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.

Keywords: cellular trajectories; computational modeling; single-cell RNA sequencing; spatiotemporal dynamics.

Figure 1

Overview of the data and models. (a) Discrete and Continuous Model: The discrete model constructs Markov chains between cells with dynamics encoded in a transition matrix, while the continuous model describes single-cell motion via stochastic differential equations (SDEs) and cell population dynamics through a corresponding partial differential equation (PDE). (b) Datasets: Snapshot data is an $n\times g$ matrix $\mathit{X}$ (n: cell count, g: gene count); temporal data provides gene expression matrices ${\mathit{X}}_i$ at time points $i\in \{0,\dots ,T-1\}$; spatial data additionally records coordinates for each cell in ${\mathit{X}}_i$.

Figure 2

Dynamic modeling of snapshot single-cell transcriptomics.

Figure 3

Dynamic modeling of temporally-resolved single-cell transcriptomics.

Figure 4

Dynamic modeling of spatial transcriptomics.