  A recent high-resolution $\alpha$, $X$-ray, and $\gamma$-ray
coincidence-spectroscopy experiment offered first glimpse of excitation schemes
of isotopes along $\alpha$-decay chains of $Z=115$. To understand these
observations and to make predictions about shell structure of superheavy nuclei
below $^{288}115$, we employ two complementary mean-field models:
self-consistent Skyrme Energy Density Functional approach and the
macroscopic-microscopic Nilsson model. We discuss the spectroscopic information
carried by the new data. In particular, candidates for the experimentally
observed $E1$ transitions in $^{276}$Mt are proposed. We find that the presence
and nature of low-energy $E1$ transitions in well-deformed nuclei around
$Z=110, N=168$ strongly depends on the strength of the spin-orbit coupling;
hence, it provides an excellent constraint on theoretical models of superheavy
nuclei. To clarify competing theoretical scenarios, an experimental search for
$E1$ transitions in odd-$A$ systems $^{275,277}$Mt, $^{275}$Hs, and $^{277}$Ds
is strongly recommended.
