Elastic Properties of DNA as the Entropic Driving Force for Dehybridization Transitions

Abstract

Through the use of a coarse-grained lattice model informed from all-atomic simulations near equilibrium, we obtain a theoretical estimate of the sequence-dependent slow melting rates (> nanoseconds) of DNA duplexes with activation free energies accurate within 3kT. We show that the change in elastic properties of short DNAs is the key entropic driving force for DNA melting and hybridization. Using a vibration and torsional continuum model, we relate this entropy to the bending and torsional persistence lengths captured from the phonon spectra in all-atomic simulations, near equilibrium, by capturing both the momentum and configuration degrees of freedom simultaneously. A key to the theory is the cooperative melting of all but one base pair at the transition state. This hinge transition state allows us to replace the hydrogen bond vibration modes with a set of out/of-phase bending modes with a much higher vibration entropy (lower phonon frequencies). A multidimensional version of Kramers transition state theory allows us to assign this change to an effective vibrational entropy term that counters the enthalpic gain required to break the hydrogen bonds, leading to an elastic theory for the melting rate of short DNAs. As the hydrogen bond enthalpies are thermodynamic quantities, we estimate them from the classical nearest-neighbor theory. The vibration entropy of the hinge transition state is strictly kinetic but, as it relates only to the persistence lengths, we are able to capture it from near-equilibrium simulations of the duplex. This theory allows us both to make quantitative estimates of the melting rates of short DNAs as well as to differentiate between unzipping and other reaction pathways that may be followed in the presence of secondary structures or mismatches. It represents the first theory for DNA melting with quantitative accuracy.