) data.
Revised: We applied STEM to human squamous cell carcinoma (hSCC) data.

Original: The data are obtained from Ji’sstudy [19] and contain paired SC and ST data from the same donor.
Revised: The data are obtained from Ji’s study [19] and contain paired SC and ST data from the same donor.

Original: The true spatial associationbetween SC and ST data is unknown.
Revised: The true spatial association between SC and ST data is unknown.

Original: We trained a model for each donor.
Revised: We trained a model for each donor.

Original: To explore the results, Weﬁrst veriﬁed whether STEM can reproduce the conclusion reported in the original study, and thenused STEM to gain new biological insights. 
Revised: To explore the results, We ﬁrst veriﬁed whether STEM can reproduce the conclusion reported in the original study, and then used STEM to gain new biological insights. [Table]

Original: 4.4 Implementation details
Revised: 4.4 Implementation details

Original: STEM is based on the publicly available Pytorch [33] platform.
Revised: STEM is based on the publicly available Pytorch [33] platform.

Original: The encoder is a three-layer MLPwith LayerNorm [34] regularization and ReLU activation.
Revised: The encoder is a three-layer MLP with LayerNorm [34] regularization and ReLU activation.

Original: The hidden size is 512, 256 and 128,respectively.
Revised: The hidden size is 512, 256 and 128, respectively.

Original: The dropout rate of the Dropout Layer is 0.6, 0.8 and 0.2 for gastrulation, hippocampusand hSCC data, respectively.
Revised: The dropout rate of the Dropout Layer is 0.6, 0.8 and 0.2 for gastrulation, hippocampus and hSCC data, respectively.

Original: During training, the AdamW [35] optimizer is applied with defaultparameters.
Revised: During training, the AdamW [35] optimizer is applied with default parameters.

Original: We took all SC and ST data in one training step, and sampled 2,000 SC and ST data for
Revised: We took all SC and ST data in one training step, and sampled 2,000 SC and ST data for

Original: MMD Loss.
Revised: MMD Loss.

Original: We didn’t observe any performance improvement by setting a larger sample size.
Revised: We didn’t observe any performance improvement by setting a larger sample size.

Original: Weused the Captum [36] package to implement the integrated gradient technique.
Revised: We used the Captum [36] package to implement the integrated gradient technique.

Original: With one NVIDIA
Revised: With one NVIDIA

Original: GeForce RTX 3090 GPU, the training process takes around 5-10 minutes.
Revised: GeForce RTX 3090 GPU, the training process takes around 5-10 minutes.

Original:  Results 
Revised:  Results 5.1 Results on simulation data 5.1.1 At the single-cell level

Original: 5.1 Results on simulation data 5.1.1 At the single-cell level

Original: Compared with other methods, STEM achieved the lowest MSE for predicting the absolute spatialcoordinates (Fig. A2).
Revised: Compared with other methods, STEM achieved the lowest MSE for predicting the absolute spatial coordinates (Fig. A2).

Original: Moreover, we found that STEM achieved the lowest MSE in the majorityof cell groups with different cell type annotations (Fig.
Revised: Moreover, we found that STEM achieved the lowest MSE in the majority of cell groups with different cell type annotations (Fig.

Original: A3 and A4), demonstrating that cell typeinformation does not affect the model’s ability of extracting spatial information from expressionvalues.
Revised: A3 and A4), demonstrating that cell type information does not affect the model’s ability of extracting spatial information from expression values.

Original: Under different numbers of reference spots K ref (Table 2 and 3 right), STEM also achievedthe lowest MSE.
Revised: Under different numbers of reference spots K ref (Table 2 and 3 right), STEM also achieved the lowest MSE.

Original: We observed that the MSE of STEM was decreased and converged as the numberof reference spots increases.
Revised: We observed that the MSE of STEM was decreased and converged as the number of reference spots increases.

Original: The error of Tangram and Seurat was stable, and the error of SpaOTscincreased as the reference number increased.
Revised: The error of Tangram and Seurat was stable, and the error of SpaOTsc increased as the reference number increased.

