Two-dimensional interfacial diffusion model of inhibitory synaptic receptor dynamics

The diffusion-trapping of protein receptors in post-synaptic regions of a neuron's plasma membrane plays a key role in determining the strength of synaptic connections and their regulation during learning and memory. In this paper, we construct and analyse a two-dimensional 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 including synaptic radius and the permeability of the synaptic interface. We then use matched asymptotic analysis to solve the corresponding problem of multiple synapses in a large, bounded domain. In particular, we show how diffusion mediates pairwise synaptic interactions that could provide a substrate for heterosynaptic plasticity. Finally, we indicate how to apply the model to the stochastic dynamics of single receptors.