  NMDA receptors (NMDA-R) typically contribute to excitatory synaptic
transmission in the central nervous system. While calcium influx through NMDA-R
plays a critical role in synaptic plasticity, experimental evidence indicates
that NMDAR-mediated calcium influx also modifies neuronal excitability through
the activation of calcium-activated potassium channels. This mechanism has not
yet been studied theoretically. Our theoretical model provides a simple
description of neuronal electrical activity that takes into account the tonic
activity of extrasynaptic NMDA receptors and a cytosolic calcium compartment.
We show that calcium influx mediated by the tonic activity of NMDA-R can be
coupled directly to the activation of calcium-activated potassium channels,
resulting in an overall inhibitory effect on neuronal excitability.
Furthermore, the presence of tonic NMDA-R activity promotes bistability in
electrical activity by dramatically increasing the stimulus interval where both
a stable steady state and repetitive firing can coexist. These results could
provide an intrinsic mechanism for the constitution of memory traces in
neuronal circuits. They also shed light on the way by which $\beta$-amyloids
can alter neuronal activity when interfering with NMDA-R in Alzheimer's disease
and cerebral ischemia.
