Predicting time-varying flux and balance in metabolic systems using structured neural-ODE processes

We develop a novel data-driven framework as an alternative to dynamic flux balance analysis, bypassing the demand for deep domain knowledge and manual efforts to formulate the optimization problem. The proposed framework is end-toend, which trains a structured neural ODE process (SNODEP) model to estimate flux and balance samples using gene-expression time-series data. SNODEP is designed to circumvent the limitations of the standard neural ODE process model, including restricting the latent and decoder sampling distributions to be normal and lacking structure between context points for calculating the latent, thus more suitable for modeling the underlying dynamics of a metabolic system. Through comprehensive experiments (156 in total), we demonstrate that SNODEP not only predicts the unseen time points of real-world gene-expression data and the flux and balance estimates well but can even generalize to more challenging unseen knockout configurations and irregular data sampling scenarios, all essential for metabolic pathway analysis. We hope our work can serve as a catalyst for building more scalable and powerful models for genome-scale metabolic analysis. A distinctive characteristic of deep neural networks is their capability to implicitly learn complicated features and dynamics from data, significantly saving human effort in composing those handcrafted features and devising complex models. Therefore, there has been a growing interest in using them in a variety of scientific contexts, such as quantum chemistry (von Glehn et al., 2022), tokamak controller design (Degrave et al., 2022), climate sciences (Lam et al., 2022; Nguyen et al., 2023), molecule generation (Hoogeboom et al., 2022) and drug discovery (Askr et al., 2023), to name a few.