Higher-Order Spike Triggered Analysis of Neural Oscillators

Keisuke Ota,Toshiaki Omori,Toru Aonishi,Masato Okada,Hiroyoshi Miyakawa,Gennady Cymbalyuk

doi:10.1371/journal.pone.0050232

Abstract

For the purpose of elucidating the neural coding process based on the neural excitability mechanism, researchers have recently investigated the relationship between neural dynamics and the spike triggered stimulus ensemble (STE). Ermentrout et al. analytically derived the relational equation between the phase response curve (PRC) and the spike triggered average (STA). The STA is the first cumulant of the STE. However, in order to understand the neural function as the encoder more explicitly, it is necessary to elucidate the relationship between the PRC and higher-order cumulants of the STE. In this paper, we give a general formulation to relate the PRC and the nth moment of the STE. By using this formulation, we derive a relational equation between the PRC and the spike triggered covariance (STC), which is the covariance of the STE. We show the effectiveness of the relational equation through numerical simulations and use the equation to identify the feature space of the rat hippocampal CA1 pyramidal neurons from their PRCs. Our result suggests that the hippocampal CA1 pyramidal neurons oscillating in the theta frequency range are commonly sensitive to inputs composed of theta and gamma frequency components.

Highlights

A neural system can be considered to be an encoder which transforms specific external stimuli into neural spikes
The linear receptive field components in V1 simple cells can be discerned from the spike triggered average (STA), which is the average of stimulus ensemble (STE) [5,6]
We used the maximum a posteriori (MAP) estimation algorithm that we proposed in our previous papers to estimate the phase response curve (PRC) from the artificial data

Summary

Introduction

A neural system can be considered to be an encoder which transforms specific external stimuli into neural spikes. Spike triggered analysis is a powerful way to achieve this goal. In this analysis, we give stochastic stimuli to a neural system and identify the set of stimuli that induce the neurons to spike [1]. We give stochastic stimuli to a neural system and identify the set of stimuli that induce the neurons to spike [1] This set is called the spike triggered stimulus ensemble (STE) [2,3,4]. The linear receptive field components in V1 simple cells can be discerned from the spike triggered average (STA), which is the average of STE [5,6]. The spike triggered covariance (STC) which is the covariance of the STE helps to clarify the receptive field structure of complex cells representing the nonlinear response [7,8]

Methods

Results

Conclusion