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NatureBioinformaticsPeer-reviewed journal article

Mapping cells through time and space with moscot

Dominik KleiniD, Giovanni PallaiD, Marius LangeiD, Michal KleiniD, Zoe PiraniD, Manuel GanderiD, Laetitia Meng-PapaxanthosiD, Michael Sterr, Lama SaberiD, Changying JingiD, Aimée Bastidas-PonceiD, Perla Cota, Marta Tarquis-MedinaiD, Shrey ParikhiD, Ilan GoldiD, Heiko LickertiD, Mostafa BakhtiiD, Mor NitzaniD, Marco CuturiiD, Fabian Joachim TheisiD

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Abstract

Single-cell genomics technologies enable multimodal profiling of millions of cells across temporal and spatial dimensions. Experimental limitations prevent the measurement of all-encompassing cellular states in their native temporal dynamics or spatial tissue niche. Optimal transport theory has emerged as a powerful tool to overcome such constraints, enabling the recovery of the original cellular context. However, most algorithmic implementations currently available have not kept up the pace with increasing dataset complexity, so that current methods are unable to incorporate multimodal information or scale to single-cell atlases. Here, we introduce multi-omics single-cell optimal transport (moscot), a general and scalable framework for optimal transport applications in single-cell genomics, supporting multimodality across all applications. We demonstrate moscots ability to efficiently reconstruct developmental trajectories of 1.7 million cells of mouse embryos across 20 time points and identify driver genes for first heart field formation. The moscot formulation can be used to transport cells across spatial dimensions as well: To demonstrate this, we enrich spatial transcriptomics datasets by mapping multimodal information from single-cell profiles in a mouse liver sample, and align multiple coronal sections of the mouse brain. We then present moscot.spatiotemporal, a new approach that leverages gene expression across spatial and temporal dimensions to uncover the spatiotemporal dynamics of mouse embryogenesis. Finally, we disentangle lineage relationships in a novel murine, time-resolved pancreas development dataset using paired measurements of gene expression and chromatin accessibility, finding evidence for a shared ancestry between delta and epsilon cells. Moscot is available as an easy-to-use, open-source python package with extensive documentation at https://moscot-tools.org.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 2 (12 May 2023) · CC BY 4.0

moscot unifies optimal transport for temporal, spatial and spatiotemporal single-cell mapping, using multimodal cost spaces and low-rank solvers to scale to 1.7 million mouse embryo cells.

Optimal transport tools that link single-cell snapshots across time or place cells into spatial coordinates were uni-modal, scaled quadratically or cubically in cell number, and relied on fragmented backends. moscot adds multimodal costs, GPU-accelerated low-rank solvers with linear complexity, and a single scverse-compatible API covering temporal, spatial and new spatiotemporal problems.

Key results

  1. Shownmoscot.time evaluates the cost on the fly and offers low-rank Sinkhorn, so it can couple atlas-scale time points where Waddington OT (WOT) runs out of memory.

    On the E11.5/E12.5 pair, moscot.time coupled 275,000 cells per time point using less than 10 GiB in about 3 hours. WOT failed beyond 100,000 cells despite 700 GiB of server memory. The benchmark used 11 subsets growing in 25,000-cell steps and tested low-rank ranks 50, 200, 500 and 2000. · Recovering trajectories of mouse embryogenesis…; Memory and runtime benchmark: moscot.time versus…; Scalability through engineering-type innovations; Scalability through methodological innovations

  2. ShownOn the 20-time-point mouse embryo atlas, moscot.time matched TOME, the k-NN method built for this dataset, on transition accuracy. It also gave more plausible growth and death rates, and its ancestor probabilities tracked known driver genes more closely.

    Germ-layer and cell-type transition scores were comparable to TOME across pre-gastrulation, gastrulation and organogenesis. Cell-level TOME (cl-TOME) implied over 19% apoptosis at E8.0/8.25, against typical rates below 10% after E7.0. moscot.time had higher absolute Spearman correlations for E8.25 first heart field (24 driver genes) and three other cell types. · Recovering trajectories of mouse embryogenesis…; Metrics for the accuracy benchmark: germ-layer…; Growth rate comparison; Comparison in terms of driver gene correlations

  3. ShownFused Gromov-Wasserstein mapping imputed held-out genes better than Tangram and gimVI. It scaled to transfer CITE-seq RNA, protein and cell type labels onto a full MERSCOPE liver section, and the alignment mode registered large mouse brain sections.

    moscot beat Tangram and gimVI on held-out-gene Spearman correlation across 14 datasets (3 seeds), though only 11 gave valid results for all methods; its accuracy rose with spatial correspondence. It mapped ∼91k CITE-seq cells onto ∼367k MERSCOPE liver cells via 336 shared genes, matched or beat PASTE on synthetic alignment, and aligned brain sections of ∼250k and ∼300k cells. · Mapping and aligning spatial samples with moscot; 2.2.1 Benchmark: moscot.space.mapping across a…; 2.2.2 Application: moscot.space.mapping on the…; Figure legends

  4. Shownmoscot.spatiotemporal adds spatial structure to temporal couplings. On whole Stereo-seq mouse embryos it predicted cell transitions better than expression-only mapping, and with CellRank it recovered known heart and brain lineage drivers.

