  Force-induced structural transitions both in relatively random and in
designed single-stranded DNA (ssDNA) chains are studied theoretically. At high
salt conditions, ssDNA forms compacted hairpin patterns stabilized by
base-pairing and base-pair stacking interactions, and a threshold external
force is needed to pull the hairpinned structure into a random coiled one. The
base-pair stacking interaction in the ssDNA chain makes this hairpin-coil
conversion a discontinuous (first-order) phase transition process characterized
by a force plateau in the force-extension curve, while lowering this potential
below some critical level turns this transition into continuous (second-order)
type, no matter how strong the base-pairing interaction is. The phase diagram
(including hairpin-I, -II, and random coil) is discussed as a function of
stacking potential and external force. These results are in quantitative
agreement with recent experimental observations of different ssDNA sequences,
and they reveal the necessity to consider the base-pair stacking interactions
in order to understand the structural formation of RNA, a polymer designed by
nature itself. The theoretical method used may be extended to study the
long-range interaction along double-stranded DNA caused by the topological
constraint of fixed linking number.
