  A new formalism for calculation of the partition function of single stranded
nucleic acids is presented. Secondary structures and the topology of structure
elements are the level of resolution that is used. The folding model deals with
matches, mismatches, symmetric and asymmetric interior loops, stacked pairs in
loop and dangling end regions, multi-branched loops, bulges and single base
stacking that might exist at duplex ends or at the ends of helices.
Calculations on short and long sequences show, that for short oligonucleotides,
a duplex formation often displays a two-state transition. However, for longer
oligonucleotides, the thermodynamic properties of the single self-folding
transition affects the transition nature of the duplex formation, resulting in
a population of intermediate hairpin species in the solution. The role of
intermediate hairpin species is analyzed in the case when a short
oligonucleotides (molecular beacons) have to reliably identify and hybridize to
accessible nucleotides within their targeted mRNA sequences. It is shown that
the enhanced specificity of the molecular beacons is a result of their
constrained conformational flexibility and the all-or-none mechanism of their
hybridization to the target sequence.
