Adapting-bump model for eccentric cells of Limulus

Light-evoked intracellular voltage noise records have been obtained from Limulus eccentric cells, from threshold light intensity to an intensity .10(5) times threshold. These data are analyzed in terms of a simple "adapting-bump" noise model. It is shown how the model yields a data reduction procedure that slightly generalizes the familiar use of Campbell's theorem for Poisson shot noise: the correlative effect of adaptation amends Campbell's theorem by a single multiplicative factor, which may be estimated directly from the power spectrum of the noise data. The model also permits direct estimation of the bump shape from the power spectrum. The bump shape estimated from noise at dim light is in excellent agreement with the average shape of bumps observed directly in the dark. The data yield a bump rate that is linear with light up through about 50 times threshold intensity but that falls short of linearity by a factor of 35 at the brightest light. The bump height decreases as the -0.4 power of light intensity across the entire range. Bump duration decreases by a factor of 2 across the entire range, and the adaptation correlation factor descends from unity to about one-third. The modest change of the adaptation correlation shows that naive application of Campbell's theorem to such data is adequate for rough estimation of the model's physiological parameters. This simple accounting for all the data gives support to the adapting-bump model.