A multicompartment model, developed by Hallermann et al. (27) to capture the properties of AP generation in pyramidal neurons in brain slices, was used for the simulations of AP initiation and spike time precision (https://senselab.med.yale.edu/modeldb/ShowModel.cshtml?model=144526). The properties of all active conductances and their spatial distribution were left unchanged from the original model. To obtain the transfer functions for different axonal channel densities, many millions of seconds had to be simulated. To reduce the computational load, the model morphology was compacted: The basal dendrites and the apical dendritic branch and the initial axon were each represented by a single process with adjusted geometry, and two axon collaterals are branching off the main axon. Compacting the morphology did not alter the characteristics of the model for AP waveform or transfer function but greatly expedited simulations. For some simulations, we exchanged the somatic sodium channel model from Schmidt-Hieber and Bischofberger (65) against a similar model we had derived from our own measurements, the AP waveforms and transfer functions changed only marginally, and this version of the model was used for the results presented here.

To obtain the transfer function, the model is driven by somatic injection of a fluctuating current, derived from an OU process with a correlation time of 35 ms. The mean and SD of the process are chosen to obtain a firing rate of 2 Hz and a coefficient of variation of the interspike interval around 0.85. This reflects a fluctuation-driven state and closely matches the experimentally obtained firing statistics. Each simulation is 200 s long with sample interval of 0.025 ms; 250 such 200-s simulation are combined to obtain approximately 106 spikes for each set of axonal channel densities. AP time is set when the somatic voltage crosses +8 mV. From AP times and the input current, we calculate the STA input, which represents the cross-correlation of input and AP output. The transfer function TF is calculated as the ratio of the Fourier transformations of the cross-correlation (STA input) multiplied with the firing rate f and the autocorrelation of the input. The latter corresponds to the PSD of the inputEmbedded Image

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