Inferring synaptic excitation/inhibition balance from field potentials.

TL;DR: A computational model is developed to show that E:I changes can be estimated from the power law exponent (slope) of the electrophysiological power spectrum, and provides evidence thatE:I ratio may be inferred from electrophysics recordings at many spatial scales, ranging from the local field potential to surface electrocorticography.

About: This article is published in NeuroImage.The article was published on 2017-09-01 and is currently open access. It has received 397 citations till now. The article focuses on the topics: Local field potential.

Summary

INTRODUCTION

• Neurons are constantly bombarded with spontaneous synaptic inputs.
• Other methods, such as magnetic resonance spectroscopy (Henry et al. 2011) and dynamic causal modeling (DCM) (Legon et al. 2015), are able to provide much greater spatial coverage, thus enabling the sampling of E:I ratio across the brain.
• Two recent lines of modeling work motivate their hypothesis.
• First, it has been shown that synaptic input fluctuations during the high conductance state can be accurately modeled by a summation of two stationary stochastic processes representing excitatory and inhibitory inputs (Alvarez & Destexhe 2004).

RESULTS

• I ratio drives 1/f changes in simulation, also known as E.
• To model LFP under the high conductance state, the authors simulate an efferent “LFP” population receiving independent Poissonic spike trains from an excitatory and an inhibitory population .
• Note that the current-PSDs begin decaying at different frequencies, due to the different rise and decay time constants of AMPA and GABAA conductance profiles, which have been previously observed in intracellular models of the balanced, high conductance state (Destexhe & Rudolph 2004).
• I ratio is positively correlated with PSD slope between 30-50 Hz, also known as (F) E.

Depth-varying synapse density in rat CA1

• To test the relationship between E:I ratio and PSD slope empirically, the authors first take advantage of the fact that excitatory and inhibitory synapse densities vary along the pyramidal dendrites in the CA1 region of the rat hippocampus (Megías et al. 2001).
• Thus, the authors find that PSD slope significantly correlates with E:I ratio in the rat CA1, as measured by synapse density, though the effect is strongly driven by the presence of inhibition.
• Additionally, the authors observe that high-frequency (140-230 Hz) power – a surrogate for spiking activity and ripples in the hippocampus (Schomburg et al. 2012) – is higher during theta troughs than peaks, further indicating the correspondence between LFP troughs and windows of excitation .
• (D) Individual-channel comparison of slopes during theta troughs vs. peaks, each channel represented by a pair of connected dots showing nearly universally more negative slope during peaks compared to troughs (* p < 10-5).
• The authors find that PSD slope dynamically tracks the stability of brain state during awake resting, followed by a rapid push towards inhibition after injection that is consistent with propofol’s time of onset (15-30 seconds), as well as the slow rebalancing during recovery from anesthesia .

DISCUSSION

• Guided by predictions from computational modeling, their analyses of existing datasets from two mammalian species with different experimental manipulations and recording equipment demonstrate that information about local E:I ratio can be robustly captured from the spectral representation of electrophysiological signals.
• There are several caveats in this study worth noting.
• In addition, the authors observe that PSD slope of cortical ECoG is much more negative than that of CA1 LFP recordings, which, in turn, is lower than slopes produced by their LFP model, suggesting that anatomical differences and dendritic integration process all contribute to the measured slope (Lindén et al. 2010; Pettersen et al. 2014).

Power Law (1/f) Decay in Neural Recordings

• Power law exponent changes of the PSD (“rotation”) have recently been observed in several empirical studies, linking it to changes in global awake and sleep states (He et al. 2010), age-related working memory decline (Voytek et al. 2015; Voytek & Knight 2015), and visuomotor task-related activation (Podvalny et al. 2015).
• The 1/f power law nature of neural recordings has been interpreted within a self-organized criticality framework (Bak et al.
• Instead, LFP and ECoG PSDs often have constant spectral power at low frequencies between 1-10 Hz, as well as different power law exponents at different frequencies.
• Ultra-low frequency region (<1 Hz) was posited to exhibit 1/f decay due to recurrent network activity (Chaudhuri et al. 2016), and power law in the very high frequency (>200 Hz) was shown to be a result of stochastic fluctuations in ion channels (Diba et al. 2004).
• The authors show that this limitation can be overcome using relatively simple metrics derived from meso- and macro-scale neural recordings, and that it can be easily applied retrospectively to existing data, opening new domains of inquiry and allowing for reanalyses within an E:I framework.

