Stochastic model of central synapses: Slow diffusion of transmitter interacting with spatially distributed receptors and transporters

A detailed mathematical analysis of the diffusion process of neurotransmitt er inside the synaptic cleft is presented and the spatio-temporal concentra tion profile is calculated. Using information about the experimentally obse rved time course of glutamate in the cleft the effective diffusion coeffici ent D-net is estimated as D-net similar to 20-50 nm(2) mu s(-1), implying a strong reduction compared with free diffusion in aqueous solution. The tor tuosity of the cleft and interactions with transporter molecules are assume d to affect the transmitter motion. We estimate the transporter density to be 5170 to 8900 mu m(-2) in the synaptic cleft and its vicinity, using the experimentally observed time constant of glutamate. Furthermore a theoretic al model of synaptic transmission is presented, taking the spatial distribu tion of post-synaptic (AMPA-) receptors into account. The transmitter diffu sion and receptor dynamics are modeled by Monte Carlo simulations preservin g the typically observed noisy character of post-synaptic responses. Distri butions of amplitudes, rise and decay times are calculated and shown to agr ee well with experiments. Average open probabilities are computed from a no vel kinetic model and are shown to agree with averages over many Monte Carl o runs. Our results suggest that post-synaptic currents are only weakly pot entiated by clustering of post-synaptic receptors, but increase linearly wi th the total number of receptors. Distributions of amplitudes and rise time s are used to discriminate between different morphologies, e.g, simple and perforated synapses. A skew in the miniature amplitude distribution can be caused by multiple release of pre-synaptic vesicles at perforated synapses. (C) 1999 Academic Press.