  The number of molecules involved in a cell or subcellular structure is
sometimes rather small. In this situation, ordinary macroscopic-level
fluctuations can be overwhelmed by non-negligible large fluctuations, which
results in drastic changes in chemical-reaction dynamics and statistics
compared to those observed under a macroscopic system (i.e., with a large
number of molecules). In order to understand how salient changes emerge from
fluctuations in molecular number, we here quantitatively define small-number
effect by focusing on a `mesoscopic' level, in which the concentration
distribution is distinguishable both from micro- and macroscopic ones, and
propose a criterion for determining whether or not such an effect can emerge in
a given chemical reaction network. Using the proposed criterion, we
systematically derive a list of motifs of chemical reaction networks that can
show small-number effects, which includes motifs showing emergence of the power
law and the bimodal distribution observable in a mesoscopic regime with respect
to molecule number. The list of motifs provided herein is helpful in the search
for candidates of biochemical reactions with a small-number effect for possible
biological functions, as well as for designing a reaction system whose behavior
can change drastically depending on molecule number, rather than concentration.
