  A novel self-assembly strategy for polypeptide nanostructure design was
presented in [Design of a single-chain polypeptide tetrahedron assembled from
coiled-coil segments, Nature Chemical Biology 9 (2013) 362--366]. The first
mathematical model (polypeptide nanostructure can naturally be presented as a
skeleton graph of a polyhedron) from [Stable traces as a model for
self-assembly of polypeptide nanoscale polyhedrons, MATCH Commun. Math. Comput.
Chem. 70 (2013) 317-330] introduced stable traces as the appropriate
mathematical description, yet we find them deficient in modeling graphs with
either very small (less or equal to 2) or large (greater or equal to 6) degree
vertices. We introduce strong traces which remedy both of the above mentioned
drawbacks. We show that every connected graph admits a strong trace by studying
a connection between strong traces and graph embeddings. Further we also
characterize graphs which admit parallel (resp. antiparallel) strong traces.
