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Nature MethodsGenomicsPeer-reviewed journal article

Reversed graph embedding resolves complex single-cell developmental trajectories

Xiaojie QiuiD, Qi MaoiD, Ying TangiD, Li WangiD, Raghav ChawlaiD, Hannah A. PlineriD, Cole TrapnelliD

Abstract

Organizing single cells along a developmental trajectory has emerged as a powerful tool for understanding how gene regulation governs cell fate decisions. However, learning the structure of complex single-cell trajectories with two or more branches remains a challenging computational problem. We present Monocle 2, which uses reversed graph embedding to reconstruct single-cell trajectories in a fully unsupervised manner. Monocle 2 learns an explicit principal graph to describe the data, greatly improving the robustness and accuracy of its trajectories compared to other algorithms. Monocle 2 uncovered a new, alternative cell fate in what we previously reported to be a linear trajectory for differentiating myoblasts. We also reconstruct branched trajectories for two studies of blood development, and show that loss of function mutations in key lineage transcription factors diverts cells to alternative branches on the a trajectory. Monocle 2 is thus a powerful tool for analyzing cell fate decisions with single-cell genomics.

In-depth summary

Claude Opus 5.5 · max effort · 8 Nov 2026 · from the full text of version 1 (21 Feb 2017) · CC BY 4.0

Monocle 2 learns branched single-cell trajectories without supervision via reversed graph embedding, revealing a non-fusing myoblast outcome and knockout myeloid cells diverted onto opposite fate branches.

Existing pseudotime tools either lean on user-supplied marker genes or experimental design, or need the number of branches fixed in advance (Wishbone assumes one branch; DPT cannot tell how many are genuine), and branch accuracy is hard to verify experimentally. Monocle 2 couples unsupervised gene selection with an explicitly learned principal tree so branching emerges from the data, and tests the resulting branches with transcription-factor knockout mice.

Key results

  1. ShownOn Paul et al. mouse myeloid progenitor data, Monocle 2 pseudotime agreed with a marker-based reference about as well as DPT and Wishbone and better than SLICER or Monocle 1, and its branch assignments stayed more accurate and consistent than Wishbone's under subsampling.

    Pearson's Rho, Kendall's Tau, adjusted Rand index (ARI) and lag-1 autocorrelation were computed on the same 300 sampled cells for all tools (SLICER and Monocle 1 could not run on all 2699); robustness used 25 subsamples of 80% of cells plus progressive downsampling, and outputs held across widely varied DDRTree parameters. No numeric scores are printed in the text. · Monocle 2 outperforms alternative reconstruction…; Comparing different algorithms to a marker-based…; Assessing robustness of pseudotime and branch…; Figure legends

  2. SuggestedHuman skeletal myoblasts previously ordered as a linear trajectory resolved into one branch with two outcomes: F1 activates contractile genes and myogenic transcription factors, consistent with myotube fusion, whereas F2 does not, which the authors interpret as failed fusion.

    94 myoblast transcriptomes; BEAM found 664 genes differing between outcomes F1 and F2 (FDR < 10%), with TNNT2, MYH2, MEF2C and MYOG high on F1, while CCNB2 behaved similarly on both; Monocle 1 on the same genes gave a linear order. The unfused reading leans on earlier MYH2 immunofluorescence. · Unsupervised feature selection identifies key…; Monocle 2 accurately reconstructs single cell…; Analysis of HSMM data; Figure legends

  3. ShownIn Olsson et al. mouse data, adding knockout cells kept a single major branch point but shifted cell fates: Gfi1-/- cells largely avoided the granulocyte branch, Irf8-/- cells the monocyte branch, and double knockouts sat on both branches near the branch point.

    A trajectory-conditioned test (knockout vs pseudotime-matched wild-type cells; FDR < 10%) found Gfi1-/- monocyte-branch cells over-expressing granulocyte genes and Irf8-/- granulocyte-branch cells over-expressing monocytic genes. In Paul et al. data, Cebpa-/- cells were absent from the erythroid branch and Cebpe-/- cells depleted from the GM branch. · Genetic perturbations divert cells along…; Trajectory-conditioned test; Figure legends

  4. ShownOn Olsson et al. FACS-sorted mouse myelopoiesis cells, Monocle 2 learned one major branch: LSK cells at the tip chosen as root, CMPs on the trunk upstream of the branch, granulocytes and monocytes on separate branches, and mixed-lineage plus rare transient cells just upstream of the branch point.

    542 branch-dependent wild-type genes (BEAM, FDR < 10% per legend; the text states FDR < 1%); many were Irf8 or Gfi1 promoter targets by ChIP-seq, and both regulators bifurcated earlier in pseudotime than direct and motif-predicted secondary targets (FIMO on GMP DHS peaks). · Monocle 2 captures granulocytic/monocytic…; Analysis of blood data; Figure legends

  5. SuggestedIn simulated cells from a 12-gene stochastic network producing neuron, astrocyte or oligodendrocyte fates, Monocle 2 recovered the three-fate tree, tracked the theoretical most-probable paths, and put branch points where Mash1/Hes5 and Scl/Olig2 turn mutually exclusive.

