Generalisation of neuronal excitability allows for the identification of an excitability change parameter that links to an experimentally measurable value

@article{Broek2020GeneralisationON,
  title={Generalisation of neuronal excitability allows for the identification of an excitability change parameter that links to an experimentally measurable value},
  author={Jantine A.C. Broek and Guillaume Drion},
  journal={arXiv: Neurons and Cognition},
  year={2020}
}
Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect information processing, such as thresholding and gain scaling. These properties can be mathematically studied using generalised phenomenological models, such as the Fitzhugh-Nagumo model and the mirrored FHN. The FHN model shows that each excitability type… 

References

SHOWING 1-10 OF 45 REFERENCES

A Novel Phase Portrait for Neuronal Excitability

The revisited model considerably enlarges the modeling power of the original one and captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model.

Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection

This work discusses the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrates the approach using single‐cell and mean‐field network models, and illustrates the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent.

A Balance Equation Determines a Switch in Neuronal Excitability

Analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.

An Organizing Center in a Planar Model of Neuronal Excitability

The excitability properties of a generalized FitzHugh--Nagumo model are studied, and two novel types of neuronal excitability are described and distinctly associated to the presence of cooperative variables.

Dynamic Input Conductances Shape Neuronal Spiking1,2

The relevance of the proposed approach for modulation, compensation, and robustness studies in a published neuron model based on data of the stomatogastric ganglion of the crab Cancer borealis is illustrated.

Mathematical models of threshold phenomena in the nerve membrane

The types of mathematical model which have been used to represent all-or-none behavior in the nerve membrane may be classified as follows: (1) thediscontinuous threshold phenomenon, in which

Type I Membranes, Phase Resetting Curves, and Synchrony

It is shown in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation and the differences between synapses that act rapidly and those that act slowly are shown.

Ion channel degeneracy enables robust and tunable neuronal firing rates

By applying recently developed analysis techniques to a number of biophysical neuron models, it is shown how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels.

Robust Modulation of Integrate-and-Fire Models

The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling, making it a good candidate for affordable computational studies of neuromodulation in large networks.

Adaptive exponential integrate-and-fire model as an effective description of neuronal activity.

The authors' simple model predicts correctly the timing of 96% of the spikes of the detailed model in response to injection of noisy synaptic conductances and has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.