Topological signatures of globular polymers

Area of Science:

• Polymer Physics
• Computational Chemistry
• Biophysics

Background:

• Understanding polymer behavior is crucial in various scientific fields.
• Knots in polymers can significantly alter their physical and statistical properties.
• Simulations provide a powerful tool to investigate complex polymer dynamics.

Purpose of the Study:

• To investigate how the topological complexity of knots in a ring polymer influences its equilibrium statistical properties.
• To analyze the length distribution of polymer loops formed under different separation conditions (slipping link vs. wall with a hole).
• To explore the interplay between topological effects and surface tension during polymer translocation through nanopores.

Main Methods:

• Computer simulations of a globular ring polymer.
• Separation of the polymer into two loops using a slipping link or a wall with a hole.
• Analysis of equilibrium statistics, including length distributions and fluctuations.
• Investigation of polymer translocation through a membrane nanopore.

Main Results:

• The minimal crossing number of polymer knots controls equilibrium statistics.
• Ring length divides between loops via a simple law, but with significant fluctuations for knotted polymers.
• Unknotted loops show suppressed fluctuations and a fast power-law decay in length distribution.
• A novel topological effect interfering with surface tension during nanopore translocation was identified.

Conclusions:

• Knot topology is a critical determinant of polymer loop statistics and behavior.
• The presence of knots leads to unpredictable fluctuations in loop length, impacting translocation.
• Unknotted polymers exhibit more regular and predictable behavior, with implications for biological and synthetic systems.
• Topological effects play a significant role in polymer translocation, alongside conventional forces like surface tension.