Single Neuron with Recurrent Excitation: Effect of the Transmission Delay

Recurrent excitatory circuits and the positive feedback they imply are assigned important roles in a variety of tasks in living organisms. Such networks obviously do not exhibit saturated behaviour in the sense of extremely fast rates and/or insensitivity to input variations, as artificial systems with positive feedback generally do. It is therefore important to identify how neural saturation is avoided. A single neuron that excites itself directly provides the simplest anatomical circuitry where this problem can be studied. Such a system was simulated experimentally by Diez-Martínez and Segundo using the pacemaker neuron in the crayfish stretch receptor organ. They showed that the feedback transmission time, called "delay", was strongly influential, and small changes led to markedly different outcomes. As the delay was increased the discharge patterns went from pacemaker spike trains to multiplets separated by silent intervals to still longer bursts and longer silent intervals. We hypothesized that neuronal sensitivity decreased along the rapid successive firings (adaptation) and prevented saturation and therefore played an important role in the observed behaviour. This hypothesis was tested using models of increasing complexity. The simplest model was an integrate and fire neuron without adaptation to repeated stimuli, in this case the dynamics were qualitatively different from the experimental data. The other models exhibited adaptation to repeated stimuli. Two were relatively simple: an integrate and fire and a leaky integrator. The last model was more complex, it included membrane conductances. Neither of these models exhibited saturation when recurrent excitation was introduced. Their dynamics were in fact similar to those in the crayfish preparation, both exhibiting pacemaker firing for short delays, and multiplets or burst for intermediate delays. Simulations were therefore compatible with the hypothesis that neuronal adaptation is important in preventing saturation. Copyright 1996 Elsevier Science Ltd