From Subthreshold to Firing-Rate Resonance

Abstract

. Many types of neurons exhibit subthreshold resonance. However, little is known about whether this frequency preference influences spike emission. Here, the link between subthreshold resonance and firing rate is examined in the framework of conductance-based models. A classification of the subthreshold properties of a general class of neurons is first provided. In particular, a class of neurons is identified in which the input impedance exhibits a suppression at a nonzero low frequency as well as a peak at higher frequency. The analysis is then extended to the effect of subthreshold resonance on the dynamics of the firing rate. The considered input current comprises a background noise term, mimicking the massive synaptic bombardment in vivo. Of interest is the modulatory effect an additional weak oscillating current has on the instantaneous firing rate. When the noise is weak and firing regular, the frequency most preferentially modulated is the firing rate itself. Conversely, when the noise is strong and firing irregular, the modulation is strongest at the subthreshold resonance frequency. These results are demonstrated for two specific conductance-based models and for a generalization of the integrate-and-fire model that captures subthreshold resonance. They suggest that resonant neurons are able to communicate their frequency preference to postsynaptic targets when the level of noise is comparable to that prevailing in vivo.

Cortical pyramidal cells as non-linear oscillators: Experiment and spike-generation theory

“…Since the θ-neuron yeilds regular (locked) and irregular responses dependent on input frequency, the link between subthreshold oscillations and complex firing patterns is not quite as straight-forward as previously suggested. Perhaps the subthreshold resonances become important under specific input regimes, when the inputs drive the cell membrane into the voltage ranges spanned by the oscillaiton as suggested in Richardson et al (2002). In any case our results clearly demonstrate that complex spike locking patterns and intermittency is not equal to impedance resonances, band-pass filtering or strong subthreshold oscialltions.…”

“…We believe that this report can be combined with the results in Richardson et al (2002) to begin to synthesize a coherent picture of when and how neurons respond to their inputs in a network setting. Therefore, when the average membrane potential of the neuron falls with in the operating range of the currents that underlie subthreshold oscillations (e.g.…”

“…In any case our results clearly demonstrate that complex spike locking patterns and intermittency is not equal to impedance resonances, band-pass filtering or strong subthreshold oscialltions. Richardson et al (2002) showed that the effects of subthreshold resonance is apparent in spiking responses when the sinusoid falls into the subthreshold region. The cell fires due to random variations in the noisy synaptic inputs.…”

“…Building on a rich history of reduced conductance based models (e.g. Fitzhugh-Nagumo, Morris-Lecar) general mathematical principles relating biophysical models of cortical neurons to reduced and canonical models of spike generation in cortical neurons are beginning to be elaborated and tested on neuronal data e.g., spike response models (Gerstner and Kistler 2002); the various versions of non-linear integrate and fire models (Richardson et al 2002,Fourcaud-Trocme, et al 2003, and more general dynamical systems approaches (Izhikevitch 2000). We suggest that identifying the dynamical structure of membrane excitability that leads to spike generation in cortical neurons can yield a powerful tool that allows a synthesis of thinking about response properties of neurons.…”

“…This in turn could imply a certain degree of nonlinearity in the firing patterns of neurons in response to stimuli of varying frequencies. (Richardson et al 2002). On the other hand, Carandini et al (1996) reported that near-linear behavior was observed for cortical regular firing cells in vitro, with little or no subthreshold resonances evident and only low-pass filtering of sinusoid inputs.…”