From response to stimulus: adaptive sampling in sensory physiology

Jan Benda, Tim Gollisch, Christian K. Machens & Andreas V. M. Herz

Current Opinion in Neurobiology 17(4): 430-436 (2007)



Sensory systems extract behaviorally relevant information from a continuous stream of complex high-dimensional input signals. Understanding the detailed dynamics and precise neural code, even of a single neuron, is therefore a non-trivial task. Automated closed-loop approaches that integrate data analysis in the experimental design ease the investigation of sensory systems in three directions: First, adaptive sampling speeds up the data acquisition and thus increases the yield of an experiment. Second, model-driven stimulus exploration improves the quality of experimental data needed to discriminate between alternative hypotheses. Third, information-theoretic data analyses open up novel ways to search for those stimuli that are most efficient in driving a given neuron in terms of its firing rate or coding quality. Examples from different sensory systems show that, in all three directions, substantial progress can be achieved once rapid online data analysis, adaptive sampling, and computational modeling are tightly integrated into experiments.


Optimal search for a neuron's receptive field

receptive field
Adaptive estimation of receptive fields, as demonstrated by a numerical simulation study. (a) The top row shows how the structure of a receptive field builds up gradually when a standard neurophysiological approach is used. Here, white-noise stimuli are presented and the receptive field is estimated as the spike-triggered average. The bottom row shows results from an adaptive sampling technique in which each new stimulus is selected such that it maximizes the information gained about the receptive field. (b) The true receptive field. (c) The uncertainty of the estimates, quantified by the entropy of the parameter distribution, drops far more rapidly for the adaptive sampling technique than for white-noise sampling (data provided by courtesy of J. Lewi). From Benda et al. 2007, as modified from Lewi J, Butera R, Paninski L: Real-time adaptive information-theoretic optimization of neurophysiology experiments. In Adv Neural Inf Process Syst, Volume 19. Edited by Scholkopf B, Platt J, Hoffman T. Cambridge, MA: MIT Press; 2007:857-864.

Search for stimuli that drive a neuron in an "optimal" way (firing rate, coding quality, mutual information)

optimal stimulus
Iterative search for optimal stimulus ensembles (OSEs). (a) In this analysis of an auditory receptor neuron, stimuli are sets of ten 80 ms-long snippets of white-noise amplitude modulations of a sine-wave carrier. Sample mean and standard deviation (colored dots in top-left panel) are drawn from a two-dimensional Gaussian distribution whose standard deviation is represented by the black ellipse. The stimuli are played repeatedly (top-right panel), resulting in spike-train responses that vary slightly from trial to trial (bottom-right panel). On the basis of the responses from several trials, the contribution of each stimulus to the mutual information is estimated; this contribution is depicted by the size of the colored dots representing the individual snippets (bottom-left panel). The contributions are taken as weight factors to update the parameters of the Gaussian distribution that is thus shifted toward the more important stimuli (new black ellipse). The updated stimulus ensemble is then used to draw new, additional test stimuli. (b) For a longer sample run with multiple iterations, intermediate estimates of the OSE (grey) rapidly converge to the final OSE (black). As shown by the iso-firing-rate lines, the OSE is centered at the steepest part of the tuning curve and triggers responses that cover almost the full range of firing rates. As desired, the OSE is thus indeed located in the most informative region in stimulus space. (c) Accordingly, the information rate initially grows rather fast with each iteration until it saturates after about 20 iterations. From Benda et al. 2007, as modified from Machens et al. 2005.

Find set's of stimulus parameter that result in the same response (iso-response method)

Discrimination of alternative response relations using the Iso-Response Method. (a and b) A hypothetical two-dimensional stimulus space is spanned by the variables s1 and s2. The drawn surfaces represent the response r(s1,s2) for two different models, which take the linear (a) and quadratic sum (b) as the argument of a sigmoid non-linearity. Although the two input-output scenarios are fundamentally different, both produce exactly the same one-dimensional response functions r(s1) and r(s2), respectively, as seen by the black areas at the sides of the surface blocks. Furthermore, any measurement along a radial direction, as is common in physiological experiments, will produce similar sigmoid response curves in both cases, as seen by the thick black lines running along the surfaces. The iso-response manifolds r=const (here: one-dimensional curves) below the surface plots, however, give a clear signature of the different underlying processes. (c) Iso-firing-rate curves for an auditory neuron stimulated by superpositions of two pure tones. The measured pairs of amplitudes s1 and s2 corresponding to a firing rate r of 150 Hz are shown together with the iso-firing-rate curves for the two scenarios which now correspond to sound-amplitude integration (a) and sound-energy integration (b), respectively. The straight line for the amplitude hypothesis deviates systematically from the data, whereas the ellipse obtained from the energy hypothesis provides an excellent fit. The different scales on the axes reflect the strong frequency dependence of the neuron's sound sensitivity. (d) As expected from the sound-energy model, iso-response lines for different output firing rates are scaled ellipses. From Benda et al. 2007, as modified from Gollisch et al. 2002.

Last modified: Fri Nov 28 13:48:40 CET 2008