  It is a long-standing question in origin-of-life research whether the
information content of replicating molecules can be maintained in the presence
of replication errors. Extending standard quasispecies models of non-enzymatic
replication, we analyze highly specific enzymatic self-replication mediated
through an otherwise neutral recognition region, which leads to
frequency-dependent replication rates. We find a significant reduction of the
maximally tolerable error rate, because the replication rate of the fittest
molecules decreases with the fraction of functional enzymes. Our analysis is
extended to hypercyclic couplings as an example for catalytic networks.
