Limits of linear rate coding of dynamic stimuli by electroreceptor afferents

We estimated the frequency-intensity (f-I) curves of P-unit electroreceptors using 4-Hz random amplitude modulations (RAMs) and using the covariance method (50-Hz RAMs). Both methods showed that P units are linear encoders of stimulus amplitude with additive noise; the gain of the f-I curve was, on average, 0.32 and 2.38 spikesxs(-1)xmicroV(-1) for the low- and high-frequency cutoffs, respectively. There were two sources of apparent noise in the encoding process: the first was the variability of baseline P-unit discharge and the second was the variation of receptor discharge due to variability of the stimulus slope independent of its intensity. The covariance method showed that a linear combination of eigenvectors representing the time-weighted stimulus intensity (E1) and its derivative (E2) could account for, on average, 92% of the total response variability; E1 by itself accounted for 76% of the variability. The low gain of the low-frequency f-I curve implies that detection of small (1 microV) signals would require integration over many receptors ( approximately 1,200) and time (200 ms); even then, signals that elicit behavioral responses could not be detected using rate coding with the estimated gain and noise levels. Weak signals at the limit of behavioral thresholds could be detected if the animal were able to extract E1 from the population of responding P units; we propose a tentative mechanism for this operation although there is no evidence as to whether it is actually implemented in the nervous system of these fish.