  Patterns and forms adopted by Nature, such as the shape of living cells, the
geometry of shells and the branched structure of plants, are often the result
of simple dynamical paradigms. Here we show that a growing self-interacting
string attached to a tracking origin, modeled to resemble nascent polypeptides
in vivo, develops helical structures which are more pronounced at the growing
end. We also show that the dynamic growth ensemble shares several features of
an equilibrium ensemble in which the growing end of the polymer is under an
effective stretching force. A statistical analysis of native states of proteins
shows that the signature of this non-equilibrium phenomenon has been fixed by
evolution at the C-terminus, the growing end of a nascent protein. These
findings suggest that a generic non-equilibrium growth process might have
provided an additional evolutionary advantage for nascent proteins by favoring
the preferential selection of helical structures.
