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.

A review of mechanistic learning in mathematical oncology

“…Neural ODEs have already been used for a variety of tasks in oncology ranging from genome-wide regulatory dynamics ( 74 ) and breast tumor segmentation in medical images ( 75 ) to time-to-event modeling ( 76 ). Importantly, neural ODEs can generate realistic synthetic data, such as longitudinal patient trajectories.…”

Biologically informed NeuralODEs for genome-wide regulatory dynamics

“…PHOENIX is available as an open-source implementation via Github: https://github.com/QuackenbushLab/phoenix [ 37 ]. The source code underlying the results presented in the article is also available at Zenodo (DOI: https://zenodo.org/doi/10.5281/zenodo.11081632) [ 81 ]. Both resources are released under the MIT License.…”

“…Explainabilty AUC was calculated by comparing encoded GRNs retrieved from each trained model (Additional File 2: Section 2 and Additional File 2: Section 3.3) against ChIP-chip data [41] Trained pseudotime. For consistency in pseudotime ordering, we reused a version of this data [44] that was already preprocessed and ordered (using a random-walk-based pseudotime approach) in the PROB paper [8].…”

“…It is interesting to note that both Fig. 5 We applied PHOENIX to a pseudotrajectory of 186 breast cancer samples (ordered along subsequent "pseudotimepoints") consisting of n g = 11, 165 genes [44]. We split up the 186 time points into contiguous intervals for training (170, 90% ), validation to tune prior (8, 5% ), and test (8, 5% ).…”

“…• All simulated data for in silico experiments has been deposited (under the MIT License) at Zenodo (DOI: https://zenodo.org/doi/10.5281/zenodo.11081632) [ 81 ].…”