  Chemical reaction systems are dynamical systems that arise in chemical
engineering and systems biology. In this work, we consider the question of
whether the minimal (in a precise sense) multistationary chemical reaction
networks, which we propose to call `atoms of multistationarity,' characterize
the entire set of multistationary networks. Our main result states that the
answer to this question is `yes' in the context of fully open continuous-flow
stirred-tank reactors (CFSTRs), which are networks in which all chemical
species take part in the inflow and outflow. In order to prove this result, we
show that if a subnetwork admits multiple steady states, then these steady
states can be lifted to a larger network, provided that the two networks share
the same stoichiometric subspace. We also prove an analogous result when a
smaller network is obtained from a larger network by `removing species.' Our
results provide the mathematical foundation for a technique used by
Siegal-Gaskins et al. of establishing bistability by way of `network ancestry.'
Additionally, our work provides sufficient conditions for establishing
multistationarity by way of atoms and moreover reduces the problem of
classifying multistationary CFSTRs to that of cataloging atoms of
multistationarity. As an application, we enumerate and classify all 386
bimolecular and reversible two-reaction networks. Of these, exactly 35 admit
multiple positive steady states. Moreover, each admits a unique minimal
multistationary subnetwork, and these subnetworks form a poset (with respect to
the relation of `removing species') which has 11 minimal elements (the atoms of
multistationarity).
