A Semiflexible Polymer Model Applied to Loop Formation in DNA Hairpins

A statistical mechanical “zipper” model is applied to describe the equilibrium 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 measurement of the persistence length of single-stranded DNA, which is found to be ∼1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of ≳7, much larger than the exponent of ∼1.5–1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of ∼−11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.