Computational modeling of single-cell dynamics data

Abstract

Deciphering the cell dynamics in complex biological systems is of great significance for understanding the mechanisms of life and facilitating disease treatment. Recent advances in single-cell sequencing technologies have enabled the measurement of single-cell characteristics over multiple time points. However, the integration and analysis of these dynamic single-cell data face many challenges and raise new demands for computational methodologies. In this review, we first elaborate these challenges in the context of experimental limitations, data features, and biological discoveries. Then, we provide an overview of the algorithmic advancements across four key tasks: inferring single-cell dynamics, dissecting dynamic mechanisms, predicting future cell fates, and integrating lineage tracing information to characterize cell dynamics. Finally, we discuss that the cutting-edge developments in biological technologies and artificial intelligence algorithms may greatly enhance our ability to explore complex life processes from a spatiotemporal systemic perspective.

Introduction

Biological systems are highly complex and dynamic, no matter whether under the processes of tissue development, disease progression, or responses to external perturbations. Dissecting the molecular mechanisms that govern cell fate during these dynamic biological processes is crucial for advancing our understanding of life and developing strategies to treat diseases. Over the past few years, advancements in single-cell omics technologies have greatly empowered the study of cell states and types under various scenarios. Furthermore, detecting time-series single-cell data provides valuable opportunities to investigate the cell dynamics. For example, tracking single-cell characteristics at different stages of tissue development facilitates the analysis of cell differentiation trajectories and the identification of key regulators of cell fates (Fig. 1A) [1–6]. Comparing tumor patient samples across different disease stages (such as precancer, diagnosis, minimal residual disease, and relapse) enables the study of tumor clonal evolution during disease progression and the identification of cellular and molecular markers associated with the diseases (Fig. 1B) [7–10]. Analyzing tumor samples before and after drug treatment provides insights into the dynamic plasticity of tumor cells and the mechanisms of drug resistance (Fig. 1C) [11–14]. Besides, the recent lineage tracing technologies, which introduce inherited DNA barcodes into cells to label the lineage relationships between cells, offer more direct evidence for investigating the dynamics of tissue development and tumor drug responses (Fig. 1D) [15–17].

Figure 1.

Biological scenarios of modeling time-series single-cell dynamics data. (A) Embryonic development process. PCM, postconception week. (B) Disease progression, illustrated by a schematic that depicts changes in tumor burden across different disease stages, including diagnosis, minimal residual disease, and relapse. (C) The cellular response to drug treatment. (D) Single-cell lineage tracing experiment.

Some traditional strategies and algorithms have been proposed to computationally analyze cellular dynamics. The first category is trajectory inference, which orders cells into linear, bifurcating, tree-like, or cyclic pseudotime trajectories based on transcriptomics similarities between cells [18, 19]. The second category is RNA velocity, which utilizes the ratio of spliced transcripts to unspliced transcripts to infer the “velocity” of gene expression change, providing a novel perspective on instantaneous dynamics of cells [20–22]. Both these kinds of approaches infer dynamics solely from a static snapshot of single cells; thus, they cannot incorporate physical time information of cell sampling when applied to time-series single-cell data. In contrast, the third category is to compare single-cell data across different time points. Direct integrated clustering [7, 14] and nonlinear distribution comparison algorithms, such as PopAlign [23] and MELD [24], are some strategies to analyze dynamics at the cluster or population level. However, this population-level modeling does not fully consider the variation among individual cells, which may overlook significant dynamics and interactions that occur at the cell level.

In recent years, cell-level algorithms have been developed specifically for modeling time-series single-cell data, with the goal of identifying cellular dynamics and molecular mechanisms at the single-cell level. This review primarily focuses on these computational advancements. We begin by elucidating the key challenges associated with computational modeling of single-cell dynamics data (Fig. 2). Subsequently, we provide an overview of the computational methods designed to overcome these challenges (Fig. 3 and Table 1).

Figure 2.

Computational challenges in modeling single-cell dynamics data. (A) Single-cell data exhibit extremely high dimensionality in their molecular characteristics. (B) Cells are destroyed during omics data detection experiment, so the time-series single-cell data are unpaired. (C) During the dynamic processes, cells can proliferate or undergo apoptosis. (D) The cell dynamics are very complex, reflecting the intricate interplay between biological signals and noise.

Figure 3.

Computational methods for modeling single-cell dynamics data. (A) Inferring single-cell dynamics through approaches such as (i) stochastic differential equations and (ii) optimal transport methods. (B) Dissecting the dynamics mechanism at (i) the cell level (such as identifying transition cells) and (ii) the gene level (such as using factor analysis to extract known, potential, or confounding factors). (C) Predicting future cell fates utilizing a conditional variational autoencoder (VAE) framework. (D) Integrating lineage tracing information with transcriptomic similarities to characterize cell dynamics. (E) Utilizing foundation models to analyze single-cell dynamics. (F) Modeling cell dynamics from a spatiotemporal perspective.

Table 1.

Summary of the algorithms for modeling dynamic single-cell data.

