A Simple Model of Nonspiking Neurons

Due to the ubiquity of spiking neurons in neuronal processes, various simple spiking neuron models have been proposed as an alternative to conductance-based models (a.k.a. Hodgkin-Huxley-type models), known to be computationally expensive and difficult to treat mathematically. However, to the best of our knowledge, there is no equivalent in the literature of a simple and lightweight model for describing the voltage behavior of nonspiking neurons, which also are ubiquitous in a large variety of nervous tissues in both vertebrate and invertebrate species and play a central role in information processing. This letter proposes a simple model that reproduces the experimental qualitative behavior of known types of nonspiking neurons. The proposed model, which differs fundamentally from classic simple spiking models unable to characterize nonspiking dynamics due to their intrinsic structure, is derived from the bifurcation study of conductance-based models of nonspiking neurons. Since such neurons display a high sensitivity to noise, the model aims at capturing the experimental distribution of single-neuron responses rather than perfectly replicating a single given experimental voltage trace. We show that such a model can be used as a building block for realistic simulations of large nonspiking neuronal networks and is endowed with generalization capabilities, granted by design.