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Computing linear approximations to nonlinear neuronal responses

Many methods used to analyze neuronal response assume that neuronal activity has a fundamentally linear relationship to the stimulus. For example, analyses based on spike-triggered average or generalized linear models (GLMs) assume that the only nonlinearity is the spiking nonlinearity, e.g. a threshold. However, many neurons have a response pattern that exhibits a more fundamental nonlinearity. For example, the nonlinearity of a neuron which is highly selective to a small class of images or songs may not be captured by a GLM because such selectivity implies strong sensitivity to multiple directions in stimulus space. Nonetheless, the response of such a neuron can be captured by a linear model if the stimulus is constrained to be close to some stimulus of interest, and the local linear approximation gives insight into neuronal behavior near that stimulus. We derive a modification of the spike-triggered average to compute such local linear approximations and demonstrate via simulation how they can reveal hidden features of the neuron's response.

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Correspondence to Duane Q Nykamp.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Koelling, M.E., Nykamp, D.Q. Computing linear approximations to nonlinear neuronal responses. BMC Neurosci 9 (Suppl 1), P118 (2008).

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