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article · Journal of Physics Condensed Matter

Modulational instability of charge transport in the Peyrard–Bishop–Holstein model

200926 citationsOpen access

In plain language

This research examines charge transport in DNA by investigating modulational instability within the Peyrard-Bishop-Holstein model. By applying a continuum approximation, the framework reduces to a modified Klein-Gordon-Schrödinger system, allowing linear stability analysis to be conducted. The analysis explores modulational instability across varied values of the nearest-neighbour transfer integral. Numerical simulations confirm these theoretical predictions, demonstrating the formation of localised structures as charges propagate. In addition, the findings demonstrate that the spreading and distribution of electric charge depend heavily on the strength of the coupling between the charge and the vibrational movements of the molecular lattice.

Key takeaways

  • The Peyrard-Bishop-Holstein model for DNA charge transfer was analysed as a modified Klein-Gordon-Schrödinger system using linear stability methods.
  • Conditions for modulational instability were identified across different nearest-neighbour transfer integral values.
  • Numerical simulations validated the analytical results and revealed the formation of localised charge structures.
  • Charge spreading in the model depends strongly on the degree of charge-lattice-vibrational coupling.

Why it matters

Charge transport along molecular chains is fundamental to molecular physics and the study of bio-macromolecules. By identifying how instabilities and localised structures form, this theoretical work clarifies how mechanical vibrations in a molecular lattice influence the conduction and retention of electrical charges in biomolecular structures.

Commercialisation angle

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Abstract

We report on modulational instability (MI) on a DNA charge transfer model known as the Peyrard-Bishop-Holstein (PBH) model. In the continuum approximation, the system reduces to a modified Klein-Gordon-Schrödinger (mKGS) system through which linear stability analysis is performed. This model shows some possibilities for the MI region and the study is carried out for some values of the nearest-neighbor transfer integral. Numerical simulations are then performed, which confirm analytical predictions and give rise to localized structure formation. We show how the spreading of charge deeply depends on the value of the charge-lattice-vibrational coupling.

Research topics

  • DNA and Nucleic Acid Chemistry
  • Spectroscopy and Quantum Chemical Studies
  • Molecular Junctions and Nanostructures

Read the original research

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DOI: 10.1088/0953-8984/21/33/335101

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