Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr""odinger Bridge

2025-05-16

AI Summary

This study addresses the critical challenge of modeling intercellular interactions from sparse single-cell temporal snapshot data. We propose CytoBridge—the first deep learning method that explicitly embeds mechanistic cell–cell interactions into a nonequilibrium mean-field Schrödinger bridge framework. Integrating optimal transport theory, nonequilibrium stochastic dynamics modeling, and neural network parameterization (supporting either graph-structured or attention-based implicit interaction encoding), CytoBridge enables end-to-end learning of joint cellular state transitions, proliferation, and interaction dynamics. Evaluated on synthetic gene regulatory networks and real scRNA-seq datasets, CytoBridge significantly improves developmental trajectory reconstruction accuracy, effectively eliminates spurious transitional states, and robustly disentangles dynamic patterns of growth, differentiation, and multicellular cooperative interactions.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr""odinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schr""odinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy.

Problem

• Modeling cell dynamics from sparse snapshot data
• Accounting for cell-cell interactions in dynamics
• Inferring stochastic, unbalanced cellular processes accurately

Innovation

• Unbalanced Mean-Field Schrödinger Bridge framework
• Deep learning algorithm CytoBridge
• Models cell transitions and interactions