Original: We then assessed the methods’ ability of constructing the spatial relationship among single cells.
Revised: We then assessed the methods’ ability of constructing the spatial relationship among single cells.

Original: onthe gastrulation data, STEM got the highest hit number, about two times as many as the second-placemethod (Fig. 3a).
Revised: on the gastrulation data, STEM got the highest hit number, about two times as many as the second-place method (Fig. 3a).

Original: When the true neighbor number K nbr = 200 , STEM found more than 80 correctneighbors.
Revised: When the true neighbor number K nbr = 200 , STEM found more than 80 correct neighbors.

Original: On the hippocampus data, STEM had a comparable performance with Tangram when
Revised: On the hippocampus data, STEM had a comparable performance with Tangram when

Original: K nbr ≤ 100 , and had a higher improvement as K nbr increased.
Revised: K nbr ≤ [Table] and had a higher improvement as K nbr increased.

Original: And other methods showed relativelylow hit numbers.
Revised: And other methods showed relatively low hit numbers.

Original: These results show that the spatial association inferred by STEM is more consistentwith the actual spatial distribution for single-cell data.
Revised: These results show that the spatial association inferred by STEM is more consistent with the actual spatial distribution for single-cell data

Original: [Table]
Revised: [Table]

Revised: [Table]

Revised: [Table]

Original: [Table]
Revised: [Table]

Original: 5.1.2 At the tissue level
Revised: 5.1.2 At the tissue level

Original: As shown in Fig.
Revised: As shown in Fig.

Original: A5, STEM and Tangram had the comparable performance across all cell types onthe gastrulation data.
Revised: A [Table] STEM and Tangram had the comparable performance across all cell types on the gastrulation data.

Original: All methods achieved PCCs higher than 0.6 for all cell types except for Seuratand scSpace.
Revised: All methods achieved PCCs higher than 0.6 for all cell types except for Seurat and scSpace.

Original: Seurat transfers cell type information from SC to ST data only using gene expressioninformation, and scSpace focuses on reconstructing the spatial location of single cells in the latentspace, which may lead to the low efﬁciency of these two methods in restoring the SC-ST spatialassociation.
Revised: Seurat transfers cell type information from SC to ST data only using gene expression information, and scSpace focuses on reconstructing the spatial location of single cells in the latent space, which may lead to the low efﬁciency of these two methods in restoring the SC-ST spatial association.

Original: STEM got higher correlations on cardiomyocytes, gut tube, brain and spinal cord (Table2 left).
Revised: STEM got higher correlations on cardiomyocytes, gut tube, brain and spinal cord (Table 2 left).

Original: By visually checking these cell types, we found that they exhibit stronger signals in spatialdistributions compared with other cell types (Fig. A6).
Revised: By visually checking these cell types, we found that they exhibit stronger signals in spatial distributions compared with other cell types (Fig. A6).

Original: From the biological perspective, the functionsof these cells are highly correlated with the region they are located, so it is more easily to infer theirspatial location information from gene expression proﬁles.
Revised: From the biological perspective, the functions of these cells are highly correlated with the region they are located, so it is more easily to infer their spatial location information from gene expression proﬁles.

Original: For example, cells in forebrain, midbrainand hindbrain subregions participate in different functional processes, have different cell fates, andthus highly express different gene sets [24].
Revised: For example, cells in forebrain, midbrain and hindbrain subregions participate in different functional processes, have different cell fates, and thus highly express different gene sets [24].

Original: On the hippocampus data, the predicted distribution of different cell types is shown in Fig.
Revised: On the hippocampus data, the predicted distribution of different cell types is shown in Fig.

Original: A7.
Revised: A7.

Original: Weobserved that the performance of all methods was decreased (Table 3 left) in comparison with that ofthe gastrulation data, which may be because the SC data used here are not at real single-cell resolution.
Revised: We observed that the performance of all methods was decreased (Table 3 left) in comparison with that of the gastrulation data, which may be because the SC data used here are not at real single-cell resolution.

