Using co-localization priors and microenvironment statistics to reconstruct tissue organization from single-cell data
Abstract
Unveiling spatial expression patterns across tissues has been key for studying developmental processes, division of labor mechanisms, as well as variations in health and disease.
Along the rapid development of improved experimental assays, computational methods have been shown to successfully recover spatial information from non-spatial single-cell data using reference atlases and/or assumptions about tissue organization such as relative smoothness of expression.
However, spatial reconstruction can still be challenging for complex tissues, especially given a limited reference atlas.
Here we show how information about tissue microenvironments statistics, such as cell type neighborhoods, or co-localization priors, can enhance tissue reconstruction in such cases.
Specifically, we incorporate co-localization priors as a generalization of novoSpaRc, an optimal transportbased framework for tissue reconstruction given single-cell data, which relies at its core on an interpolation between a structural correspondence assumption between expression and physical space and a potential reference atlas.
We demonstrate that incorporating cell type co-localization priors can enhance the reconstruction of the mammalian organ of Corti and testicular spatial structure.
Introduction
The collective behavior and division of labor of cells in tissues, in health and disease, relies on their interactions and global organization [1, 2, 3].
Computationally inferring such organization and spatial expression patterns from single-cell data, such as single-cell RNA-sequencing (scRNA-seq) data, is a rapidly-developing field which includes diverse methodologies, relying on multiple types of prior knowledge [4, 5, 6].
Still, methods struggle with reconstruction of complex, disordered tissues, especially where a reference atlas is limited.
Importantly, different tissues, even complex and globally disordered, were shown to exhibit specific spatial features and cell type co-localization rules [7, 8, 9], which thus can potentially contribute to spatial reconstruction.
Here we integrate such spatial features and generalize novoSpaRc, an optimal-transport-based method for tissue reconstruction [4, 10].
novoSpaRc relies on an interpolation between a potentially available reference atlas and a structural correspondence assumption which expresses a hypothesis about an underlying tissue organization principle reflecting relative, averaged smoothness of gene expression across tissues.
This assumption, however, generally holds within a single cell type and not for complex, disordered tissues[4].
We leverage information about local cellular microenvironments statistics, and as a proof of concept, focus on cell-type co-localization statistics, as an additional weighted term in the novoSpaRc framework.
Specifically, we first construct a co-localization matrix which captures cell-type neighborhood statistics which can either be learned from existing data or known a-priori.
Then, the co-localization matrix is integrated into a quadratic term which is added to the objective of the generalized optimal transport formulation of novoSpaRc.
Using two examples of the mouse organ of Corti and testis, we show that co-localization prior can be used for both layered and islet-patterned tissues, and can aid in recovering tissue structure and spatial gene expression patterns.
Methods
Given scRNA-seq gene expression data, X ∈ R N × K ( N cells and K genes), and a target space of M locations corresponding to the physical tissue structure we wish to reconstruct, we aim to infer an embedding T ∈ [0 , 1] N × M of N cells to M locations which takes into consideration and interpolates between three factors: (1) structural correspondence assumption, (2) a reference atlas, and (3) a co-localization prior, in a way which generalizes the novoSpaRc framework [4, 10] to include local microenvironment statistics.
Together, we optimize T via the following generalized optimal-transport formulation:
[Equation] [Equation]
where C P cell ,P loc = (cid:8) T | T ∈ [0 , 1] N × M , T 1 = P cell , 1 T =
P loc (cid:9) , 1 P cell = 1 , P loc 1 = 1 .
The first three terms are interpolated using the non-negative coefficients α, β such that α + β ∈ [0 , 1] .
The first term corresponds to the structural correspondence assumption,
[Equation]
where D exp ∈ R N × N is cell-cell similarity matrix, D phys ∈ R M × M is location-location similarity matrix, and L is a loss function which we take to be the quadratic loss (as described in [4, 10]).
The second term corresponds to the discrepancy between an embedding and knowledge regarding a partial reference atlas,
[Equation]
where D exp,phys ∈ R N × M is a cell-location discrepancy matrix between cells and locations according to an available reference atlas (as described in [4, 10]).
The third term corresponds to co-localization priors,
[Equation]
where L = a · b , D neigh ∈ { 0 , 1 } M × M is the kNN adjacency matrix of locations in the target space.
D coLoc is a matrix corresponding to the agreement between the cellular embedding and the cell types co-localization prior,
[Equation]
where X label ∈ [0 , 1] N × t is a labelled single-cell dataset, and A ∈ R t × t is the co-localization matrix, which captures the ‘attraction’ between t different labels, such as cell types.
Specifically,
A t 1 t 2 describes the likelihood of cell type t 1 to be located in the neighborhood (defined below) of cell type t 2 .
A can be based either on quantitative estimates of spatially-informed measurements of labels (such as those inferred from Slide-seq [11, 12] captured expression), or based on qualitative description of organization.
In the former case, based on label indicators/compositional annotations across the spatial sample, X ′ label ∈ [0 , 1] M ′ × t ( M ′ locations in spatial sample, t labels), and their radius-based nearest neighbors adjacency indicator matrix B ∈ { 0 , 1 } M ′ × M ′ , we compute A = X ′ labelT
· B ·
X ′ label .
