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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, and Pan and Zhang 2023 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

Lineage tracing on transcriptional landscapes

Software: Multiple repositories

Manuscript: Lineage tracing on transcriptional landscapes links state to fate during differentiation

CALISTA

Software: https://github.com/CABSEL/CALISTA

Manuscript: CALISTA: Clustering And Lineage Inference in Single-Cell Transcriptional Analysis

TRACER

Manuscript: Mapping Lung Cancer Epithelial-Mesenchymal Transition States and Trajectories with Single-Cell Resolution

psupertime

Software: https://github.com/wmacnair/psupertime

Manuscript: psupertime: supervised pseudotime inference for single cell RNA-seq data with sequential labels

OscoNet

Software: https://github.com/alexisboukouvalas/OscoNet

Manuscript: OscoNet: Inferring oscillatory gene networks

Cyclum

Software: https://github.com/KChen-lab/cyclum

Manuscript: Latent periodic process inference from single-cell RNA-seq data

MERLoT

Software: https://github.com/soedinglab/merlot

Manuscript: Reconstructing complex lineage trees from scRNA-seq data using MERLoT

scVelo

Software: https://scvelo.org

Manuscript: Generalizing RNA velocity to transient cell states through dynamical modeling

Tempora

Software: https://github.com/BaderLab/Tempora

Manuscript: Tempora: cell trajectory inference using time-series single-cell RNA sequencing data

CellCycleTRACER

Software: https://ibm.biz/cellcycletracer-aas

Manuscript: CellCycleTRACER accounts for cell cycle and volume in mass cytometry data

TrajectoryNet

Software: https://github.com/krishnaswamylab/TrajectoryNet and https://github.com/KrishnaswamyLab/Cell-Dynamics-Pipeline

Manuscript: TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

Additional manuscript: Learning transcriptional and regulatory dynamics driving cancer cell plasticity using neural ODE-based optimal transport

redPATH

Software: https://github.com/tinglab/redPATH

Manuscript: redPATH: Reconstructing the Pseudo Development Time of Cell Lineages in Single-Cell RNA-Seq Data and Applications in Cancer

GraphDR and StructDR

Software: https://github.com/jzthree/quasildr

Manuscript: An analytical framework for interpretable and generalizable 'quasilinear' single-cell data analysis

Pseudocell Tracer

Software: https://github.com/akds/pseudocell

Manuscript: Inferring cellular trajectories from scRNA-seq using Pseudocell Tracer

TinGa

Software: https://github.com/Helena-todd/TinGa

Manuscript: TinGa: fast and flexible trajectory inference with Growing Neural Gas

scDEC

Software: https://github.com/kimmo1019/scDEC

Manuscript: Simultaneous deep generative modeling and clustering of single cell genomic data

VeTra

Software: https://github.com/wgzgithub/VeTra

Manuscript: VeTra: a new trajectory inference tool based on RNA velocity

DTFLOW

Software: https://github.com/statway/DTFLOW

Manuscript: DTFLOW: Inference and Visualization of Single-cell Pseudo-temporal Trajectories Using Diffusion Propagation

CellPath

Software: https://github.com/PeterZZQ/CellPath

Manuscript: Inference of multiple trajectories in single cell RNA-seq data from RNA velocity

CellRank / CellRank 2

Software: https://cellrank.org

CellRank manuscript: CellRank for directed single-cell fate mapping

CellRank 2 manuscript: Unified fate mapping in multiview single-cell data

Revelio

Software: https://github.com/danielschw188/Revelio

Manuscript: The transcriptome dynamics of single cells during the cell cycle

Cytopath

Software: https://github.com/aron0093/cytopath

Manuscript: Cytopath: Simulation based inference of differentiation trajectories from RNA velocity fields

VIA

Software: https://github.com/ShobiStassen/VIA

Manuscript: VIA: Generalized and scalable trajectory inference in single-cell omics data

Global Waddington-OT

Software: https://github.com/zsteve/gWOT

Manuscript: Towards a mathematical theory of trajectory inference

StationaryOT

Software: https://github.com/zsteve/StationaryOT

Manuscript: Optimal transport analysis reveals trajectories in steady-state systems

Condiments

Software: https://github.com/HectorRDB/condiments

Vignettes: https://hectorrdb.github.io/condimentsPaper/

Manuscript: Trajectory inference across multiple conditions with condiments: differential topology, progression, differentiation, and expression

