A simplified model of NMDA-receptor-mediated dynamics in leaky integrate-and-fire neurons

A model for NMDA-receptor-mediated synaptic currents in leaky integrate-and-fire neurons, first proposed by Wang (J Neurosci, 1999), has been widely studied in computational neuroscience. The model features a fast rise in the NMDA conductance upon spikes in a pre-synaptic neuron followed by a slow decay. In a general implementation of this model which allows for arbitrary network connectivity and delay distributions, the summed NMDA current from all neurons in a pre-synaptic population cannot be simulated in aggregated form. Simulating each synapse separately is prohibitively slow for all but small networks, which has largely limited the use of the model to fully connected networks with identical delays, for which an efficient simulation scheme exists. We propose an approximation to the original model that can be efficiently simulated for arbitrary network connectivity and delay distributions. Our results demonstrate that the approximation incurs minimal error and preserves network dynamics. We further use the approximate model to explore binary decision making in sparsely coupled networks.