| Summary: | Deoxyribonucleic acid (DNA) is a long polymer consisting of two chains of bases, in which the genetic information is stored. A base from one chain has a corresponding base on the other chain which together form a so-called base-pair. Molecular-dynamics simulations of a normal DNA duplex show that breathing events – the temporary opening of one or more base-pairs – typically occur on the microsecond time-scale. Using the molecular dynamics package AMBER, we analyse, for different twist angles in the range 30-40 degrees of twist, a 12 basepair DNA duplex solvated in a water box, which contains the ’rogue’ base difluorotoluene (F) in place of a thymine base (T). This replacement makes breathing occur on the nanosecond time-scale. The time spent simulating such large systems, as well as the variation of breathing length and frequency with helical twist, determined us to create a simplified model, which is capable to predict with accuracy the DNA behaviour. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping to our system, we obtain a new mesoscopic model of the DNA duplex, close to that observed in experiments and all-atom MD simulations. Defects are considered in the inter-chain interactions as well as in the along-chain interactions. The system parameters are fitted to AMBER data using the maximum likelihood method. This model enables us to discuss the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices and how breathing can be viewed as competition between the along-chain elastic energy, the inter-chain binding energy and the entropy term of the system’s free energy. Using traditional analysis methods, such as principal component analysis, data autocorrelation, normal modes and Fourier transform, we compare the AMBER and SDE simulations to emphasize the strength of the proposed model. In addition, the Fourier transform of the trajectory of the A-F base-pair suggests that DNA is a self-organised system and our SDE model is also capable of preserving this behaviour. However, we reach the conclusion that the critical DNA behaviour needs further investigations, since it might offer some information about bubble nucleation and growth and even about DNA transcription and replication.
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