Simple model neurons with AMPA and NMDA filters: role of synaptic time scales

Many central neurons receive inputs that are filtered by a variety of synaptic types with very different time constants. We study the response properties of a leaky integrate-and-fire (LIF) model neuron in the presence of both fast AMPA and slow NMDA filters and find an analytical formula valid when the membrane time constant τm of the neuron is short. When the NMDA/AMPA abundances are similar to those found in cerebral cortex and deep cerebellar nuclei, the neuron mainly responds to particular large fluctuations in its inputs. These results suggest that NMDA receptors play a crucial role in shaping the response of central neurons.