A Hidden Markov Random Field Model for Detecting Domain Organizations from Spatial Transcriptomic Data

  • Qian ZhuEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 1935)


Cells in complex tissues are organized by distinct microenvironments and anatomical structures. This spatial environment of cells is thought to be important for division of labor and other specialized functions of tissues. Recently developed spatial transcriptomic technologies enable the quantification of expression of hundreds of genes while accounting for cells’ spatial coordinates, providing an opportunity to study spatially organized structures. Here, we describe a computational pipeline for detecting the spatial organization of cells based on a hidden Markov random field model. We illustrate this pipeline with data generated from multiplexed smFISH from the adult mouse visual cortex.

Key words

Hidden Markov random field Spatial organization Sequential fluorescence in situ hybridization Multiplexed fluorescence in situ hybridization 


  1. 1.
    Deng Q, Ramsköld D, Reinius B, Sandberg R (2014) Single-cell RNA-seq reveals dynamic, random monoallelic gene expression in mammalian cells. Science 343:193–196. Scholar
  2. 2.
    Jaitin DA, Kenigsberg E, Keren-Shaul H et al (2014) Massively parallel single cell RNA-Seq for marker-free decomposition of tissues into cell types. Science 343:776–779. Scholar
  3. 3.
    Macosko EZ, Basu A, Regev A et al (2015) Highly parallel genome-wide expression profiling of individual cells using Nanoliter droplets. Cell 161:1202–1214. Scholar
  4. 4.
    Schiffenbauer YS, Kalma Y, Trubniykov E et al (2011) Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells. Cell 161:1187–1201. Scholar
  5. 5.
    Halpern KB, Shenhav R, Matcovitch-Natan O et al (2017) Single-cell spatial reconstruction reveals global division of labour in the mammalian liver. Nature 542:1–5. Scholar
  6. 6.
    Lein ES, Hawrylycz MJ, Ao N et al (2006) Genome-wide atlas of gene expression in the adult mouse brain. Nature 445:168–176. Scholar
  7. 7.
    Raj A, van den Bogaard P, Rifkin SA et al (2008) Imaging individual mRNA molecules using multiple singly labeled probes. Nat Methods 5:877–879. Scholar
  8. 8.
    Lubeck E, Cai L (2012) Single-cell systems biology by super-resolution imaging and combinatorial labeling. Nat Methods 9:743–748. Scholar
  9. 9.
    Chen KH, Boettiger AN, Moffitt JR et al (2015) Spatially resolved, highly multiplexed RNA profiling in single cells. Science 348. Scholar
  10. 10.
    Moffitt JR, Hao J, Bambah-Mukku D et al (2016) High-performance multiplexed fluorescence in situ hybridization in culture and tissue with matrix imprinting and clearing. Proc Natl Acad Sci 113:14456–14461. Scholar
  11. 11.
    Shah S, Lubeck E, Zhou W, Cai L (2016) In situ transcription profiling of single cells reveals spatial organization of cells in the mouse Hippocampus. Neuron 92:342–357. Scholar
  12. 12.
    Zhu Q, Shah S, Dries R et al (2018) Identification of spatially associated subpopulations by combining scRNAseq and sequential fluorescence in situ hybridization data. Nat Biotechnol. Scholar
  13. 13.
    Ståhl PL, Salmén F, Vickovic S et al (2016) Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353:78–82. Scholar
  14. 14.
    Wang Q (2012) HMRF-EM-image: implementation of the hidden markov random field model and its expectation-maximization algorithm. arXiv PreprGoogle Scholar
  15. 15.
    Li SZ (2009) Markov random field modeling in image analysisGoogle Scholar
  16. 16.
    Li SZ (2003) Modeling image analysis problems using Markov random fields. Stoch Process Model Simul 473Google Scholar
  17. 17.
    Obayashi T, Kinoshita K (2011) COXPRESdb: a database to compare gene coexpression in seven model animals. Nucleic Acids Res 39:D1016–D1022CrossRefGoogle Scholar
  18. 18.
    Tasic B, Menon V, Nguyen TN et al (2016) Adult mouse cortical cell taxonomy revealed by single cell transcriptomics. Nat Neurosci 19:335–346. Scholar
  19. 19.
    Chung NC, Storey JD (2015) Statistical significance of variables driving systematic variation in high-dimensional data. Bioinformatics 31:545–554. Scholar
  20. 20.
    Brélaz D (1979) New methods to color the vertices of a graph. Commun ACM 22:251–256. Scholar
  21. 21.
    Finak G, McDavid A, Yajima M et al (2015) MAST: a flexible statistical framework for assessing transcriptional changes and characterizing heterogeneity in single-cell RNA sequencing data. Genome Biol 16:278. Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dana-Farber Cancer InstituteBostonUSA

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