A simple biophysically plausible model for long time constants in single neurons

Recent work in computational neuroscience and cognitive psychology suggests that a set of cells that decay exponentially could be used to support memory for the time at which events took place. Analytically and through simulations on a biophysical model of an individual neuron, we demonstrate that exponentially decaying firing with a range of time constants up to minutes could be implemented using a simple combination of well-known neural mechanisms. In particular, we consider firing supported by calcium-controlled cation current. When the amount of calcium leaving the cell during an interspike interval is larger than the calcium influx during a spike, the overall decay in calcium concentration can be exponential, resulting in exponential decay of the firing rate. The time constant of the decay can be several orders of magnitude larger than the time constant of calcium clearance, and it could be controlled externally via a variety of biologically plausible ways. The ability to flexibly and rapidly control time constants could enable working memory of temporal history to be generalized to other variables in computing spatial and ordinal representations.