Tracking recurrence of correlation structure in neuronal recordings
Introduction
Brain states are hypothesized to provide snapshots of ongoing neural and functional dynamics across multiple temporal and spatial scales. Analysis of large-scale brain dynamics has revealed that such patterns occur during a resting state (default mode), forming a complex network across regions (Greicius et al., 2003, Greicius et al., 2009, Hebb, 2002, von der Malsburg, 1981, Allen et al., 2012, Chen et al., 2013, Lu et al., 2007). Considerable research has been performed at the macroscale using fMRI to determine these recurring connectivity patterns and their relation to cognitive function (Gilbert and Sigman, 2007, Hagmann et al., 2008, Lungarella and Sporns, 2006, Sporns and Zwi, 2004) and to disease (de Haan et al., 2012, Kühn and Gallinat, 2013, Moncrieff and Cohen, 2006, Uddin et al., 2014). Oscillatory states provide one set of operational modes which occur in thalamocortical and hippocampal systems at multiple spatial (microcircuit to brain area) and temporal scales (millisecond to minutes) (Buzsáki, 2010, Palva and Palva, 2011). Understanding the signatures and origins of these modes will form a bridge from micro- to macro-scale brain states (Colgin et al., 2009, Schomburg et al., 2014, Fukushima et al., 2012, Hunter et al., 2006, Kumar et al., 2013, Schroeder and Lakatos, 2012). Evaluating the expression of the different brain states will also enable a deeper understanding of the strategies the brain uses to perform cognitive computations – the brain's coding languages (Treisman, 1996, von der Malsburg, 1995). New techniques for high dimensional neural system evaluation will become increasingly important as new micro and macro imaging methods are developed under the auspices of the U.S. BRAIN (Brain Research through Advancing Innovative Neurotechnologies) project and related projects elsewhere in the world (Bargmann et al., 2014).
In addition to the macro level, analysis of neural systems is also done at the level of neuronal ensemble through spike-train analysis, and at the meso level through analysis of local field potentials (LFPs). At the lower levels, most previous work on neuronal spiking activity has used measures of similarity of spike patterns of single neurons in different contexts (Fellous et al., 2004). Other work includes determining the correlation of smoothed ensemble population firing vectors during distinct behavioral states such as sleep, run and rest, at behaviorally relevant time-scales. However, these methods do not take into account the single cell or local area correlation structure across ensembles (Gothard et al., 1996, Kelemen and Fenton, 2013, Louie and Wilson, 2001). Other work that does include assessment of ensemble correlation structure and dynamics in different behavioral states (Song et al., 2009, Song et al., 2015, Chan et al., 2011), does not include visualization techniques that help interpret how the correlation structure recurs over time (Kudrimoti et al., 1999).
We propose a new method which enables tracking how the correlation structure of neuronal ensembles changes over time. Our method, Population Coordination, PCo, facilitates visualizing the recurrence of correlation structure of neuronal ensembles. PCo is intrinsically a multiscale measure in the temporal domain since it looks at recurrence at a high time scale of a spatiotemporal pattern measured at one or more shorter time scales. PCo is tunable to allow choice of view at faster or slower time scales. It is also applicable to data recorded at different spatial scales, from ensembles of single cells or multi-site LFP recordings, as shown here, on up to larger scale recordings using EEG or other measures. Measures from different scales could also be combined. In this study, we develop the PCo method and show how it may be used to determine correlation structure in different experimental conditions. We use PCo on two databases of electrophysiological data: hippocampal place cell data and multi-site LFP activity. We demonstrate the usefulness of PCo in identifying and following brain states.
Section snippets
Place cell electrophysiology
Adult male LongEvans hooded rats were obtained from a commercial breeder (Taconic Farms). The rats were 350–400 g at the start of training. Two recording environments were used (Fenton et al., 2008). One was a standard apparatus for place cell recordings. It was a 68-cm-diameter gray cylinder with a polarizing card on the wall that occupied 90° of arc. The other apparatus was a 150 cm × 140 cm chamber with stairs on three sides. The rat could traverse the stairs to access two drinking spouts. One
Recurrence of correlation structure
Population Coordination (PCo) quantifies repetitive Population Correlation (PCorr) activity structure at multiple locations, allowing for intuitive display of temporal recurrence of specific correlation structure patterns.
We start by describing the formation of the PCorr vectors, itself a multistep process (Fig. 1). Brain Activity vectors (AVs) will either reflect local area activity (from local field potentials – LFPs), or can be formed by binning individual single-unit recordings. In Fig. 1a,
Discussion
We developed a technique for measuring the recurrence of neural correlation structure over time, applicable to data recorded from multiple spatial scales of the brain (neuronal ensembles, local field potentials, EEG). The method, PCo, evaluates continuous signals, EEG or LFP, but can be readily adapted to look at spike trains by using binning or other methods to create a piecewise continuous signal. The multiple potential uses of PCo suggest that it may become a useful tool to facilitate
Acknowledgements
Supported by grants from the Simons Foundation (294388), and National Institutes of Health: R01EB022903; R01MH084038; R01MH099128; R01MH086638; R42NS064474; U01EB017695.
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