Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

FLOW-MAP: a graph-based, force-directed layout algorithm for trajectory mapping in single-cell time course datasets


High-dimensional single-cell technologies present new opportunities for biological discovery, but the complex nature of the resulting datasets makes it challenging to perform comprehensive analysis. One particular challenge is the analysis of single-cell time course datasets: how to identify unique cell populations and track how they change across time points. To facilitate this analysis, we developed FLOW-MAP, a graphical user interface (GUI)-based software tool that uses graph layout analysis with sequential time ordering to visualize cellular trajectories in high-dimensional single-cell datasets obtained from flow cytometry, mass cytometry or single-cell RNA sequencing (scRNAseq) experiments. Here we provide a detailed description of the FLOW-MAP algorithm and how to use the open-source R package FLOWMAPR via its GUI or with text-based commands. This approach can be applied to many dynamic processes, including in vitro stem cell differentiation, in vivo development, oncogenesis, the emergence of drug resistance and cell signaling dynamics. To demonstrate our approach, we perform a step-by-step analysis of a single-cell mass cytometry time course dataset from mouse embryonic stem cells differentiating into the three germ layers: endoderm, mesoderm and ectoderm. In addition, we demonstrate FLOW-MAP analysis of a previously published scRNAseq dataset. Using both synthetic and experimental datasets for comparison, we perform FLOW-MAP analysis side by side with other single-cell analysis methods, to illustrate when it is advantageous to use the FLOW-MAP approach. The protocol takes between 30 min and 1.5 h to complete.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Conceptual overview of FLOWMAPR software.
Fig. 2: FLOW-MAP software GUI interface.
Fig. 3: FLOW-MAP output with extreme parameter settings.
Fig. 4: Comparison of FLOW-MAP to other single-cell analysis tools.
Fig. 5: FLOW-MAP analysis of combined mESC differentiation time course.
Fig. 6: Comparison of protein expression levels in combined mESC differentiation time course.
Fig. 7: FLOW-MAP analysis of mESC differentiation by individual culture conditions.
Fig. 8: FLOW-MAP analysis of hematopoietic transitions in bone marrow measured by scRNAseq.

Data availability

Mass cytometry datasets have been placed on Cytobank for the stem cell differentiation time course ( and synthetic 2D single-cell data ( Original scRNAseq data from Nestorowa et al.42 and Kee et al.65 can be found on NCBI GEO (accession numbers GSE81782 and GSE87069, respectively).

Code availability

The code to run FLOW-MAP has been shared on Github (


  1. 1.

    Spitzer, M. H. & Nolan, G. P. Mass cytometry: single cells, many features. Cell 165, 780–791 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. 2.

    Wagner, A., Regev, A. & Yosef, N. Revealing the vectors of cellular identity with single-cell genomics. Nat. Biotechnol. 34, 1145–1160 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. 3.

    Jolliffe, I. T. Principal Component Analysis (Springer-Verlag, 2002).

  4. 4.

    Ringnér, M. What is principal component analysis? Nat. Biotechnol. 26, 303–304 (2008).

    PubMed  Google Scholar 

  5. 5.

    van der Maaten, L. & Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008).

    Google Scholar 

  6. 6.

    Amir, E. D. et al. viSNE enables visualization of high dimensional single-cell data and reveals phenotypic heterogeneity of leukemia. Nat. Biotechnol. 31, 545–552 (2013).

    CAS  PubMed Central  Google Scholar 

  7. 7.

    Linderman, G. C., Rachh, M., Hoskins, J. G., Steinerberger, S. & Kluger, Y. Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data. Nat. Methods 16, 243–245 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Coifman, R. R. & Lafon, S. Diffusion maps. Appl. Comput. Harmon. Anal. 21, 5–30 (2006).

    Google Scholar 

  9. 9.

    Haghverdi, L., Buettner, F. & Theis, F. J. Diffusion maps for high-dimensional single-cell analysis of differentiation data. Bioinformatics 31, 2989–2998 (2015).

    CAS  PubMed  Google Scholar 

  10. 10.

    Angerer, P. et al. Destiny: diffusion maps for large-scale single-cell data in R. Bioinformatics 32, 1241–1243 (2016).

    CAS  PubMed  Google Scholar 

  11. 11.

    Qiu, P. et al. Extracting a cellular hierarchy from high-dimensional cytometry data with SPADE. Nat. Biotechnol. 29, 886–891 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. 12.

    Anchang, B. et al. Visualization and cellular hierarchy inference of single-cell data using SPADE. Nat. Protoc. 11, 1264–1279 (2016).

    CAS  PubMed  Google Scholar 

  13. 13.

    Bendall, S. C. et al. Single-cell mass cytometry of differential immune and drug responses across a human hematopoietic continuum. Science 332, 687–696 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Trapnell, C. et al. The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells. Nat. Biotechnol. 32, 381–386 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  15. 15.

