Kinetic theory for DNA melting with vibrational entropy

Abstract

By treating DNA as a vibrating nonlinear lattice, an activated kinetic theory for DNA melting is developed to capture the breakage of the hydrogen bonds and subsequent softening of torsional and bending vibration modes. With a coarse-grained lattice model, we identify a key bending mode with GHz frequency that replaces the hydrogen vibration modes as the dominant out-of-phase phonon vibration at the transition state. By associating its bending modulus to a universal in-phase bending vibration modulus at equilibrium, we can hence estimate the entropic change in the out-of-phase vibration from near-equilibrium all-atom simulations. This and estimates of torsional and bending entropy changes lead to the first predictive and sequence-dependent theory with good quantitative agreement with experimental data for the activation energy of melting of short DNA molecules without intermediate hairpin structures.

Acceleration of DNA melting kinetics using alternating electric fields

“…A Nose-Hoover Langevin piston was applied to keep the pressure at 1.013 25 bars. 44,45 The suggested mechanism for melting of short DNA molecules without secondary structures is through an unzipping process; 26 however, when melting the DNA molecule "ACAAGTCCT" through the use of an AC field, we observe that the molecule aligns with the field and stretches until one of the strands slides from the other (see Fig. 5), suggesting a very different mechanism than the thermal 26 and the resonance-induced 32,33 ones.…”

“…44,45 The suggested mechanism for melting of short DNA molecules without secondary structures is through an unzipping process; 26 however, when melting the DNA molecule "ACAAGTCCT" through the use of an AC field, we observe that the molecule aligns with the field and stretches until one of the strands slides from the other (see Fig. 5), suggesting a very different mechanism than the thermal 26 and the resonance-induced 32,33 ones. Hence, the suggested definition of the melting time as the time when the center of mass of the central five bases of each single strand is larger than a certain constant 46 is not sufficient, and we also require all of the hydrogen bonds and base stacking interactions between interacting strands to be broken.…”

“…To analyze the capacity of discriminating different sequences with this method, we analyzed the enhanced melting rates of sequences "CAAAAAG," "ACAAGTCCT," "CACG-GCTC," and "AGATTAGCAGGTTTCCCACC" at 298.15 K, which are among the few melting rates of short DNA sequences within our simulation capabilities that have been measured and published. 26,50 The free energy barriers of these sequences take the values of 16.3, 18.7, 20.1, and 24.3 kcal/mol, respectively, at this temperature, corresponding to melting rates of 6.9, 0.1, 0.01, and 9.5 × 10 −5 s −1 . These disparate melting rates for very different DNA lengths and sequences are chosen to demonstrate the isothermal field-enhanced melting mechanism.…”

“…We also fitted the permittivities to the Cole-Cole 31 and Havriliak-Negami 21 models, fittings which coincided with the Debye and Cole-Davidson fittings, respectively. It is important to mention that resonance effects (which are observed in the terahertz spectrum 26,32,33 ) are not captured by either of these approximations.…”

Computing transition rates for rare events: When Kramers theory meets the free-energy landscape

“…As the transition rate defined in Eq. 9 may account for the activation entropy captured by the MFEP, such as rotational and vibrational entropy [22][23][24], it does not account for the configurational entropy, S conf , in the metastable basin [15,25]:…”