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.

Wishbone identifies bifurcating developmental trajectories from single-cell data


Recent single-cell analysis technologies offer an unprecedented opportunity to elucidate developmental pathways. Here we present Wishbone, an algorithm for positioning single cells along bifurcating developmental trajectories with high resolution. Wishbone uses multi-dimensional single-cell data, such as mass cytometry or RNA-Seq data, as input and orders cells according to their developmental progression, and it pinpoints bifurcation points by labeling each cell as pre-bifurcation or as one of two post-bifurcation cell fates. Using 30-channel mass cytometry data, we show that Wishbone accurately recovers the known stages of T-cell development in the mouse thymus, including the bifurcation point. We also apply the algorithm to mouse myeloid differentiation and demonstrate its generalization to additional lineages. A comparison of Wishbone to diffusion maps, SCUBA and Monocle shows that it outperforms these methods both in the accuracy of ordering cells and in the correct identification of branch points.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Alignment of cells along bifurcating trajectories.
Figure 2: Wishbone robustly recovers hallmarks of T-cell differentiation.
Figure 3: Heterogeneity in gated populations is explained in part by variance along a trajectory.
Figure 4: Transcription factors show distinct dynamics in SP populations.
Figure 5: Generalization of Wishbone to branches in human and mouse myeloid development spanning mass cytometry and single-cell RNA-Seq.
Figure 6: Wishbone outperformed competing methods in both ordering of cells and branch associations.

Accession codes


Gene Expression Omnibus


  1. Tang, F. et al. mRNA-Seq whole-transcriptome analysis of a single cell. Nat. Methods 6, 377–382 (2009).

    CAS  Article  Google Scholar 

  2. 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  Article  Google Scholar 

  3. 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  Article  Google Scholar 

  4. Shin, J. et al. Single-cell RNA-Seq with waterfall reveals molecular cascades underlying adult neurogenesis. Cell Stem Cell 17, 360–372 (2015).

    CAS  Article  Google Scholar 

  5. 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  Article  Google Scholar 

  6. Paul, F. et al. Transcriptional heterogeneity and lineage commitment in myeloid progenitors. Cell 163, 1663–1677 (2015).

    CAS  Article  Google Scholar 

  7. Coifman, R.R. et al. Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc. Natl. Acad. Sci. USA 102, 7426–7431 (2005).

    CAS  Article  Google Scholar 

  8. Koch, U. & Radtke, F. Mechanisms of T cell development and transformation. Annu. Rev. Cell Dev. Biol. 27, 539–562 (2011).

    CAS  Article  Google Scholar 

  9. Yui, M.A. & Rothenberg, E.V. Developmental gene networks: a triathlon on the course to T cell identity. Nat. Rev. Immunol. 14, 529–545 (2014).

    CAS  Article  Google Scholar 

  10. Egawa, T. Regulation of CD4 and CD8 coreceptor expression and CD4 versus CD8 lineage decisions. Adv. Immunol. 125, 1–40 (2015).

    CAS  Article  Google Scholar 

  11. Wang, L. et al. Distinct functions for the transcription factors GATA-3 and ThPOK during intrathymic differentiation of CD4(+) T cells. Nat. Immunol. 9, 1122–1130 (2008).

    CAS  Article  Google Scholar 

  12. Love, P.E. & Bhandoola, A. Signal integration and crosstalk during thymocyte migration and emigration. Nat. Rev. Immunol. 11, 469–477 (2011).

    CAS  Article  Google Scholar 

  13. Mingueneau, M. et al. The transcriptional landscape of αβ T cell differentiation. Nat. Immunol. 14, 619–632 (2013).

    CAS  Article  Google Scholar 

  14. Yamashita, I., Nagata, T., Tada, T. & Nakayama, T. CD69 cell surface expression identifies developing thymocytes which audition for T cell antigen receptor-mediated positive selection. Int. Immunol. 5, 1139–1150 (1993).

    CAS  Article  Google Scholar 

  15. Singer, A., Adoro, S. & Park, J.H. Lineage fate and intense debate: myths, models and mechanisms of CD4- versus CD8-lineage choice. Nat. Rev. Immunol. 8, 788–801 (2008).

    CAS  Article  Google Scholar 

  16. Heng, T.S. & Painter, M.W. The Immunological Genome Project: networks of gene expression in immune cells. Nat. Immunol. 9, 1091–1094 (2008).

    CAS  Article  Google Scholar 

  17. Rosenbauer, F. & Tenen, D.G. Transcription factors in myeloid development: balancing differentiation with transformation. Nat. Rev. Immunol. 7, 105–117 (2007).