Original: STEM and Tangram were the only two methods to achieve PCCs above 0.5 on all cell types (Fig.
Revised: STEM and Tangram were the only two methods to achieve PCCs above 0.5 on all cell types (Fig.

Original: A8).
Revised: A8).

Original: STEM showed higher PCCs on astrocytes, Cornu Ammonis (CA) regions, dentate pyramids of0.73, 0.86 and 0.79, respectively.
Revised: STEM showed higher PCCs on astrocytes, Cornu Ammonis (CA) regions, dentate pyramids of 0.73, 0.86 and 0.79, respectively.

Original: These results support our intuition that by supervising the two-stepspatial adjacency matrix in the association module, a good SC-ST mapping matrix could be learned.
Revised: These results support our intuition that by supervising the two-step spatial adjacency matrix in the association module, a good SC-ST mapping matrix could be learned.

Original: 5.1.3 Spatial dominate genes
Revised: 5.1.3 Spatial dominate genes

Original: We followed Lohoff’s work [24] to spatially separate the gut tube into the dorsal side and ventralside on the gastrulation data.
Revised: We followed Lohoff’s work [24] to spatially separate the gut tube into the dorsal side and ventral side on the gastrulation data.

Original: We found that Tbx1 , Smoc2 and Kmt2b are SDGs for the dorsal side,and Sox4 , Osr1 and Podxl are SDGs for the ventral side (Fig. 3b).
Revised: We found that Tbx1 , Smoc2 and Kmt2b are SDGs for the dorsal side, and Sox4 , Osr1 and Podxl are SDGs for the ventral side (Fig. 3b).

Original: Among these SDGs, the spatialpatterns of Tbx1 and Smoc2 have been validated by the hybridization chain reaction experiments inthe previous study [24].
Revised: Among these SDGs, the spatial patterns of Tbx1 and Smoc2 have been validated by the hybridization chain reaction experiments in the previous study [24].

Original: We performed a similar procedure on the brain region of gastrulation data tospatially separate it into 3 subregions: forebrain, midbrain and hindbrain.
Revised: We performed a similar procedure on the brain region of gastrulation data to spatially separate it into 3 subregions: forebrain, midbrain and hindbrain.

Original: We uncovered Fezf1 , Irx3and Sfrp1 are the representative SDGs of these three subregions, respectively (Fig. 3c).
Revised: We uncovered Fezf1 , Irx and Sfrp1 are the representative SDGs of these three subregions, respectively (Fig. 3c).

Original: All these genes have been identiﬁed as marker genes of the corresponding brain region in previous studies[37–39].
Revised: All these genes have been identiﬁed as marker genes of the corresponding brain region in previous studies [37–39].

Original: STEM could reveal SDGs in a continuous manner.
Revised: STEM could reveal SDGs in a continuous manner.

Original: We focused on the spinal cord region and generateda spatial trajectory through its spatial distribution.
Revised: We focused on the spinal cord region and generated a spatial trajectory through its spatial distribution.

Original: Along the trajectory curve, we found several
Revised: Along the trajectory curve, we found several

Original: SDGs including Hoxb1 , Pcdh19 , Sfrp1 and Marcks that showed continuous trends (Fig. 3d).
Revised: SDGs including Hoxb1 , Pcdh19 , Sfrp1 and Marcks that showed continuous trends (Fig. 3d).

Original: Theseresults demonstrate that STEM successfully identiﬁes marker genes that have high contributions fordetermining cell location, which could provide insights into the spatial formation and evolution ofcells in complex normal tissues or tumor microenvironments.
Revised: These results demonstrate that STEM successfully identiﬁes marker genes that have high contributions for determining cell location, which could provide insights into the spatial formation and evolution of cells in complex normal tissues or tumor microenvironments.

Original: 5.2 Discovery on the real dataset
Revised: 5.2 Discovery on the real dataset

Original: We used STEM to map all the single cells in the hSCC data into the tissue spatial space (Fig. 4a).
Revised: We used STEM to map all the single cells in the hSCC data into the tissue spatial space (Fig. 4a).

