Elsevier

Neurocomputing

Volumes 52–54, June 2003, Pages 525-530
Neurocomputing

Analyzing mechanosensory transduction by identifying invariant directions in stimulus space

https://doi.org/10.1016/S0925-2312(02)00771-3Get rights and content

Abstract

Extended receptive fields are characteristic for the integrative properties of sensory neurons. How this integration is performed is an important aspect in understanding neural coding and can give insight into the computations and the biophysics involved. We present a method of systematically investigating the nature of spectral integration in auditory receptor neurons by analyzing how these neurons combine intensities contained in different parts of the stimulus spectrum. The method consists of identifying regions in parameter space that lead to the same neural response, and it is also applicable to other stimulus domains.

Introduction

Auditory receptor neurons, such as hair cells and chordotonal sensilla, transduce vibrations of the basilar or tympanal membrane into deflections of the cell-membrane potential and, possibly, spikes. In doing so, the neuron performs an integration in the frequency domain as well as over a certain temporal window. Together, these two domains can be viewed as the spectro-temporal receptive field of the neuron. Auditory receptor neurons thus share with most sensory neurons that they respond to a multi-dimensional stimulus space.

There have been a number of approaches to describe and characterize the input–output relations of sensory neurons in order to understand the underlying coding strategies [2], [6]. The simplest phenomenological models describe both the input and output by single scalars, the amplitude A of a one-dimensional stimulus and the firing rate R, respectively: R=g(A), where g(x) denotes some, generally nonlinear function.

The simplest extension of those models is to include a multi-dimensional input space with stimulus components given by A1,A2,…,AN. The response R is now given by a (nonlinear) function of all stimulus components. This is often simplified by taking the effect of the receptive field explicitly into account and using a weighted sum of all stimulus components (cf. [1]):R=gn=1NFn·An.The model parameters F1,F2,…,FN define the structure of the receptive field. This “ad hoc” integration over the receptive field is not the only way, of course, to combine the stimulus components. A better description may be found if one regards an appropriate nonlinear transformation h(An) of the components:R=gn=1NFn·h(An).Finding the right transformation h(An) or some other description of how the stimulus components are combined may help to interpret the stimulus encoding in a mechanistic fashion. If, e.g., A denotes the amplitude of an acoustic stimulus and h(A)=A2, the neuron can be interpreted as an energy detector.

In this work, we present an experimental approach to systematically discriminate different models of stimulus integration over the receptive field. This is applied to spectral integration in auditory receptors of locusts, i.e., the combining of intensities contained in different parts of the stimulus spectrum.

Section snippets

Stimulus-response curves and iso-activity regions

Sensory neurons are often characterized by stimulus-response curves where the response, such as the firing rate, is measured at different stimulus intensities. Fig. 1 shows the firing rate of a locust auditory receptor in response to pure-tone stimulation of f1=4kHz and f2=9.55kHz. For a generic model R=g(∑Fn·h(An)), where the An denote the amplitudes of the tones of frequency fn, the shape of the response curves is determined by the combination of the functions g and h, while the parameters Fn

Experiments

We performed intracellular recordings from the axons of receptor cells in the auditory nerve of Locusta migratoria. Stimuli were combinations of pure tones played over loudspeakers, S(t)=A1sin(2πf1t)+A2sin(2πf2t), with sound frequencies f1=4kHz and f2=9.55kHz. Stimulus generation and spike detection were controlled by the custom-made Online Electrophysiology Laboratory (OEL) software. Stimulus length was 100ms, during which the receptor cells fire tonically with a small phasic part due to

Results

Examples of measured iso-activity regions in a two-dimensional stimulus space for locust auditory receptors can be seen in Fig. 4. Several amplitude combinations (A1,A2) were measured that all led to the same firing rate, and the data points are well fitted by ellipses. This corresponds to case (b) in Fig. 2, Fig. 3.

The findings can be summarized in a phenomenological input–output relation for sound-intensity coding in the locust ear. In the generalized form, the firing-rate response R to a

Conclusion

Many sensory neurons integrate inputs over a large receptive field in producing their responses. Analyzing the nature of this integration can lead to valuable insights into the coding properties or the mechanisms of stimulus transduction. Determining iso-activity regions in stimulus space, i.e., regions that leave the response invariant, can be used for an analysis that is independent of static nonlinearities as typically occur when a stimulus is encoded into a firing rate. A systematic

Acknowledgements

We thank J. Benda and C. Machens for making the framework of the OEL software available to us and for their assistance in maintenance and in the development of the algorithms used in this work, and H. Schütze for his support during the experiments.

References (6)

  • O. Estévez et al.

    The ‘silent substition’ method in visual research

    Vis. Res.

    (1982)
  • E.J. Chichilnisky

    A simple white noise analysis of neuronal light responses

    Network

    (2001)
  • P. Dayan et al.

    Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems

    (2001)
There are more references available in the full text version of this article.

Cited by (0)

1

Supported by Boehringer Ingelheim Fonds.

2

Supported by the Deutsche Forschungsgemeinschaft.

View full text