  Loops are essential secondary structure elements in folded DNA and RNA
molecules and proliferate close to the melting transition. Using a theory for
nucleic acid secondary structures that accounts for the logarithmic entropy c
ln m for a loop of length m, we study homopolymeric single-stranded nucleic
acid chains under external force and varying temperature. In the thermodynamic
limit of a long strand, the chain displays a phase transition between a low
temperature / low force compact (folded) structure and a high temperature /
high force molten (unfolded) structure. The influence of c on phase diagrams,
critical exponents, melting, and force extension curves is derived
analytically. For vanishing pulling force, only for the limited range of loop
exponents 2 < c < 2.479 a melting transition is possible; for c <= 2 the chain
is always in the folded phase and for 2.479 < c always in the unfolded phase. A
force induced melting transition with singular behavior is possible for all
loop exponents c < 2.479 and can be observed experimentally by single molecule
force spectroscopy. These findings have implications for the hybridization or
denaturation of double stranded nucleic acids. The Poland-Scheraga model for
nucleic acid duplex melting does not allow base pairing between nucleotides on
the same strand in denatured regions of the double strand. If the sequence
allows these intra-strand base pairs, we show that for a realistic loop
exponent c ~ 2.1 pronounced secondary structures appear inside the single
strands. This leads to a lower melting temperature of the duplex than predicted
by the Poland-Scheraga model. Further, these secondary structures renormalize
the effective loop exponent c^, which characterizes the weight of a denatured
region of the double strand, and thus affect universal aspects of the duplex
melting transition.
