Nonlinear charge transport in the helicoidal DNA molecule

Area of Science:

• Biophysics
• Computational Biology
• Condensed Matter Physics

Background:

• Charge transport is crucial for DNA functionality.
• Understanding charge migration mechanisms in DNA is key to its biological roles.
• The twist-opening model provides a framework for studying DNA dynamics.

Purpose of the Study:

• To explore charge transport in the DNA twist-opening model.
• To investigate the role of modulational instability in charge dynamics.
• To analyze the impact of hopping interaction correction (α) on charge transport patterns.

Main Methods:

• Modulational instability analysis of a plane wave.
• Adiabatic approximation leading to a modified discrete nonlinear Schrödinger equation.
• Linear stability analysis and numerical verification of analytical predictions.
• Direct integration of radial and torsional dynamics equations.

Main Results:

• Modulational instability governs charge dynamics, approximated by a modified discrete nonlinear Schrödinger equation.
• Increasing hopping interaction correction (α) reduces the instability domain, favoring pattern formation.
• Soliton-like, localized structures, and polaronic structures are observed and confirmed numerically.
• Charge migration impacts radial and torsional dynamics, with polarons generated via modulational instability.

Conclusions:

• Modulational instability is a key mechanism for charge transport and polaron formation in the DNA twist-opening model.
• The parameter α effectively controls the stability and potential for pattern formation.
• The study reinforces the robustness of polaronic charge transport in this DNA model.