  The bulk-surface wave pinning model is a reaction-diffusion system for
studying cell polarisation. It is constituted by a surface reaction-diffusion
equation, coupled to a bulk diffusion equation with a non-linear boundary
condition. Cell polarisation arises as the surface component develops specific
patterns. Since proteins diffuse much faster in the cell interior than on the
membrane, in the literature, the bulk component is often assumed to be
spatially homogeneous. {\re Therefore, the model can be reduced to a single
surface equation}. However, {\re in real applications} a spatially non-uniform
bulk component might be an important player to take into account. In this
paper, we study, through numerical computations, the role of the bulk component
and, more specifically, how different bulk diffusion rates might affect the
polarisation response. We find that the bulk component is indeed a key factor
in {\re determining the surface polarisation response}. Moreover, for certain
geometries, it is the spatial heterogeneity of the bulk component that triggers
the polarisation response, which might not be possible in a reduced model.
  Understanding how polarisation depends on bulk diffusivity might be crucial
when studying models of migrating cells, which are naturally subject to domain
deformation.
