Reversed graph embedding resolves complex single-cell trajectories

Abstract

Single-cell trajectories can unveil how gene regulation governs cell fate decisions. However, learning the structure of complex trajectories with multiple branches remains a challenging computational problem. We present Monocle 2, an algorithm that uses reversed graph embedding to describe multiple fate decisions in a fully unsupervised manner. We applied Monocle 2 to two studies of blood development and found that mutations in the genes encoding key lineage transcription factors divert cells to alternative fates.

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Figure 1: Monocle 2 discovers a cryptic alternative outcome in myoblast differentiation.
Figure 2: Monocle 2 trajectories reveal that genetic perturbations divert cells to alternative outcomes.

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References

  1. 1

    Trapnell, C. et al. Nat. Biotechnol. 32, 381–386 (2014).

    CAS  Article  Google Scholar 

  2. 2

    Kumar, P., Tan, Y. & Cahan, P. Development 144, 17–32 (2017).

    CAS  Article  Google Scholar 

  3. 3

    Setty, M. et al. Nat. Biotechnol. 34, 637–645 (2016).

    CAS  Article  Google Scholar 

  4. 4

    Haghverdi, L., Büttner, M., Wolf, F.A., Buettner, F. & Theis, F.J. Nat. Methods 13, 845–848 (2016).

    CAS  Article  Google Scholar 

  5. 5

    Mao, Q., Wang, L., Goodison, S. & Sun, Y. in Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 765–774 (ACM, 2015).

  6. 6

    Mao, Q., Wang, L., Tsang, I. & Sun, Y. IEEE Trans. Pattern Anal. Mach. Intell. https://doi.org/10.1109/TPAMI.2016.2635657 (2016).

    Article  Google Scholar 

  7. 7

    Rodriguez, A. & Laio, A. Science 344, 1492–1496 (2014).

    CAS  Article  Google Scholar 

  8. 8

    Treutlein, B. et al. Nature 509, 371–375 (2014).

    CAS  Article  Google Scholar 

  9. 9

    Olsson, A. et al. Nature 537, 698–702 (2016).

    CAS  Article  Google Scholar 

  10. 10

    Paul, F. et al. Cell 163, 1663–1677 (2015).

    CAS  Article  Google Scholar 

  11. 11

    Hastie, T. & Stuetzle, W. J. Am. Stat. Assoc. 84, 502–516 (1989).

    Article  Google Scholar 

  12. 12

    Gorban, A.N. & Zinovyev, A.Y. in Handbook of Research on Machine-learning Applications and Trends: Algorithms, Methods, and Techniques 28–59 (Information Science Reference, Hershey, Pennsylvania, USA, 2009).

  13. 13

    Bellman, R. The Theory of Dynamic Programming (DTIC Document, 1954).

  14. 14

    Welch, J.D., Hartemink, A.J. & Prins, J.F. Genome Biol. 17, 106 (2016).

    Article  Google Scholar 

  15. 15

    Qiu, X. et al. Nat. Methods 14, 309–314 (2017).

    CAS  Article  Google Scholar 

  16. 16

    Qiu, X., Ding, S. & Shi, T. PLoS One 7, e49271 (2012).

    CAS  Article  Google Scholar 

  17. 17

    Tang, Y., Yuan, R., Wang, G., Zhu, X. & Ao, P. arXiv:1611.07140 (2016).

  18. 18

    Tirosh, I. et al. Nature 539, 309–313 (2016).

    Article  Google Scholar 

  19. 19

    Cusanovich, D.A. et al. Science 348, 910–914 (2015).

    CAS  Article  Google Scholar 

  20. 20

    Ramani, V. et al. Nat. Methods 14, 263–266 (2017).

    CAS  Article  Google Scholar 

  21. 21

    Mao, Q., Yang, L., Wang, L., Goodison, S. & Sun, Y. . in Proceedings of the 2015 SIAM International Conference on Data Mining 792–800 (Society for Industrial and Applied Mathematics, 2015).

  22. 22

    Boyd, S. & Vandenberghe, L. Convex Optimization (Cambridge University Press, Cambridge, 2004).

  23. 23

    Rand, W.M. J. Am. Stat. Assoc. 66, 846–850 (1971).

    Article  Google Scholar 

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Acknowledgements

We thank I. Tirosh for discussions on marker-based ordering, F. Theis and F.A. Wolf for discussions on the data analysis with DPT from Paul et al.9, and members of the Trapnell laboratory for comments on the manuscript. This work was supported by US National Institutes of Health (NIH) grants DP2 HD088158 (C.T.) and U54 DK107979 (C.T.); C.T. is partly supported by a Dale. F. Frey Award for Breakthrough Scientists and an Alfred P. Sloan Foundation Research Fellowship; and H.A.P. is supported by a National Science Foundation (NSF) Graduate Research Fellowship (DGE-1256082).

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Contributions

X.Q., Q.M., and C.T. designed and implemented Monocle 2; X.Q. performed the analysis; Y.T. and L.W. contributed to the technical design; R.C. and H.A.P. performed the testing; C.T. conceived the project; and all authors wrote the manuscript.

Corresponding author

Correspondence to Cole Trapnell.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–20 and Supplementary Note. (PDF 20516 kb)

Life Sciences Reporting Summary

Life Sciences Reporting Summary. (PDF 129 kb)

Supplementary Data 1

Zipped file for the neuron simulation data. (ZIP 35169 kb)

Supplementary Data 2

Zipped file for the least action path data. (ZIP 401 kb)

Supplementary Data 3

Zipped file for the complicate tree structure data. (ZIP 3 kb)

Supplementary Software

Software and analysis code used in this study which can reproduce all results. (ZIP 15812 kb)

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Qiu, X., Mao, Q., Tang, Y. et al. Reversed graph embedding resolves complex single-cell trajectories. Nat Methods 14, 979–982 (2017). https://doi.org/10.1038/nmeth.4402

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