Name	Description	Taska	Code, environment, and requirement	Ref.
Waddington-OT	A framework that uses OT to infer the evolution of cell-state distributions over time from scRNA-seq time-course data, capturing probable origins and cell fates in gene expression space	I, II	https://github.com/broadinstitute/wot, Python (anndata, POT), CPU	[32]
TrajectoryNet	Dynamic-OT-based algorithm constructing the continuous paths taken between distributions to infer cellular dynamics	I, II	https://github.com/KrishnaswamyLab/TrajectoryNet, Python (torch, scanpy, scprep, POT), GPU	[39]
			https://github.com/KrishnaswamyLab/Cell-Dynamics-Pipeline, Python (torch, scanpy, scprep, POT), GPU	[38]
PRESCIENT	A generative framework that models single-cell dynamics in real-time using population-level time-series data, modeling cellular differentiation as a diffusion process	I, III	https://github.com/gifford-lab/prescient, Python (torch, scanpy), GPU	[29]
GraphFP	A nonlinear Fokker–Planck equation on graph-based model to reconstruct the cell-state-transition potential energy landscape from time-series scRNA-seq data	I	https://github.com/QiJiang-QJ/GraphFP, R (deSolve, igraph), CPU	[30]
PI-SDE	A physics-informed neural stochastic differential equation framework to learning the cellular dynamics and potential energy landscape based on time-series scRNA-seq data	I, III	https://github.com/QiJiang-QJ/PI-SDE, Python (torch, POT), GPU	[31]
Cstreet	A KNN-graph-based cell-state trajectory inference method for time-series scRNA-seq data	I	https://github.com/TongjiZhanglab/CStreet, Python (scanpy, networkx), CPU	[95]
UPMM	Application of unbalanced parameterized Monge maps for trajectory inference on real-world developmental single-cell data	I	No source code provided	[96]
TIGON	A dynamic, unbalanced OT method to reconstruct dynamic trajectories and population growth simultaneously as well as the underlying GRN from multiple snapshots	I, II	https://github.com/yutongo/TIGON, Python (torch, torchdiffeq), GPU	[40]
CellOT	A neural OT framework for learning the response of individual cells to a given perturbation by mapping these unpaired distributions, solved by convex neural networks	I, III	https://github.com/bunnech/cellot, Python (torch, scanpy), CPU	[37]
CINEMA-OT	Causal-inference-based approach separating confounding sources of variation from perturbation effects to obtain an optimal transport matching that reflects counterfactual cell pairs	I, II, III	https://github.com/vandijklab/CINEMA-OT, Python (scanpy, statsmodels), CPU	[33]
scTIE	An autoencoder-based method that integrates temporal multimodal data and infers GRNs predictive of cellular state	I, II	https://github.com/SydneyBioX/scTIE, Python (torch), GPU	[52]
scStateDynamics	Inferring single-cell dynamics and identifying cluster-shared and cluster-specific gene factors from the cell-level expression changes to dissect the drug action mechanisms	I, II	https://github.com/wguo-research/scStateDynamics, Python (torch, scanpy, POT, pyro-ppl), CPU	[35]
Perturb-OT	A single-cell-level cross-modality matching and perturbation response prediction method based on Gromov–Wasserstein OT	I, III	https://github.com/Genentech/Perturb-OT, Python (torch, scanpy, POT, scvi-tools), GPU	[34]
Moscot	A general and scalable framework for mapping multimodal cellular distributions through time and space based on Gromov–Wasserstein OT	I	https://github.com/theislab/moscot, Python (ott-jax, scanpy, networkx), GPU	[36]
Dynamo	A computational framework utilizing scRNA-seq together with RNA velocity and metabolic labeling to infer absolute RNA velocity and reconstruct continuous vector fields	I	https://github.com/aristoteleo/dynamo, Python (anndata, statsmodels, networkx), CPU	[41]
CellRank	A method that combines the robustness of trajectory inference and RNA velocity for single-cell fate mapping in diverse scenarios, including regeneration, reprogramming, and disease	I	https://github.com/theislab/cellrank, Python (pyGPCCA, scanpy, network, scvelo), CPU	[42]
CellRank2	A versatile and scalable framework to infer cellular fate using multiview single-cell data, consistently recovering terminal states and fate probabilities across data modalities	I	https://github.com/theislab/cellrank, Python (pyGPCCA, scanpy, network, scvelo), CPU	[43]
MuTrans	Modeling cell-fate transitions as multiscale stochastic dynamics, using random walk probabilities and Langevin dynamics to identify stable attractors, transition states, and regulatory genes	II	https://github.com/cliffzhou92/MuTrans-release, Python (PyEMMA, scanpy) or MATLAB (optimization toolbox), CPU	[44]
MEFISTO	A factor analysis framework for modeling single-cell multiomics data when spatial or temporal dependencies between the samples are known	II	https://github.com/bioFAM/MOFA2, R (Seurat) or https://github.com/bioFAM/mofapy2, Python (dtw-python), GPU	[45]
TDL	Deep learning methods (RNNs, LSTM networks, or 3D CNNs) for gene interaction prediction from time-course scRNA-seq data	II	https://github.com/xiaoyeye/TDL, Python (keras, theano), GPU	[50]
dynDeepDRIM	A 4D-CNN-based deep learning model to reconstruct GRNs using time-course scRNA-seq data, representing the joint expression of a gene pair as an image	II	https://github.com/ericcombiolab/dynDeepDRIM, Python (keras), GPU	[51]
PROB	A latent temporal progression based Bayesian method to infer GRNs from the cross-sectional transcriptomic data of tumor samples	II	https://github.com/SunXQlab/PROB, MATLAB	[49]
CellDrift	Generalized linear models designed to identify covarying temporal patterns across different cell types in response to perturbations	II, III	https://github.com/KANG-BIOINFO/CellDrift, Python (scanpy, statsmodels), CPU	[97]
RENGE	A computational method inferring GRNs using time-series single-cell CRISPR datasets	II	https://github.com/masastat/RENGE, Python (jax, statsmodels), GPU	[98]
GSFA	Guided sparse factor analysis method inferring latent factors that represent coregulated genes or gene modules	II	https://github.com/xinhe-lab/GSFA, C++ (RcppArmadillo), CPU	[46]
contrastiveVI	Contrastive variational inference framework for deconvolving variations in treatment–control scRNA-seq datasets into shared and treatment-specific latent variables	II, III	https://github.com/suinleelab/contrastiveVI, Python (torch, scanpy, scvi-tools), GPU	[61]
Genes2Genes	A Bayesian information-theoretic dynamic programming framework for gene-level alignment of single-cell trajectories	II	https://github.com/Teichlab/Genes2Genes, Python (torch, anndata, gseapy), CPU	[47]
TDEseq	A temporal gene expression analysis approach built upon the linear additive mixed models to characterize the temporal gene expression changes for time-course scRNA-seq datasets	II	https://github.com/fanyue322/TDEseq, R (Seurat), CPU	[48]
biolord	A deep generative method for disentangling single-cell multiomics data to multiple attributes and predictions of cellular response to unseen drugs and genetic perturbations	II, III	https://github.com/nitzanlab/biolord, Python (torch, scanpy, scvi-tools), GPU	[58]
scGen	A model combining variational autoencoders and latent space vector arithmetic for scRNA-seq, aiming at modeling perturbation response of cells across cell types, studies, and species	III	https://github.com/theislab/scgen, Python (torch, scanpy, scvi-tools), GPU	[57]
trVAE	Out-of-distribution generation by regularizing the joint distribution across the categorical variable in the framework of a cVAE	III	https://github.com/theislab/trVAE, Python (keras, scanpy), GPU	[56]
scDEAL	A deep transfer learning framework for predicting single-cell cancer drug response labels (sensitive and resistant) by leveraging large-scale bulk cell line datasets	III	https://github.com/OSU-BMBL/scDEAL, Python (torch, scanpy), GPU	[54]
chemCPA	A compositional perturbation autoencoder that incorporates knowledge about the compounds’ structure, enabling the prediction of drug perturbations at a single-cell level from molecular representations	III	https://github.com/theislab/chemCPA, Python (torch, scanpy), GPU	[55]
GEARS	A deep learning method leveraging prior knowledge graphs to predict transcriptional responses to single and multigene perturbations using scRNA-seq	III	https://github.com/snap-stanford/GEARS, Python (torch, torch_geometric, scanpy, networkx), GPU	[60]
Sagittarius	A transformer-based model that can accurately extrapolate gene expression profiles outside the range of measured time points	III	https://github.com/addiewc/Sagittarius, Python (torch, statsmodels, anndata), GPU	[64]
PRnet	A perturbation-conditioned deep generative model that predicts transcriptional responses to novel chemical perturbations that have never experimentally perturbed at bulk and single-cell levels	III	https://github.com/Perturbation-Response-Prediction/PRnet, Python (torch, scanpy), GPU	[59]
scDiff	A general single-cell analysis framework based on a conditional diffusion generative model by unifying various tasks as posterior modeling problems	III	https://github.com/OmicsML/scDiff, Python (transformers, scanpy, scprep, scvi-tools), GPU	[65]
LineageOT	A unified framework leveraging OT to reconstruct developmental trajectories from LT-scSeq	I, IV	https://github.com/aforr/LineageOT, Python (scanpy, networkx, POT), CPU	[67]
CoSpar	A robust computational approach based on coherent and sparse optimization to infer cell dynamics from LT-scSeq	I, II, IV	https://github.com/AllonKleinLab/cospar, Python (scanpy, statsmodels), CPU	[68]
Moslin	A Gromov–Wasserstein OT model to map lineage-traced cells across time points	I, IV	https://github.com/theislab/moslin, Python (moscot), GPU	[69]
scTrace+	A method combining lineage tracing and multifaceted transcriptomic similarity information to enhance cell-fate inference	I, IV	https://github.com/czythu/scTrace, Python (scanpy, node2vec), CPU	[70]
Geneformer	A context-aware, attention-based pretraining model on single-cell transcriptome data to enable predictions in network biology with limited data through transfer learning	V	https://huggingface.co/ctheodoris/Geneformer, Python (scanpy, torch), GPU	[73]
scGPT	A foundation model in the single-cell multiomics data with a generative pretraining approach	V	https://github.com/bowang-lab/scGPT, Python (scanpy, torch, scvi-tools), GPU	[74]
scFoundation	A large pretrained model using asymmetric transformer-like architecture to capture complex context relations among genes in a variety of cell types and states	V	https://github.com/biomap-research/scFoundation, Python (scanpy, torch, scvi-tools), GPU	[75]
SLAT	A graph adversarial matching algorithm to align heterogenous spatial data across distinct technologies and modalities	VI	https://github.com/gao-lab/SLAT, Python (scanpy, torch), GPU	[92]
STAligner	A graph attention neural network to integrate and align ST datasets across different conditions, technologies, and developmental stages	VI	https://github.com/zhanglabtools/STAligner, Python (scanpy, torch), GPU	[93]
Spateo	A framework for 3D reconstruction and characterization of spatial gradients and cellular interactions at whole-organ and embryo levels, using spatial transcriptomics	VI	https://github.com/aristoteleo/spateo-release, Python (anndata, torch), GPU	[94]

