  The emergence of autocatalytic sets of molecules seems to have played an
important role in the origin of life context. Although the possibility to
reproduce this emergence in laboratory has received considerable attention,
this is still far from being achieved. In order to unravel some key properties
enabling the emergence of structures potentially able to sustain their own
existence and growth, in this work we investigate the probability to observe
them in ensembles of random catalytic reaction networks characterized by
different structural properties. From the point of view of network topology, an
autocatalytic set have been defined either in term of strongly connected
components (SCCs) or as reflexively autocatalytic and food-generated sets
(RAFs). We observe that the average level of catalysis differently affects the
probability to observe a SCC or a RAF, highlighting the existence of a region
where the former can be observed, whereas the latter cannot. This parameter
also affects the composition of the RAF, which can be further characterized
into linear structures, autocatalysis or SCCs. Interestingly, we show that the
different network topology (uniform as opposed to power-law catalysis systems)
does not have a significantly divergent impact on SCCs and RAFs appearance,
whereas the proportion between cleavages and condensations seems instead to
play a role. A major factor that limits the probability of RAF appearance and
that may explain some of the difficulties encountered in laboratory seems to be
the presence of molecules which can accumulate without being substrate or
catalyst of any reaction.
