Statistical mechanical model for a closed loop plectoneme with weak helix specific forces.

Area of Science:

• Statistical mechanics
• Biophysics
• Polymer physics

Background:

• Plectonemes are complex DNA structures crucial for genome organization.
• Understanding their statistical mechanics is vital for comprehending DNA packaging and manipulation.
• Existing models often simplify or neglect helix structure-dependent forces and topological constraints.

Purpose of the Study:

• To develop a statistical mechanical framework for describing closed loop plectonemes.
• To incorporate weak helix structure-dependent forces into free energy and average structure calculations.
• To systematically enforce the topological constraint of closed loop supercoiling within a variational approximation.

Main Methods:

• Utilized a variational approximation framework.
• Incorporated helix structure-dependent forces and their chiral nature.
• Employed a Lagrange multiplier to enforce topological constraints (sum of average twist and writhe).
• Calculated average writhe via thermal average of Gauss' integral.
• Applied mean-field Kornyshev-Leikin theory for interaction energies.

Main Results:

• Developed a framework for closed loop plectonemes with chiral force incorporation.
• Demonstrated that helix forces break symmetry between left and right-handed supercoiling.
• Showed left-handed supercoils exhibit looser structures than right-handed ones.
• Identified lower free energy in left-handed supercoils, contrasting with prior ground state calculations.

Conclusions:

• The developed framework accurately describes closed loop plectonemes under weak helix forces.
• Helix-induced chirality leads to asymmetric plectoneme structures and energetics.
• The approach provides a method for calculating finite size corrections due to topological constraints.