    Qiu, X. et al. Reversed graph embedding resolves complex single-cell trajectories. Nat. Methods 14, 979–982 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    McInnes, L., Healy, J., Saul, N. & Großberger, L. UMAP: uniform manifold approximation and projection. JOSS 3, 861 (2018).

    Google Scholar 

  17. 17.

    Becht, E. et al. Dimensionality reduction for visualizing single-cell data using UMAP. Nat. Biotechnol. 37, 38–44 (2018).

    Google Scholar 

  18. 18.

    Bendall, S. C. et al. Single-cell trajectory detection uncovers progression and regulatory coordination in human B cell development. Cell 157, 714–725 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Levine, J. H. et al. Data-driven phenotypic dissection of AML reveals progenitor-like cells that correlate with prognosis. Cell 162, 184–197 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Chen, H. et al. Cytofkit: a bioconductor package for an integrated mass cytometry data analysis pipeline. PLoS Comput. Biol. 12, e1005112 (2016).

    PubMed  PubMed Central  Google Scholar 

  21. 21.

    DeTomaso, D. & Yosef, N. FastProject: a tool for low-dimensional analysis of single-cell RNA-Seq data. BMC Bioinforma. 17, 315 (2016).

    Google Scholar 

  22. 22.

    Setty, M. et al. Wishbone identifies bifurcating developmental trajectories from single-cell data. Nat. Biotechnol. 34, 637–645 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

    Li, H. et al. Reference component analysis of single-cell transcriptomes elucidates cellular heterogeneity in human colorectal tumors. Nat. Genet. 49, 708–718 (2017).

    CAS  PubMed  Google Scholar 

  24. 24.

    Wang, B., Zhu, J., Pierson, E., Ramazzotti, D. & Batzoglou, S. Visualization and analysis of single-cell RNA-seq data by kernel-based similarity learning. Nat. Methods 14, 414–416 (2017).

    CAS  PubMed  Google Scholar 

  25. 25.

    Marco, E. et al. Bifurcation analysis of single-cell gene expression data reveals epigenetic landscape. Proc. Natl Acad. Sci. USA 111, E5643–E5650 (2014).

    CAS  PubMed  Google Scholar 

  26. 26.

    Herring, C. A. et al. Unsupervised trajectory analysis of single-cell RNA-Seq and imaging data reveals alternative tuft cell origins in the gut. Cell Syst. 6, 37–51.e9 (2018).

    CAS  PubMed  Google Scholar 

  27. 27.

    Spitzer, M. H. et al. An interactive reference framework for modeling a dynamic immune system. Science 349, 1259425 (2015).

    PubMed  PubMed Central  Google Scholar 

  28. 28.

    Zunder, E. R., Lujan, E., Goltsev, Y., Wernig, M. & Nolan, G. P. A continuous molecular roadmap to iPSC reprogramming through progression analysis ource

  29. 29.

    Jacomy, M., Venturini, T., Heymann, S. & Bastian, M. ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the Gephi software. PLoS ONE 9, e98679 (2014).

    PubMed  PubMed Central  Google Scholar 

  30. 30.

    Bastian, M., Heymann, S. & Jacomy, M. Gephi: an open source software for exploring and manipulating networks. Third Int. AAAI Conf. Weblogs Soc. Media 361–362 (2009).

  31. 31.

    Weinreb, C., Wolock, S. & Klein, A. M. SPRING: a kinetic interface for visualizing high dimensional single-cell expression data. Bioinformatics 34, 1246–1248 (2018).

    CAS  PubMed  Google Scholar 

  32. 32.

    Tusi, B. K. et al. Population snapshots predict early haematopoietic and erythroid hierarchies. Nature 555, 54–60 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. 33.

    Saelens, W., Cannoodt, R., Todorov, H. & Saeys, Y. A comparison of single-cell trajectory inference methods. Nat. Biotechnol. 37, 547–554 (2019).

    CAS  PubMed  Google Scholar 

  34. 34.

    Cannoodt, R., Saelens, W. & Saeys, Y. Computational methods for trajectory inference from single-cell transcriptomics. Eur. J. Immunol. 46, 2496–2506 (2016).

    CAS  PubMed  Google Scholar 

  35. 35.

    Wolf, F. A. et al. PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells. Genome Biol. 20, 59 (2019).

    PubMed  PubMed Central  Google Scholar 

  36. 36.

    Setty, M. et al. Characterization of cell fate probabilities in single-cell data with Palantir. Nat. Biotechnol. 37, 451–460 (2019).

    CAS  PubMed  Google Scholar 

  37. 37.

