Figure 9. A simple adaptation model. A. A schematic plot of the adaptation channel centered on fo = f1 with s = 0.34 (left ordinate) and three of the sequences that included this frequency with probability of 5% (right ordinate), all three with Df = 44%. The Deviant f1 sequence (probability of f1 marked in red) included also tones at frequency f2 with a probability of 95% (blue). Frequency f2 lies within the effective range of the kernel centered on f1, thus causing a significant amount of adaptation. The Diverse-broad sequence includes f2 with probability of 5% and 10 other frequencies with a probability of 9% each (yellow). These additional frequencies are marked here fA to fJ (some of them are omitted from the figure due to space limitations). The Deviant-alone f1 sequence (green) does not contain any other frequency. The bars representing tone probabilities at f1 and f2 for the different sequences are shown side by side. B. Upper bars - the adaptation load for the three conditions, P pf Kðfo,f Þ. Lower bars – the predicted normalized steady- f state response. Note that the Deviant response is appreciably smaller than the Diverse-broad response, which is about the same as the Deviant-alone response. In the measured data, the Deviant and Diverse- broad responses had about the same size. C. The half-width of the kernel computed for each of the LFP recording sites with Df = 44% when derived from Deviant responses (abscissa) plotted against the half-width of the kernel derived from Diverse-Broad responses (ordinate). The normalized adaptation load when the center frequency was the Standard was assumed to be 0.90, the minimum possible. The results were virtually the same when the normalized adaptation load for the standard was assumed to be maximal, 0.95. doi:10.1371/journal.pone.0023369.g009 In the Diverse-broad condition, the additional terms in the adaptation load span a relatively large frequency band. If the width of the kernel K(f0,f) is on the order of the spacing between the frequencies used in the sequence, only a few terms will contribute significantly to the adaptation load, because of the shape of the kernel. For example, if the width of the kernel is s = 0.34 (which is a typical value for the data, see below) and the spacing between frequencies is Df = 44%, only two additional terms will contribute significantly to the adaptation load, one frequency on each side of the center frequency (Fig. 9A, yellow bars: the two contributing frequencies are f2, with probability 0.05, and fE, with probability 0.09). The adaptation load in the Deviance Detection in Rat Auditory Cortex Diverse-broad condition is therefore approximately 0:05K (f0,f0) z0:14K (f0,f0 1:44). Thus, the normalized response in the Diverse-broad condition is expected to be about B0:14K(f0,f0 1:44). Since in the majority of cases the normalized response in the Diverse-broad condition is smaller than 1 (Figs. 5C, 5D), it follows that K (f0,f0 1:44)w0 must hold – in other words, the width of the adaptation channel is non-zero. In the Deviant condition, the additional term in the adaptation load is solely due to the standard, and the adaptation load is 0:05K (f0,f0)z0:95K (f0,f0 1:44) (Fig. 9A, red and blue bars; Fig. 9B). The normalized response to the Deviant is therefore B0:95K(f0,f0 1:44). Intuitively, the adaptation load in the Deviant case will be larger than that in the Diverse-broad condition, because in the Deviant condition, all sound presentations that contribute to the adaptation have been brought closer to the deviant frequency (the blue bar is as high as the sum of probabilities of all the yellow bars except for the one at f1). In fact, under the assumptions we made about the rate of decrease of K, the model makes the prediction that the response in the Deviant condition should be smaller than in the Diverse-broad condition, and by appreciable amounts: with the approximations made above, if the normalized response in the Diverse broad condition is 0.9, the normalized response in the Deviant condition is expected to be less than 0.6 (Fig. 9B). The normalized responses in the Deviant and in the Diverse- broad conditions can be used to derive estimates for the width of the adaptation channel. For that purpose, it is necessary to estimate B, which we do by using the normalized response to the Standard condition. In the Standard condition, f0 is presented in a probability of 0.95, complemented by the other frequency, Df apart. The adaptation load is therefore 0:95z0:05K (f0,f0 1:44), and the normalized response is therefore B0:9z0:05K(f0,f0 1:44). The kernel is smaller than 1, so the normalized response to the Standard lies between B0.95 and B0.90. The calculations below set the Standard responses to B0.90; setting the Standard responses to B0.95 resulted in practically the same values. We estimated the width of the adaptation channel using the responses to the Diverse-broad condition and separately using the responses to the Deviant condition. In both conditions, we calculated the predicted normalized response as a function of the width of the adaptation channel, and selected the width that corresponded exactly to the measured response. For this analysis, we used only the data for which the responses in the Deviant condition were smaller than the responses in the Diverse-broad condition, and both were smaller than in the Deviant-alone condition (these conditions are necessary for a solution to exist with B,1 and K (f0,f )w0). It should be remembered, however, that these cases comprise only about half of the total data (see Fig. 5). Figure 9C shows the two estimates of the width of the adaptation channel plotted against each other for the LFP data collected with Df = 44%. Clearly, the Diverse-broad responses required a consistently wider adaptation channel than the Deviant responses. To recapitulate, this discrepancy is due to the experimental findings that the responses in the Diverse-broad condition are smaller than in the Deviant-alone condition (requiring a large enough adaptation bandwidth), but are about the same size as in the Deviant condition (an equality that can hold only for small adaptation bandwidth). Thus, these two findings are PLoS ONE | www.plosone.org 9 August 2011 | Volume 6 | Issue 8 | e23369