    MOSTA data: one slide per time point from E9.5 to E16.5, ∼500,000 cells. Transition scores beat the expression-only W-type problem and were robust to hyperparameters. Drivers included Gata4, Tbx20, Myl7 and Myh6 (heart) and Tcf7l2, Sox11 and Neurod2 (neurons). SPATEO needed downsampling to 2,000 cells per embryo. · Charting the spatiotemporal dynamics of mouse…; Discussion; Mapping accuracy; CellRank analysis

  5. SuggestedIn a new paired RNA/ATAC time course of mouse pancreas, multimodal moscot.time couplings point to epsilon progenitors as a shared origin of epsilon and delta cells. They also suggest that Fev+ delta cells can still become any of the four endocrine fates.

    Multiome of Ngn3-Venus-enriched epithelium at E14.5 (9,811 nuclei) and E15.5 (7,107 nuclei), with 228,259 peaks; most coupled transitions are supported by literature. Shared ancestry is backed by similar ATAC profiles, co-accessible Hhex and Ghrl promoters, and Isl1/Tead1 motif activity matched to progenitor expression. · Disentangling lineage relationships of delta and…; Preprocessing; moscot.time model; Motif analysis

Methods, data and reproducibility

Mapping tasks are cast as Wasserstein, Gromov-Wasserstein or fused Gromov-Wasserstein optimal transport (OT) problems on shared multimodal latent spaces. These are solved with entropic, unbalanced or low-rank solvers in the JAX-based OTT backend, and the resulting couplings drive ancestor/descendant, imputation, annotation-transfer and slide-alignment analyses.

  • Mouse embryogenesis scRNA-seq atlas compiled and annotated by Qiu et al. (TOME), spanning E3.5-13.5 · mouse · n = almost 1.7 million cells; 20 time points
  • Spatial transcriptomics datasets from the Li et al. benchmark, each split 50% pseudo-reference and 50% spatial query · n = 14 datasets
  • Mouse liver CITE-seq reference (Guilliams et al., Liver Cell Atlas) · mouse · n = ∼91k cells
  • Vizgen MERSCOPE mouse liver section · mouse · n = ∼367k cells
  • Vizgen MERSCOPE (MERFISH) mouse brain coronal sections; three samples from three mice per section · mouse · n = ∼250k cells (section 1); ∼300k cells (section 2)
  • MOSTA Stereo-seq spatiotemporal mouse embryo atlas (Chen et al.), one slide per time point, E9.5-E16.5 · mouse · n = ∼500,000 cells
  • New single-nucleus RNA + ATAC multiome of Ngn3-Venus fusion embryonic pancreas, endocrine-progenitor enriched by FACS · mouse · n = 9,811 nuclei (E14.5); 7,107 nuclei (E15.5)
  • Synthetic gridded gene-expression datasets for the alignment benchmark, randomly subsampled · n = four synthetic datasets
Methods & tools
moscot (moscot.time, moscot.space, moscot.spatiotemporal), OTT (Optimal Transport Tools, JAX), Waddington OT (WOT), TOME and cell-level TOME (cl-TOME), Tangram, gimVI (scVI-tools), PASTE, GPSA, CellRank (GPCCA estimator), SCANPY and squidpy, MultiVI (PoissonATAC) and MUON, Signac with chromVAR and cisBP motifs
Software & environment
OTT (JAX) backend with just-in-time compilation and GPU execution; scverse stack (SCANPY, AnnData, squidpy); Seurat v3 for embryo atlas preprocessing; benchmarks managed with SEML. No pinned package versions or containers reported.
Assay conditions & compute
Mapping benchmark on Helmholtz Cluster GPUs (mix of V100 and A100) with a 5 GPU-hour cap per method; memory benchmark on CPU, with WOT given 700 GiB; moscot.time coupled 275,000 cells per time point in under 10 GiB in about 3 hours.
Reproducibility gaps
The new pancreas multiome data are not yet deposited (promised soon); the Li et al. benchmark datasets are cited only via the original publication, with no accessions; package versions are not pinned apart from naming Seurat v3.
Limitations (6)
  • Low-rank solvers, which are needed at atlas scale, have not yet been combined with unbalanced OT. That combination matters when cell type proportions shift strongly between time points or spatial slides. · stated by the authors
  • Discrete OT couplings cannot be applied to new, out-of-sample cells without refitting; the authors point to Neural OT as a possible future remedy. · stated by the authors
  • Pancreas cells were FACS-sorted, so cell type proportions are strongly biased and predicted transitions keep their direction but not their true biological magnitude. The shared delta/epsilon ancestry hypothesis still requires experimental validation. · stated by the authors
  • Brain alignment was judged only by agreement in neighborhood gene-expression densities, because the sections lacked cell type labels; mismatches could also reflect intrinsic biological variability between sections. · stated by the authors
  • The apoptosis-rate advantage over cl-TOME is partly built in: the left unbalancedness parameter was tuned so moscot.time's predicted apoptotic fraction fell inside preset biological ranges. · noted in this summary
  • The main text gives no numeric scores for the spatial mapping, alignment or spatiotemporal gains (these are deferred to supplementary figures). The runtime test also pitted GPU moscot.time against CPU-only WOT, mixing algorithm and hardware effects. · noted in this summary

Read this if you need optimal transport to link single-cell time courses, map multimodal references onto spatial data, or align large spatial slides at atlas scale in Python.

Citations
154
FWCI
45.97
Field percentile
top 1%

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