  The information content of a non-enzymatic self-replicator is limited by
Eigen's error threshold. Presumably, enzymatic replication can maintain higher
complexity, but in a competitive environment such a replicator is faced with
two problems related to its twofold role as enzyme and substrate: as enzyme, it
should replicate itself rather than wastefully copy non-functional substrates,
and as substrate it should preferably be replicated by superior enzymes instead
of less-efficient mutants. Because specific recognition can enforce these
propensities, we thoroughly analyze an idealized quasispecies model for
enzymatic replication, with replication rates that are either a decreasing
(self-specific) or increasing (cross-specific) function of the Hamming distance
between the recognition or "tag" sequences of enzyme and substrate. We find
that very weak self-specificity suffices to localize a population about a
master sequence and thus to preserve its information, while simultaneous
localization about complementary sequences in the cross-specific case is more
challenging. A surprising result is that stronger specificity constraints allow
longer recognition sequences, because the populations are better localized.
Extrapolating from experimental data, we obtain rough quantitative estimates
for the maximal length of the recognition or tag sequence that can be used to
reliably discriminate appropriate and infeasible enzymes and substrates,
respectively.
