Wavelet Analysis of Nonstationary Fluctuations of Monte Carlo-Simulated Excitatory Postsynaptic Currents

Abstract

Tracking spectral changes of rapidly varying signals is a demanding task. In this study, we explore on Monte Carlo-simulated glutamate-activated AMPA patch and synaptic currents whether a wavelet analysis offers such a possibility. Unlike Fourier methods that determine only the frequency content of a signal, the wavelet analysis determines both the frequency and the time. This is owing to the nature of the basis functions, which are infinite for Fourier transforms (sines and cosines are infinite), but are finite for wavelet analysis (wavelets are localized waves). In agreement with previous reports, the frequency of the stationary patch current fluctuations is higher for larger currents, whereas the mean-variance plots are parabolic. The spectra of the current fluctuations and mean-variance plots are close to the theoretically predicted values. The median frequency of the synaptic and nonstationary patch currents is, however, time dependent, though at the peak of synaptic currents, the median frequency is insensitive to the number of glutamate molecules released. Such time dependence demonstrates that the "composite spectra" of the current fluctuations gathered over the whole duration of synaptic currents cannot be used to assess the mean open time or effective mean open time of AMPA channels. The current (patch or synaptic) versus median frequency plots show hysteresis. The median frequency is thus not a simple reflection of the overall receptor saturation levels and is greater during the rise phase for the same saturation level. The hysteresis is due to the higher occupancy of the doubly bound state during the rise phase and not due to the spatial spread of the saturation disk, which remains remarkably constant. Albeit time dependent, the variance of the synaptic and nonstationary patch currents can be accurately determined. Nevertheless the evaluation of the number of AMPA channels and their single current from the mean-variance plots of patch or synaptic currents is not highly accurate owing to the varying number of the activatable AMPA channels caused by desensitization. The spatial nonuniformity of open, bound, and desensitized AMPA channels, and the time dependence and spatial nonuniformity of the glutamate concentration in the synaptic cleft, further reduce the accuracy of estimates of the number of AMPA channels from synaptic currents. In conclusion, wavelet analysis of nonstationary fluctuations of patch and synaptic currents expands our ability to determine accurately the variance and frequency of current fluctuations, demonstrates the limits of applicability of techniques currently used to evaluate the single channel current and number of AMPA channels, and offers new insights into the mechanisms involved in the generation of unitary quantal events at excitatory central synapses.

Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

“…The evaluation of power spectra using parametric methods differs significantly from the estimation using non-parametric methods such as Fourier and Wavelet analyses (Fishman 1973;Rioul and Vetterli 1991;Aristizabal and Glavinović 2003). The evaluation is not done directly from the data.…”

“…The time course of variance of current fluctuations is also available from the Kalman-AR-model fits to individual quantal events. They are thus uncontaminated by the variable contribution of 'instantaneous' glutamate concentration (Kruk et al 1997;Glavinović 1999), although the rapidly developing desensitization of AMPA receptors limits their usefulness in determining the number of AMPA receptors post-synaptically using a binomial theorem (Aristizabal and Glavinović 2003). Nevertheless the changes of variance and median frequency of current fluctuations are likely to provide useful information about the gating kinetics of AMPA channels and the time course of glutamate in the synaptic cleft.…”

“…At present the method is used when the single channel conductance is low and channels inaccessible, as is often the case with synaptic currents in the central nervous system (Robinson et al 1991;Traynelis and Jaramillo 1998;Benke et al 2001;Mozrzymas 2004). It is now clear that the fluctuations of the excitatory post-synaptic currents are highly non-stationary (Aristizabal and Glavinović 2003). A high degree of non-stationarity is not surprising given the time course of glutamate concentration in the synapse, which rises very quickly and decays in a multi-exponential manner, though more slowly (Clements 1996;Glavinović and Rabie 1998), and the concentration dependence of several rates of the kinetic scheme of AMPA channels (Colquhoun et al 1992).…”

“…Moreover, the desensitization of AMPA receptors, which develops rapidly during the time course of unitary excitatory post-synaptic currents, contributes significantly to shaping the time course of mEPSCs (Jones and Westbrook 1996;Glavinović and Rabie 1998;Hirasawa et al 2001;Wall et al 2002;Jackson et al 2003;Yelshansky et al 2004). The gating mechanism of transmitter-activated channels, such as ACh and AMPA channels are complex (Katz and Thesleff 1957;Trussell and Fischbach 1989), and their desensitization is associated with a progressively changing pattern of bursts and clusters (Sakmann et al 1980), which renders the spectra of their current fluctuations non-stationary, even when activated by constant and spatially uniform pulses of transmitter (Aristizabal and Glavinović 2003). An assessment of the spectral or variance changes of non-stationary current fluctuations ought to provide important insights into the time course of the transmitter in the synaptic cleft, and the kinetics of gating of transmitter-activated channels.…”

“…Even if the individual quantal event is taken as a single current segment its duration is rarely so long. Wavelet transform, which localizes not only in frequency but also in time, and which has a frequency dependent windowing, provides an alternative (Rioul and Vetterli 1991;Aristizabal and Glavinović 2003).…”