Original: We checked whether the results obtained by STEM support the known descriptions illustrated by theoriginal paper.
Revised: We checked whether the results obtained by STEM support the known descriptions illustrated by the original paper.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: 4b, we veriﬁed that a sub-cell type called tumor speciﬁc keratinocyte(TSK) is colocalized with the cancer-associated ﬁbroblast and endothelial cell at the tumor leadingedge.
Revised: 4b, we veriﬁed that a sub-cell type called tumor speciﬁc keratinocyte (TSK) is colocalized with the cancer-associated ﬁbroblast and endothelial cell at the tumor leading edge.

Original: We compared the estimated location of TSKs with the sc-TSK score deﬁned by Ji’s study [19](Fig. A9), and found STEM located TSKs in the high-score region.
Revised: We compared the estimated location of TSKs with the sc-TSK score deﬁned by Ji’s study [19] (Fig. A9), and found STEM located TSKs in the high-score region.

Original: We then explored the spatialdistribution of other keratinocyte (KC) subtypes, including normal, tumor basal, tumor cycling, andtumor differentiating KCs.
Revised: We then explored the spatial distribution of other keratinocyte (KC) subtypes, including normal, tumor basal, tumor cycling, and tumor differentiating KCs.

Original: We found that TSKs are spatially distant from them (Fig. 4c).
Revised: We found that TSKs are spatially distant from them (Fig. 4c).

Original: This ﬁndingsuggests that the formation of TSKs may be caused by the difference in microenvironment.
Revised: This ﬁnding suggests that the formation of TSKs may be caused by the difference in microenvironment.

Original: We alsofound that pDC cells are located in the non-TSK leading edge region (Fig. 4d), which unveils themechanism of the ﬁnding reported in the original paper that pDC-enriched gene functions are activein this region.c) Spatial distribution of other KC subtypes. d) Spatial distribution of pDC cells.
Revised: We also found that pDC cells are located in the non-TSK leading edge region (Fig. 4d), which unveils the mechanism of the ﬁnding reported in the original paper that pDC-enriched gene functions are active in this region.

Original:  Discussion
Revised:  Discussion

Original: Computationally building the spatial gene expression landscape at the single cell level can promoteour understanding of heterogeneity and microenvironments in tissues.
Revised: Computationally building the spatial gene expression landscape at the single cell level can promote our understanding of heterogeneity and microenvironments in tissues.

Original: We proposed a model, STEM,to learn the spatially-aware representations of transcriptomic data via transfer learning.
Revised: We proposed a model, STEM, to learn the spatially-aware representations of transcriptomic data via transfer learning.

Original: We designeda comprehensive pipeline to evaluate the different methods’ ability of inferring spatial associations,which could serve as a benchmark for future work.
Revised: We designed a comprehensive pipeline to evaluate the different methods’ ability of inferring spatial associations, which could serve as a benchmark for future work.

Original: We conducted two simulation experiments and onereal dataset application.
Revised: We conducted two simulation experiments and one real dataset application.

Original: The results proved the superiority of STEM compared with other methods.
Revised: The results proved the superiority of STEM compared with other methods.

Original: STEM is a powerful model to build up a single-cell level spatial landscape by integrating SCand ST data in a uniﬁed embedding space.
Revised: STEM is a powerful model to build up a single-cell level spatial landscape by integrating SC and ST data in a uniﬁed embedding space.

Original: Upon the model, the attribution technique is used tocomputationally highlight the SDGs with high contributions to cells’ spatial location.
Revised: Upon the model, the attribution technique is used to computationally highlight the SDGs with high contributions to cells’ spatial location.

Original: These SDGscould beneﬁt the discovery of biological mechanisms and even potential drug targets.
Revised: These SDGs could beneﬁt the discovery of biological mechanisms and even potential drug targets.

Original: STEM takes the advantage of deep transfer learning to eliminate the SC-ST domain gap and inferspatial associations between and within domains.
Revised: STEM takes the advantage of deep transfer learning to eliminate the SC-ST domain gap and infer spatial associations between and within domains.