    Moffitt, J. R. et al. High-throughput single-cell gene-expression profiling with multiplexed error-robust fluorescence in situ hybridization. Proc. Natl Acad. Sci. USA 113, 11046–11051 (2016).

    CAS  PubMed  Google Scholar 

  38. 38.

    Angelo, M. et al. Multiplexed ion beam imaging of human breast tumors. Nat. Med. 20, 436–442 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. 39.

    Giesen, C. et al. Highly multiplexed imaging of tumor tissues with subcellular resolution by mass cytometry. Nat. Methods 11, 417–422 (2014).

    CAS  PubMed  Google Scholar 

  40. 40.

    Buettner, F. & Theis, F. J. A novel approach for resolving differences in single-cell gene expression patterns from zygote to blastocyst. Bioinformatics 28, i626–i632 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  41. 41.

    Fischer, D. S. et al. Inferring population dynamics from single-cell RNA-sequencing time series data. Nat. Biotechnol. 37, 461–468 (2019).

    CAS  PubMed  Google Scholar 

  42. 42.

    Nestorowa, S. et al. A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation. Blood 128, e20–e31 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. 43.

    Butler, A., Hoffman, P., Smibert, P., Papalexi, E. & Satija, R. Integrating single-cell transcriptomic data across different conditions, technologies, and species. Nat. Biotechnol. 36, 411–420 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Tenenbaum, J. B., de Silva, V. & Langford, J. C. A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000).

    CAS  PubMed  Google Scholar 

  45. 45.

    Cacciatore, S., Luchinat, C. & Tenori, L. Knowledge discovery by accuracy maximization. Proc. Natl Acad. Sci. USA 111, 5117–5122 (2014).

    CAS  PubMed  Google Scholar 

  46. 46.

    Morrison, G. M. et al. Anterior definitive endoderm from ESCs reveals a role for FGF signaling. Cell Stem Cell 3, 402–415 (2008).

    CAS  PubMed  Google Scholar 

  47. 47.

    Nostro, M. C., Cheng, X., Keller, G. M. & Gadue, P. Wnt, activin, and BMP signaling regulate distinct stages in the developmental pathway from embryonic stem cells to blood. Cell Stem Cell 2, 60–71 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. 48.

    Ying, Q.-L., Stavridis, M., Griffiths, D., Li, M. & Smith, A. Conversion of embryonic stem cells into neuroectodermal precursors in adherent monoculture. Nat. Biotechnol. 21, 183–186 (2003).

    CAS  PubMed  Google Scholar 

  49. 49.

    Zunder, E. R. et al. Palladium-based mass tag cell barcoding with a doublet-filtering scheme and single-cell deconvolution algorithm. Nat. Protoc. 10, 316–333 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Bandura, D. R. et al. Mass cytometry: technique for real time single cell multitarget immunoassay based on inductively coupled plasma time-of-flight mass spectrometry. Anal. Chem. 81, 6813–6822 (2009).

    CAS  PubMed  Google Scholar 

  51. 51.

    Ornatsky, O. et al. Highly multiparametric analysis by mass cytometry. J. Immunol. Methods 361, 1–20 (2010).

    CAS  PubMed  Google Scholar 

  52. 52.

    Finck, R. et al. Normalization of mass cytometry data with bead standards. Cytom. A 83, 483–494 (2013).

    Google Scholar 

  53. 53.

    Fread, K. I., Strickland, W. D., Nolan, G. P. & Zunder, E. R. An updated debarcoding tool for mass cytometry with cell type-specific and cell sample-specific stringency adjustment. Pac. Symp. Biocomput. 22, 588–598 (2017).

    PubMed  Google Scholar 

  54. 54.

    Kotecha, N., Krutzik, P. O. & Irish, J. M. Web-based analysis and publication of flow cytometry experiments. Curr. Protoc. Cytom. Chapter 10, Unit 10.17 (2010).

    Google Scholar 

  55. 55.

    Chen, T. J. & Kotecha, N. Cytobank: providing an analytics platform for community cytometry data analysis and collaboration. Curr. Top. Microbiol. Immunol. 377, 127–157 (2014).

    CAS  PubMed  Google Scholar 

  56. 56.

    Lujan, E. et al. Early reprogramming regulators identified by prospective isolation and mass cytometry. Nature 521, 352–356 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. 57.

    Blondel, V. D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. Fast unfolding of communities in large networks. J. Stat. Mech. 2008, P10008 (2008).

    Google Scholar 

  58. 58.

    Ying, Q.-L. et al. The ground state of embryonic stem cell self-renewal. Nature 453, 519–523 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  59. 59.

    Tesar, P. J. et al. New cell lines from mouse epiblast share defining features with human embryonic stem cells. Nature 448, 196–199 (2007).

    CAS  PubMed  Google Scholar 

  60. 60.

