Learning collective multicellular dynamics with an interacting mean field neural SDE model.

The advent of temporal single-cell RNA sequencing (scRNA-seq) data has enabled in-depth investigation of dynamic processes in heterogeneous multicellular systems. Despite remarkable advancements in computational methods for modeling cellular dynamics, integrating cell-cell interactions (CCIs) into these models remains a major challenge. This is particularly true when dealing with high-dimensional gene expression profiles from large populations of interacting cells, where the intricate interplay between cells can be obscured by data complexity. To address this, we present scIMF, a single-cell deep-generative Interacting Mean Field model that learns collective multicellular dynamics. Leveraging the McKean-Vlasov stochastic differential equation framework, scIMF provides a mathematical foundation for describing interacting multicellular systems, where each cell's evolution depends on the population's empirical distribution. By incorporating a cell-wise attention mechanism, the model efficiently captures nonlocal and asymmetric CCIs, enabling realistic reconstruction of complex intercellular relationships in high-dimensional spaces. Benchmarking across diverse temporal scRNA-seq datasets demonstrates that scIMF outperforms state-of-the-art methods in reconstructing gene expression at unobserved time points and in inferring cellular velocities. Furthermore, scIMF uncovers biologically interpretable, non-reciprocal interaction patterns of cells, providing a principled framework for studying complex, particularly non-equilibrium biological systems.