LOGARITHMIC TIME-COURSE OF SENSORY ADAPTATION IN ELECTROSENSORY AFFERENT NERVE-FIBERS IN A WEAKLY ELECTRIC FISH

1. We recorded single unit activity from individual primary electrosen sory afferent axons in the posterior branch of the anterior lateral li ne nerve of gametoid weakly electric fish, Apteronotus leptorhynchus. We analyzed the responses of P-type (probability-coding afferent fiber s to externally applied amplitude step changes in the quasi-sinusoidal transdermal potential established by the fish's own electric organ di scharge (EOD). 2. In response to AM step increases in transdermal pote ntial, the firing rate of P-type afferents exhibited an abrupt increas e followed by an initially rapid and subsequently more gradual decay b ack toward the baseline level. Afferent responses continued to adapt s lowly throughout the duration of prolonged step stimuli lasting > 100 s. The time course of sensory adaptation was similar for all units tes ted. 3. We introduce a new functional form for describing the time cou rse of sensory adaptation in which the change in firing rate Delta r d ecays logarithmically with time: Delta r(t) = A/[B In (t) + I]. This l ogarithmic form accurately describes the adaptation time course of P-t ype afferents over five decades in time, from milliseconds to hundreds of seconds, with only two free parameters. Using a nonlinear least-sq uares fitting technique, we obtained a mean value of the parameter B, which characterizes the adaptation time course, of 0.149 +/- 0.028 (me an +/- SD, n = 49). 4. We compare logarithmic fits with traditional mu ltiexponential and power law forms and demonstrate that the logarithmi c form yields a better characterization of P-type afferent responses. This analysis helps explain the variability in previously reported ada ptation time constants, which have ranged from 0.2 to 3.4 s, in gymnot id P-type afferents. 5. We tested the linearity of P-type afferent res ponses using positive and negative AM steps of varying amplitudes. Asi de from nonlinearities associated with rectification (firing rates can not be negative) and saturation (firing rates cannot exceed the EOD fr equency), we found that P-type afferent responses scaled linearly with stimulus amplitude. 6. Based on the observed linearity, we predict th e frequency domain response characteristics of P-type afferents and fi nd that the predicted gain and phase are in good agreement with experi mental measurements using sinusoidal AM stimuli over a range of AM fre quencies from 1 to 100 Hz. Thus the logarithmic parameterization of th e step response appears to accurately capture the response dynamics of P-type afferents over a wide range of behaviorally relevant AM freque ncies. 7. We conclude that the temporal filtering properties of pyrami dal cells in the medullary electrosensory nucleus, the electrosensory lateral line lobe (ELL), need to be reevaluated in light of the logari thmic adaptation time course in the periphery, and we discuss implicat ions for the role of P-type afferents in driving a feedback gain contr ol mechanism that regulates ELL pyramidal cell responsiveness.