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Science 18 January 1974:
Vol. 183. no. 4121, pp. 161 - 172
DOI: 10.1126/science.183.4121.161
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Articles

Distributed Relaxation Processes in Sensory Adaptation

Spatial nonuniformity in receptors can explain both the curious dynamics and logarithmic statics of adaptation

John Thorson 1 and Marguerite Biederman-Thorson 1

1 Max-Planck-Institut für Verhaltensphysiologie, 8131 Seewiesen, Germany

Dynamic description of most receptors, even in their near-linear ranges, has not led to understanding of the underlying physical events—in many instances because their curious transfer functions are not found in the usual repertoire of integral-order control-system analysis. We have described some methods, borrowed from other fields, which allow one to map any linear frequency response onto a putative weighting over an ensemble of simpler relaxation processes. One can then ask whether the resultant weighting of such processes suggests a corresponding plausible distribution of values for an appropriate physical variable within the sensory transducer.

To illustrate this approach, we have chosen the fractional-order low-frequency response of Limulus lateral-eye photoreceptors. We show first that the current "adapting-bump" hypothesis for the generator potential can be formulated in terms of local first-order relaxation processes in which local light flux, the cross section of rhodopsin for photon capture, and restoration rate of local conductance-changing capability play specific roles. A representative spatial distribution for one of these parameters, which just accounts for the low-frequency response of the receptor, is then derived and its relation to cellular properties and recent experiments is examined.

Finally, we show that for such a system, nonintegral-order dynamics are equivalent to nonhyperbolic statics, and that the efficacy distribution derived to account for the small-signal dynamics in fact predicts several decades of near-logarithmic response in the steady state.

Encouraged by the result that one plausible proposal can account approximately for both the low-frequency dynamics (the transfer function sk) and the range-compressing statics (the Weber-Fechner relationship) measured in this photoreceptor, we have described some formally similar applications of these distributed effects to the vertebrate retina and to analogous properties of mechanoreceptors and chemoreceptors.


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