  We study the secondary structure of RNA determined by Watson-Crick pairing
without pseudo-knots using Milnor invariants of links. We focus on the first
non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg
invariant, which is an integer, can be interpreted in terms of the Heisenberg
group as well as in terms of lattice paths.
  We show that the Heisenberg invariant gives a lower bound on the number of
unpaired bases in an RNA secondary structure. We also show that the Heisenberg
invariant can predict \emph{allosteric structures} for RNA. Namely, if the
Heisenberg invariant is large, then there are widely separated local maxima
(i.e., allosteric structures) for the number of Watson-Crick pairs found.
