LOTUS
Lineage-Aware Dynamics
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RESEARCH OVERVIEW
A lineage-aware optimal transport framework for reconstructing continuous, lineage-consistent single-cell fate dynamics from time-resolved single-cell data.
LOTUS framework
LOTUS integrates time-resolved single-cell transcriptomes with clonal barcodes to infer continuous, lineage-consistent cell-fate dynamics. A clone-level optimal transport constraint complements Sinkhorn reconstruction, mass matching and energy regularization, helping resolve transcriptome-only transport ambiguities and supporting lineage-tree reconstruction, fate-boundary inference, fate-potential estimation and in silico perturbation analysis.
Major advances
LOTUS uses experimentally observed clonal information as an explicit constraint, capturing how cells move through transcriptional space and how clones propagate, expand or disappear across time.
LOTUS estimates fate potential at single-cell and clone resolution, distinguishing single-fate, dual-fate and multi-fate programs and identifying meta-clones with divergent downstream fate biases.
LOTUS can use endogenous TCR clonotypes as lineage constraints, extending the framework to clonotype-resolved TR1 dynamics during malaria infection.
Clone-level dynamics view
LARRY Hematopoiesis
CellTagging Reprogramming
Evaluation and biological meaning
Figure 2
Across ten independent tests, LOTUS achieved a 1.10% mean off-target rate, compared with 5.20% for DeepRUOT, 4.94% for TIGON and 14.84% for scDiffEq.
a, Schematic of simulated dataset 1. b, Off-target rates across repeated simulations. c-f, Representative simulated-dataset-1 reconstructions for LOTUS, DeepRUOT, TIGON and scDiffEq. g, Schematic of simulated dataset 2. h, Off-target rates across increasing clone numbers.
Fig. 2 | LOTUS improves lineage-consistent trajectory reconstruction in simulated lineage-tracing datasets.
a, Two barcoded progenitor populations give rise to distinct terminal fates. b, Across ten test datasets, LOTUS achieved the lowest mean off-target rate (1.10%), versus DeepRUOT (5.20%), TIGON (4.94%) and scDiffEq (14.84%).
c-f, PCA visualizations of reconstructed trajectories for LOTUS (c), DeepRUOT (d), TIGON (e) and scDiffEq (f) in one representative test dataset of simulated dataset 1. The annotated off-target values therefore refer to this single dataset, whereas panel b summarizes ten independent test datasets. True cells from the two barcode-associated fates are shown in blue and orange, correctly routed predicted cells are shown in green, and off-target predictions are shown in red. Dashed contours indicate the expected fate regions.
g, Schematic of simulated dataset 2, in which multiple barcoded progenitor populations give rise to two distinct terminal fates. Compared to simulated dataset 1, more clones have been added to this dataset. This setting evaluates the robustness of lineage-aware reconstruction under increasing clonal complexity.
h, Distribution of test off-target rates across different numbers of clones. The upper panel shows the distribution of off-target rates for LOTUS, DeepRUOT, TIGON and scDiffEq under each clone number, where each point represents an independent test run performed on a newly generated simulated dataset. The lower panel shows, for each test dataset, the performance margin between the top-ranked and second-ranked methods, computed as the second-lowest off-target rate minus the lowest off-target rate. LOTUS maintains lower off-target rates across clone numbers compared with DeepRUOT, TIGON and scDiffEq.
Figure 3
LOTUS recovers branch-resolved hematopoietic trajectories, clone-specific propagation, early fate-boundary structure and temporal ordering in LARRY.
a, LOTUS-derived lineage tree for LARRY hematopoiesis. b, SPRING reference embedding. c-e, Continuous trajectories and clone-level propagation. f, Neu-Mo fate-boundary prediction. g, Temporal lineage-supervision ablation. h-j, Pseudotime and temporal ordering.
