Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models

TL;DR

This paper investigates the mechanisms behind Type III neuronal responses to transient inputs in hybrid nonlinear neuron models, revealing new insights into their computational properties and response behaviors.

Contribution

It provides a geometric and analytical framework for understanding Type III responses, including post-inhibitory facilitation and slope detection, in hybrid neuron models.

Findings

Identifies conditions for post-inhibitory facilitation in hybrid models.

Provides a geometric characterization of PIF phenomena.

Analyzes slope detection analytically for tent inputs.

Abstract

Experimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons, less is known about the dynamic mechanisms shaping their responses to transient inputs, although these bear significant physiological relevance. Here, we study responses to transient inputs in a widely used class of neuron models (nonlinear adaptive hybrid models) well-known to reproduce a number of biologically realistic behaviors. We focus on responses to transient inputs that have been previously associated with Type III neurons, arguably the least studied category in Hodgkin's classification, which are those neurons that never exhibit continuous firing in response to sustained excitatory currents. The two phenomena that we study are post-inhibitory facilitation, in which an otherwise subthreshold excitatory input can induce a spike if it is applied with proper timing after an inhibitory pulse, and slope detection, in which a neuron spikes to a transient input only when the input's rate of change is in a specific, bounded range. We analyze the origin of these phenomena in nonlinear hybrid models and provide a geometric characterization of dynamical structures associated with PIF in the system and an analytical study of slope detection for tent inputs. While the necessary and sufficient conditions for these behaviors are easily satisfied in neurons with Type III excitability, our proofs are quite general and valid for neurons that do not exhibit Type III excitability as well. This study therefore provides a framework for the mathematical analysis of these responses to transient inputs associated with Type III neurons in other systems and for advancing our understanding of these systems' computational properties.