Characterizing the computation in single neurons with an LN model. *A*, A neuron is driven to fire action potentials (in voltage *V*(*t*)) by stimulating with Gaussian noise input current *i*(*t*). Increasing the SD, σ, of the input from σ_{1} (top, black) to σ_{2} (bottom, red) results in higher frequency firing. *B*, The optimal single input feature correlated with spiking is the STA stimulus, the mean current preceding a spike. The feature is normalized such that STA · STA = 1. In this example, STA_{σ1} (black) and STA_{σ2} (red dashed) are identical. *C*, The computation is characterized by the spike-triggered, scaled, filtered stimulus distribution, *p*_{σ}[*ŝ* | sp] (*ŝ* ≡ *s*/σ). This neuron shows large error in gain scaling as the distribution changes shape significantly with changes in *P*_{σ1}, [*ŝ* | sp]≠*p*_{σ2}[*ŝ* | sp]; this change is quantified by *D*_{σ} (see Materials and Methods). The prior stimulus distribution, *p*[*ŝ*], is a unit variance Gaussian (shaded). *D*, Scaled nonlinear input–output relations, *R̂*_{σ}[*ŝ*]& #x2261; *R*_{σ}[*ŝ*]*R̄*_{σ}, are calculated by dividing *p*_{σ}[*ŝ* | sp] by *p*[*ŝ*] (see Materials and Methods); as in *C*, the two input–output relations do not overlap for different σ.

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