Deviance Detection in Rat Auditory Cortex Figure 8. Respones as a function of ISI. A. Average LFP responses at five different ISIs. The examples, from different animals, show the responses to the low frequency (f1) in each pair. B. The population average of the responses to different ISIs for the two groups of rats (continuous and dashed lines) used in testing the effects of ISI. The error bars are s.e.m. For more details, see text. C. The distributions of the individual CSIs at each ISI. Circles are ‘common’ averages, computed as the sum of all numerators of contrasts in each ISI value, divided by sum of all denominators. doi:10.1371/journal.pone.0023369.g008 results in a steady state response after a few stimulus presentations [19]. The steady state response to tones of frequency f0 within a sequence composed only of tones of frequency f0, normalized by the unadapted response, will be denoted by B,1. The responses to very rare tones at frequency f0 embedded in a sequence of tones of a frequency f that is different from f0 should still be adapted, but only partially. To capture this frequency dependence, the model posits that the normalized response to a tone at frequencyfo after a long sequence of tones of frequency f is BKðfo,f Þ, where the kernel K is a (non-normalized) Gaussian, K ðfo,f Þ~ exp { ðlog2f {log2foÞ2! 2s2 : The half-width of the cross-frequency adaptation band, s, is the main parameter of interest of the model. For f = f0, the K(f0,f0) is 1 and we recover the steady state response level B. As f gets farther away from f0, K(f0,f) decreases to 0 so that the normalized response level BKðfo,f Þ approaches 1 (the unadapted response). The sequences we used consisted of tones of multiple frequencies. To combine the effects of all of these frequencies multiplicatively, the average contribution of all the presentations of tones at frequency f that appeared with probability pf in the sequence was modeled as Bpf Kðfo,f Þ. The overall adaptation depth is a product of the ideal unadapted response, A, and the adaptation contributed by each of the frequencies that appeared in the sequence: P pf Kðfo,f Þ RðfoÞ~A:B f , where the sum is taken over the frequencies of all tones in the sequence. The last formula should be considered as an estimate of the steady-state adapted response to frequency fo during a ‘typical’ stationary sequence of stimuli, in which the different frequencies were randomly intermixed with the overall proportions given by pf . The model has three parameters: B, s and A. To motivate the comparison that will be made between the model and the data, we start by giving a semi-quantitative description of the behavior of the model applied to the type of sequences used here. Obviously, the responses that are predicted by the model are inversely related to the sum in the exponent, which will be called ‘the adaptation load’. In the Standard, Equal- probability and Diverse-narrow conditions, it is clear why the adaptation load is relatively large: f0 and/or nearby frequencies, for which the kernel is large, are highly probable. The interesting cases consist of the three conditions that give rise to large responses: Deviant-alone, Diverse-broad, and Deviant (in a decreasing order of the average responses). The adaptation load is least (and therefore the predicted responses largest) in the Deviant-alone condition, where it is equal to 0:05K (f0,f0)~0:05, 0.05 being the probability of the deviant, and K(f0,f0)~1 (see Figs. 9A, green bar and 9B; in Fig. 9A the adaptation channel is centered on frequency f1). In the Diverse- broad and Deviant conditions the adaptation load includes this term as well, but has additional contributions. PLoS ONE | www.plosone.org 8 August 2011 | Volume 6 | Issue 8 | e23369