Single-cell RNA-seq pseudotime estimation algorithms

Single cells, many algorithms. The goal of this page is to catalog the many algorithms that estimate pseudotimes for cells based on their gene expression levels. This problem is also referred to as single-cell trajectory inference or ordering. It contains method names, software links, and manuscript links and simply seeks to list as many methods as possible without commentary. Some related methods not specifically designed for RNA-seq (e.g. mass cytometry) are included as well, as are some methods for estimating RNA velocity. The list also includes methods that are specifically designed to take pseudotemporal data as input.

The initial list was created by Anthony Gitter, but pull requests are very welcome. Thank you to the other contributors.

Citation

Anthony Gitter. Single-cell RNA-seq pseudotime estimation algorithms. 2018. doi:10.5281/zenodo.1297422 https://github.com/agitter/single-cell-pseudotime

Problem overview

Informally, the pseudotime estimation problem can be stated as:

• Given: single-cell gene expression measurements for a heterogeneous collection of cells that is transitioning from biological state A to state B
• Return: a quantitative value for each cell that represents its progress in the A to B transition

There are many ways to approach this problem, and major algorithmic steps that are common to most (but not all) methods are:

• Reduce the dimension of the dataset
• Find a smooth progression through the low dimensional data, assuming that cells that are nearby one another in the low dimensional space have similar expression levels because they are at similar points in to A to B process

Dimension reduction sometimes relies on knowledge of important marker genes and sometimes uses the full gene expression matrix. The trajectory through the low dimensional space can be identified using graph algorithms (e.g., minimum spanning tree or shortest path), principal curves, or probabilistic models (e.g., Gaussian process).

Bacher and Kendziorski 2016, Trapnell 2015, Tanay and Regev 2017, Moon et al. 2017, Tritschler et al. 2019, Weiler et al. 2021, Ding et al. 2022, Pan and Zhang 2023, Hutton and Meyer 2025, and Richter et al. 2026 provide a more comprehensive overview of single-cell RNA-seq and the pseudotime estimation problem. Cannoodt et al. 2016 reviews pseudotime inference algorithms. Pablo Cordero's blog post discusses why it is hard to recover the correct dynamics of a system from single-cell data. For more general lists of methods for single-cell RNA-seq see seandavi/awesome-single-cell and scRNA-tools. The Hemberg lab single-cell RNA-seq course has an overview of five pseudotime algorithms with usage examples. Many modern ideas for pseudotime estimation are descended from Magwene et al. 2003 on reconstructing the order of microarray expression samples.

Single-cell expression data have also inspired new methods for gene regulatory network reconstruction, as reviewed by Fiers et al. 2018 and Todorov et al. 2018. Several of these, such as SINGE, treat pseudotime annotations as time points and extend traditional time series network inference algorithms for single-cell data. BEELINE, SERGIO, and McCalla et al. 2023 benchmark many of these specialized network inference methods.

Choosing a method

Some of the distinguishing factors among algorithms include:

• Use of prior knowledge such as capture times (DeLorean) or switch-like marker genes (Ouija)
• Modeling specific types of biological processes such as branching processes in differentiation (multiple methods) or cyclic processes (Oscope)
• Return a single pseudotime or a posterior distribution over pseudotimes for each cell
• Perform additional analyses after inferring pseudotimes such as regulatory network inference or identifying differentially expressed genes over pseudotime

Saelens et al. 2019 performed a comprehensive evaluation of 29 different single-cell trajectory inference methods and discuss the different types of algorithms in more detail. They benchmark both quantitative performance and assess software quality. See their website and GitHub repository as well. Tian et al. 2018 also include trajectory inference algorithms in their single-cell RNA-seq benchmarking study. Escort is a framework to help guide the selection of a suitable trajectory inference algorithm for a dataset.