Fig. 3 | Temporal order reconstruction of lineage-resolved differentiation trajectories and fate-boundary dynamics.
a, LOTUS-derived lineage-tree representation of LARRY hematopoietic differentiation. Barcoded cells were grouped into PCA-based Leiden microclusters and arranged along a LOTUS potential-derived developmental stage, with the undifferentiated-enriched microcluster used as the root. Candidate microcluster connections were obtained from the PCA-neighbor graph, constrained to proceed from earlier to later stages, and refined by LOTUS-inferred velocity alignment to favor forward developmental transitions. Cells were projected onto the resulting root-to-leaf paths and colored by annotated cell state. Branch widths encode downstream growth-weighted branch strength based on subtree cell abundance and LOTUS-inferred growth rate. Lineage-end labels indicate terminal dominant states, and local labels show dominant cell-state compositions within lineage-stage bins.
b, SPRING visualization of the LARRY scRNA-seq hematopoietic differentiation dataset, coloured by cell type annotations.
c, LOTUS-inferred trajectory reconstruction on the SPRING embedding. Ground-truth cells at different time points are shown together with model-predicted cell states and sampled stochastic trajectories, illustrating the ability of the model to recover continuous developmental paths across discrete sampling days.
d, Reconstruction of monocyte-associated differentiation routes. Inferred trajectories capture divergent paths from early progenitor states toward Mo-DC and Mo-Neu branches, consistent with the topology of the reference manifold.
e, Representative clone-level dynamics across day 2, day 4 and day 6. True clone distributions and predicted future states are shown for individual barcoded clones, demonstrating clone-specific propagation along lineage-consistent differentiation paths.
f, Fate-boundary prediction between neutrophil and monocyte fates in clone-disjoint held-out test cells. LOTUS attained the highest agreement with the clone-derived reference boundary (R = 0.597).
g, Ablation analysis of temporal lineage supervision. Removing the day 2-day 4 clone loss caused a larger reduction in agreement with the ground-truth fate boundary than removing the day 4-day 6 clone loss, indicating that early lineage information plays a more critical role in fate-boundary reconstruction.
h, Schematic representation of pseudotime progression along the myeloid differentiation continuum, spanning MPP, GMP, pMy and My states.
i, Reconstructed temporal ordering of cell differentiation stages over simulated time. For each simulated time point, the stage value was calculated as the average ordinal differentiation-stage score of cells, with MPP, GMP, pMy and My encoded as stages 0-3, respectively. The inferred stage value increases from early to late simulated days, indicating that the learned dynamics are temporally consistent with progressive myeloid differentiation.
j, Pseudotime progression from day 2 to day 4. Each cell was assigned a pseudotime value at the observed day 2 state and predicted day 4 state by weighted nearest-neighbor mapping in PCA space to reference cells with known pseudotime. The two-dimensional density map shows the paired pseudotime values of the same cells, with the x axis indicating pseudotime at day 2 and the y axis indicating pseudotime at day 4. The dashed diagonal denotes no pseudotime change. Enrichment of density above the diagonal indicates that most cells acquire higher pseudotime values from day 2 to day 4, consistent with forward progression along the inferred developmental trajectory.
Figure 4
LARRY and STRACK perturbation screens prioritize fate-associated regulators and recover branch-specific transcription-factor programs.
a-d, LARRY perturbation analyses and transcription-factor dynamics. e-i, LOTUS lineage-tree reconstruction, perturbation analyses and transcription-factor dynamics in STRACK hematopoiesis.
Fig. 4 | Lineage-aware in silico perturbation analysis and transcription-factor prediction generalize across datasets.
a-d show in silico perturbation analyses and transcription-factor dynamics based on the LARRY hematopoietic differentiation dataset from Weinreb et al. (2020).
a, In silico perturbation of neutrophil-monocyte fate allocation in the LARRY dataset. The perturbation was applied to Cebpe, Mxd1 and Dach1: in the perturbation input, day-2 progenitor cells were displaced in PCA space along the PCA-loading directions of these genes, while the control input was generated without gene perturbation. Lineage trees show control and perturbed trajectories, with neutrophil and monocyte branches highlighted in red and blue, respectively. Stacked area plots quantify the corresponding temporal changes in cell-type proportions from day 2 to day 6.
