Kinetic theory for DNA melting with vibrational entropy ...

1 Kinetic theory for DNA melting with vibrational entropySebastian Sensale, Zhangli Peng, and Hsueh-Chia ChangCitation: The Journal of Chemical physics 147, 135101 (2017);View online: Table of Contents: by the american institute of PhysicsArticles you may be interested in Removing the barrier to the calculation of activation energies: Diffusion coefficients and reorientation times inliquid waterThe Journal of Chemical physics 147, 134103 (2017); First passage times for multiple particles with reversible target-binding kineticsThe Journal of Chemical physics 147, 134112 (2017); diagram of two-dimensional hard rods from fundamental mixed measure density functional theoryThe Journal of Chemical physics 147, 134908 (2017); passage, looping, and direct transition in expanding and narrowing tubes: Effects of the entropy potentialThe Journal of Chemical physics 147, 134104 (2017).

2 Decoupling of translational and rotational diffusion in quasi-2D colloidal fluidsThe Journal of Chemical physics 147, 134502 (2017); coarse-grained potentials for waterThe Journal of Chemical physics 147, 134108 (2017); JOURNAL OF CHEMICAL PHYSICS147, 135101 (2017) Kinetic theory for DNA melting with vibrational entropySebastian Sensale,1 Zhangli Peng,1,a)and Hsueh-Chia Chang2,a)1 Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame,Indiana 46556-5637, USA2 Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame,Indiana 46556-5637, USA(Received 14 July 2017; accepted 19 September 2017.

3 Published online 4 October 2017)By treating DNA as a vibrating nonlinear lattice, an activated Kinetic theory for DNA melting isdeveloped to capture the breakage of the hydrogen bonds and subsequent softening of torsional andbending vibration modes. With a coarse-grained lattice model, we identify a key bending mode withGHz frequency that replaces the hydrogen vibration modes as the dominant out-of-phase phononvibration at the transition state. By associating its bending modulus to a universal in-phase bendingvibration modulus at equilibrium, we can hence estimate the entropic change in the out-of-phasevibration from near-equilibrium all-atom simulations.

4 This and estimates of torsional and bendingentropy changes lead to the first predictive and sequence-dependent theory with good quantitativeagreement with experimental data for the activation energy of melting of short DNA molecules withoutintermediate hairpin by AIP INTRODUCTIONB iological systems are characterized by their metabolismand self-replication. In DNA, self-replication initiates withthe local formation of denaturation bubbles by overcomingenergy barriers, making denaturation, and hybridization ofDNA among the most important processes in biology.

5 Thesereactions, in response to physical or chemical stimuli, are alsothe cornerstones of many laboratory techniques such as poly-merase chain reaction (PCR) and DNA sequencing, as wellas many oligo-based biosensors where a single-stranded DNAbinds selectively to its complementary and kinetics are two fundamentalaspects of DNA denaturation and hybridization. Throughextensive benchmarking against melting temperature measure-ments, nearest-neighbor models have proven to accuratelyrepresent the thermodynamics of these reactions, at least forsequences of up to 24 base pairs (bps).

6 2,3 Kinetic propertiesare harder to capture both through simulations and theories, asthe reaction pathway is not well defined4and the time scales ofthese processes are large enough to prevent extensive studiesthrough all-atom molecular dynamics (MD) 7As most relevant melting and hybridization conditionsoccur away from the thermodynamic melting temperature andare under non-equilibrium external forces like shear and elec-tric stress,8,9irreversible Kinetic rates are often more importantthan thermodynamic equilibrium constants.

7 Irreversible melt-ing has been shown to produce higher selectivity for base-pairs with comparable thermodynamic equilibrium dissocia-tion models have been developedto meet this need for melting and hybridization rates. Theyhave the ability to predict trends in the kinetics but typicallya)Authors to whom correspondence should be addressed: rates many orders of magnitude faster than experi-mental 12 Irreversible DNA melting kinetics are known experi-mentally to obey the Eyring-Polanyi activated rate5 7,13 15k=kBThexp( G kBT), wherekis the melting rate,kBis the Boltz-mann constant,Tis the temperature,his the Planck constant,and G is the activation free energy, which can be decom-posed into its enthalpy and entropy terms G = H T S.

8 As the separation of the strands during the melting is smallenough such that the rate is, within reasonable values, bothconcentration and salt content independent,6,16the determi-nation of the free energy of activation is sufficient to providegood estimates for the Kinetic rate of melting . Nevertheless, weare not aware of any current theory on the activation energy ofmelting, even from the coarse-grained major obstacle is the estimate of the activationentropy S , which is expected to involve cooperative vibra-tion dynamics with both in-phase and out-of-phase phononfluctuations with respect to the hydrogen bonds at the transi-tion state.

9 Such long-wavelength and slow vibration dynam-ics are in violation of energy equi-partition as some of thevibration modes will dominate due to the long-range tracking of this coupling and the evolutionof the slow and long-range vibrations are beyond all-atomsimulations except for dedicated efforts with large ,11,18 There are, however, coarse-grained models that may allowus to capture these cooperative vibrations at the transition statewithout directly simulating the dynamics. The most extensiveall-atom molecular dynamics simulations of the DNA meltingprocess to date present a mechanistic description where theduplex untwists until reaching a conformation which resem-bles a planar ladder.

10 Then, the bases fray and peel until bothstrands are held together by a single base pair (see Fig. 1).Finally, this base pair breaks, leading to two fully ,18 The melting process appears to be quite stochastic,0021-9606/2017/147(13)/135101 /11/$ , 135101-1 Published by AIP Sensale, Peng, and ChangJ. Chem. , 135101 (2017)FIG. 1. Conformations of the DNA duplex CAAAAAG sampled during an enhanced melting different routes with different fluxes and residencetimes, and thus making the definition of a simple reactioncoordinate quite sequences longer than 10 bps,loops or cruciform secondary structures form during denat-uration, further complicating the dynamics and the energylandscape,19with typically lower activation 22 Nevertheless, for a transition state theory .