Computing linear approximations to nonlinear neuronal responses

Melinda E Koelling¹ and Duane Q Nykamp²

¹Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA

²School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

author email corresponding author email

from Seventeenth Annual Computational Neuroscience Meeting: CNS*2008
Portland, OR, USA. 19–24 July 2008

BMC Neuroscience 2008, 9(Suppl 1):P118doi:10.1186/1471-2202-9-S1-P118


Published:	11 July 2008

First paragraph (this article has no abstract)

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.