Dashed line represents patch boundary moving with velocity
, with patch to left of boundary. Uncomplexed SNAREs (density profile
,
blue) bind within patch forming complexes (density profile
,
red). Far outside (inside) patch
(
) approaches the initial SNARE density,
. The vertical axis indicates the density scale and shows how
compares to two constant density values,
and
. (A) Slow patch growth (
). SNAREs bind rapidly inside the boundary and a diffusion-depleted zone of SNAREs develops outside the patch. The SNARE profile penetrates a small distance
into the patch. Because the boundary moves slowly compared to complex diffusion the complex diffusion length
exceeds
so
is relatively flat and the boundary density is undepleted,
. (B) Intermediate patch growth (
.) As for the slow regime the SNARE profile is diffusion-depleted near the boundary. However patch growth is now fast relative to complex diffusion such that
; only a portion of those complexes generated in the patch catch up with the boundary before it moves on and the boundary density is depleted,
. (C) Fast patch growth (
). SNARE binding is slow compared to patch growth so SNARE density is little depleted at the boundary and
is large. As for the intermediate regime,
but the complex boundary density is even more depleted relative to
.