A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibr ium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurem ent of the persistence length of single-stranded DNA, which is found to be similar to1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of th e hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of greater than or similar to7, much larger than the exponent of similar to1.5-1.8 expected from considerations of loo p entropy alone. This result indicates a strong dependence of the excess st ability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arisi ng from favorable hydrophobic interactions among the bases in tight loops a nd which diminish as the loops get larger. Free energy profiles along a gen eralized reaction coordinate are calculated from the equilibrium zipper mod el. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a low er enthalpy than the random coil state. The equilibrium model predicts appa rent activation energy of similar to -11 kcal/mol for the hairpin closing s tep, in remarkable agreement with the value obtained from kinetics measurem ents.