  DNA supercoiling plays an important role on a biological point of view. One
of its consequences at the supra-molecular level is the formation of DNA
superhelices named plectonemes. Normally separated by a distance on the order
of 10 nm, the two opposite double-strands of a DNA plectoneme must be brought
closer if a protein or protein complex implicated in genetic regulation is to
be bound simultaneously to both strands, as if the plectoneme was locally
pinched. We propose an analytic calculation of the energetic barrier, of
elastic nature, required to bring closer the two loci situated on the opposed
double-strands. We examine how this energy barrier scales with the DNA
supercoiling. For physically relevant values of elastic parameters and of
supercoiling density, we show that the energy barrier is in the $k_{\rm B} T$
range under physiological conditions, thus demonstrating that the limiting step
to loci encounter is more likely the preceding plectoneme slithering bringing
the two loci side by side.
