article · Chaos An Interdisciplinary Journal of Nonlinear Science
Charge transport within the twist-opening model of DNA has been investigated through the modulational instability of plane waves. Under an adiabatic approximation, the movement of charge follows a modified discrete nonlinear Schrödinger equation incorporating next-nearest neighbour interactions. Linear stability analysis reveals how modulational instability behaves relative to a parameter that measures corrections to hopping interactions. As this parameter increases, the domain of instability contracts, which improves the likelihood of selecting conditions that foster pattern formation in the twist-opening framework. Numerical integration of equations governing radial and torsional motions confirms these analytical findings. The migration of charge affects both radial and torsional dynamics across various parameter values. Furthermore, numerical simulations reveal soliton-like and localised formations, demonstrating that polaronic structures emerge via modulational instability and confirming the stability of polarons in this DNA transport model.
Understanding how electrical charge travels along DNA molecules provides fundamental insight into molecular-scale biophysics. By demonstrating how stable, localised charge packets like polarons form and persist through physical twisting and radial motions, this theoretical framework helps explain how energy and electrical signals can propagate along complex helical biomolecules without immediately dispersing.
The abstract does not indicate an application pathway, presenting early-stage theoretical and numerical modelling of molecular charge transport without referencing practical uses or end users.
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Charge transport in the twist-opening model of DNA is explored via the modulational instability of a plane wave. The dynamics of charge is shown to be governed, in the adiabatic approximation, by a modified discrete nonlinear Schrödinger equation with next-nearest neighbor interactions. The linear stability analysis is performed on the latter and manifestations of the modulational instability are discussed according to the value of the parameter α, which measures hopping interaction correction. In so doing, increasing α leads to a reduction of the instability domain and, therefore, increases our chances of choosing appropriate values of parameters that could give rise to pattern formation in the twist-opening model. Our analytical predictions are verified numerically, where the generic equations for the radial and torsional dynamics are directly integrated. The impact of charge migration on the above degrees of freedom is discussed for different values of α. Soliton-like and localized structures are observed and thus confirm our analytical predictions. We also find that polaronic structures, as known in DNA charge transport, are generated through modulational instability, and hence reinforces the robustness of polaron in the model we study.
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DOI: 10.1063/1.4766594
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