Adaptation in simple neurons: dependence of feature selectivity on stimulus statistics
The relationship between a neuron’s complex inputs and its spiking output defines the neuron’s coding strategy. A linear/nonlinear cascade model - a linear filter or set of filters that extracts the features of the stimulus that are relevant for triggering spikes and a nonlinear function that relates stimulus to firing probability- captures much of the computation of single neurons. In many sensory systems, these two components of the coding strategy adapt to changes in the statistics of the inputs, in such a way as to improve information transmission. Here we explore analytically the contributions to adaptation to stimulus statistics that are due to neuronal dynamics, without change in the underlying neuronal parameters.
Following the pioneering work of Hodgkin and Huxley, it is known that the space-clamped behavior of a neuron can be accurately modeled by a nonlinear dynamical system. Thus, to understand adaptation in the phenomenological LN model, we want to understand how an LN model arises from the underlying dynamical system. Here, we consider the simplest intrinsically-spiking model neuron: the Quadratic Integrate-and-Fire model, or QIF.
First, we use reverse correlation methods to find the elements of the LN model corresponding to the QIF. The simplest correlation measure is the Spike-triggered Average stimulus, or STA, which is the mean stimulus preceding a spike; the STA is the optimal linear filter for firing rate estimation and is a good choice for the filter in an LN model. For the QIF, for Gaussian white noise stimuli with constant mean, the STA is found empirically to be a function of the variance the LN model of the QIF adapts to stimulus statistics.
To gain an understanding of how the STA adapts, we present methods to analytically derive the outcome of the reverse correlation analysis. As the low variance limit has been explored previously by others, we focus here on applying a technique known as Stochastic Linearization to calculate the STA in the high variance limit. This technique captures the affects on the sampled features due to how driving the neuron with different stimulus statistics changes the exploration of the subthreshold regime in the approach to a spike. This method provides us with explicit expressions for how the STA depends on the spike-generating mechanism, the spike history, and the variance of the stimulus.
While we focus here on a very simple model, the techniques and the conceptual picture they embody generalize to more complex models. Further, our results underscore the difficulty of inferring underlying biophysical parameters from the output of reverse correlation, independent of a consideration of the stimulus properties.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). Adaptation in simple neurons: dependence of feature selectivity on stimulus statistics.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.015
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Received:
29 Jan 2009;
Published Online:
29 Jan 2009.