    Brons, I. G. M. et al. Derivation of pluripotent epiblast stem cells from mammalian embryos. Nature 448, 191–195 (2007).

    CAS  PubMed  Google Scholar 

  61. 61.

    Vallier, L., Reynolds, D. & Pedersen, R. A. Nodal inhibits differentiation of human embryonic stem cells along the neuroectodermal default pathway. Dev. Biol. 275, 403–421 (2004).

    CAS  PubMed  Google Scholar 

  62. 62.

    Takahashi, K. et al. Induction of pluripotent stem cells from adult human fibroblasts by defined factors. Cell 131, 861–872 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  63. 63.

    Villani, A.-C. et al. Single-cell RNA-seq reveals new types of human blood dendritic cells, monocytes, and progenitors. Science 356, eaah4573 (2017).

    PubMed  PubMed Central  Google Scholar 

  64. 64.

    Habib, N. et al. Massively parallel single-nucleus RNA-seq with DroNc-seq. Nat. Methods 14, 955–958 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  65. 65.

    Kee, N. et al. Single-cell analysis reveals a close relationship between differentiating dopamine and subthalamic nucleus neuronal lineages. Cell Stem Cell 20, 29–40 (2017).

    CAS  PubMed  Google Scholar 

  66. 66.

    Grass, J. A. et al. Distinct functions of dispersed GATA factor complexes at an endogenous gene locus. Mol. Cell. Biol. 26, 7056–7067 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

Download references


We thank G.-C. Yuan for his assistance in performing SCUBA analysis. We are grateful to N. Kee (formerly of the Perlmann lab) for helpful discussions and advice. We thank P. Fabris for sharing synthetic datasets for comparison of dimensionality-reduction techniques. M.E.K. was supported by the National Science Foundation Graduate Research Fellowship under grant no. DGE-4747, the National Cancer Institute and the NIH under Award Number F99CA21223, and Stanford University’s Diversifying Academia, Recruiting Excellence Fellowship. C.M.W. was supported by NIH grant CVTG 5T32HL007284. K.I.F. was supported by NIGMS training grant 5T32GM008715. S.M.G. was supported by the BDS training grant (NIH 5T32LM012416). G.K.F. was supported by the CMB training grant (NIH T32GM007276). E.R.Z. was supported by NIH NRSA F32 (GM093508-01), AHA/Allen Frontiers Group Distinguished Investigator Program and the Simons Foundation SFARI Pilot Grant program. This work was further supported by grants to G.P.N.: U19 AI057229, 1U19AI100627, Department of Defense (CDMRP), Northrop-Grumman Corporation, R01CA184968, 1R33CA183654-01, R33CA183692, 1R01GM10983601, 1R21CA183660, 1R01NS08953304, OPP1113682, 5UH2AR067676, 1R01CA19665701, R01HL120724 and CIRM (RB2–01592). G.P.N. is supported by the Rachford & Carlotta A. Harris Endowed Chair.

Author information




E.R.Z. conceptualized the FLOW-MAP algorithm. E.R.Z., G.K.F., and G.P.N. designed the mESC differentiation experiment. E.R.Z. and G.K.F. performed the mESC differentiation experiment and collected cell samples. E.R.Z. performed antibody staining and mass cytometry measurement. M.E.K., E.R.Z., S.M.G., C.M.W. and R.S.R. wrote the FLOW-MAP code. M.E.K., C.M.W., K.I.F. and E.R.Z. analyzed and interpreted the data. M.E.K., C.M.W. and E.R.Z. wrote the manuscript. All authors edited, read and approved the manuscript.

Corresponding author

Correspondence to Eli R. Zunder.

Ethics declarations

Competing interests

G.P.N. is a paid consultant for Fluidigm, the manufacturer that produced some of the reagents and instrumentation used in this study. The remaining authors declare no competing interests.

Additional information

Peer review information Nature Protocols thanks Evan Newell and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related link

Key reference using this protocol

Zunder, E. R., Lujan, E., Goltsev, Y., Wernig, M. & Nolan, G. P. Cell Stem Cell 16, 323–337 (2015):

Supplementary information

Supplementary Information

Supplementary Table 1, Supplementary Methods and Supplementary Figs. 1–18.

Reporting Summary

Supplementary Data 1

Parameter optimization graphs

Supplementary Data 2

Synthetic datasets

Supplementary Data 3

mESC differentiation dataset

Supplementary Data 4

Nestorowa et al.42: scRNAseq data and code

Supplementary Data 5

Kee et al.65: scRNAseq data and code

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ko, M.E., Williams, C.M., Fread, K.I. et al. FLOW-MAP: a graph-based, force-directed layout algorithm for trajectory mapping in single-cell time course datasets. Nat Protoc 15, 398–420 (2020).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing