Knots," and "Knot
Energies:" Can the knot type be determined from the `ideal'
shape of the curve that minimizes a particular (two-body) potential?
Simon in Ideal Knots (1998):
a Charged Trefoil
charged knots ... are tight
Composite charged knots ... are factored
- The above results are obtained from
off-lattice Monte Carlo simulations of N monomers,
- each a sphere of diameter b;
- connected by tethers such that
most physically relevant situations, Coulomb interactions are highly screened;
for DNA in vivo, but larger values can be achieved in vitro.
(dimensionless) screened Coulomb interaction depends on two lengths:
- The screening
the range of interactions,
- The Bjerrum length gives
the strength of potential, through
tight knots disappear for finite screening lengths?
Electrostatic (Odijk-Skolnick-Fixman) persistence length:
- The tight knot is the global energy minimum as
long as is comparable
to size of the open chain.
- The tight knot is a local energy minimum
as long as is
larger than the bare persistence length.
- Tight knots (metastable) slow down the relaxational dynamics:
- The higher the charge density, the slower is the relaxation
to the final state.
- A knot in an open chain is untied by