  Inferring chemical reaction networks (CRN) from concentration time series is
a challenge encouragedby the growing availability of quantitative temporal data
at the cellular level. This motivates thedesign of algorithms to infer the
preponderant reactions between the molecular species observed ina given
biochemical process, and build CRN structure and kinetics models. Existing
ODE-basedinference methods such as SINDy resort to least square regression
combined with sparsity-enforcingpenalization, such as Lasso. However, we
observe that these methods fail to learn sparse modelswhen the input time
series are only available in wild type conditions, i.e. without the possibility
toplay with combinations of zeroes in the initial conditions. We present a CRN
inference algorithmwhich enforces sparsity by inferring reactions in a
sequential fashion within a search tree of boundeddepth, ranking the inferred
reaction candidates according to the variance of their kinetics on
theirsupporting transitions, and re-optimizing the kinetic parameters of the
CRN candidates on the wholetrace in a final pass. We show that Reactmine
succeeds both on simulation data by retrievinghidden CRNs where SINDy fails,
and on two real datasets, one of fluorescence videomicroscopyof cell cycle and
circadian clock markers, the other one of biomedical measurements of
systemiccircadian biomarkers possibly acting on clock gene expression in
peripheral organs, by inferringpreponderant regulations in agreement with
previous model-based analyses. The code is available
athttps://gitlab.inria.fr/julmarti/crninf/ together with introductory
notebooks.
