Extracting information from the power spectrum of voltage noise

doi:10.1016/j.neucom.2004.10.110

Neurocomputing

Volumes 65–66, June 2005, Pages 901-906

https://doi.org/10.1016/j.neucom.2004.10.110 Get rights and content

Abstract

We outline an approximation for obtaining an analytic expression of the power spectral density (PSD) of the membrane potential $(V_{m})$ in neurons subject to synaptic noise. In high-conductance states, there is a remarkable agreement between this approximation and PSDs computed numerically. This analytic expression can be used to predict how the PSD depends on the exact kinetic model for synaptic currents, as well as on the values of the rate constants. This approach can therefore yield methods to estimate the characteristics of the kinetics of individual synaptic conductances from the analysis of the $V_{m}$ activity in intracellular recordings in vivo.

Introduction

Neocortical neurons during active states in vivo display intense and irregular subthreshold synaptic activity (“synaptic noise”) which may strongly affect their integrative properties [6]. It is possible to characterize synaptic background activity using voltage-clamp methods applied in vivo [1] or in vitro [8]. However, most experiments, in particular in vivo recordings, are performed in current-clamp mode, in which the membrane potential activity is recorded. One therefore needs methods to extract the characteristics of the synaptic inputs under current-clamp by analyzing the voltage fluctuations, which is our goal in the present paper.

Section snippets

Methods

To simulate synaptic noise, we used a single-compartment model described by the passive membrane equation $C_{m} \frac{d V}{d t} = - g_{leak} (V - E_{leak}) - \sum_{j} g_{j} (t) [V (t) - E_{j}],$ where V is the membrane potential, $C_{m} = 1 μ F / {cm}^{2}$ is the specific membrane capacitance, $g_{leak} = 0.1 mS / {cm}^{2}$ and $E_{leak} = - 70 mV$ are the leak conductance and reversal potential, respectively. The last term represents a large number of conductance-based synaptic inputs, where, for each synapse j, $g_{j}$ denotes the conductance and $E_{j}$ is the reversal potential. $g_{j}$ can be

Results

We start by providing a general expression for the power spectral density (PSD) of the membrane potential $(V_{m})$ , then consider the expression for two particular kinetic models.

Taking the Fourier transform of the membrane equation (Eq. (1)) yields $i ω C_{m} V (ω) = - g_{leak} [V (ω) - E_{leak} δ (ω)] - \sum_{j} g_{j} (ω) * [V (ω) - E_{j}],$ where $*$ is the convolution operator. This equation is not solvable because of this convolution, which is a consequence of the multiplicative aspect of conductances.

To solve this equation, we make an

Conclusions

We showed that, under an effective leak approximation, one can derive an analytic expression for the PSD of the $V_{m}$ for neurons subject to synaptic noise. This analytic expression can be used to yield two types of information about synaptic conductances. The first type of information is qualitative and concerns the kinetic model underlying synaptic conductances. The exact type of model will affect the scaling of the PSD at high frequencies. This scaling is determined by the number of exponential

Acknowledgements

Research supported by CNRS and HFSP.

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Neurocomputing

Extracting information from the power spectrum of voltage noise

Abstract

Introduction

Section snippets

Methods

Results

Conclusions

Acknowledgements

Visual input evokes transient and strong shunting inhibition in visual cortical neurons

Nature

Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition

J. Comput. Neurosci.

Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism

J. Comput. Neurosci.

Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo

J. Neurophysiol.