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Loops are essential secondary structure elements in folded DNA and RNAmolecules and proliferate close to the melting transition. Using a theory fornucleic acid secondary structures that accounts for the logarithmic entropy cln m for a loop of length m, we study homopolymeric single-stranded nucleicacid chains under external force and varying temperature. In the thermodynamiclimit of a long strand, the chain displays a phase transition between a lowtemperature / 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 derivedanalytically. For vanishing pulling force, only for the limited range of loopexponents 2 < c < 2.479 a melting transition is possible; for c <= 2 the chainis always in the folded phase and for 2.479 < c always in the unfolded phase. Aforce induced melting transition with singular behavior is possible for allloop exponents c < 2.479 and can be observed experimentally by single moleculeforce spectroscopy. These findings have implications for the hybridization ordenaturation of double stranded nucleic acids. The Poland-Scheraga model fornucleic acid duplex melting does not allow base pairing between nucleotides onthe same strand in denatured regions of the double strand. If the sequenceallows these intra-strand base pairs, we show that for a realistic loopexponent c ~ 2.1 pronounced secondary structures appear inside the singlestrands. This leads to a lower melting temperature of the duplex than predictedby the Poland-Scheraga model. Further, these secondary structures renormalizethe effective loop exponent c^, which characterizes the weight of a denaturedregion of the double strand, and thus affect universal aspects of the duplexmelting transition.

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: implications for DNA hybridization