Molecular diffusion model of neurotransmitter homeostasis around synapses supporting gradients

Neurotransmitter homeostasis in and around a synapse involves complex random processes such as diffusion, molecular binding, and uptake by glial transporters. A three-dimensional stochastic diffusion model of a synapse was developed to provide molecular-level details of neurotransmitter homeostasis not predicted by alternative models based on continuum approaches. The development was illustrated through an example case cortico-accumbens synapse that successfully integrated neuroadaptations observed after chronic cocaine. By incorporating cystine-glutamate exchanger as a nonsynaptic release site for glutamate, the stochastic model was used to quantify the relative contributions of synaptic and nonsynaptic sources to extracellular concentration and to estimate molecular influx rates into the perisynapse. A perturbation analysis showed that among the parameters considered, variation in surface density of glial transporters had the largest effect on glutamate concentrations. The stochastic diffusion model of the example synapse was further generalized to characterize glial morphology by studying the role of diffusion path length in supporting neurotransmitter gradients and isolating the synapse. For the same set of parameters, diffusion path length was found to be proportional to the gradient supported.