DeepCycle

Software: https://github.com/andreariba/DeepCycle

Manuscript: Cell cycle gene regulation dynamics revealed by RNA velocity and deep-learning

Tricycle

Software: https://github.com/hansenlab/tricycle

Manuscript: Universal prediction of cell cycle position using transfer learning

scShaper

Software: https://github.com/elolab/scshaper

Manuscript: scShaper: ensemble method for fast and accurate linear trajectory inference from single-cell RNA-seq data

CCPE

Software: https://github.com/LiuJJ0327/CCPE

Manuscript: CCPE: Cell Cycle Pseudotime Estimation for Single Cell RNA-seq Data

scDVF

Software: https://github.com/gersteinlab/scDVF

Manuscript: scDVF: Data-driven Single-cell Transcriptomic Deep Velocity Field Learning with Neural Ordinary Differential Equations

Tempo

Software: https://github.com/bauerbach95/tempo

Manuscript: Tempo: an unsupervised Bayesian algorithm for circadian phase inference in single-cell transcriptomics

DeepVelo

Software: https://github.com/bowang-lab/DeepVelo

Manuscript: DeepVelo: Deep Learning extends RNA velocity to multi-lineage systems with cell-specific kinetics

LRT

Software: https://github.com/JuanXie19/LRT

Manuscript: LRT: T Cell Trajectory Inference by Integrative Analysis of Single Cell TCR-seq and RNA-seq data

scTour

Software: https://github.com/LiQian-XC/sctour

Manuscript: scTour: a deep learning architecture for robust inference and accurate prediction of cellular dynamics

UniTVelo

Software: https://github.com/StatBiomed/UniTVelo

Manuscript: UniTVelo: temporally unified RNA velocity reinforces single-cell trajectory inference

VITAE

Software: https://github.com/jaydu1/VITAE

Manuscript: Model-based Trajectory Inference for Single-Cell RNA Sequencing Using Deep Learning with a Mixture Prior

Real-time axis for T cells

Manuscript: From pseudotime to true dynamics: reconstructing a real-time axis for T cells differentiation

GeneTrajectory

Software: https://github.com/KlugerLab/GeneTrajectory

Manuscript Gene Trajectory Inference for Single-cell Data by Optimal Transport Metrics

scFates

Software: https://scfates.readthedocs.io/en/latest/

Manuscript: scFates: a scalable python package for advanced pseudotime and bifurcation analysis from single cell data

veloVI

Software: https://github.com/YosefLab/velovi

Manuscript: Deep generative modeling of transcriptional dynamics for RNA velocity analysis in single cells

MIRA

Software: https://github.com/cistrome/MIRA

Manuscript: MIRA: joint regulatory modeling of multimodal expression and chromatin accessibility in single cells

Pyro-Velocity

Software: https://github.com/pinellolab/pyrovelocity

Manuscript: Pyro-Velocity: Probabilistic RNA Velocity inference from single-cell data

Totem

Software: https://github.com/elolab/Totem

Manuscript: Cell-connectivity-guided trajectory inference from single-cell data

scLTNN

Software: https://github.com/Starlitnightly/scltnn

Manuscript: Identify the origin and end cells and infer the trajectory of cellular fate automatically

UPMM

Manuscript: Modeling Single-Cell Dynamics Using Unbalanced Parameterized Monge Maps

PhyloVelo

Software: https://github.com/kunwang34/PhyloVelo

Manuscript: Cell division history encodes directional information of fate transitions

MultiVelo

Software: https://github.com/welch-lab/MultiVelo

Manuscript: Multi-omic single-cell velocity models epigenome–transcriptome interactions and improves cell fate prediction

SCTC

Software: https://github.com/hailinphysics/sctc

Manuscript: SCTC: inference of developmental potential from single-cell transcriptional complexity

MIOFlow

Software: https://github.com/KrishnaswamyLab/MIOFlow

Manuscript: Manifold Interpolating Optimal-Transport Flows for Trajectory Inference

DEAPLOG

Software: https://github.com/ZhangHongbo-Lab/DEAPLOG

Manuscript: A method for differential expression analysis and pseudo-temporal locating and ordering of genes in single-cell transcriptomic data

GCSTI

Software: https://github.com/xznhy/rna-seq

Manuscript: GCSTI: A Single-Cell Pseudotemporal Trajectory Inference Method Based on Graph Compression

moscot

Software: https://moscot-tools.org/

Manuscript: Mapping cells through time and space with moscot

DELVE

Software: https://github.com/jranek/delve

Manuscript: Feature selection for preserving biological trajectories in single-cell data

