Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

Abstract

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors-number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.

Establishing and validating a new source analysis method using phase

“…The main motivation for choosing second order model was that it provides more control over the estimated parameters (eg., phase) than higher order AR processes. Additionally, in this paper [12] the authors have shown with second order AR processes the phase estimation for narrow band frequency spectrum is optimal than higher order AR processes. In our case the phase estimation was based on a single peak frequency and not on a broad band frequency spectrum.…”

“…However, before utilizing any of these approaches, the forward problem must be solved. The solution is based on either spherical head models (single sphere [11] and concentric spheres [12]) or realistic head models (boundary element method (BEM) [13] and finite element method (FEM) [14]). After developing any new method, the best way to test its robustness is to apply the simulation to a dataset in which the results are already known.…”