  Proteins form a very important class of polymers. In spite of major advances
in the understanding of polymer science, the protein problem has remained
largely unsolved. Here, we show that a polymer chain viewed as a tube not only
captures the well-known characteristics of polymers and their phases but also
provides a natural explanation for many of the key features of protein
behavior. There are two natural length scales associated with a tube subject to
compaction -- the thickness of the tube and the range of the attractive
interactions. For short tubes, when these length scales become comparable, one
obtains marginally compact structures, which are relatively few in number
compared to those in the generic compact phase of polymers. The motifs
associated with the structures in this new phase include helices, hairpins and
sheets. We suggest that Nature has selected this phase for the structures of
proteins because of its many advantages including the few candidate strucures,
the ability to squeeze the water out from the hydrophobic core and the
flexibility and versatility associated with being marginally compact. Our
results provide a framework for understanding the common features of all
proteins.