In special cases, we can construct a proxy for the co-localization matrix A without requiring a spatial sample of the data, as we show for the layered structure of the organ of Corti example below.
The fourth term corresponds to entropic regularization, where H ( T )
= − (cid:80) ij T ij log ( T ij ) , and ε is a non-negative regularization constant.
Expression over the target space, S ∈ R K × M , is consequently inferred by S = X T T ∗ .
Likewise, labels over the target space, X ∗ label ∈ [0 , 1] M × t , are inferred by X ∗ label =
T ∗ T X label .
We solve this minimization problem using projected gradient descent, a projection based on the Kullback-Leibler metric rewritten as an instance of entropically-regularized optimal transport ([13]), which is then computed using Sinkhorn’s fixed point iteration [14], similarly to [4].
Results Reconstruction of the organ of Corti
The organ of Corti, a hearing receptor located in the mammalian cochlea, consists of ten layers of different cell types that spiral from its base to its apex [15](Figure 1A).
Based on data of the transcriptional profiles of cells in the mammalian organ of Corti collected in [15], the variation in expression across the base-apex axis was recently utilized to computationally order the cells along this axis, for each cell type separately, both in the original study [15] and using novoSpaRc [10].
However, using a similar approach to map all cells together onto a 2-dimensional target space representing the unrolled tissue fails in recovering the layered-cell-type structure (Figure 1C, Figure 1E).
We used the layered structure exhibited by different cell types in the organ of Corti to construct a co-localization matrix of cell types, reflecting the distances between layers along the medial-lateral axis (Figure 1I).
We then mapped all cells simultaneously onto the 2-dimensional target space, using both the cell type co-localization prior and the structural correspondence prior ( Figure 1B,
Figure 1D, Figure 1F).
We find that the two axes of the target space following reconstruction correspond to medial-lateral cell type ordering (X-axis, Figure 1B, Figure 1D) and basal-apical ordering (Y-axis,Figure 1F) of the cells.
The cell type co-localization prior is crucial for faithful reconstruction in this case, which is optimized at an intermediate level of interpolation between the two priors ( β = 0 .
3 ; Figure 1H).
Reconstruction mouse testicular microenvironment
The testis are a well-structured organ consisting of seminiferous tubules with spermatogonial stem cells at their basement membrane, and separated from each other with interstitial space that contains supporting cells like macrophages and endothelial, and cells involved in the regulation of spermatogenesis like Sertoli, and Leydig cells.
Here we aimed to reconstruct a Slide-seq puck of the mouse testis based on its synthetic dissociation [16] (Figure 2A).
First, we tested our method on a patch from the Slide-seq puck, where we both constructed the cell-type co-localization matrix and used it to reconstruct the same patch (Figure 2E).
Similarly to the organ of Corti reconstruction, the co-localization prior enhances the quality of reconstruction of the testicular spatial structure (Figure 2B, Figure 2C).
When interpolating between the co-localization prior and a reference atlas composed of spatial expression of several marker genes (chosen as highly variable genes), we find that while the quality of reconstruction increases with the size of the reference atlas (the number of marker genes used for reconstruction), optimal reconstruction is achieved at intermediate interpolation value ( β = 0 . 4 ), leveraging co-localization information (Figure 2D).
To further test whether co-localization statistics can be learned from one sample and transferred to recover the organization of another, we divided the Slide-seq puck into 16 patches and tested the contribution of the co-localization prior across patches (Figure 3A, Figure 3B, Figure 3C).
We find that even in this more challenging case given an effectively noisy version of a co-localization prior, it contributes to the spatial reconstruction of the tissue with a similar intermediate interpolation value ( β = 0 .
Figure 3D).
Discussion
Here we showed how cell type co-localization statistics can be used to enhance the spatial reconstruction of complex tissues, including the mammalian organ of Corti and testicular spatial structure.
We built on the novoSpaRc [4, 10] framework and demonstrated how interpolating between terms capturing information about either the structural correspondence prior or a reference atlas and colocalization statistics can improve the quality of spatial tissue reconstruction, compared to using only the former terms, respectively.
In this work we aimed to show the potential for using spatial features, such as cell type colocalization statistics, to enhance spatial reconstruction of single-cell data.
We envision that the analysis and incorporation of additional, more complex and more diverse, spatial features could improve tissue reconstruction further, although such complexity will pose more challenging optimization problems.
More complex spatial features could potentially be analyzed and incorporated using flexible frameworks such as Graph Neural Networks.
Together, improving computational methodologies for tissue reconstruction will aid in exposing the structural design principles that shape functional, ordered and disordered tissues.
Acknowledgments and Disclosure of Funding
We thank Zoe Piran and members of our lab for meaningful discussions, and Shahar Nahum for the illustration of the organ of Corti.
This work was funded by the Center for Interdisciplinary
Data Science Research at the Hebrew University of Jerusalem (NM and MN), the Council of Higher
Education (NM), Azrieli Foundation Early Career Faculty Fellowship, Google Research Scholar program, and the European Union (ERC, DecodeSC, 101040660) (MN).
Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European
Union or the European Research Council.
Neither the European Union nor the granting authority can be held responsible for them.
The authors declare no competing interests.