Frequency filter interactions in network of non-oscillatory cells

Abstract

Resonance refers to the ability of dynamical systems to exhibit a peak in their amplitude response to oscillatory inputs at a preferred (resonant) frequency. In neuronal cir- cuits, resonance is typically measured by using the imped- ance amplitude profile Z defined as the absolute value of the quotient of the Fourier transforms of the output and the input. Resonance has been investigated in single neurons by many authors both experimentally and theoretically (Cichon & Gan, 2015 Apr; Sajikumar et al., 2014 Aug 19). Network resonance has received much less attention. Two important questions are (i) whether and under what condi- tions a network of neurons exhibits resonance in one or more neurons in response to inputs to one or more neurons, and (ii) whether and under what conditions the information is communicated between neurons in a frequency-dependent manner. In this project we address these issues by using a minimal network consisting of two passive cells (linear, non-reso- nant neurons) recurrently connected via graded synaptic inhibition or excitation and receiving oscillatory inputs in either one or the two nodes (Sezener et al., 2021). In order to investigate how network resonance emerges we extend the concept of impedance to nonlinear systems by comput- ing the peak-to-trough amplitudes normalized by the input amplitude. In order to investigate the communication of frequency-dependent information across neurons in the network we borrow the concept of the coupling coefficient from the gap junction literature. The coupling coefficient K, defined as the quotient between the postsynaptic and pre- synaptic membrane potentials of two electrically coupled neurons, is used to measure the strength of the connection in the presence of constant (DC) inputs. Here we extend this metrics to synaptically connected neurons and to the fre- quency domain. Linear networks (linear neurons and linear connectivity) can only show a low-pass filter K profile (K as a function of the input frequency). We show that the pres- ence of the more realistic nonlinear synaptic connectivity can produce band-pass K profiles. We note that the concept of communication of information we use here is different than the standard one used in information theory.