Introduction Subthreshold dynamics play a key role in spike generation, and it is well-known that some neurons exhibit a frequency preference when integrating subthreshold input– so-called resonators [1,2]. It has been shown, however, that despite the existence of subthreshold resonance, a single resonator neuron exhibits low-pass, i.e., monotonic, information filtering (as measured by the spectral coherence). In other words, in the subthreshold regime, band-pass impedance does not translate to band-pass information filtering. Instead, nonlinearities, such as spiking dynamics, are needed to create band-pass information transfer [3,4].
Methods Here, we study a similar question in electrically and synaptically coupled pairs of neurons. Our goal is to evaluate whether this resonance profile imparts non-trivial information filtering capabilities to the coupled systems. We numerically simulate an integrate-and-fire coupled to a resonate-and-fire system in both the subthreshold and suprathreshold regime, and we investigate the stimulus-response spectral coherence function of the system under perturbation by coloured noise (Ornstein-Uhlenbeck process), as well as the lower bound of mutual information rate.
Results With an electrical coupling between a resonator and an integrator, we show that a Fano-like resonance profile appears in the impedance, i.e., a narrow, asymmetric peak with anti-resonance [5]. Moreover, we observe that the coherence function is non-monotonic, with a minimum around the frequency of the opposite neuron. We also find that with a synaptic-like coupling, a similar Fano-like peak appears in the coherence function, and the lower bound of mutual information rate is generally higher.
Discussion This challenges the claim that neurons require nonlinearities to relay bandpass information filtering properties. This also gives rise to a new type of coherence function and superior information transmission rate overall. This new perspective places information filtering in the context of connection motifs where a small number of resonators and integrators interact, rather than the context of individual neurons.
References [1] Izhikevich, Eugene M. Dynamical systems in neuroscience. MIT press, 2007. [2] Izhikevich, Eugene M. "Resonate-and-fire neurons." Neural networks 14.6-7 (2001): 883-894. [3] Lindner, Benjamin. "Mechanisms of information filtering in neural systems." IEEE Transactions on Molecular, Biological and Multi-Scale Communications 2.1 (2016): 5-15. [4] Blankenburg, Sven, et al. "Information filtering in resonant neurons." Journal of computational neuroscience 39 (2015): 349-370. [5] Joe, Yong S., Arkady M. Satanin, and Chang Sub Kim. "Classical analogy of Fano resonances." Physica Scripta 74.2 (2006): 259.
Acknowledgement I would like thank Prof. Serge Gauvin for the initial inspiration.
