<p>Knots are discovered in a wide range of systems, from DNA and proteins to catheters and umbilical cords, and have thus attracted much attention from physicists and biophysicists. Langevin dynamics simulations were performed to study the knotting properties of coarsegrained knotted circular semiflexible polyelectrolyte (PE) in solutions of different concentrations of trivalent salt. We find that the length and position of the knotted region can be controlled by tuning the bending rigidity <i>b</i> of the PE and the salt concentration <i>C</i><sub>S</sub>. We find that the knot length varies nonmonotonically with <i>b</i> in the presence of salt, and the knot localizes and is the tightest at <i>b</i>=5. As <i>b</i>&gt;5, the knot swells with <i>b</i> increase. In addition, similar modulations of the knot size and position can be achieved by varying the salt concentration <i>C</i><sub>S</sub>. The knot length varies nonmonotonically with <i>C</i><sub>S</sub> for <i>b</i>&gt;0. The knot localizes and becomes tightest at <i>C</i><sub>S</sub>=1.5×10<sup>−4</sup> mol/L in the range of <i>C</i><sub>S</sub>≤1.5×10<sup>−4</sup> mol/L. As <i>C</i><sub>S</sub>&gt;1.5×10<sup>−4</sup> mol/L, the knot of the circular semiflexible PE swells at the expense of the overall size of the PE. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and knot length.</p>

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Tuning Knot Size of Knotted Circular Semiflexible Polyelectrolyte via Salt Concentration

  • Dan Lu,
  • Ai-Hua Chai,
  • Xiu-Xia Hu,
  • Pei-Hua Zhong,
  • Jian Wu,
  • Nian-Qian Kang,
  • Xian-Fei Kuang,
  • Zhi-Yong Yang

摘要

Knots are discovered in a wide range of systems, from DNA and proteins to catheters and umbilical cords, and have thus attracted much attention from physicists and biophysicists. Langevin dynamics simulations were performed to study the knotting properties of coarsegrained knotted circular semiflexible polyelectrolyte (PE) in solutions of different concentrations of trivalent salt. We find that the length and position of the knotted region can be controlled by tuning the bending rigidity b of the PE and the salt concentration CS. We find that the knot length varies nonmonotonically with b in the presence of salt, and the knot localizes and is the tightest at b=5. As b>5, the knot swells with b increase. In addition, similar modulations of the knot size and position can be achieved by varying the salt concentration CS. The knot length varies nonmonotonically with CS for b>0. The knot localizes and becomes tightest at CS=1.5×10−4 mol/L in the range of CS≤1.5×10−4 mol/L. As CS>1.5×10−4 mol/L, the knot of the circular semiflexible PE swells at the expense of the overall size of the PE. Our results lay the foundation for achieving broader and more precise external adjustability of knotted PE size and knot length.