The frequency transfer function was calculated from responses to injected fluctuating current, using a method originally introduced by Bryant and Segundo (64) with modifications. AP time was registered when the somatic membrane voltage crossed 3 mV, which corresponds to the steepest point on the AP waveform. The STA current was calculated for each cell from ~600 spikes by averaging stimulus waveform in a temporal window of 500 ms before and after the spike. To improve signal-to-noise ratio, the STA was filtered in the frequency domain using a Gaussian window w(f′), centered at frequency f′ = f, with an SD of f/2πEmbedded Image

This averages out neighboring frequency components of similar amplitude but random phase, that is, noise. Deterministic frequency components with a phase that changes only mildly within the Gaussian window are not affected by this windowing. ThusEmbedded Image

If the train of APs is idealized as a discrete sequence of numbers with zero for empty samples and 1/dt for samples carrying an AP, then the product of the STA current and the firing rate ν equals the cross-correlation between input current and AP output. The frequency response function (or the dynamic gain), G(f), was then calculated as the ratio between the Fourier transform of this cross-correlation Embedded Imageand the Fourier transform of the autocorrelation of the input current Embedded Image. The latter is equal to the power spectral density (PSD) of the input current, and for an OU process, the analytical expression of the PSD can replace the numerical autocorrelationEmbedded Imagewhere σ is the SD of the input current and τcorr is the correlation time of the noise.

To average the gain curves from N cells, we averaged the STA currents. To avoid overrepresentation of cells with a smaller input resistance, that is, cells that require a larger amplitude of current fluctuations, we weighted the STA curves: Embedded Image with the average input variance Embedded Image. The average cross-correlation was obtained by multiplication with the average firing rateEmbedded Image

For each neuron and for the population average, we calculated the confidence intervals of the gain curve and the noise floor by balanced bootstrap. The confidence interval at a given frequency f′ was defined by the 2.5th and 97.5th percentile of GBST(f′) for 200 bootstrap gain curves calculated from 200 random samples of actual AP times. The noise floor at a certain frequency is understood as 95th percentile of Embedded Image calculated not from measured but from random AP times. To obtain random AP times without changing the statistics of the AP time series, we applied a cyclic shift of the injected current by a random value larger than five correlation times. This results in a random triggered average of the input, which replaces the STA current in the calculations for Embedded Image. Neurons were excluded from the analysis if signs of nonstationarity in AP shape or other signs of cell instability, such as a drifting baseline potential, were detected.

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