Variational Mixtures of ODEs for Inferring Cellular Gene Expression Dynamics

TL;DR

This paper introduces a variational mixture of ODEs model to infer cellular gene expression dynamics, accurately estimating latent cell states and future gene expression from snapshot data.

Contribution

It presents a novel deep generative model that combines mixture of ODEs with variational inference to handle bifurcating cell trajectories and unknown observation timings.

Findings

Significantly improves data fit for single-cell gene expression

Enhances accuracy of latent time inference

Better predicts future cell states compared to previous methods

Abstract

A key problem in computational biology is discovering the gene expression changes that regulate cell fate transitions, in which one cell type turns into another. However, each individual cell cannot be tracked longitudinally, and cells at the same point in real time may be at different stages of the transition process. This can be viewed as a problem of learning the behavior of a dynamical system from observations whose times are unknown. Additionally, a single progenitor cell type often bifurcates into multiple child cell types, further complicating the problem of modeling the dynamics. To address this problem, we developed an approach called variational mixtures of ordinary differential equations. By using a simple family of ODEs informed by the biochemistry of gene expression to constrain the likelihood of a deep generative model, we can simultaneously infer the latent time and latent state of each cell and predict its future gene expression state. The model can be interpreted as a mixture of ODEs whose parameters vary continuously across a latent space of cell states. Our approach dramatically improves data fit, latent time inference, and future cell state estimation of single-cell gene expression data compared to previous approaches.