Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods

Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.Author summary: Reconstructing the correlated reactions that govern a system of biochemical species from observational temporal data is an essential step in understanding many biological systems. To facilitate this process, we propose a robust, data-driven approach based on a sparse Bayesian statistical model. Our approach exploits sparse Bayesian priors and an unbiased observational model to recover a parsimonious, interpretable reaction system from mass-action relations, utilizing very little user input. On a set of simulated test problems, the method demonstrates increased robustness and decreased bias at different levels of measurement variability, while also producing interpretable reaction systems and quantifying uncertainty. As a tool, the approach can be used to flexibly interrogate biological systems while allowing incorporation of potentially uncertain domain knowledge to improve the efficiency and identifiability of the problem.