Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains

Area of Science:

• Soft Matter Physics
• Computational Biology
• Polymer Physics

Background:

• Simulating the dynamics of semi-flexible polymers like DNA is crucial for understanding biological processes.
• Existing methods often struggle with complex topological constraints (knots) and computational efficiency.
• Conditioned path generation is essential for studying transitions between specific states.

Purpose of the Study:

• To develop a computationally efficient stochastic method for generating overdamped Langevin dynamics of semi-flexible Gaussian chains.
• To enable the simulation of chains evolving between arbitrary initial and final conformations, including any knotted states.
• To analyze the topological transitions and routes between different knot types in filamentous structures.

Main Methods:

• A novel stochastic method is proposed to generate conditioned Langevin dynamics.
• The method utilizes local stochastic differential equations for exact path generation.
• Statistically independent paths are generated in a computationally efficient manner.

Main Results:

• The method successfully generates conditioned paths for semi-flexible Gaussian chains between unrestricted initial and final conformations.
• Analysis of transition routes between knots in crossable filamentous structures was performed.
• Topological properties like crossings, writhe, and unknotting number were found to be non-monotonic in time.
• More complex topologies than initial or final states can be visited during transitions.

Conclusions:

• The proposed stochastic method provides an efficient and exact way to simulate conditioned dynamics of semi-flexible chains with complex topologies.
• This approach offers new insights into topological reconnections in soft matter and DNA manipulation by enzymes.
• The study highlights the dynamic and complex nature of topological changes during polymer transitions.