Algebraic Statistics of Poincaré Recurrences in a DNA Molecule

Area of Science:

• * Biophysics and Physical Chemistry
• * Computational Biology and Biochemistry

Background:

• * Understanding DNA dynamics is crucial for molecular biology and drug design.
• * Previous studies have explored DNA base-pair breathing but lacked detailed statistical analysis in realistic environments.

Purpose of the Study:

• * To statistically analyze the Poincaré recurrences in the base-pair breathing dynamics of an all-atom DNA molecule.
• * To investigate the relationship between DNA dynamics, chaotic systems, and experimental observations.

Main Methods:

• * Employed molecular dynamics simulations of an all-atom DNA molecule in an aqueous environment.
• * Analyzed Poincaré recurrence statistics and low-frequency noise.
• * Applied the virial theorem to analyze chaotic dynamics in polynomial potentials.

Main Results:

• * Found an algebraic decay law for Poincaré recurrences over five time decades with an exponent β≈1.2.
• * Demonstrated analytically that β≈1.2 arises from dipole-dipole interactions in DNA dynamics.
• * Observed strong low-frequency noise with exponent η≈1.6.
• * Found parallels with chaotic dynamics in symplectic maps (β~1.5).

Conclusions:

• * The statistical properties of DNA base-pair breathing dynamics align with predictions from chaotic dynamics theory.
• * The findings provide a theoretical link between molecular dynamics simulations, experimental data (Stokes shift), and fundamental physics principles.