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DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

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Maximum entropy principle applied to semiflexible ring polymers.

Maxim Dolgushev¹, Ganna Berezovska, Alexander Blumen

¹Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany. dolgushev@physik.uni-freiburg.de

The Journal of Chemical Physics

|September 15, 2011

Summary

This summary is machine-generated.

The maximum entropy principle (MEP) was extended to analyze semiflexible polymer rings. This approach reveals solutions that may correspond to knotted polymer structures.

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Area of Science:

Polymer Physics
Statistical Mechanics
Computational Chemistry

Background:

The maximum entropy principle (MEP) has proven successful for treelike polymer analysis.
Extending MEP to polymers with loops, specifically polymer rings, presents a significant challenge.
Previous work utilized a discrete beads-and-bonds model for treelike polymers.

Purpose of the Study:

To investigate the applicability of the maximum entropy principle (MEP) to discrete semiflexible polymer rings.
To develop a theoretical framework for understanding the behavior of polymer rings using MEP.
To explore potential solutions arising from MEP analysis and their physical interpretations.

Main Methods:

A Rouse-type scheme was employed for discrete semiflexible polymer rings.
A reduced variational approach with Lagrange multipliers was utilized.
Analytical solutions involving Chebyshev polynomials were derived.
Monte Carlo simulations incorporating excluded volume interactions were performed.

Main Results:

An analytically closed-form expression for discrete polymer rings was obtained.
Multiple solutions emerged, including a regular solution and others with non-positive definite potential energy matrices.
These additional solutions were interpreted as potentially representing knotted polymer rings.
Simulations supported the interpretation of these solutions relating to knots.

Conclusions:

The maximum entropy principle can be successfully applied to analyze discrete semiflexible polymer rings.
The derived solutions offer insights into the complex topological states of polymer rings, including knots.
The study provides a theoretical foundation for further investigations into the statistical mechanics of cyclic polymers.