b, Volcano plots showing gene perturbation effects on neutrophil and monocyte fate probabilities. Genes with significant positive and negative effects are highlighted in orange and purple, respectively, whereas non-significant genes are shown in grey. Representative lineage-associated regulators are annotated. The dashed horizontal line denotes the FDR threshold.
c, Fraction of expected lineage markers and transcription factors recovered across Top-N ranked perturbation genes (N = 50-250) for monocyte- and neutrophil-associated screens. Lines show recovery for LOTUS and DeepRUOT across ranking depth.
d, Temporal expression dynamics of transcription factors associated with major hematopoietic lineages in the Larry dataset. Heatmap values represent gene-wise expression z-scores across inferred differentiation time, grouped by neutrophil, monocyte, basophil, megakaryocyte and mast-cell programs.
e-i show lineage-tree reconstruction, in silico perturbation analyses and transcription-factor dynamics based on the STRACK hematopoietic differentiation dataset from Singh et al. (2025).
e, LOTUS-derived lineage-tree representation of STRACK hematopoietic differentiation. The inferred lineage tree integrates velocity-guided edges, growth-weighted branch structure and stage-informed layout, revealing branching trajectories from HSC and MPP states toward erythroid, megakaryocytic, basophil, monocyte and neutrophil fates.
f, UMAP visualization of the STRACK scRNA-seq hematopoietic differentiation dataset, coloured by cell type annotations.
g, Temporal transcription factors dynamics along GMP- and MEP-associated differentiation programs in the STRACK dataset. Heatmap values indicate expression z-scores over inferred developmental time.
h, Volcano plots of GMP- and MEP-associated lineage perturbation screens. Significant genes with positive and negative perturbation effects are highlighted in orange and purple, respectively, and representative regulators are annotated.
i, Quantification of expected marker and transcription-factor recovery in GMP- and MEP-side screens among the top 200 ranked perturbation genes. Bars show the fraction of lineage-associated markers recovered by LOTUS, DeepRUOT or both methods.
Figure 5
Clone-potential analysis connects predicted fate allocation with dual-fate states, inferred chromatin accessibility and clone-associated regulatory signatures.
a-b, LOTUS-estimated cell and clone fate potential. c-f, Molecular characterization of Neu-Mo double-fate cells. g-k, Meta-clone trajectories and linked transcriptional and chromatin programs.
Fig. 5 | LOTUS resolves multi-fate clone potential, meta-clone identity and clone-associated regulatory programs.
a, LOTUS estimated cell differentiation potential. Top, representative double-fate and multi-fate clones are shown across simulated time, with predicted states colored by simulation time and experimentally observed clone states marked at days 2, 4 and 6. Bottom left, predicted fate allocation of a multi-fate clone across terminal hematopoietic states, with the inset pie chart showing the corresponding fate composition. Bottom right, total variation distance between predicted and observed clone fate distributions, highlighting regions where clone-level fate prediction is more or less concordant with the measured lineage output.
b, Comparison between observed and LOTUS-predicted fate-potential matrices across cell types. Rows represent individual clones or clone groups, and columns denote potential downstream fate states. The leftmost column represents the number of possible differentiation directions for the clone.
c, Differential expression analysis of Neu-Mo double-fate cells compared with Neu-only and Mo-only cells. Cells were defined as Neu-Mo double-fate when predicted probabilities for both neutrophil and monocyte fates exceeded 0.05 at any simulated time point. The upper part compares double-fate cells with Neu-only cells, while the lower part compares double-fate cells with Mo-only cells.
d, Mean AUCell activity of differentially active regulons across Neu-only, double-fate and Mo-only cells. The top 25 regulons with differences across the three groups are shown; colors indicate the mean regulon AUC in each group.
e, MultiVI-inferred marker-promoter accessibility profiles across fate groups, showing lineage-associated genes in Neu-only, Neu-Mo double-fate and Mo-only populations. These inferred accessibility profiles reflect cell states represented in the reference multiome dataset.