^aTask I: single-cell dynamics inference; task II: dynamic mechanism dissecting; task III: cell-fate prediction; task IV: integrating lineage tracing information; task V: foundation model-based dynamics analysis; and task VI: spatiotemporal dynamics modeling.

We categorize these algorithms into four main tasks: (i) inferring the single-cell dynamics, which involves aligning the cells from different time points to construct a temporal landscape of cellular dynamics (Fig. 3A); (ii) dissecting dynamic mechanisms, which aims to identify important cell subpopulations during dynamic processes, as well as key genes and pathways associated with the cell fate determination (Fig. 3B); (iii) predicting cell fates, which seeks to infer future cell states, such as predicting the cellular responses to perturbation (Fig. 3C); and (iv) integrating lineage tracing information to elucidate

cell dynamics, which incorporates additional experimental data to achieve a more comprehensive characterization of cell dynamics (Fig. 3D). Furthermore, we summarize the cutting-edge advances in biotechnology and artificial intelligence (AI) technology related to cell dynamics analysis, as well as the new paradigm of spatiotemporal dynamics modeling (Fig. 3E and F). Relevant information on these algorithms, including method descriptions, task categories, code repositories, programming languages (Python, R, or MATLAB), primary dependency packages (such as scanpy [25] and Seurat [26]), hardware requirements (CPU/GPU), as well as benchmarking methods with evaluation metrics, is summarized in Tables 1 and S1.

Challenges of modeling single-cell dynamics data

The limitations of single-cell sequencing experiments, coupled with the inherent characteristics of the data, pose significant challenges for the computational modeling and biological interpretation of single-cell dynamics data.

First, the state space of single cells is extremely high dimensional (Fig. 2A). Current single-cell RNA sequencing (scRNA-seq) technologies can detect gene expression values of over 20 000 genes. Despite this high dimensionality, cellular dynamics typically follow a low-dimensional manifold [27]. Therefore, it is necessary to identify a latent manifold space that more intuitively reflects cellular dynamics and to measure distances between cells based on their intrinsic manifold structure.

Second, because the experiment of detecting single-cell omics characteristics results in cell destruction, time-series single-cell data are not from the same set of cells (Fig. 2B). To capture cell-level dynamics, we need to assume that the sampled cells are representative of the overall cell population and computationally align the cells across different time points.

Third, changes in cell population abundance are also critical aspects of cellular dynamics. During biological processes, cells proliferate or undergo apoptosis (Fig. 2C). In the scenarios of development and differentiation, distinct cell types may exhibit unique trends of cell population abundance changes. Similarly, under drug perturbation conditions, different cell clusters may display varying degrees of sensitivity or resistance to the drug. Thus, incorporating changes in cell population abundance into algorithm modeling is also important.

Fourth, the observed cell dynamics is a highly complex process, reflecting a confluence of meaningful biological signals and various confounding factors (Fig. 2D). These coupled factors pose significant challenges in mitigating technological noise to identify biologically meaningful and interpretable factors underlying cell dynamics. Moreover, some important cell subpopulations, such as transition cells, are often rare and difficult to capture. This brings great challenges for identifying the cellular or molecular mechanisms involved in natural or perturbed processes, and further complicates the prediction of future cell fates.

