Neuronal Morphology Generates High-Frequency Firing Resonance

Abstract

The attenuation of neuronal voltage responses to high-frequency current inputs by the membrane capacitance is believed to limit single-cell bandwidth. However, neuronal populations subject to stochastic fluctuations can follow inputs beyond this limit. We investigated this apparent paradox theoretically and experimentally using Purkinje cells in the cerebellum, a motor structure that benefits from rapid information transfer. We analyzed the modulation of firing in response to the somatic injection of sinusoidal currents. Computational modeling suggested that, instead of decreasing with frequency, modulation amplitude can increase up to high frequencies because of cellular morphology. Electrophysiological measurements in adult rat slices confirmed this prediction and displayed a marked resonance at 200 Hz. We elucidated the underlying mechanism, showing that the two-compartment morphology of the Purkinje cell, interacting with a simple spiking mechanism and dendritic fluctuations, is sufficient to create high-frequency signal amplification. This mechanism, which we term morphology-induced resonance, is selective for somatic inputs, which in the Purkinje cell are exclusively inhibitory. The resonance sensitizes Purkinje cells in the frequency range of population oscillations observed in vivo.

Noisy Juxtacellular StimulationIn VivoLeads to Reliable Spiking and Reveals High-Frequency Coding in Single Neurons

“…Two-compartment model. We also use a two-compartment model that contains one somatic compartment and one dendritic compartment (Ostojic et al, 2015). To allow for electrotonic coupling, both compartments are connected via an Ohmic conductance.…”

“…A recent computational study by Eyal et al (2014) and in vitro experiments and modeling on Purkinje cells by Ostojic et al (2015) revealed that the presence of a purely passive dendritic tree can enhance the response at high frequencies. We tested whether similar models as used in these studies can reproduce, not only the rate modulation factor, but also all of the second-order statistics that were accessible in our in vivo experiments: spike train power spectrum, cross-spectra between stimulus and spike train and between two different spike trains (i.e., two different trials) for a frozen stimulus, and the coherence function.…”

“…In Figure 9D, the different parameters that belong to the 10 cells below threshold are presented. For some of the parameters, specific values can be found in the literature (Rall, 1959;Koch et al, 1996;Badel et al, 2008;Bekkers, 2011;Harrison et al, 2015;Ostojic et al, 2015), whereas, for others (D s , D d , I base ), the order of magnitude can be estimated based on biophysical considerations. For all parameters, we found a reasonable agreement between the expected order of magnitude and the values shown in Figure 9D.…”

“…Finally, we used a multicompartment model (Eyal et al, 2014) and a two-compartment model (Ostojic et al, 2015) to reproduce quantitatively the statistics measured in vivo and compared the performance of the latter model with a one-compartment model.…”

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

“…Additional variables may describe synaptic filtering [11], external sources of colored noise [12,13], dendritic compartments [14], and subthreshold oscillations [15].…”