Stochastic Properties of Coincidence-Detector Neural Cells

Abstract

Neural information is characterized by sets of spiking events that travel within the brain through neuron junctions that receive, transmit, and process streams of spikes. Coincidence detection is one of the ways to describe the functionality of a single neural cell. This letter presents an analytical derivation of the output stochastic behavior of a coincidence detector (CD) cell whose stochastic inputs behave as a nonhomogeneous Poisson process (NHPP) with both excitatory and inhibitory inputs. The derivation, which is based on an efficient breakdown of the cell into basic functional elements, results in an output process whose behavior can be approximated as an NHPP as long as the coincidence interval is much smaller than the refractory period of the cell's inputs. Intuitively, the approximation is valid as long as the processing rate is much faster than the incoming information rate. This type of modeling is a simplified but very useful description of neurons since it enables analytical derivations. The statistical properties of single CD cell's output make it possible to integrate and analyze complex neural cells in a feedforward network using the methodology presented here. Accordingly, basic biological characteristics of neural activity are demonstrated, such as a decrease in the spontaneous rate at higher brain levels and improved signal-to-noise ratio for harmonic input signals.