In an LN model, differences in gain manifest through changes in the shape of the output nonlinearity. To quantify these changes, we calculated the set of linear transformations required to map the output nonlinearity for high-contrast stimulation (σL = 8.7 dB, c = 92%) onto those

for other stimulus conditions. In principle, this mapping could combine a scaling of the curve along the horizontal and vertical axes and a translation of the curve along these axes (x- and y-offset, respectively). However, none of the units under investigation operated near their saturation point, making an estimate of vertical scaling difficult. Thus, we measured changes in the remaining three degrees of freedom ( Equation 6; Model 4 in Table S2). Horizontal scaling corresponds to a change in gain, x-offset to a threshold shift and y-offset ISRIB cost to a change in minimum firing rate. We observed a robust relationship between stimulus contrast and gain across the population of units. An approximately OSI-744 order 3-fold decrease in contrast from 8.7 dB (c = 92%) to 2.9 dB (c = 33%) increased gain by a median factor of 2.01; for an ∼1.5-fold decrease in contrast from 8.7 dB (c = 92%) to 5.8 dB (c = 64%), gain increased by 1.34× ( Figure 4A). The gain effect was also strongest among units with the most robust, repeatable spike trains ( Figure S3D). Gain therefore changes in the appropriate direction to compensate for changes in stimulus

contrast, but this compensation is not complete. Decreasing stimulus new contrast also caused nonlinearities to shift by a small amount to the right (median x-offset of 5.5% and 1.4% for low and medium contrast; p < 0.001 and p < 0.05, respectively, sign-rank test; Figure 4B),

but there was no corresponding vertical translation of these curves (Figure 4C). Although the change in x-offset is nominally indicative of a small increase in threshold, the gain and x-offset measures were correlated with each other across units (r2 = 0.195 in high-to-low- and 0.11 in high-to-medium-contrast curve transformations; Figure 4D), suggesting that the rightwards shift in curves partly acts to compensate for gain (see Figure S3E). The lack of systematic y-offset changes indicated that minimum firing rate did not change across conditions. Therefore, the primary consequence of decreasing stimulus contrast is that cortical cells increase their gain. By transforming output nonlinearities across conditions, we could predict neural responses to each contrast stimulus as successfully as by using separate nonlinearities for each condition as described above (median difference in prediction scores of 0.7%; sign-rank, p > 0.5). These effects are similar to the changes in coding accuracy previously observed in the IC (Dean et al., 2005). Neuronal firing is most sensitive to and hence most informative about stimulus changes when the slope of the input/output function is at its greatest. This occurs at a median position of X⋅vX⋅v = 5.