Velvet

Software: https://github.com/rorymaizels/velvet

Manuscript: Deep dynamical modelling of developmental trajectories with temporal transcriptomics

ENTRAIN

Software: https://github.com/theimagelab/entrain

Manuscript: ENTRAIN: integrating trajectory inference and gene regulatory networks with spatial data to co-localize the receptor-ligand interactions that specify cell fate

TFvelo

Software: https://github.com/xiaoyeye/TFvelo

Manuscript: TFvelo: gene regulation inspired RNA velocity estimation

TopGen

Manuscript: Unraveling cell differentiation mechanisms through topological exploration of single-cell developmental trajectories

cell2fate

Software: https://github.com/BayraktarLab/cell2fate

Manuscript: Model-based inference of RNA velocity modules improves cell fate prediction

FBSDE

Software: https://github.com/Diebrate/population_model

Manuscript: Modeling Single Cell Trajectory Using Forward-Backward Stochastic Differential Equations

cy2path

Software: https://github.com/aron0093/cy2path

Manuscript: Factorial state-space modelling for kinetic clustering and lineage inference

scEGOT

Software: https://github.com/yachimura-lab/scEGOT

Manuscript: scEGOT: Single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport

Ricci flow

Manuscript: Charting cellular differentiation trajectories with Ricci flow

Flat NB-VAE

Manuscript: Modelling single-cell RNA-seq trajectories on a flat statistical manifold

Sceptic

Software: https://github.com/Noble-Lab/Sceptic

Manuscript: Pseudotime analysis for time-series single-cell sequencing and imaging data

VeloCycle

Software: https://github.com/lamanno-epfl/velocycle/

Manuscript: Statistical inference with a manifold-constrained RNA velocity model uncovers cell cycle speed modulations

Chronocell

Software: https://github.com/pachterlab/FGP_2024

Manuscript: Trajectory inference from single-cell genomics data with a process time model

PSEUDOTIMEABC

Software: https://github.com/keita-iida/PSEUDOTIMEABC

Manuscript: Identifying key regulatory genes in drug resistance acquisition: Modeling pseudotime trajectories of single-cell transcriptome

scTEP

Software: https://cran.r-project.org/package=scTEP

Manuscript: A robust and accurate single-cell data trajectory inference method using ensemble pseudotime

TrajAtlas

Software: https://github.com/GilbertHan1011/TrajAtlas

Manuscript: Trajectory-centric Framework TrajAtlas reveals multi-scale differentiation heterogeneity among cells, genes, and gene module in osteogenesis

SNOW

Software: https://bitbucket.org/biocomplexity/snow/src/main/

Manuscript Variational inference of single cell time series

Meta Flow Matching

Software: https://github.com/lazaratan/meta-flow-matching

Manuscript: Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold

scMultiNODE

Software: https://github.com/rsinghlab/scMultiNODE

Manuscript: scMultiNODE: Integrative Model for Multi-Modal Temporal Single-Cell Data

Related topics

Cicero

Manuscript: Chromatin accessibility dynamics of myogenesis at single cell resolution

Effects of imputation on cell ordering

Manuscript: Comparison of computational methods for imputing single-cell RNA-sequencing data

PROSSTT

Software: https://github.com/soedinglab/prosstt

Manuscript: PROSSTT: probabilistic simulation of single-cell RNA-seq data for complex differentiation processes

CellAlign

Software: https://github.com/shenorrLab/cellAlign

Manuscript: Alignment of single-cell trajectories to compare cellular expression dynamics

CONFESS

Software: http://bioconductor.org/packages/release/bioc/html/CONFESS.html

Manuscript: CONFESS: Fluorescence-based single-cell ordering in R

Trajectory alignment

Software: https://www.cell.com/cms/10.1016/j.cels.2018.07.006/attachment/2b57ebff-a502-4819-b8ed-8a87d17a4ae7/mmc4.zip

Manuscript: Aligning Single-Cell Developmental and Reprogramming Trajectories Identifies Molecular Determinants of Myogenic Reprogramming Outcome

ImageAEOT

Manuscript: Autoencoder and Optimal Transport to Infer Single-Cell Trajectories of Biological Processes