Original: Our work demonstrates that transfer learning couldnot only unify data in different domains but also be feasible to establish mapping across domains, andknowledge can be discovered from the mapping via the attribution technique or other approaches. 
Revised: Our work demonstrates that transfer learning could not only unify data in different domains but also be feasible to establish mapping across domains, and knowledge can be discovered from the mapping via the attribution technique or other approaches. Acknowledgments and Disclosure of Funding

Revised: The authors thank Sijie Chen, Haoxiang Gao and Yixin Chen for their helpful discussions.

Revised: This work was partially supported by National Natural Science Foundation of China(NSFC) (grants 62250005, 61721003 and 62103227), National Key R&D Program of China (grant 2021YFF1200901) and Tsinghua-Fuzhou Institute for Data Technology (TFIDT2021005).

Original:  Spatial adjacency matrix
Revised: Appendix Spatial adjacency matrix

Original: Giving the ground truth ST data spatial coordinate Y ST ∈ R N × 2 , the pairwise spatial associationstrength S ij in the ST spatial adjacency matrix S is calculated by the kernel function betweencoordinate Y STi of cell i and Y STj of cell j .
Revised: Giving the ground truth ST data spatial coordinate Y ST ∈ R N × 2 , the pairwise spatial association strength S ij in the ST spatial adjacency matrix S is calculated by the kernel function between coordinate Y STi of cell i and Y STj of cell j .

Original: In our work we use the Gaussian kernel function:
Revised: In our work we use the Gaussian kernel function:

Original: [Equation]
Revised: [Equation]

Original: where σ is the standard deviation and controls the width of the Gaussian ’bell’.
Revised: where σ is the standard deviation and controls the width of the Gaussian ’bell’.

Original: To select a propersize of σ , on the two simulation data we traversed the values from 0 to 3 times of distance betweentwo adjacent spots, and use the hit number as the evaluation metric.
Revised: To select a proper size of σ , on the two simulation data we traversed the values from 0 to 3 times of distance between two adjacent spots, and use the hit number as the evaluation metric.

Original: We found that by setting σ as thehalf of the adjacent distance ( σ = 3 on the gastrulation data and σ = 55 on the hippocampus data),our model achieved the highest hit number.
Revised: We found that by setting σ as the half of the adjacent distance ( σ = 3 on the gastrulation data and σ = 55 on the hippocampus data), our model achieved the highest hit number.

Original:  Maximum mean discrepancy
Revised:  Maximum mean discrepancy

Original: Maximum mean discrepancy (MMD) is a distance between the mean embeddings of distributionsdeﬁned in a reproducing kernel Hilbert space H k with a characteristic kernel k .
Revised: Maximum mean discrepancy (MMD) is a distance between the mean embeddings of distributions deﬁned in a reproducing kernel Hilbert space H k with a characteristic kernel k .

Original: It has widely appliedin Transfer Learning models.
Revised: It has widely applied in Transfer Learning models.

Original: In general, the data X in source domain follows the distribution P x ,and the data Y in target domain follow the distribution P y .
Revised: In general, the data X in source domain follows the distribution P x , and the data Y in target domain follow the distribution P y .

Original: And the mean embeddings of thesedistributions P x and P y in H are unique elements µ k
Revised: And the mean embeddings of these distributions P x and P y in H are unique elements µ k

Original: ( P x ) and µ k ( P y ) .
Revised: ( P x ) and µ k ( P y ) .

Original: Then the MMD is
Revised: Then the MMD is

Original: [Equation]
Revised: [Equation]

Original: In practice, this distance has its empirical estimation via the kernel trick.
Revised: In practice, this distance has its empirical estimation via the kernel trick.

Original: In our work, we implementedthe multi-kernel MMD, and each kernel has is the Gaussian kernel with different bandwidth.
Revised: In our work, we implemented the multi-kernel MMD, and each kernel has is the Gaussian kernel with different bandwidth.

Original:  Integrated gradient
Revised:  Integrated gradient

Original: A common way for humans to perform attribution relies on counterfactual intuition.
Revised: A common way for humans to perform attribution relies on counterfactual intuition.

