  The physical approach of a small particle (virus, medical drug) to the cell
membrane represents the crucial first step before active internalization and is
governed by thermal diffusion. Using a fully analytical theory we show that the
stretching and bending of the elastic membrane by the approaching particle
induces a memory in the system which leads to anomalous diffusion, even though
the particle is immersed in a purely Newtonian liquid. For typical cell
membranes the transient subdiffusive regime extends beyond 10 ms and can
enhance residence times and possibly binding rates up to 50\%. Our analytical
predictions are validated by numerical simulations.
