  The lateral diffusion and trapping of protein receptors within the
postsynaptic membrane of a neuron plays a key role in determining the strength
of synaptic connections and their regulation during learning and memory. In
this paper we construct and analyze a 2D interfacial diffusion model of
inhibitory synaptic receptor dynamics. The model involves three major
components. First, the boundary of each synapse is treated as a semi-permeable
interface due to the effects of cytoskeletal structures. Second, the effective
diffusivity within a synapse is taken to be smaller than the extrasynaptic
diffusivity due to the temporary binding to scaffold protein buffers within the
synapse. Third, receptors from intracellular pools are inserted into the
membrane extrasynaptically and internalized extrasynaptically and synaptically.
We first solve the model equations for a single synapse in an unbounded domain
and explore how the non-equilibrium steady-state number of synaptic receptors
depends on model parameters. We then use matched asymptotic analysis to solve
the corresponding problem of multiple synapses in a large, bounded domain.
Finally, treating a synapse as a phase separated condensate of scaffold
proteins, we describe how diffusion of individual scaffold proteins can also be
modeled in terms of interfacial diffusion. We thus establish interfacial
diffusion as a general paradigm for exploring synaptic dynamics and plasticity.
