Abstract 5371: Modeling single-cell dynamics using stochastic generative models based on neural differential equations
Authors: Vinyard Michael E. , Rasmussen Anders W. , Li Ruitong , Pinello Luca , Getz Gad 
Published: June 2023

Hematopoietic malignancies arise from driver alterations acquired during specific, often intermediate and transient, differentiation states. When adequately sampled, “snapshot” single-cell measurements can capture dynamic biological processes, including transient states. While there are effective computational modeling solutions to order and capture the relationships among these cell states (often projecting onto a lower dimensional manifold with directionality), methods to infer the causal gene regulatory mechanisms driving cell state transitions remain limited.

Recently, a mathematical framework for modeling cell dynamics from snapshot data using a physics-based drift-diffusion equation was proposed. This drift-diffusion equation framework describes the dynamics of cell distributions with respect to time, wherein stereotypical driving forces (e.g., hematopoietic development) are captured by the drift term, and biological stochasticity is attributed to the diffusion term. The existing modeling solutions within this framework are forced to assume a fixed diffusion parameter across cell states, ascribing all observed dynamics to drift alone. Here, we expand on current drift-diffusion models to learn both the drift and diffusion terms that describe every observed cell state. These models are constructed from stochastic neural differential equations, continuous deep neural networks that approximate the theoretically complex differential equations underlying gene regulatory networks in hematopoiesis.

Lineage-barcoded, multi-time point single-cell RNA sequencing experiments can approximate ground truth cellular dynamics. Using such data, we demonstrate the predictive accuracy of our proposed approach through benchmarking against the state-of-the-art methods. Through our drift-diffusion model, we can now distinguish, for the first time, between the deterministic and stochastic contributions to cell fate decision making. In doing so, we identify genes whose expression is associated with cellular drift and indeed show that they correspond to well-known markers of specific cell types; moreover, we identify genes that are associated with cell states that exhibit notable diffusion. Finally, we demonstrate the potential of such models to capture the essence of the dynamic processes through prediction on out-of-distribution data (referred to as “transfer learning” in the machine learning field). For example, when the model is trained on in vitro hematopoiesis data, our model is able to accurately predict cell trajectories in the corresponding in vivo mouse model. We anticipate that such insights will be useful in identifying key dynamic and time-dependent regulatory processes in normal development and cancer.

Citation Format: Michael E. Vinyard, Anders W. Rasmussen, Ruitong Li, Luca Pinello, Gad Getz. Modeling single-cell dynamics using stochastic generative models based on neural differential equations. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5371.