Besides, the computational resource requirements of models are also important. More complex models (such as deep learning architectures) may achieve better performance but typically demand greater memory usage, longer runtime, and the use of hardware acceleration by GPUs. Therefore, it is crucial to consider the trade-offs between model complexity and practical efficiency.

Computational methods for modeling single-cell dynamics data

Single-cell dynamics inference

Temporal alignment of single-cell dynamics transcriptomic data is a fundamental computational task aimed at reconstructing the progression of dynamic biological processes. ScRNA-seq captures high-dimensional snapshots of the cellular states at multiple time points. An accurate alignment enables researchers to reconstruct developmental trajectories, uncover transition states, and map lineage decisions. For instance, in stem cell differentiation, alignment methods reveal how intermediate states emerge and resolve into specific fates. Similarly, in disease progression studies, temporal alignment can be used to identify critical stages and regulatory shifts, providing insights into therapeutic targets. Moreover, in response to perturbations such as drug treatments, these methods facilitate the understanding of cellular adaptation and resistance mechanisms.

However, cells are often sampled asynchronously, which makes it challenging to understand their temporal relationships. To overcome this challenge, some novel methods are proposed, which incorporate time-series data and leverage temporal constraints to improve alignment accuracy and biological interpretability. Current mainstream algorithms for aligning temporal scRNA-seq data include stochastic differential equation (SDE)-based and optimal transport (OT)-based modeling (Fig. 3A). SDE-based methods capture cellular dynamics by modeling transitions as continuous stochastic processes [Fig. 3A(i)], while OT leverages the distributional similarity of cell states to map cells across time points and experimental conditions [Fig. 3A(ii)].

Previous work has shown that a global potential function of a time series can be inferred through a diffusion-based model that is fitted to well-mixed, cross-sectional observations. Based on this, differential equations are widely used to modeling the cellular dynamics [28–31]. For example, PRESCIENT is a generative framework that models single-cell dynamics in real time using population-level time-series data [29]. It models cellular differentiation as a diffusion process given by the SDE, describing the cell-state evolution as governed by a drift term, representing deterministic changes along the negative gradient of a potential function, and a noise term, accounting for stochastic variability [Fig. 3A(i)]. The model is trained on observed time-series data and can simulate future cell states, capturing both the deterministic and random components of cellular dynamics. This approach enables realistic modeling of development processes in physical time, bridging population-level observations and single-cell differentiation trajectories.

Recently, OT has emerged as a robust and scalable framework for temporal alignment of single-cell time-series data. OT provides a mathematical approach for mapping one probability distribution to another, while minimizing a predefined cost function. In the context of scRNA-seq, cells sampled at different time points are treated as distributions in the gene expression space, and OT finds the optimal mapping that aligns these distributions. OT-based models (such as Waddington-OT [32], CINEMA-OT [33], Perturb-OT [34], scStateDynamics , [35], and Moscot [36]) compute the “transport plan,” which minimizes the cost of aligning cells from one time point to the next [Fig. 3A(ii)]. The cost function can be based on distances in the gene expression space, and often incorporates biological priors, such as temporal smoothness or trajectory continuity, to ensure plausible alignments.

Recent developments have combined OT with additional modeling techniques to enhance its biological relevance. Neural OT methods offer powerful tools for analyzing complex distributions in both static and dynamic contexts. The approach using convex neural networks parameterizes the dual formulation of an OT with a convex neural network, ensuring stable optimization and accurately solving static OT problems. This method is well suited for aligning two static distributions, such as single-cell transcriptomic profiles under different experimental conditions, enabling cross-condition comparisons and uncovering correspondences between datasets. For instance, CellOT models the effects of perturbations on single-cell distributions by learning mappings ​that transform untreated distributions ​ into perturbed ones​ through neural OT [37]. These mappings, parameterized as gradients of dual potentials, are learned independently for each perturbation, enabling CellOT to generalize predictions to untreated cells from new, unseen samples. Finally, CellOT is validated through drug response predictions in melanoma cell lines, revealing reprogramming of the MEK and PI3K pathways and identifying cellular adaptations associated with resistance to MEK inhibitors. It also predicted transcriptomic responses in lupus patients to interferon-β, highlighting changes in genes such as CXCL11 and CCL2. Additionally, CellOT accurately modeled innate immune responses across species, particularly in lipopolysaccharide-induced reactions.

By contrast, neural ordinary differential equation (ODE)-based dynamic OT extends OT into the temporal domain by leveraging neural ODEs to model the continuous evolution of distributions over time [38–40]. This approach explicitly incorporates temporal trends and accounts for dynamic changes and unbalanced mass variations, such as cell proliferation and apoptosis, making it particularly effective for analyzing single-cell time-series data and developmental trajectories. For example, TIGON is a dynamic, unbalanced OT model that connects unpaired time-series single-cell transcriptomic data to infer cell velocity, growth, and cellular dynamics [40]. Using the Wasserstein–Fisher–Rao distance, TIGON captures changes in gene expression and cell populations over time, leverages a neural-ODE-based mesh-free formulation for efficient computation, and infers temporal gene regulatory networks (GRNs) and growth-associated genes.

In addition to OT-based approaches, integrating the RNA velocity [20] remains a powerful strategy for inferring cell dynamics. The RNA velocity can infer directional information about the future state of individual cells based on unspliced and spliced mRNA abundances. Although the inference of RNA velocity is not the same task as modeling cell dynamics using physical time-series (rather than a snapshot) single-cell data, it still offers helpful information. Dynamo is a method that integrates metabolic labeling with RNA velocity to infer single-cell dynamics quantitatively [41]. By directly measuring nascent RNA through time-resolved scRNA-seq, Dynamo overcomes the limitations of traditional methods that rely on the balance between spliced and unspliced transcripts, and provides absolute estimates of RNA kinetic parameters such as transcription, splicing, and degradation rates. It integrates RNA metabolic labeling with splicing kinetics to model expression dynamics and RNA turnover. Then, it robustly reconstructs continuous transcriptomic vector fields from discrete single-cell data based on machine learning and utilizes differential geometry (e.g. Jacobian, acceleration, curvature, and divergence) to enhance biological interpretation. Finally, the framework predicts optimal cell-fate transitions and identifies key regulatory drivers via least-action paths and in silico perturbation. Dynamo is validated using time-resolved scRNA-seq data from human hematopoiesis, accurately recapitulating established lineage hierarchies and predicting optimal cell-fate transitions. Dynamo identifies key regulators such as FLI1, KLF1, SPI1, and GATA1, revealing critical regulatory motifs and pathways driving megakaryocyte and basophil differentiation. CellRank is a method that integrates transcriptomic-similarity-based trajectory inference with RNA velocity cues to construct directed, probabilistic state-change trajectories [42]. Building on it, CellRank2 is an upgraded framework designed to reconstruct cell-fate decisions by leveraging multiview single-cell data [43]. It infers the cell–cell transition probability matrices by incorporating dynamic information from multiple kernels, including the RNA velocity, gene expression similarities, pseudotime, developmental potential, experimental time points, and metabolic labels. This unified modular framework effectively maximizes the potential of diverse dynamic information sources.

