  A coarse-grained computational model is used to investigate how the bending
rigidity of a polymer under tension affects the formation of a trefoil knot.
Thermodynamic integration techniques are applied to demonstrate that the
free-energy cost of forming a knot has a minimum at non-zero bending rigidity.
The position of the minimum exhibits a power-law dependence on the applied
tension. For knotted polymers with non-uniform bending rigidity, the knots
preferentially localize in the region with a bending rigidity that minimizes
the free-energy.
