New Research on Untying Knots in Polymers - Comments

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Discussion Overview

The discussion revolves around the recent research on untying knots in polymers, exploring the implications of knot formation, energy states, and potential applications. It includes theoretical considerations, practical examples, and questions about the stability of knotted states in polymers.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether knots in polymers immediately re-knot when stretching forces are removed and asks about the potential energy of knotted versus straight configurations.
  • Another participant explains that the lowest energy state of a polymer is a random coil, which maximizes entropy, and discusses the likelihood of spontaneous knot formation upon relaxation.
  • It is proposed that a knotted polymer has higher free energy than an unknotted one, with knots being described as metastable and unlikely to expand significantly once formed.
  • A participant raises concerns about whether knots create extra stress at specific bonds that could lead to bond breakage, suggesting that a stable knotted state implies bonds do not break easily.
  • Practical applications of knots beyond DNA are queried, with one participant mentioning that knots can be useful but expressing uncertainty about the relevance of their research to these applications.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the stability and implications of knots in polymers, and no consensus has been reached on the questions raised.

Contextual Notes

Participants discuss the thermodynamic stability of knots under the assumption that polymer length remains constant, which may not account for scenarios involving breaking or growing.

klotza
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Greg Bernhardt submitted a new PF Insights post

New Research on Untying Knots in Polymers
dna_stretch.png


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That was fun to read. Good article.

When you remove the stretching forces, do they immediately re-knot?

Can you calculate the potential energy of the configurations? Is a knotted state lower energy than straight?
 
Good question. The lowest energy state of a polymer is a random coil, that is the one that maximizes entropy. When you stretch a polymer and let it relax, it returns to the coiled state as entropy increases (this is also why rubber is elastic). However, if there's no knot it is unlikely (but not impossible) for knots to spontaneously form as it relaxes.

A polymer with a knot is thought to have a higher free energy than one without a knot (there's more configurations without a knot than with a knot, so unknot has higher entropy). What has been theorized is that knots are metastable, meaning there is an equilibrium size for the knot once it exists, and it is unlikely to expand to much bigger than that, so the molecule will remain knotted for a long time, until it diffuses to the end of the molecule and unties. There might also be scenarios in which knots are favourable, like a molecule under extreme confinement (the DNA of a virus is an example).
 
Do the knots put extra stress at particular bonds that might make the bond break? If the knotted state is stable, that suggests they don't break.

How about non-DNA practical applications?
 
They do. You can try tying a cooked spaghetti noodle into a knot and pulling on the ends. The noodle will break at the knot. All this stuff about thermodynamic stability though basically assumes that the length is constant (no breaking or growing).

There are lots of things that knots are useful for, but I'm not sure my research really improved any of those.
 
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