Chaos in Coupled Nerve Cells

Abstract

A model for the impulse transmission between nerve cells is presented. The model is compared with experiments on nerve cell bodies of the large land snail Helix pomatia. Synaptic input is simulated by equal-sized square current pulses applied at a constant rate. The output pattern consists of a mixture of spikes and dropouts, where the response fraction depends on stimulus strength and frequency in a non-trivial manner. In the periodic model, the output locks to the input at simple ratios (1:1, 2:1, 3:2, etc.) resulting in the fractal relation called the “Devil’s staircase” between response fraction and stimulation strength or rate. In the chaotic model the near-threshold behavior of the nerve cell is included, resulting in a breakdown of the staircase into a mixture of regions with regular behavior and regions with chaotic behavior. In the chaotic regions, the mean output frequency differs from the mean frequency of nearby regions. The behavior of this model is close to the behavior of the nerve cell. Coupling is mimicked by applying the output from one cell to another cell with the same model parameters. Even in very simple systems, the resulting output depends not only on the strength of the coupling, but also on the precise timing of the incoming impulses. The signal processing of a nerve cell is therefore not just a function of the mean firing frequency. It is a result of subtly timed mixtures of regular and chaotic firing patterns.