f, Distribution of promoter or marker scores for Neu-associated, Mo-associated, fate-bias and dual-priming gene sets across double, Neu and Mo fate groups.
g, The distribution of clone clusters constructed based on predicted trajectories in the initial cell embedding space.
h, Representative trajectories of two meta clones, MC1 and MC5, indicating that clone-level fate differences can emerge even among cells with highly similar transcriptomic profiles.
i, Differential expression analysis between MC1 and MC5 cells, identifying clone-associated transcriptional programs.
j, Mean MultiVI-inferred lineage-module accessibility of MC1 and MC5 across major hematopoietic lineage modules.
k, Coupling between RNA expression changes and promoter inferred-ATAC accessibility for lineage-associated genes. The x axis shows RNA log2 fold change between MC1 and MC5, and the y axis shows promoter inferred-ATAC accessibility difference.
Figure 6
LOTUS distinguishes reprogrammed from failed trajectories in the CellTagging dataset and resolves the early fate boundary with R = 0.670.
a, Lineage tree inferred for the Biddy et al. reprogramming dataset. b, UMAP visualization. c, iEP-enriched and iEP-depleted simulated trajectories. d, Fate-boundary prediction. e, Foxd2 perturbation. f, Reprogrammed- and failed-fate perturbation screens. g-h, Top-200 and Top-K recovery. i, Temporal transcription-factor dynamics.
Fig. 6 | LOTUS reconstructs lineage-dependent reprogramming dynamics.
a, Lineage tree inferred for the Biddy et al. reprogramming dataset. Edges are guided by local velocity, branch width reflects inferred growth, and the layout is arranged according to developmental potential. Cells are colored by experimentally annotated outcomes.
b, UMAP visualization of reprogramming dataset, showing the global organization of reprogrammed, failed and other cell states.
c, Simulated differentiation pathways for iEP-enriched and iEP-depleted initial populations. Ground-truth cells are shown together with inferred trajectories across days 12, 15, 21 and 28, illustrating divergence between reprogramming-prone and reprogramming-resistant routes.
d, Fate-boundary prediction comparing the observed reprogrammed-to-failed fate ratio for day-12 cells with LOTUS, DeepRUOT, TIGON, scDiffEq, Super-OT and DestinyNet predictions. LOTUS achieved the highest agreement with the reference boundary (R = 0.670).
e, In silico perturbation of the reprogramming landscape after Foxd2 perturbation. Control and Foxd2-perturbed UMAPs show changes in final cell-state distributions, with stacked area plots summarizing temporal shifts in cell-type proportions.
f, Volcano plots showing genes whose perturbation is predicted to promote reprogrammed or failed fates.
g, Recovery of known marker and transcription-factor genes among the top 200 perturbation candidates.
h, Top-K recovery of differentiation-associated genes in the reprogramming screen.
i, Temporal dynamics of transcription factors associated with reprogrammed and failed outcomes.
Figure 7
LOTUS preserves clone-family structure, reconstructs longitudinal TR1 states and identifies state-associated temporal regulatory networks.
a, Observed clone-family distribution and LOTUS-inferred trajectories. b-c, Reconstructed clone-family expression. d-e, Longitudinal TR1 dynamics and clonotype composition. f, Scribe-inferred temporal regulatory networks.
Fig. 7 | LOTUS reconstructs clonal identity and TR1 dynamics in malaria-responsive CD4+ T cells.
a, Observed clone-family distribution and LOTUS-inferred trajectories. Left, observed CD4+ T cells projected in UMAP space, with colors indicating clone families 1-7. Right, LOTUS-inferred clonal trajectories originating from 10 sampled cells per clone family, projected onto the same embedding; colors denote clone-family identity.
b, Observed and LOTUS-reconstructed gene expression in family 7 cells. Mean log-normalized expression was compared at the matched time point. Pearson's r = 0.98 reflects in-sample agreement at an observed training time point, not independent validation.
c, LOTUS-reconstructed gene expression across clone families. Heatmap showing genes broadly expressed across CD4+ T cells or selectively enriched in specific clone families following TCR activation. Expression patterns were reconstructed by LOTUS.