RNA velocity

Software: http://velocyto.org/

Manuscript: RNA velocity of single cells

devMap

Manuscript: High Resolution Comparison of Cancer-Related Developmental Processes Using Trajectory Alignment

Trajan

Software: https://github.com/canzarlab/Trajan

Manuscript: Dynamic pseudo-time warping of complex single-cell trajectories

SINGE

Software: https://github.com/gitter-lab/SINGE

Manuscript: Network inference with Granger causality ensembles on single-cell transcriptomics

GPseudoClust

Software: https://github.com/magStra/GPseudoClust

Manuscript: GPseudoClust: deconvolution of shared pseudo-trajectories at single-cell resolution

tradeSeq

Software: http://www.bioconductor.org/packages/release/bioc/html/tradeSeq.html

Manuscript: Trajectory-based differential expression analysis for single-cell sequencing data

CORGI

Software: https://github.com/YutongWangUMich/corgi

Manuscript: A gene filter for comparative analysis of single-cell RNA-sequencing trajectory datasets

BEELINE

Software: https://github.com/murali-group/Beeline

Manuscript: Benchmarking algorithms for gene regulatory network inference from single-cell transcriptomic data

Dynamo

Software: https://github.com/aristoteleo/dynamo-release

Manuscript: Mapping Vector Field of Single Cells

SERGIO

Software: https://github.com/PayamDiba/SERGIO

Manuscript: A single-cell expression simulator guided by gene regulatory networks

GeneSwitches

Software: https://geneswitches.ddnetbio.com/

Manuscript: GeneSwitches : Ordering gene-expression and functional events in single-cell experiments

CAPITAL

Software: https://github.com/ykat0/capital

Manuscript: Alignment of time-course single-cell RNA-seq data with CAPITAL

Transcriptional uncertainty landscapes

Manuscript: Universality of cell differentiation trajectories revealed by a reconstruction of transcriptional uncertainty landscapes from single-cell transcriptomic data

Pseudo-Location

Manuscript: Pseudo-Location: A novel predictor for predicting pseudo-temporal gene expression patterns using spatial functional regression

fishpond

Software: http://bioconductor.org/packages/devel/bioc/html/fishpond.html and https://github.com/skvanburen/scUncertaintyPaperCode

Manuscript: Compression of quantification uncertainty for scRNA-seq counts

scHOT

Software: https://bioconductor.org/packages/scHOT

Manuscript: Investigating higher-order interactions in single-cell data with scHOT

PRESCIENT

Software: https://github.com/gifford-lab/prescient

Manuscript: Generative modeling of single-cell population time series for inferring cell differentiation landscapes

Mathematics of RNA Velocity

Manuscript: On the Mathematics of RNA Velocity I: Theoretical Analysis

Mathematics of RNA Velocity II

Manuscript: On the Mathematics of RNA Velocity II: Algorithmic Aspects

PseudotimeDE

Software: https://github.com/SONGDONGYUAN1994/PseudotimeDE

Manuscript: PseudotimeDE: inference of differential gene expression along cell pseudotime with well-calibrated p-values from single-cell RNA sequencing data

TIPS

Manuscript: TIPS: Trajectory Inference of Pathway Significance through Pseudotime Comparison for Functional Assessment of single-cell RNAseq Data

VeloSim

Software: https://github.com/PeterZZQ/VeloSim

Manuscript: VeloSim: Simulating single cell gene-expression and RNA velocity

<details> <summary>Abstract</summary> The availability of high throughput single-cell RNA-Sequencing data allows researchers to study the molecular mechanisms that drive the temporal dynamics of cells during differentiation or development. Recent computational methods that build upon single-cell sequencing technology, such as trajectory inference or RNA-velocity estimation, provide a way for researchers to analyze the state of each cell during a continuous dynamic process. However, with the surge of such computational methods, there is still a lack of simulators that can model the cell temporal dynamics, and provide ground truth data to benchmark the computational methods.

Hereby we present VeloSim, a simulation software that can simulate the gene-expression kinetics in cells along continuous trajectories. VeloSim is able to take any trajectory structure composed of basic elements including “linear” and “cycle” as input, and outputs unspliced mRNA count matrix, spliced mRNA count matrix, cell pseudo-time and true RNA velocity of the cells. We demonstrate how VeloSim can be used to benchmark trajectory inference and RNA-velocity estimation methods with different amounts of biological and technical variation within the datasets. VeloSim is implemented into an R package available at https://github.com/PeterZZQ/VeloSim.

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