On RAF Sets and Autocatalytic Cycles in Random Reaction Networks

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 re
exively 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 diffculties encountered in laboratory seems to
be the presence of molecules which can accumulate without being substrate
or catalyst of any reaction.