# A Statistical Unsupervised Learning Algorithm for Inferring Reaction Networks from Time Series Data

Julien Martinelli, Jeremy Grignard, Sylvain Soliman, François Fages

June 2019
### Abstract

With the automation of biological experiments and the increase of quality of single cell data that can now be obtained by phosphoproteomic and time lapse videomicroscopy, automating the building of mechanistic models from these time series data becomes conceivable and a necessity for many new applications. While learning numerical parameters to fit a given model structure to observed data is now a quite well understood subject, learning the structure of the model is a more challenging problem that previous attempts failed to solve without relying quite heavily on prior knowledge about that structure. In this paper , we consider mechanistic models based on chemical reaction networks (CRN) with their continuous dynamics based on ordinary differential equations, and finite time series about the time evolution of concentration of molecular species for a given time horizon and a finite set of perturbed initial conditions. We present a statistical learning algorithm to learn CRNs with a time complexity for inferring one reaction in O(t.n 2) where n is the number of species and t the number of observed transitions in the traces. We learn both the structure and the reaction rates of the CRN. We evaluate this algorithm and its sensitivity to its statistical threshold parameters, first on simulated data from a hidden CRN, and second on real videomicroscopy single cell time series data over three days about the circadian clock and cell cycle progression of NIH3T3 embryonic fi-broblasts. In all cases, our algorithm is able to reconstruct meaningful CRNs. We discuss some limits according to the existence of multiple time scales and highly variable traces.

Publication

In *ICML 2019 - Workshop on Computational Biology*