Error thresholds for self- and cross-specific enzymatic replication

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