In summary, OT provides a mathematically principled and flexible framework for addressing the task of cell dynamics inference, excelling in scenarios where data are high dimensional and noisy. It aligns cell distributions across time by minimizing transition costs, effectively capturing discrete state transitions. In contrast, ODE-based models capture the continuous evolution of cellular states, offering mechanistic insights into underlying regulatory processes and enabling precise trajectory predictions. OT-based methods achieve robust distributional alignment, while ODE-based models offer fine-grained temporal dynamics and biological interpretability, making them complementary tools for elucidating complex cell-fate decisions. In the continuous perspective, both dynamic OT- and ODE-based methods model temporal dynamics as continuous flows, allowing a unified interpretation of dynamical systems. Except for the usage of transcriptomic data, incorporating additional information such as RNA velocity and metabolic labeling significantly enhances the inference of cell dynamics. By integrating these dynamic measures, researchers can achieve a more comprehensive and robust understanding of cellular state transitions, leading to more precise predictions of dynamic biological processes. As these methods continue to evolve, their integration with multiomics data and advanced computational techniques promises to further enhance our understanding of cellular dynamics and the underlying regulatory mechanisms.

Dissecting dynamic mechanisms

Time-resolved scRNA-seq is a powerful approach for understanding the dynamic mechanisms underlying cellular processes, providing insights into cellular transitions, regulatory drivers, and temporal patterns. By capturing the transcriptomic profiles of individual cells at multiple time points, these datasets reveal both the temporal and population-level heterogeneity of gene expression. The ability to analyze dynamic changes in single-cell transcriptomic data is central for understanding how biological systems function and respond to stimuli. For instance, during differentiation, cells transition through transient intermediate states, often termed “transition states,” before reaching stable terminal fates [Fig. 3B(i)]. Identifying these states can uncover bottlenecks or decision points in cellular trajectories. Similarly, the identification of driver genes, those whose expression changes are crucial for guiding transitions, provides insights into regulatory mechanisms and potential therapeutic targets. Additionally, studying the dynamics of GRNs over time offers a system-level view of how cellular behavior emerges from the interactions of regulatory elements [Fig. 3B(ii)]. These insights can be applied in developmental biology, cancer research, immunology, and regenerative medicine.

However, high dimensionality, with thousands of genes measured across relatively few cells per time point, leads to sparse and noisy data, which complicates the reliable inference of underlying biological patterns. Furthermore, variability across cells stemming from both biological heterogeneity and technical noise can obscure true temporal trends and regulatory relationships. These challenges necessitate the development of advanced computational methods capable of disentangling signals from noise, capturing complex temporal dependencies, and identifying biologically meaningful features. Robust computational methods are essential for deciphering these dynamics and extracting actionable insights from such data. They focus on addressing fundamental questions in biology, such as identifying intermediate cellular states, identifying key regulatory drivers, and characterizing the temporal evolution of GRNs.

Transition states represent critical points where cells shift between distinct functional or developmental stages, offering insights into biological processes. Computational methods for this task often leverage probabilistic modeling to capture temporal patterns. For example, MuTrans models cell-fate transitions as multiscale stochastic dynamics, capturing the switch process between stable attractor states mediated by transition cells [Fig. 3B(i)] [44]. It conceptualizes transitions as overdamped Langevin dynamics in multistable potential wells, where stable states correspond to attractors and transition states to saddle points. Using iterative learning, it constructs a random walk transition matrix across cell–cell, cluster–cluster, and cell–cluster scales, and identifies attractor basins and transition probabilities. This approach distinguishes stable and transition cells via a transition cell score and identifies key gene types (e.g. transition-driver genes) involved in the transition process.

As for dynamic mechanisms at the gene level, factor analysis (FA) with probabilistic modeling provides a powerful framework for modeling temporal scRNA-seq data by decomposing the observed gene expression into interpretable components. This approach assumes that the observed data matrix can be represented as a combination of underlying low-dimensional factors, noise, and possibly time-dependent terms, thereby facilitating the analysis of complex temporal dynamics. The core idea of FA is to factorize the gene expression matrix , where rows represent cells and columns represent genes, into components such as . Here, denotes the latent cell states, captures the contributions of latent factors to gene expression, and accounts for the stochastic noise [Fig. 3B(ii)]. Based on this, scStateDynamics implements a Bayesian FA model to decompose the expression changes into static cluster-specific variations, dynamic cluster-shared gene factors, and residual noise [35]. The identified gene factors can be annotated with biological significance by calculating pathway scores (the average weights of the genes within each respective pathway). This offers a new approach for integrating dynamic information to analyze drug effects and compare heterogeneities across clusters.

Time-dependent extensions of the FA model incorporate temporal information by explicitly modeling dynamics using techniques such as Gaussian processes. Temporal priors can also be introduced to enforce smooth transitions in , allowing the reconstruction of continuous cell trajectories. MEFISTO is a time-aware framework that decomposes high-dimensional, multiview data (e.g. omics, tissues, or time-series) into a small number of interpretable factors, capturing both shared and group-specific temporal variations. Each factor value is modeled as the realization of a Gaussian process. It enables data-driven alignment of misaligned groups, interpolation of missing data, and supports clustering and outlier detection. The inferred factors can be further annotated by performing gene set enrichment analysis [45].

Moreover, by incorporating regulatory priors or sparsity constraints on , these methods can identify key genes driving dynamic changes and infer time-dependent GRNs. Guided sparse factor analysis (GSFA) method combines sparse FA and multivariate linear modeling to study perturbation effects on gene expression [46]. It decomposes the expression matrix into latent factors and sparse gene loadings while linking these factors to perturbations using a coefficient matrix . Outputs include the effects of perturbations on gene targets, gene loadings, and lists of genes significantly affected by each perturbation.

