  Recent observations have revealed a gallery of substructures in the dust
component of nearby protoplanetary discs, including rings, gaps, spiral arms,
and lopsided concentrations. One interpretation of these substructures is the
existence of embedded planets. Not until recently, however, most of the
modelling effort to interpret these observations ignored the dust back reaction
to the gas. In this work, we conduct local-shearing-sheet simulations for an
isothermal, inviscid, non-self-gravitating, razor-thin dusty disc with a planet
on a fixed circular orbit. We systematically examine the parameter space
spanned by planet mass ($0.1M_\text{th} \le M_\text{p} \le 1M_\text{th}$, where
$M_\text{th}$ is the thermal mass), dimensionless stopping time ($10^{-3} \le
\tau_\text{s} \le 1$), and solid abundance ($0 < Z \le 1$). We find that when
the dust particles are tightly coupled to the gas ($\tau_\text{s} < 0.1$), the
spiral arms are less open and the gap driven by the planet becomes deeper with
increasing $Z$, consistent with a reduced speed of sound in the approximation
of a single dust-gas mixture. By contrast, when the dust particles are
marginally coupled ($0.1 \lesssim \tau_\text{s} \lesssim 1$), the spiral
structure is insensitive to $Z$ and the gap structure in the gas can become
significantly skewed and unidentifiable. When the latter occurs, the pressure
maximum radially outside of the planet is weakened or even extinguished, and
hence dust filtration by a low-mass ($M_\text{p} < M_\text{th}$) planet could
be reduced or eliminated. Finally, we find that the gap edges where the dust
particles are accumulated as well as the lopsided large-scale vortices driven
by a massive planet, if any, are unstable, and they are broken into numerous
small-scale dust-gas vortices.
