Force distribution in a semiflexible loop.

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Biophysics

Background:

• Looped polymers, including DNA and macromolecules, are common in nature.
• Thermodynamics often uses free energy (an average quantity) to describe stability, but local forces also play a role.
• Understanding force distributions provides insights into mechanochemistry beyond traditional thermodynamics.

Purpose of the Study:

• To investigate the force exerted by an inextensible semiflexible polymer in a looped configuration.
• To analyze the full distribution of constraint forces, not just their average values.
• To explore how factors like chain length, extension, and stiffness influence these forces.

Main Methods:

• Utilized a simulation technique called "phase-space sampling" to generate equilibrium distributions of chain conformations.
• Employed Lagrangian mechanics to compute constraint forces between the loop's ends.
• Analyzed kinetic and potential energy contributions to the forces.

Main Results:

• The mean constraint force equals the thermodynamic force.
• The mean force promotes extension despite bending stress.
• Force distribution is asymmetric, deviates from Gaussian, and depends on chain length, extension, and stiffness.
• Increased contour length reduces average force but increases force fluctuations.

Conclusions:

• Local force distributions offer insights into polymer behavior not captured by thermodynamics alone.
• Large-amplitude fluctuations in looped polymers can occur unexpectedly.
• The study provides computational tools for simulating constrained polymer systems efficiently and without bias.