In addition to probabilistic FA, there are alternative approaches for modeling gene expression to uncover dynamic mechanisms at the gene level. Genes2Genes is a Bayesian information-theoretic dynamic programming framework designed to align single-cell transcriptomic trajectories by capturing sequential matches (one-to-one, expansion, or compression) and mismatches (insertions or deletions) of individual genes [47]. For each gene of interest, it compares the expression dynamics across pseudotime by interpolating the data and applying an adapted Gotoh’s algorithm with the five alignment states to infer the optimal alignment strings. TDEseq is a method for detecting temporal differentially expressed genes, which employs linear additive mixed models (LAMMs) to analyze temporal gene expression changes in time-course scRNA-seq data [48]. It detects four key temporal patterns (growth, recession, peak, or trough) using quadratic I-splines and cubic C-splines as the basis functions for individual gene analysis.

Regarding dynamic mechanisms at the gene interaction level, a critical task is to infer GRNs that capture the temporal dependencies and causal relationships between genes. One of the approaches is using linear regression model to fit the dynamics of gene expression over time by estimating the gene regulatory coefficients [49]. Another common modeling approach is to represent gene interaction matrices across multiple time points as 3D tensors [50]. Therefore, deep-learning-based temporal models, such as recurrent neural networks (RNNs) and long short-term memory (LSTM) networks, are powerful tools for this task. Another modeling approach treats joint gene expression of a gene pair (or including neighbor gene pairs) as a primary image using joint histograms, leveraging 3D (or 4D) convolutional neural networks (CNNs) to process these images [50, 51]. When extended to cross-modal data, integration can be performed first, followed by temporal alignment and GRN inference. For example, scTIE integrates single-cell RNA and chromatin accessibility data using an autoencoder. Then, it employs iterative OT to align cells across time points while preserving biological signals [52]. By embedding data into a common space, scTIE identifies genes and chromatin features that are predictive of cell fate transitions and uses these features to build context-specific GRNs, which are vital for understanding cellular differentiation during developmental processes. This approach directly links embeddings to biological features such as genes and peak regions, offering superior predictive accuracy for gene regulation.

In summary, understanding the dynamic mechanisms underlying cellular transitions and gene regulation has profound implications in biology and medicine. Identifying transition states provides insights into plasticity and heterogeneity in systems such as development and cancer. Discovering driver genes and dynamic GRNs enables researchers to manipulate cellular behavior for therapeutic purposes, such as reprogramming cells for regenerative medicine or targeting key regulators in disease.

Cell-fate prediction

Predicting cell fate from single-cell transcriptomic data is a fundamental challenge in understanding cellular dynamics and decision-making processes. Accurately forecasting a cell’s future state is essential for deciphering developmental pathways, identifying transitional states, and characterizing responses to environmental cues. Among the factors influencing cell fate, external perturbations, such as drug treatment, genetic modifications, and environmental changes, may exert intricate effects on the reshaping of cellular trajectories. Understanding and predicting how cells respond to perturbations is particularly important for applications in drug discovery, regenerative medicine, and disease modeling, which is a critical goal in systems biology and medicine [53].

Time-series scRNA-seq offers a dynamic view of cellular states and their heterogeneity, which makes it a powerful tool for studying these responses. The scientific significance of this task lies in its potential applications across multiple domains. For example, in drug discovery, predicting the response of different cell types to candidate compounds can help prioritize experiments and reduce costs. In developmental biology, computational modeling of how cells transition between states under various conditions can provide insights into their differentiation trajectory. Similarly, in personalized medicine, these models enable the prediction of individual-specific responses to therapies, facilitating more precise treatment strategies.

Several OT-based approaches, such as CellOT [37], seek to learn a mapping function between unperturbed and perturbed cells using an OT strategy. This allows them not only to align the cells effectively but also to predict the perturbed states of previously unseen cells based on their preperturbation states. However, these approaches have limitations in modeling novel perturbations, such as previously unseen compounds or cell types. The experimental generation of transcriptomic profiles for all possible perturbations is infeasible owing to the high cost and complexity of such experiments. Computational methods, particularly those based on generative models, have emerged as effective tools to address this challenge.

Generative models are well suited for this task because they can learn the complex, high-dimensional relationships between cellular states and perturbations from available data and generalize to unseen conditions. These methods often use a latent-space representation, which captures the essential structure of the data, including variations across cell types, perturbations, and experimental conditions. Perturbation effects are modeled as transformations in this latent space, enabling the simulation of postperturbation states from the preperturbation data. Variational autoencoders (VAEs) and their extensions are the most common architecture for this purpose [54–61]. Conditional VAEs (cVAE) provide a robust framework for predicting single-cell transcriptomic responses and generating gene expression profiles under perturbation conditions [62]. By conditioning on both the observed gene expression and experimental perturbations, the cVAE learns a probabilistic mapping between the input data and the corresponding perturbed states, enabling the simulation and prediction of cellular responses to unseen conditions (Fig. 3C). In the cVAE framework, the input data (e.g., gene expression profile) and perturbation labels (e.g. drug type and genetic knockout) are encoded into a latent representation using a neural-network-based encoder. The decoder then reconstructs the perturbed gene expression using and . This probabilistic setup captures the inherent variability in gene expression while leveraging the conditional structure to model perturbation-specific effects. For example, Biolord [58] utilizes control cells along with unseen labels as inputs to predict gene expression for unobserved cellular states, enabling counterfactual predictions through the cVAE framework. It encodes multiple cellular attributes into a decomposed latent space with separate subnetworks for the known and unknown attributes. These latent representations are then fed into a generative module to predict measured features, such as gene expression profiles. It can also identify features associated with specific cellular states by altering known attributes (e.g. shifting control cells to an infected state) and analyzing the resulting changes. Additionally, it enables latent-space exploration to uncover structural insights into individual attributes and performs classification for cells with missing labels.

Recent developments have incorporated domain-specific knowledge, such as the chemical properties of drugs or regulatory network constraints, to enhance the biological validity of predictions. GEARS combines prior knowledge, including gene coexpression graphs and perturbation relationship graphs, to predict postperturbation expression profiles using a deep generative model [60]. ChemCPA [55] and PRnet [59] leverage the Simplified Molecular-Input Line Entry System (SMILES) to encode chemical structures, allowing them to be generalized to novel compounds without requiring prior knowledge. The key advantages of the cVAE include its ability to generalize across diverse perturbations and its capacity to disentangle latent factors driving expression changes. By training the model on a dataset spanning multiple conditions, the cVAE can interpolate and extrapolate responses to perturbations that are not directly observed in the training data. Additionally, the latent space learned by the encoder provides insights into cellular heterogeneity and the underlying mechanisms of the perturbation effects.