    CAS  Article  Google Scholar 

  18. Doulatov, S. et al. Revised map of the human progenitor hierarchy shows the origin of macrophages and dendritic cells in early lymphoid development. Nat. Immunol. 11, 585–593 (2010).

    CAS  Article  Google Scholar 

  19. Klein, A.M. et al. Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells. Cell 161, 1187–1201 (2015).

    CAS  Article  Google Scholar 

  20. Subramanian, A. et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proc. Natl. Acad. Sci. USA 102, 15545–15550 (2005).

    CAS  Article  Google Scholar 

  21. Buettner, F. et al. Computational analysis of cell-to-cell heterogeneity in single-cell RNA-Sequencing data reveals hidden subpopulations of cells. Nat. Biotechnol. 33, 155–160 (2015).

    CAS  Article  Google Scholar 

  22. Pinkus, G.S. & Pinkus, J.L. Myeloperoxidase: a specific marker for myeloid cells in paraffin sections. Mod. Pathol. 4, 733–741 (1991).

    CAS  PubMed  Google Scholar 

  23. Kaneko, H., Shimizu, R. & Yamamoto, M. GATA factor switching during erythroid differentiation. Curr. Opin. Hematol. 17, 163–168 (2010).

    CAS  Article  Google Scholar 

  24. 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  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  26. Moignard, V. et al. Decoding the regulatory network of early blood development from single-cell gene expression measurements. Nat. Biotechnol. 33, 269–276 (2015).

    CAS  Article  Google Scholar 

  27. Stegle, O., Teichmann, S.A. & Marioni, J.C. Computational and analytical challenges in single-cell transcriptomics. Nat. Rev. Genet. 16, 133–145 (2015).

    CAS  Article  Google Scholar 

  28. 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  Article  Google Scholar 

  29. Waddington, C.H. An Introduction to Modern Genetics (George Allen & Unwin, 1939).

  30. Macosko, E.Z. et al. Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets. Cell 161, 1202–1214 (2015).

    CAS  Article  Google Scholar 

  31. de Silva, V. & Tenenbaum, J.B. Global versus local methods in nonlinear dimensionality reduction. Advances in Neural Information Processing Systems 15, 721–728 (2003).

    Google Scholar 

  32. Amir, A.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  Article  Google Scholar 

  33. Gut, G., Tadmor, M.D., Pe'er, D., Pelkmans, L. & Liberali, P. Trajectories of cell-cycle progression from fixed cell populations. Nat. Methods 12, 951–954 (2015).

    CAS  Article  Google Scholar 

  34. von Luxburg, U. A tutorial on spectral clustering. Stat. Comput. 17, 395–416 (2007).

    Article  Google Scholar 

  35. Gautier, L., Cope, L., Bolstad, B.M. & Irizarry, R.A. affy--analysis of Affymetrix GeneChip data at the probe level. Bioinformatics 20, 307–315 (2004).

    CAS  Article  Google Scholar 

  36. Grün, D. et al. Single-cell messenger RNA sequencing reveals rare intestinal cell types. Nature 525, 251–255 (2015).

    Article  Google Scholar 

  37. Huang, W., Sherman, B.T. & Lempicki, R.A. Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources. Nat. Protoc. 4, 44–57 (2009).

    CAS  Article  Google Scholar 

Download references


We would like to thank A. Bloemendal, Z. Good, N. Hacohen, S. Krishnaswamy, J. Levine and A.J. Carr for their helpful comments. M.D.T. is supported by an NSF graduate fellowship. This work was supported by NSF MCB-1149728, NIH DP1- HD084071, NIH R01CA164729 to D.P. D.P. holds a Packard Fellowship for Science and Engineering. This work was also supported by David and Fela Shapell Family Foundation INCPM Fund, the WIS staff scientists grant from the Nissim Center, for the Development of Scientific Resources, and ISF 1184/15 to N.F.

Author information

Authors and Affiliations



S.B. and D.P. conceived the study. M.S., M.D.T., O.A., and D.P. designed and developed Wishbone. M.S. and D.P. performed statistical analysis and comparison of Wishbone. S.R.-Z., T.M.S., and N.F. performed all bench experiments and data acquisition. M.S., S.R.-Z., N.F., and D.P. performed the biological analysis and interpretation. M.D.T., M.S., P.K., and K.C. programmed the software tools. M.S., S.R.-Z., N.F., and D.P. wrote the manuscript.

Corresponding author

Correspondence to Dana Pe'er.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figure 1–25 and Supplementary Notes 1–4 (PDF 4787 kb)

Supplementary Table 1 (XLSX 13 kb)

Supplementary Software (ZIP 20989 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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