Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-seq Data Analysis

Abstract

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schrödinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

References in corpus (27)

• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• Score-Based Generative Modeling through Stochastic Differential Equations
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems
• Optimal Transport for structured data with application on graphs
• Realization of Waddington's Metaphor: Potential Landscape, Quasi-potential, A-type Integral and Beyond
• Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling
• Unnormalized Optimal Transport
• TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics
• Improving and generalizing flow-based generative models with minibatch optimal transport
• Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology
• Building Normalizing Flows with Stochastic Interpolants
• Neural Parametric Fokker-Planck Equations
• Convergence of flow-based generative models via proximal gradient descent in Wasserstein space
• EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation
• Single-cell entropy to quantify the cellular transcription from single-cell RNA-seq data
• Quantifying energy landscape of high-dimensional oscillatory systems by diffusion decomposition
• Variational Mixtures of ODEs for Inferring Cellular Gene Expression Dynamics
• Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory
• Simulation-free Schrödinger bridges via score and flow matching
• A Computational Framework for Solving Wasserstein Lagrangian Flows
• Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation
• Trajectory Inference via Mean-field Langevin in Path Space
• Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport
• The Schrödinger Bridge between Gaussian Measures has a Closed Form
• Neural Lagrangian Schrödinger Bridge: Diffusion Modeling for Population Dynamics
• Action Matching: Learning Stochastic Dynamics from Samples