Moreover, advanced methods for AI-generated content (AIGC) are increasingly being applied to cell-fate prediction tasks, leveraging their ability to model complex distributions. The transformer architecture has demonstrated superior performance in many fields of AIGC, utilizing an encoder–decoder framework built on self-attention mechanisms to represent input data. This architecture excels at handling long-range and contextual relationships. By using a transformer to model single-cell dynamics, it can effectively capture complex long-range dependencies in time-series data and to model gene–gene interactions [63]. Sagittarius is a transformer-based model that extrapolates gene expression profiles at unmeasured time points by learning a shared reference space for time-series data, addressing unaligned time points and batch effects [64]. Sagittarius employs an encoder–decoder architecture​​ to jointly model ​​continuous temporal variables​​ (e.g. biological age or treatment duration through high-frequency sinusoidal encoding), ​​discrete conditional variables​​ (e.g. organ or drug types through learnable conditional embeddings), and ​​high-dimensional transcriptomic profiles​​. Moreover, biological time is mapped to a unified pseudotemporal axis via trainable nonlinear transformations for cross-dataset time-series alignment. Validated on benchmarks spanning developmental biology, pharmacogenomics, and cancer genomics, Sagittarius demonstrates superior performance in capturing and extrapolating temporal dynamics. Diffusion models (e.g. scDiff [65]) have also been used to generate realistic single-cell gene expression profiles under perturbations by modeling the data distribution through a stepwise denoising process. Diffusion models generate biologically realistic and diverse single-cell gene expression profiles by capturing stochasticity and complex nonlinear relationships of cellular responses to perturbations. Their flexibility allows for the robust modeling of high-dimensional data and effective generalization to novel or hypothetical perturbations, enabling deeper insights into cellular heterogeneity and perturbation effects.

In summary, generative modeling provides a scalable and versatile approach for cell-fate prediction, particularly for predicting single-cell transcriptomic responses to perturbations. By learning from existing datasets and simulating untested conditions, these methods accelerate biological discovery and therapeutic innovation, address fundamental questions regarding cellular behavior, and enable practical applications in medicine. As these models continue to evolve, they promise to deepen our understanding of cellular systems and support the development of effective treatments.

Integrating lineage tracing information

The computational alignment of cells at two distinct time points offers a valuable approach for analyzing cell dynamics, as discussed in the section “Single-cell dynamics inference.” However, the destruction of cells caused by current omics detection technologies limits our ability to obtain the ground truth of cell dynamics, hindering the validation of the inferred cell alignment relationships. Recently developed single-cell lineage tracing (scLT) technologies introduce unique inherited DNA sequences (barcodes) into cells to label the clonal lineages of individual cells, enabling the simultaneous acquisition of transcriptomic characteristics and lineage information of cells through scRNA-seq. These DNA barcodes can either label cells in a single step to distinguish different clones in parallel or cumulatively label dividing cell clones (such as through CRISPR-Cas9 genome editing) to enable the reconstruction of hierarchical cell lineage trees [15, 66]. This provides some experimental evidence elucidating the cell lineage relationships over time, significantly advancing our understanding of cell dynamics and the molecular characteristics associated with cell fate.

Despite these advancements, current scLT approaches still exhibit several limitations. Lineage tracing experiments often face substantial off-target effects or loss, resulting in a large proportion of cells remaining unlabeled by lineage barcodes. Additionally, cells sharing the same lineage barcode may exhibit high intraclonal heterogeneity due to long-term evolution, complicating the understanding of the step-by-step changes in cell states. Therefore, integrating the experimental lineage tracing information with single-cell gene expression profiles may facilitate a more comprehensive and accurate cellular dynamics landscape (Fig. 3D). Recently, several algorithmic frameworks have been proposed to achieve this information integration.

The LineageOT framework reconstructs the lineage trees based on accumulated lineage barcoding information and then utilizes the relationships within the tree to adjust the positions of the cells at the later time point, moving them closer toward the estimated ancestral states if they share the same lineage. Next, the classical OT strategy is applied to align the cells between the earlier and later time points by maximizing the likelihood of cell coupling [67]. Finally, LineageOT is validated using the Caenorhabditis elegans (C. elegans) embryogenesis dataset, where the complete cell lineage is known. It outperforms Waddington-OT in this scenario, using the metrics of ancestor error and descendant error. The CoSpar approach infers cell dynamics by iteratively optimizing a cell transition matrix between the earlier and later time points, leveraging three types of constraints. The first constraint is the sparsity of the cell transition matrix, indicating that the cells can only transition to just a few states over time. The second is the coherence constraint, indicating that cells with similar gene expression profiles generally showcase similar fates. Moreover, the cell transition matrix should maintain a constant cell density distribution for a given lineage clone over time [68]. The moslin algorithm employs a fused Gromov–Wasserstein-based model to align cells across time points based on the gene expression similarity and lineage concordance. On the one hand, it utilizes the OT strategy to encourage aligning cells with similar gene expression profiles; on the other hand, it links cells with similar lineage history within each time point and restricts the cell pairs at the earlier time point that should be aligned to those at the later time point with similar relative lineage distances [69]. Besides, scTrace+ provides a unified framework to enhance the cell dynamics traces by comprehensively integrating lineage tracing information and multifaceted transcriptomic similarities both within and across time points. It first incorporates the lineage relationships and transcriptomic similarities across time points to generate a basic cell-state transition matrix. Next, scTrace+ employs the cell–cell clonal relationships and transcriptomic similarity networks within each time point as side information and conducts matrix completion based on low-rank constraints to infer the fates of cells lacking lineage labels [70]. These methods greatly contribute to many insights about various biological processes, such as hematopoiesis differentiation, embryogenesis, fibroblast reprogramming, and tumor drug responses.

In summary, classical methods based on transcriptomic similarity provide a strategy for inferring cell dynamics under the assumption that cells gradually change their states. Lineage tracing technologies offer some experimental evidence for tracking cell evolution. The integration of these two aspects holds great potential for advancing our understanding of cellular dynamics.

Outlook

Cutting-edge advances in biotechnology

While tracing the dynamics of an individual cell is valuable, it remains challenging with the current omics detection technologies due to their destructive nature. Lineage tracing approaches can label the cells from a common origin but do not accurately reflect true ancestor–descendant relationships. Computational alignment of cells provides a potential strategy; however, it relies on the assumption that the sampled cells at each time point can represent the entire population and that the cells gradually change their molecular states over time. Recent Live-seq technologies make an attempt to address the need to physically trace the transcriptome of individual cells by extracting RNA through cytoplasmic biopsy using fluidic force microscopy, allowing for transcriptome profiling without compromising cell viability [71]. Despite their current limitations in scalability, sensitivity, and cell throughput, Live-seq technologies represent a significant advancement. Future iterations may overcome these limitations and achieve more efficient analysis of the temporal molecular or functional characteristics of individual cells.

