Belayer: Modeling discrete and continuous spatial variation in gene expression from spatially resolved transcriptomics
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Abstract
Spatially resolved transcriptomics (SRT) technologies measure gene expression at known locations in a tissue slice, enabling the identification of spatially varying genes or cell types. Current approaches for these tasks assume either that gene expression varies continuously across a tissue or that a tissue contains a small number of regions with distinct cellular composition. We propose a model for SRT data from layered tissues that includes both continuous and discrete spatial variation in expression and an algorithm, Belayer, to learn the parameters of this model. Belayer models gene expression as a piecewise linear function of the relative depth of a tissue layer with possible discontinuities at layer boundaries. We use conformal maps to model relative depth and derive a dynamic programming algorithm to infer layer boundaries and gene expression functions. Belayer accurately identifies tissue layers and biologically meaningful spatially varying genes in SRT data from the brain and skin.
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CUT&Tag and RNA showed good concordance in spatial patterns.
“These clusters agreed with the anatomical annotation by Nissl staining and showed good concordance between CUT&Tag and RNA in spatial patterns (Fig. 3a–c), which was further confirmed by Belayer34 analysis (Supplementary Fig. 7c).”
From Spatial epigenome–transcriptome co-profiling of mammalian tissues (2023) · cites this paper as [34]
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Wang, W., Zhong, Q., Teng, L., Bhatnagar, N., Sharma, B., Zhang, X., Luther, W., Haynes, L. P., Burgoyne, R. D., Vidal, M., et al. (2013) · Oncogene · doi:10.1038/onc.2013.290 · Cited by 28 · see citing works
Cell type-specific inference of differential expression in spatial transcriptomicsPreprint
Cable, D. M., Murray, E. M., Shanmugam, V., et al. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.12.26.474183 · Cited by 26 · see citing works
Anisotropic Interpolation on Graphs: The Combinatorial Dirichlet Problem
Grady, L. J., & Schwartz, E. L. (2003) · Cited by 24 · see citing works
Estimating and testing multiple structural changes in linear models using band spectral regressions
Yamamoto, Y., & Perrón, P. (2013) · Econometrics Journal · doi:10.1111/ectj.12010 · Cited by 22 · see citing works
Complexin2 modulates working memory-related neural activity in patients with schizophrenia
Haß, J., Walton, E., Kirsten, H., Turner, J. A., Wolthusen, R. P. F., Roessner, V., Sponheim, S. R., Holt, D. J., Gollub, R. L., Calhoun, V. D., et al. (2014) · European Archives of Psychiatry and Clinical Neuroscience · doi:10.1007/s00406-014-0550-4 · Cited by 20 · see citing works
Walter, F. C., Stegle, O., & Velten, B. (2023) · Bioinformatics · doi:10.1093/bioinformatics/btad183 · Cited by 20 · see citing works
Fast Algorithms for Segmented RegressionPreprint
Acharya, J., Diakonikolas, I., Li, J. C. F., et al. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1607.03990 · Cited by 19 · see citing works
Functional Anatomy of the Neural Retina
Marc, R. E. (2008) · Elsevier eBooks · doi:10.1016/b978-1-4160-0016-7.50125-9 · Cited by 17 · see citing works
Hexagonal grid methods with applications to partial differential equations
Lee, D., Tien, H.-C., Luo, C. P., et al. (2013) · International Journal of Computer Mathematics · doi:10.1080/00207160.2013.864392 · Cited by 15 · see citing works
SPICEMIX: Integrative single-cell spatial modeling of cell identityPreprint
Chidester, B., Zhou, T., Alam, S., & Ma, J. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.11.29.383067 · Cited by 11 · see citing works
Nonnegative spatial factorizationPreprint
Townes, F. W., & Engelhardt, B. E. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.06122 · Cited by 7 · see citing works
Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions
Yamamoto, Y., & Perrón, P. (2012) · Institutional Repositories DataBase (IRDB) · Cited by 2 · see citing works
Mapping gradients in the mouse cortex
Bras, A. L. (2019) · Lab Animal · doi:10.1038/s41684-019-0295-9 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- Ahlfors LV (n.d.), Complex Analysis, 2 edn, McGraw-Hill Book Company.
- Martini F, Timmons MJ, Tallitsch RB, Ober WC, Garrison CW, Welch KB & Hutchings RT (2006), Human anatomy, Pearson/Benjamin Cummings San Francisco, CA.
Cited by
Sorted by citations
Spatial epigenome–transcriptome co-profiling of mammalian tissues
Zhang, D., Deng, Y., Kukanja, P., Agirre, E., Bartosovic, M., Dong, M., Ma, C., Ma, S., Su, G., Bao, S., et al. (2023) · Nature · doi:10.1038/s41586-023-05795-1 · Cited by 483 · see citing works
Self-citation
- Authors
- Ma, C., Chitra, U., Zhang, S., & Raphael, B. J.
- Affiliations
- Princeton University (US)
- Corresponding author
- Raphael, Benjamin J.
- Venue
- Cell Systems
- Publisher
- Elsevier BV
- Published
- 2022-10
- Volume
- 13
- Issue
- 10
- Pages
- 786-797.e13
- ISSN
- 2405-4712 (ISSN-L)
- PMC
- PMC9814896
- OpenAlex
- W4306797744
- Cited by
- 27
- References
- 109
- Citations by year
- 2026: 7 · 2025: 5 · 2024: 11 · 2023: 3 · 2022: 1
- FWCI
- 1.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/legal/tdmrep-license (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 383 d)
- doi.org/10.15223/policy-017 (stm-asf)
- doi.org/10.15223/policy-037 (stm-asf)
- doi.org/10.15223/policy-012 (stm-asf)
- doi.org/10.15223/policy-029 (stm-asf)
- doi.org/10.15223/policy-004 (stm-asf)
- Locations
- Cell Systems (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Cancer Institute (U24CA264027)
- National Science Foundation (DGE 2039656)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Keywords
- spatial transcriptomics, layered tissue, conformal mapping, dynamic programming, brain, skin
- MeSH terms
- Algorithms, Transcriptome
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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