  In this note we prove that the Kalton interlaced graphs do not equi-coarsely
embed into the James space $\mathcal J$ nor into its dual $\mathcal J^*$. It is
a particular case of a more general result on the non equi-coarse embeddability
of the Kalton graphs into quasi-reflexive spaces with a special asymptotic
stucture. This allows us to exhibit a coarse invariant for Banach spaces,
namely the non equi-coarse embeddability of this family of graphs, which is
very close to but different from the celebrated property $\mathcal Q$ of
Kalton. We conclude with a remark on the coarse geometry of the James tree
space $\mathcal J \mathcal T$ and of its predual.