Cutting-edge advances in AI technology

In parallel with the innovation of experimental technologies, the latest advances of AI also provide some novel perspectives. Leveraging the powerful capabilities of GPUs for large-scale matrix operations and parallel computation, foundation models, which are pretrained on large-scale data through self-supervision and often built on transformer-based architectures, have driven revolutionary breakthroughs in the fields of natural language processing and computer vision. Inspired by this success, some foundation models have also been developed for single-cell biology [63, 72], such as Geneformer [73], scGPT [74], and scFoundation [75]. These models are pretrained on large-scale single-cell omics data across various organs, cell types, and experimental conditions, utilizing a transformer-based architecture to learn meaningful representations of cells and genes. This effectively captures the complex relationships among them and empowers various downstream tasks, including the time-series analysis of genetic perturbation, disease processes, or drug treatment (Fig. 3E). For example, by fine-tuning on the Perturb-seq datasets [76–79], the scGPT [74] model can effectively learn complex gene interactions from known genetic perturbation responses, enabling in silico predictions of cellular transcriptomic states after previously unseen genetic perturbations. This capability allows for the exploration of a vast combinatorial space of potential multiple gene perturbations, which would be impractical to obtain solely through biological experiments. Similarly, the Geneformer [73] model can be fine-tuned to distinguish cardiomyocytes from nonfailing hearts or hearts affected by hypertrophic or dilated cardiomyopathy. Based on it, candidate therapeutic targets can be identified through in silico manipulation, specifically by deleting or activating genes to assess whether these perturbations can drive the cells of nonfailing hearts toward the hypertrophic or dilated cardiomyopathy states. Thus, foundation models provide novel insights into understanding gene functions, identifying disease-associated therapeutic targets and predicting drug responses. With the further accumulation of single-cell dynamics data, particularly perturbation data, it is expected that more advanced pretrained models can be developed. The paradigm of “AI + omics,” which integrates cutting-edge AI technologies with large-scale single-cell omics data, may hold great potential for uncovering the mechanisms of dynamic biological processes.

New paradigm of spatiotemporal dynamics modeling

Building on the modeling of dynamic single-cell data in the temporal dimension, the incorporation of the spatial-dimensional information holds significant promise. Recent advances in spatial transcriptomics (ST) technologies have enabled the simultaneous detection of gene expression profiles and the spatial positioning of cells through sequence-based [80] or image-based [81, 82] approaches. These innovations facilitate the investigation of spatial heterogeneity in tumor [83–85] or normal tissues [86]. Further, time-series ST enables the spatiotemporal modeling to elucidate the dynamics of spatial structures and intercellular interactions [87]. This perspective on modeling spatiotemporal dynamics holds significant potential for systematically unveiling the black box of various biological processes [88]. To align time-series ST slides, several algorithms and tools have been developed [89–93]. In these models, the spatial constraints (such as cell–cell proximity) are taken into account to construct spatial graphs and infer their temporal dynamics (Fig. 3F). For example, the Spatially-Linked Alignment Tool (SLAT) method utilizes graph adversarial matching to align heterogenous ST slices [92]. STAligner designs a graph attention neural network to integrate and align ST slides across different conditions, technologies, and stages [93]. When applied to ST data of mouse embryonic development from multiple time points, both SLAT and STAligner demonstrate their effectiveness in dissecting the spatiotemporal dynamics of organ development. The recently proposed Spateo framework provides a unified and powerful approach to computationally model the 3D spatiotemporal dynamics of mouse embryos at the whole-organ levels [94]. It first introduces digitization methods to reconstruct 3D maps and characterize spatial gradients and cellular interactions of whole embryo. Then, it proposes “morphometric vector fields” and spatial differential geometry to identify the molecular programs underlying organogenesis. This molecular hologram modeling in the 3D spatiotemporal dimension enables a more comprehensive study of organ ecology. Moreover, as demonstrated by Spateo, the analysis of single-cell data is shifting from conventional reductionist approaches to a systemic spatiotemporal framework, i.e. from a focus on the cell level to an emphasis on tissue or organ levels. Life is a super complex system compared to physical or social systems. Further advancements in spatiotemporal omics technologies, along with associated computational methods, will offer new perspectives to explore the 3D dynamics of life systems.

Conclusions

Measuring time-series single-cell omics data provides a novel dynamic perspective for investigating various biological processes at the cellular level. Developing powerful computational methods to model these dynamics data can further enhance our understanding of the mechanisms underlying these biological processes. To characterize the dynamic landscape at the single-cell level, several differential-equation-based and OT-based methods have been proposed, enabling temporal alignment and modeling of cells at different time points. Based on the inferred cell dynamics, some key cell subpopulations, such as transition cell states or drug-resistant cells, can be computationally distinguished, and the fate-associated genes or pathways can be identified through FA or some other strategies. To predict the future fates of cells, particularly after external perturbation, some generative models have been developed to identify the latent spaces that interpret the cellular responses to perturbation. Additionally, the experimental lineage tracing information is integrated into some algorithms to provide a more comprehensive analysis of the cell dynamics.

In the future, with the development of biotechnologies and AI, establishing a life-specific complex systems theory based on large-scale spatiotemporal data and cutting-edge AI algorithms may greatly deepen our understanding of life and even facilitate innovative life-engineering approaches, paving the way for the development of more effective therapeutic strategies for various diseases.

Key Points

• Investigating single-cell dynamics during complex biological processes, such as tissue development, disease progression, and responses to perturbations, is crucial for understanding the underlying biological mechanisms.

• We summarize the computational challenges associated with modeling dynamic single-cell data.

• We provide a comprehensive overview of recent algorithmic advancements in four key tasks: inferring single-cell dynamics, dissecting dynamic mechanisms, predicting future cell fates, and integrating lineage tracing information to analyze cell dynamics.

• Advanced biological technologies, combined with artificial intelligence algorithms, have the potential to facilitate our exploration of complex life processes from a spatiotemporal systemic perspective.

Conflict of interest

None declared.

Funding

This work was supported by funding from the National Key Research and Development Program of China (nos 2020YFA0712403 and 2021YFF1200901), the National Natural Science Foundation of China (nos 62133006 and 92268104), and the China Postdoctoral Science Foundation (no. 2022 M721839).