Identifying dynamic regulation with machine learning using adversarial surrogates

Biological systems maintain stability of their function in spite of external and internal perturbations. An important challenge in studying biological regulation is to identify the control objectives based on empirical data. Very often these objectives are time-varying, and require the regulation system to follow a dynamic set-point. For example, the sleep-wake cycle varies according to the 24 hours solar day, inducing oscillatory dynamics on the regulation set-point; nutrient availability fluctuates in the organism, inducing time-varying set-points for metabolism. In this work, we introduce a novel data-driven algorithm capable of identifying internal regulation objectives that are maintained with respect to a dynamic reference value. This builds on a previous algorithm that identified variables regulated with respect to fixed set-point values. The new algorithm requires adding a prediction component that not only identifies the internally regulated variables, but also predicts the dynamic set-point as part of the process. To the best of our knowledge, this is the first algorithm that is able to achieve this. We test the algorithm on simulation data from realistic biological models, demonstrating excellent empirical results.