Inferring synaptic excitation/inhibition balance from field potentials
Introduction
Neurons are constantly bombarded with spontaneous synaptic inputs. This state of fluctuating activity is referred to as the high-conductance state (Destexhe et al., 2003), and gives rise to the asynchronous, irregular (Poisson-like) firing observed in vivo (Destexhe et al., 2001). In this state, neural circuits sit in a balance between synaptic excitation (E) and inhibition (I), typically consisting of fast glutamate and slower GABA inputs, respectively, where inhibition is two to six times the strength of excitation (Alvarez and Destexhe, 2004, Xue et al., 2014). Physiologically, the balance of E:I interaction is essential for neuronal homeostasis (Turrigiano and Nelson, 2004) and the formation of neural oscillations (Atallah and Scanziani, 2009). Computationally, E:I balance allows for efficient information transmission and gating (Salinas and Sejnowski, 2001, Vogels and Abbott, 2009), network computation (Mariño et al., 2005), and working memory maintenance (Lim and Goldman, 2013). Conversely, an imbalance between excitation and inhibition, during key developmental periods or tonically thereafter, is implicated in neurological and psychiatric disorders such as epilepsy (González-Ramírez et al., 2015, Symonds, 1959), schizophrenia (Uhlhaas and Singer, 2010), and autism (Dani et al., 2005, Mariani et al., 2015, Rubenstein and Merzenich, 2003), as well as impairments in information processing and social exploration (Yizhar et al., 2011).
Given such a state of intricate balance and its profound consequences when disturbed, quantifying the E:I ratio could aid in better characterizing the functional state of the brain. Existing methods for estimating E:I ratio focus predominantly on interrogation of precisely selected cells, either through identification of excitatory and inhibitory neurons based on extracellular action potential waveforms (Peyrache et al., 2012), or by intracellular voltage-clamp recordings to measure synaptic currents (Monier et al., 2008), often combined with pharmacological or optogenetic manipulations (Reinhold et al., 2015, Xue et al., 2014). These methods are invasive and are restricted to small populations of cells, making them difficult to apply clinically and to in vivo population-level analyses critical for understanding neural network functioning. Other methods, such as magnetic resonance spectroscopy (Henry et al., 2011) and dynamic causal modeling (Legon et al., 2015), are able to provide greater spatial coverage, enabling the sampling of E:I ratio across the brain. However, this gain comes at a cost of temporal resolution – requiring several minutes of data for a single snapshot – and are based on restrictive connectivity assumptions.
Here, we aim to address this important gap in methodology to measure E:I ratio with broad population coverage and fine temporal resolution. Two recent lines of modeling work motivate our starting 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 and Destexhe, 2004). These inputs have different rates of decay, corresponding to a faster AMPA current and a slower GABAA current, which can be readily differentiated in the frequency domain and computationally inferred from single membrane voltage traces (Pospischil et al., 2009, Fig. 1B). Second, population-level neural field recordings, such as the local field potential (LFP) and electrocorticography (ECoG), have been shown to be primarily dominated by postsynaptic currents (PSC) across large populations (Buzsáki et al., 2012, Mazzoni et al., 2015, Miller et al., 2009). Additionally, recent work by (Haider et al., 2016) observed tight coupling between the LFP and synaptic inputs in the time domain. Thus, we combine these two findings and reason that changes in the relative contribution between excitatory and inhibitory synaptic currents must also be reflected in the field potential, and in particular, in the frequency domain representation (power spectral density, or PSD) of LFP and ECoG recordings. In this work, we derive a straightforward metric that closely tracks E:I ratio via computational modeling, and demonstrate its empirical validity by reanalyzing publically available databases from two different mammalian species. Specifically, we test the hypotheses that anatomical and theta oscillation-modulated changes in excitation and inhibition in the rat hippocampus can be inferred from CA1 local field potentials, and that anesthesia-induced global inhibition is reflected in macaque cortical electrocorticography.
Section snippets
LFP simulation
We simulate local field potentials under the high conductance state (Alvarez and Destexhe, 2004), with the assumption that the LFP is a linear summation of total excitatory and inhibitory currents (Mazzoni et al., 2015). Poisson spike trains from one excitatory and one inhibitory population are generated by integrating interspike intervals (ISI) drawn from independent exponential distributions, with specified mean rate parameter (Fig. 1A). Each spike train is convolved with their respective
E:I ratio drives 1/f changes in simulation
To model LFP under the high conductance state, we simulate an efferent “LFP” population receiving independent Poissonic spike trains from an excitatory and an inhibitory population, as detailed in the Methods. In the frequency domain, we observe that the power spectral density of the LFP (LFP-PSD) follows a decaying (1/f) power law for frequencies past 20 Hz (negatively linear in log-log plot), which directly results from adding the two current components, both following power law decays (Fig. 1
Discussion
Guided by predictions from our computational modeling results, our 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 captured from the spectral representation of electrophysiological signals. Specifically, we show that LFP-PSD slope correlates with both anatomical E:I ratio—represented by changes in synaptic density ratio across CA1 layers—and dynamic E:I ratio as
Author contributions
R.G., E.J.P., and B.V. initiated and designed the study. R.G., E.J.P., and B.V. developed the computational model. R.G. analyzed the data. All authors discussed the results and wrote the manuscript.
Acknowledgements
We thank S.R. Cole, T. Donoghue, C. Holdgraf, R. van der Meij, E. Mukamel, D. Nitz, T. Noto, J. Olson, B. Postle, and T. 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
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