    Stochastic differential equations integrated by the Euler method for 400 time steps and run 200 times; one simulated path per fate was given to Monocle 2 at default settings (DDRTree in a two-dimensional latent space; SimplePPT in the original 12 dimensions) and compared graphically with ODE fixed-point paths; no error metric is printed. · Monocle 2 accurately reconstructs single cell…; Simulating the neuronal differentiation…; Figure legends

Methods, data and reproducibility

dpFeature selects ordering genes via PCA, t-SNE, density peak clustering and negative-binomial GLM tests; DDRTree jointly learns a low-dimensional embedding and a spanning tree on soft K-means centroids, giving pseudotime (geodesic distance from a chosen root) and branches; BEAM and a trajectory-conditioned test find branch- or genotype-dependent genes.

  • Human skeletal muscle myoblast (HSMM) single-cell RNA-seq time course (0, 24, 48, 72 h) from the authors' earlier study, converted to transcript counts with Census · human · n = 94 cells
  • Developing lung epithelial cells (E14.5, E16.5, E18.5 and adult AT2 labels) with spike-in-based transcript counts, used for feature selection comparisons · n = 183 cells
  • Paul et al. MAR-seq UMI profiles of differentiating blood cells (lymphoid removed) plus Cebpa-/- and Cebpe-/- cells; ordered using the study's 3004 informative genes · mouse · n = 2699 cells (erythroid 1095, CMP 451, GMP 1123, DC 30)
  • Olsson et al. FACS-sorted myelopoiesis cells (LSK, CMP, GMP, LKCD34+ gates), wild type plus Gfi1-/-, Irf8-/- and double-knockout cells; FPKM converted with Census · mouse · n = several hundred FACS-sorted cells · Synapse syn4975060
  • Downloaded Gfi1 and Irf8 ChIP-seq data, peak-called with MACS2 to nominate direct regulatory targets among branch genes
  • DNase I hypersensitive site (DHS) peaks for GMP cells, motif-scanned with FIMO against JASPAR vertebrate motifs to infer secondary targets · GSE59992
  • Simulated 12-gene stochastic differential equation network (neural progenitor to neuron, astrocyte or oligodendrocyte), 400 Euler time steps per run · n = 200 simulation runs
Methods & tools
Monocle 2 (reversed graph embedding, DDRTree by default), dpFeature (PCA, t-SNE, density peak clustering, negative-binomial GLM likelihood ratio test), BEAM (Branch Expression Analysis Modeling), Trajectory-conditioned differential expression test (new in this work), Census (transcript count estimation), SimplePPT, SGL-tree and L1-graph principal graph learners, Monocle 1 (ICA plus minimum spanning tree), Wishbone, DPT diffusion pseudotime (destiny 2.0.3), SLICER 0.2.0, MACS2; FIMO with JASPAR vertebrate motifs (version 2016), irlba, lle, diffusionMap and piano (GO enrichment) packages
Software & environment
Monocle 2 reduceDimension/orderCells (DDRTree default; Monocle 1 run with ICA, num_paths = 2); prcomp (R), irlba, lle, diffusionMap and piano packages; destiny 2.0.3 (DPT), SLICER 0.2.0, Wishbone, MACS2, FIMO, JASPAR 2016. Monocle 2 version unstated.
Reproducibility gaps
No repository for Monocle 2, DDRTree or dpFeature code is printed (the only code link is the third-party Wishbone repo); HSMM, lung and Gfi1/Irf8 ChIP-seq inputs lack accessions in the text; no hardware or runtime figures are reported.
Limitations (6)
  • No gold-standard ordering exists for real single-cell data, and the authors concede their marker-score reference is imperfect, adding lag-1 autocorrelation of marker spline fits as a complementary accuracy check. · stated by the authors
  • SLICER and Monocle 1 could not be run on all 2699 cells, so accuracy comparisons used a 300-cell random sample; SLICER was left out of subsampling robustness tests owing to long runtimes and occasional instability. · stated by the authors
  • The trajectory-conditioned test was applied as a plain two-group comparison within the knockouts' pseudotime range, because spline models with a genotype term need more cells per group; the authors expect the full model to be more accurate when both groups are well represented. · stated by the authors
  • The authors cannot yet explain why some loss-of-function mutations create new trajectory branches whereas others, such as Gfi1 or Irf8 loss here, divert cells along existing branches. · stated by the authors
  • Although framed as fully unsupervised, the pipeline involves manual choices: PC counts and density peak ρ/δ cutoffs are set per dataset from decision plots, the root tip is user-selected, and the MAR-seq benchmark used the original study's 3004 genes rather than dpFeature output. · noted in this summary
  • Cross-method accuracy rests on a single real dataset scored against a reference built from marker expression in the same cells, plus simulations; the knockout analyses test Monocle 2 alone, so comparative performance on other systems or with orthogonal lineage ground truth is untested. · noted in this summary

Read this if you build or apply pseudotime methods for branched differentiation and want an unsupervised principal-tree approach checked against simulations, competing tools, and knockout-driven fate shifts.

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