Capturing adaptation properties of retinal ganglion cell responses with a generalized linear model

C Ekanadham, J Shlens, L Jepson, A M Litke, D Tranchina, L Paninski, EJ Chichilnisky and E P Simoncelli

Published in Proc. AREADNE: Research in Encoding And Decoding of Neural Ensembles, Jun 2010.

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    • Neurons throughout the visual system adapt to the statistics of visual inputs. In particular, the spike rates of retinal ganglion cells (RGCs), the output neurons of the retina, adapt to changes in luminance and contrast over time scales of several seconds (Chander & Chichilnisky 2001). This observation is often not accounted for in spiking models of RGC light response whose parameters can be fit directly from data. For example, generalized linear models (GLMs) provide a tractable framework in which a neuron's instantaneous firing rate is modeled as the exponentiated linear combination of time-dependent explanatory variables, such as stimulus history and the recent history of its own spiking and any afferents (Truccolo et al. 2005, Pillow et al. 2008). These models can effectively capture RGC spiking responses to white noise in the primate retina (Pillow et al., 2008). However, it is unclear to what extent they can characterize responses to correlated stimuli, and in particular whether they can account for adaptive responses to stimuli whose statistics are varying on timescales longer than a few hundred milliseconds.

    To address this question, we recorded the activity of parasol cells in the primate retina in response to binary white noise and a structured stimulus constructed from a Gaussian band signal and a log-normal contrast envelope with spatiotemporal correlations matched to that of natural scenes (Frazor & Geisler, 2006).. We parametrized the GLM to allow for long time scale effects of spiking history (up to six sec), and fit the model to RGC responses using maximum likelihood techniques. For each stimulus condition, the fitted model was cross-validated on responses to novel stimuli with the same statistics. The model provided an accurate characterization of the steady-state responses under both stimulus conditions. We also examined the adaptive behaviors of both fitted models by simulating responses to contrast-switching stimuli (Smirnakis et al. 1997; Fairhall et al. 2001; Chander et al. 2001). The model fitted under the correlated stimulus condition exhibited spike rate adaptation on the timescale of several seconds in most cells. In particular, the model exhibits a transient overshoot (undershoot) in mean spike rate after a step increase (decrease) in contrast. This behavior is due to the inhibitory effect of previous spikes, arising from a slowly decaying negative tail in the fitted spike history filter, and can be further analyzed using a mean-field approximation of the model. On the other hand, the spike history filter fitted under the white noise condition did not have this negative tail, and thus did not exhibit spike rate adaptation in the contrast-switching simulations.

    Finally, we compared the response of the model fitted to correlated stimulus to that of real cells for the contrast-switching paradigm. We selected eight cells which exhibited strong spike rate adaptation to both an increase and decrease in contrast. We found that the model captured both the magnitude and timescale of spike rate adaptation in these cells. We conclude that GLMs can provide a flexible framework for capturing long time-scale behaviors such as spike rate adaptation in RGCs. We are currently working to quantify the capacity of the model to explain neural responses to both traditional stimuli known to induce spike rate adaptation, as well as richer stimulus ensembles with statistics closely matched to the properties of natural scenes.

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