title: Distributed relaxation processes in sensory adaptation.
abstract: 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 s(k)) 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.
mesh_terms: D000200:Action Potentials; D000222:Adaptation, Physiological; D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D003386:Brachyura; D002628:Chemoreceptor Cells / Q000502:physiology; D003058:Cockroaches; D004175:Diptera; D004553:Electric Conductivity; D004558:Electric Stimulation; D007313:Insecta; D008433:Mathematics; D008465:Mechanoreceptors / Q000502:physiology; D008954:Models, Biological; D010775:Photic Stimulation; D010786:Photoreceptor Cells / Q000502:physiology; D011984:Sensory Receptor Cells / Q000502:physiology*