Algorithms

Temporal Reconstruction Algorithm

Manuscript: Reconstructing the temporal ordering of biological samples using microarray data

Monocle / Monocle 2 / Monocle 3 / Census

Software: https://bioconductor.org/packages/release/bioc/html/monocle.html

Monocle manuscript: The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells

Census manuscript: Single-cell mRNA quantification and differential analysis with Census

Monocle 2 manuscript: Reversed graph embedding resolves complex single-cell trajectories

Monocle 3 manuscript: The single-cell transcriptional landscape of mammalian organogenesis

Wanderlust / Cycler / Wishbone

Wanderlust software: http://www.c2b2.columbia.edu/danapeerlab/html/wanderlust.html

Wanderlust manuscript: Single-Cell Trajectory Detection Uncovers Progression and Regulatory Coordination in Human B Cell Development

Cycler manuscript: Trajectories of cell-cycle progression from fixed cell populations

Wishbone software: http://www.c2b2.columbia.edu/danapeerlab/html/wishbone.html

Wishbone manuscript: Wishbone identifies bifurcating developmental trajectories from single-cell data

SCUBA

Software: https://github.com/gcyuan/SCUBA

Manuscript: Bifurcation analysis of single-cell gene expression data reveals epigenetic landscape

Oscope

Software: https://www.biostat.wisc.edu/~kendzior/OSCOPE/

Manuscript: Oscope identifies oscillatory genes in unsynchronized single-cell RNA-seq experiments

Diffusion maps / destiny

destiny software: http://bioconductor.org/packages/release/bioc/html/destiny.html

Diffusion maps manuscript (a): Decoding the regulatory network of early blood development from single-cell gene expression measurements

Diffusion maps manuscript (b): Diffusion maps for high-dimensional single-cell analysis of differentiation data

destiny manuscript: destiny: diffusion maps for large-scale single-cell data in R

DeLorean

Software: https://github.com/JohnReid/DeLorean

Manuscript: Pseudotime estimation: deconfounding single cell time series

Waterfall

Manuscript: Single-Cell RNA-Seq with Waterfall Reveals Molecular Cascades underlying Adult Neurogenesis

Embeddr

Software: https://github.com/kieranrcampbell/embeddr

Manuscript: Laplacian eigenmaps and principal curves for high resolution pseudotemporal ordering of single-cell RNA-seq profiles

GP-LVM and pseudogp

GP-LVM software: https://github.com/kieranrcampbell/gpseudotime

GP-LVM manuscript: Bayesian Gaussian Process Latent Variable Models for pseudotime inference in single-cell RNA-seq data

pseudogp software: https://github.com/kieranrcampbell/pseudogp

pseudogp manuscript: Order Under Uncertainty: Robust Differential Expression Analysis Using Probabilistic Models for Pseudotime Inference

GP-LVM

Analysis code: https://github.com/Teichlab/spectrum-of-differentiation-supplements

Manuscript: Single-Cell RNA-Sequencing Reveals a Continuous Spectrum of Differentiation in Hematopoietic Cells

SLICER

Software: https://github.com/jw156605/SLICER

Manuscript: SLICER: inferring branched, nonlinear cellular trajectories from single cell RNA-seq data

TSCAN

Software: https://github.com/zji90/TSCAN

Manuscript: TSCAN: Pseudo-time reconstruction and evaluation in single-cell RNA-seq analysis

SCOUP

Software: https://github.com/hmatsu1226/SCOUP

Manuscript: SCOUP: a probabilistic model based on the Ornstein–Uhlenbeck process to analyze single-cell expression data during differentiation

Topslam

Software: https://github.com/mzwiessele/topslam

Manuscript: Topslam: Waddington Landscape Recovery for Single Cell Experiments

Ouija

Software: https://github.com/kieranrcampbell/ouija and http://www.github.com/kieranrcampbell/ouijaflow

Manuscript: A descriptive marker gene approach to single-cell pseudotime inference

CellTrails

Sofware: https://bioconductor.org/packages/release/bioc/html/CellTrails.html

Manuscript: Transcriptional dynamics of hair-bundle morphogenesis revealed with CellTrails

Slingshot

Software: https://github.com/kstreet13/slingshot

Extended vignette: https://github.com/drisso/bioc2016singlecell/tree/master/vignettes

Manuscript: Slingshot: Cell lineage and pseudotime inference for single-cell transcriptomics

Workflow manuscript: Bioconductor workflow for single-cell RNA sequencing: Normalization, dimensionality reduction, clustering, and lineage inference

GPfates

Software: https://github.com/Teichlab/GPfates

Manuscript: [Temporal mixture modelling of single-cell RNA-seq data resol