Low-energy DNA bubble dynamics via the quantum Coulomb potential

Area of Science:

• Computational physics
• Biophysics
• Molecular dynamics

Background:

• Understanding DNA dynamics is crucial for molecular biology.
• Existing models often provide only asymptotic results for DNA bubble dynamics.

Purpose of the Study:

• To develop a versatile low-energy model for DNA bubble dynamics.
• To derive closed-form expressions for probability density, first-passage time, and correlation functions.

Main Methods:

• Solving the Schrödinger equation in imaginary time with a quantum Coulomb potential.
• Approximating the physical solution using a linear combination of low-energy states.
• Expressing results using Bessel functions.

Main Results:

• A novel low-energy model for DNA bubble dynamics below the melting point.
• Closed-form expressions for probability density, first-passage time density, and correlation functions.
• Consistency with Fokker-Planck equation results and comparison with Gamma and diffusion models.

Conclusions:

• The developed model offers a comprehensive approach to DNA bubble dynamics.
• The closed-form expressions provide a more complete description than previous asymptotic results.
• This model enhances the understanding of DNA behavior at the molecular level.