Elemental Spiking Neuron Model for Reproducing Diverse Firing Patterns and Predicting Precise Firing Times

Abstract

In simulating realistic neuronal circuitry composed of diverse types of neurons, we need an elemental spiking neuron model that is capable of not only quantitatively reproducing spike times of biological neurons given in vivo-like fluctuating inputs, but also qualitatively representing a variety of firing responses to transient current inputs. Simplistic models based on leaky integrate-and-fire mechanisms have demonstrated the ability to adapt to biological neurons. In particular, the multi-timescale adaptive threshold (MAT) model reproduces and predicts precise spike times of regular-spiking, intrinsic-bursting, and fast-spiking neurons, under any fluctuating current; however, this model is incapable of reproducing such specific firing responses as inhibitory rebound spiking and resonate spiking. In this paper, we augment the MAT model by adding a voltage dependency term to the adaptive threshold so that the model can exhibit the full variety of firing responses to various transient current pulses while maintaining the high adaptability inherent in the original MAT model. Furthermore, with this addition, our model is actually able to better predict spike times. Despite the augmentation, the model has only four free parameters and is implementable in an efficient algorithm for large-scale simulation due to its linearity, serving as an element neuron model in the simulation of realistic neuronal circuitry.

Impact of Neuronal Properties on Network Coding: Roles of Spike Initiation Dynamics and Robust Synchrony Transfer

“…This is similarly true for more sophisticated integrate-and-fire (IF) models such as the adaptive exponential IF model (Brette and Gerstner, 2005; for review, see Brunel, 2010). In principle, stimulus-dependent variations in the voltage trajectory toward threshold can be replaced with stimulus-dependent variations in threshold (Yamauchi et al, 2011). What is important is that the model includes different time-scales so that intrinsic processes can interact with timescales present in the input, thus enabling inputs with power at lower or higher frequencies to preferentially elicit spikes.…”

Estimating nonstationary input signals from a single neuronal spike train

“…Nevertheless, the OUP should be replaced by a more realistic model [52][53][54][55] to improve the estimation. One advantage of the transforming method is that any spiking neuron model can replace the LIF model.…”

Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

“…The Izhikevich model constitutes a simplified version of the Hodgkin-Huxley model. Other appropriate models would be ones whose subthreshold dynamics can be integrated exactly (Rotter and Diesmann 1999), which can be simulated with similar computationally efficient strategies (Yamauchi et al 2011). For Izhikevich-type neurons, membrane variables v and u are given as: With the following after-spike reset conditions: where the dimensionless variable v represents the membrane potential in mV and the dimensionless variable u represents the membrane recovery variable, which accounts for the activation of the K + currents and inactivation of Na + currents (Izhikevich 2003).…”