Biologically informed NeuralODEs for genome-wide regulatory dynamics

Abstract

Models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the causal gene-regulatory network (GRN) governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impedes scalability and/or explainability. To overcome these limitations, we developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that can flexibly incorporate prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of ODEs. We test accuracy of PHOENIX in a series of in silico experiments benchmarking it against several currently used tools for ODE estimation. We also demonstrate PHOENIX's flexibility by studying oscillating expression data from synchronized yeast cells and assess its scalability by modelling genome-scale breast cancer expression for samples ordered in pseudotime. Finally, we show how the combination of user-defined prior knowledge and functional forms from systems biology allows PHOENIX to encode key properties of the underlying GRN, and subsequently predict expression patterns in a biologically explainable way. PHOENIX will be available as open source at: https://github.com/QuackenbushLab/phoenix.

Simultaneous estimation of gene regulatory network structure and RNA kinetics from single cell gene expression

“…However, inherent limitations in the ability to capture intronic reads make this approach challenging ( 27 ), particularly with scRNA-seq methods that target the 3’ end of transcripts. The use of RNA velocity in GRN inference is still preliminary ( 30, 31 ) although recent work has extended the concept of RNA velocity to predictive models based on deep learning combined with ordinary differential equation models to predict gene expression at future states and to infer GRNs ( 32–34 ).…”