Nonlinear systems analysis of computer models of repetitive firing

The inhibitory influences of recurrent inhibition and afterhyperpolarization are studied theoretically insofar as they affect the density of the interspike interval and the frequency transfer characteristic. The methods employed involve exact results for excitation with decay and constant threshold, computer simulations for decaying thresholds representing afterhyperpolarization, and the diffusion approximation for excitation with inhibition and a constant threshold. Afterhyperpolarization tends to preserve the linearity of the frequency transfer characteristic and the lognormality of the interspike time. Recurrent inhibition which grows linearly with frequency of excitation can lead to frequency limiting. Some forms of nonlinear recurrent inhibition may lead to a filter type effect whereby the neuron responds significantly only over certain ranges of input intensity. A simple network model is analysed which exhibits recurrent inhibitory frequency growing linearly with frequency of excitation. An estimate of 10 to 50 is made for the number of Renshaw cells which connect with a spinal motoneuron. The frequency limiting of motoneurons is discussed and the stabilizing influence attributed to Renshaw cells is questioned. It is postulated that Renshaw recurrent inhibition is of functional significance at low levels of excitatory drive to motoneurons and that its effect is diminished by reciprocal inhibition at high excitatory input frequencies.