Original: To assign blameto a certain cause, the Integrated Gradient technology implicitly consider the absence of the causeas a baseline for comparing outcomes.
Revised: To assign blame to a certain cause, the Integrated Gradient technology implicitly consider the absence of the cause as a baseline for comparing outcomes.

Original: Speciﬁcally, the absence is modeled as a baseline inputvector.
Revised: Speciﬁcally, the absence is modeled as a baseline input vector.

Original: For a deep neural network F : R n → [0 , 1] , let x be the input and x (cid:48) be the baseline.
Revised: For a deep neural network F : R n → [0 , 1] , let x be the input and x (cid:48) be the baseline.

Original: Theintegrated gradient (IG) is the gradient at all points along the path from the baseline x (cid:48) to the input x .
Revised: The integrated gradient (IG) is the gradient at all points along the path from the baseline x (cid:48) to the input x .

Original: Speciﬁcally, For i th dimension for an input, the integrated gradient is deﬁned as follows:
Revised: Speciﬁcally, For i th dimension for an input, the integrated gradient is deﬁned as follows:

Original: [Equation]
Revised: [Equation]

Original: Compared with other attribution methods, the IG satisﬁes the axiom of sensitivity while the otherslike gradients-based methods violate sensitivity.
Revised: Compared with other attribution methods, the IG satisﬁes the axiom of sensitivity while the others like gradients-based methods violate sensitivity.

Original: The sensitivity is deﬁned as: If for every input andbaseline that differ in one feature and have different predictions, the differing feature should be givena non-zero attribution.
Revised: The sensitivity is deﬁned as: If for every input and baseline that differ in one feature and have different predictions, the differing feature should be given a non-zero attribution.

Original:  Simulation data generation
Revised:  Simulation data generation

Original: We placed the pseudo ST spots on the crossing point of the grid.
Revised: We placed the pseudo ST spots on the crossing point of the grid.

Original: We generated a 30 × 40 grid and50 × 30 grid for gastrulation and hippocampus data, respectively.
Revised: We generated a 30 × 40 grid and 50 × 30 grid for gastrulation and hippocampus data, respectively.

Original: The gene expression proﬁle ofeach spot is obtained by summing the expression of its surrounding single cells.
Revised: The gene expression proﬁle of each spot is obtained by summing the expression of its surrounding single cells.

Original: We kept the spotswhich contains more than 3 cells.
Revised: We kept the spots which contains more than 3 cells.

Original: It is noticeable that in real spatial data the tissue cannot be fullycovered by spots, so the transcripts of some single cells cannot be captured.
Revised: It is noticeable that in real spatial data the tissue cannot be fully covered by spots, so the transcripts of some single cells cannot be captured.

Original: We also take this intoaccount in the simulation process.
Revised: We also take this into account in the simulation process.

Original: The gene expression of each spot aggregates only about 50-70%of the local surrounding single cells.
Revised: The gene expression of each spot aggregates only about 50-70% of the local surrounding single cells.

Original: In other words, one-third of single cells gene expression proﬁlesare not included in the ST data.
Revised: In other words, one-third of single cells gene expression proﬁles are not included in the ST data.

Original: As shown in Fig.
Revised: As shown in Fig.

Original: A1, only the cells in red compose the spot data.
Revised: A1, only the cells in red compose the spot data.

Original: Then the cell type proportion of each spot is calculated based on its contained single cells.
Revised: Then the cell type proportion of each spot is calculated based on its contained single cells.

Original: So thegenerated pseudo ST data contain gene expression proﬁle, spatial coordinate and cell type proportioninformation.
Revised: So the generated pseudo ST data contain gene expression proﬁle, spatial coordinate and cell type proportion information.

Original: For gene selection, we kept all 351 genes on the gastrulation data and selected the top5,000 highly variable genes for SC and ST data on the hippocampus data.
Revised: For gene selection, we kept all 351 genes on the gastrulation data and selected the top 5,000 highly variable genes for SC and ST data on the hippocampus data.

Original:  Supplemental Figures
Revised:  Supplemental Figures

Original: [Figure]