d, Reconstruction of longitudinal TR1 clonal dynamics in participant 3481 during malaria infection. Background points indicate the observed distribution of all TR1 cells at each time point, whereas highlighted points represent LOTUS-reconstructed descendant cells from clonotypes containing at least two cells.
e, Predicted clonal state composition of TR1 clonotypes at the time points shown in d. Each heatmap is vertically aligned with the corresponding UMAP panel above. Columns represent individual clonotypes, rows represent TR1 cell states, and color intensity indicates the proportion of cells in each clonotype occupying the corresponding state.
f, Scribe-inferred TF-to-gene temporal regulatory networks derived from LOTUS-reconstructed effector TR1 (left), memory TR1 (middle), and activated TR1 (right) dynamics. Yellow nodes represent transcription factors, green nodes represent genes, and edge width is proportional to the inferred temporal dependency strength (cRDI score).
Supplementary analyses
Additional benchmarks, trajectory reconstructions and biological analyses from the LOTUS manuscript.
a-d, PCA visualizations of reconstructed trajectories for LOTUS, DeepRUOT, TIGON and scDiffEq. True barcode-associated fates are blue and orange, correctly routed predictions green, and off-target predictions red. e, Final-time-point Wasserstein-2 distance across ten simulations; lower values indicate better agreement.
a, Stochastic trajectories on the SPRING embedding. b, LOTUS velocity streamlines, with cells colored by inferred differentiation potential. c, Three-dimensional potential landscape. d, Representative generated trajectories in gene-expression space. e, Comparison of LOTUS-predicted and reference growth-rate patterns.
a, Ground-truth and method-predicted neutrophil-to-monocyte fate ratios for day-2 cells; Pearson correlation quantifies agreement. b, Boundary-associated ratio maps for the reference, LOTUS, DeepRUOT and CoSpar, including LOTUS ablations removing the day 2-4 or day 4-6 clone loss.
a, Reference fate labels from Weinreb et al. (2020). b-c, LOTUS and DeepRUOT predictions on the SPRING embedding. d-e, Predictions after removing the day 2-4 or day 4-6 clone loss; accuracy quantifies the effect of each temporal lineage constraint.
a-b, LOTUS lineage-tree visualizations under control and perturbation conditions. c, Cebpe, Mxd1 and Dach1 dose-response analysis. d, DeepRUOT LARRY perturbation screens. e-f, LOTUS trajectory and velocity visualizations in STRACK. g, DeepRUOT GMP- and MEP-associated perturbation screens.
a, Distribution of Neu-only, Neu-Mo double-fate and Mo-only cells on SPRING. b-c, Neutrophil and monocyte module scores across groups. d, KEGG enrichment comparing double-fate and Neu-only cells. e, RNA-expression and promoter inferred-ATAC coupling for lineage-associated genes.
a, Predicted trajectories for meta-clones MC1-MC10. b, MC1 and MC5 distributions in SPRING. c, Commitment-score comparison, where lower values indicate broader multi-lineage priming. d, Heatmap of top MC1- and MC5-biased pseudo-ATAC peaks.
a, LOTUS trajectories across sampled reprogramming time points. b, Velocity streamlines with inferred potential. c, Correlation after ablating the day 12-15 or day 15-21 clone loss (ten independent runs). d, Reference and predicted reprogrammed-to-failed fate-ratio maps, including CoSpar and LOTUS ablations.
a, DeepRUOT-predicted perturbation effects on reprogrammed and failed fate probabilities. b, Reactome pathway-enrichment heatmap of top-ranked LOTUS and DeepRUOT perturbation genes; color indicates minus log10 adjusted P value.
a, Velocity stream plot of LOTUS-reconstructed CD4+ T cells on the reference UMAP. b, pySCENIC AUCell regulon-activity heatmap. c, Reconstructed and observed TR1-state abundance trends during malaria infection. d, Reconstructed proportions of naïve-like, activated, effector and memory TR1 states over time.
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