Neutral networks of sequence to shape maps

In this paper we present a combinatorial model of sequence to shape maps. Our particular construction arises in the context of representing nucleotide interactions beyond Watson-Crick base pairs and its key feature is to replace biophysical steric by combinatorial constraints. We show that these combinatory maps produce exponentially many shapes and induce sets of sequences which contain extended connected subgraphs of diameter n, where n denotes the length of the sequence. Our main result is to prove the existence of exponentially many shapes that have neutral networks.