EXPERIMENTAL PROCEDURES

• The authors simulate local field potentials under the high conductance state (Alvarez & Destexhe 2004), with the assumption that the LFP is a linear summation of total excitatory and inhibitory currents (Mazzoni et al. 2015).
• Each spike train is convolved with their respective conductance profiles, which are modeled as a difference-of-exponentials defined by the rise and decay time constants of AMPA and GABAA receptors (Eq.1).
• For all time series data (simulated and recorded LFP, ECoG), the PSD is estimated by computing the median of the square magnitude of the sliding window (short-time) Fourier transform (STFT).
• Tran for invaluable discussion and comments, the Buzsáki Lab and CRCNS for their public repository of rat LFP data, and the Fujii Lab and NeuroTycho for their public repository of monkey ECoG data.
• B.V. is supported by the University of California, San Diego, Qualcomm Institute, California Institute for Telecommunications and Information Technology, Strategic Research Opportunities Program, and a Sloan Research Fellowship.

Figure S2. Region of interest in CA1.

• Synaptic density values corresponding to the segment of CA1 LFP data were taken from Megias et al, 2001.
• Figure 2 shows aligned slope and E:I density variations along the depth of interest, centered on the middle of the pyramidal layer, highlighted by the gray box.
• Both figures are identical, with only the filtered region removed for the main text for aesthetic reasons.
• (C) Fit errors for 30-50 Hz fit are significantly greater than when fit over 40-60 Hz for majority of channels, leading to the analysis decision of choosing the latter for analysis.
• Table S1. Multivariate Linear Model Coefficients and R2 for Slope vs. E, I, and E:I Ratio Note that univariate models produce coefficients with consistent signs (positive for E, E:I ratio; negative for I).

Figures

Figure 1. E:I ratio correlates with PSD slope in simulation.

Figure 3. PSD slope tracks theta-modulated changes in E:I balance.

Table 1. LFP Simulation Parameters

Figure 4. ECoG-PSD slope tracks propofol-induced global inhibition.

Figure 2. LFP-PSD slope varies with E:I synapse density ratio in rat CA1. (A) Example shank spanning across CA1 (rad: stratum radiatum; pyr: stratum pyramidale; or: stratum oriens; adapted from (Mizuseki et al. 2011)). (B) Example PSDs computed from electrodes along one recording shank. (C) Aggregate slope profile across depth, centered to the middle of pyramidal layer (0 μm) (horizontal bars denote standard deviation). (D) Excitatory (AMPA) and inhibitory (GABAA) synapse density varies across CA1 depth. (E and F) LFP-PSD slope correlates positively with E:I synapse density ratio (E) and negatively with GABAA density (F) (vertical bars denote standard deviation).

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Inferring synaptic excitation/inhibition balance from field potentials" ?

Fluctuations in this E: I balance have been shown to influence neural computation, working memory, and information processing. This has limited the ability to examine the full impact that E: I shifts have in neural computation and disease. In this study, the authors develop a computational model to show that E: I ratio can be estimated from the power law exponent ( slope ) of the electrophysiological power spectrum, and validate this relationship using previously published datasets from two species ( rat local field potential and macaque electrocorticography ). 

Q2. What are the key words in this article?

Key Words: excitation-inhibition balance, local field potential, electrocorticography, power spectral density, power law, simulation, high-conductance state. 

Q3. What is the name of the author?

While more drastic shifts and aberrant E:I patterns are implicated in numerous neurological and psychiatric disorders, current methods for measuring E:I dynamics require invasive procedures that are difficult to perform in behaving animals, and nearly impossible in humans. 

Q4. Who is the author of this article?

Richard D. Gao1,*, Erik J. Peterson1, Bradley Voytek1,2,3,41Department of Cognitive Science, 2Neurosciences Graduate Program, 3Institute for Neural Computation, and 4Kavli Institute for Brain and Mind, University of California, San Diego, La Jolla, CA, USA.*Correspondence: rigao@ucsd.eduNeural circuits sit in a dynamic balance between excitation (E) and inhibition (I).