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Inferring chemical reaction networks (CRN) from concentration time series isa challenge encouragedby the growing availability of quantitative temporal dataat the cellular level. This motivates thedesign of algorithms to infer thepreponderant reactions between the molecular species observed ina givenbiochemical process, and build CRN structure and kinetics models. ExistingODE-basedinference methods such as SINDy resort to least square regressioncombined with sparsity-enforcingpenalization, such as Lasso. However, weobserve that these methods fail to learn sparse modelswhen the input timeseries are only available in wild type conditions, i.e. without the possibilitytoplay with combinations of zeroes in the initial conditions. We present a CRNinference algorithmwhich enforces sparsity by inferring reactions in asequential fashion within a search tree of boundeddepth, ranking the inferredreaction candidates according to the variance of their kinetics ontheirsupporting transitions, and re-optimizing the kinetic parameters of theCRN candidates on the wholetrace in a final pass. We show that Reactminesucceeds both on simulation data by retrievinghidden CRNs where SINDy fails,and on two real datasets, one of fluorescence videomicroscopyof cell cycle andcircadian clock markers, the other one of biomedical measurements ofsystemiccircadian biomarkers possibly acting on clock gene expression inperipheral organs, by inferringpreponderant regulations in agreement withprevious model-based analyses. The code is availableathttps://gitlab.inria.fr/julmarti/crninf/ together with introductorynotebooks.

Reactmine: a statistical search algorithm for inferring chemical reactions from time series data