Untying Knotted DNA with Elongational Flows.

Area of Science:

• Polymer Physics
• Biophysics
• Computational Biology

Background:

• Knotted DNA molecules are prevalent in biological systems and nanotechnology.
• Understanding knot dynamics is crucial for manipulating DNA and other polymers.
• Elongational flows offer a method for studying polymer behavior and knot untying.

Purpose of the Study:

• To investigate the behavior of initially knotted double-stranded DNA molecules in elongational flows using Brownian dynamics simulations.
• To determine the governing principles of knot motion and translation along the DNA strand.
• To elucidate the distinct dynamics of different knot types, specifically torus versus nontorus knots.

Main Methods:

• Brownian dynamics simulations were employed to model DNA molecules with initial knots.
• Scalings were derived to analyze simulation data and establish governing equations for knot motion.
• Analysis focused on nonaffine displacement, translation rates, and rotational dynamics of knots.

Main Results:

• Knot motion in elongational flow follows a diffusion-convection equation.
• Knot translation rates are dependent on topology and exhibit nonaffine displacement.
• Torus knots display a characteristic "corkscrew" motion, unlike nontorus knots, due to a flow-induced rotation-translation coupling.

Conclusions:

• The study provides a quantitative understanding of how DNA knots untie and move in flow.
• A mechanism explaining the coupling between knot rotation and translation was identified.
• These findings have implications for nanoscale DNA manipulation, genomic sequencing, and polymer processing.