Strong Traces Model of Self-Assembly Polypeptide Structures

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 (≤ 2) or large (≥ 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.

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