The asynchronous state's relation to large-scale potentials in cortex

Abstract

Understanding the relation between large-scale potentials (M/EEG) and their underlying neural activity can improve the precision of research and clinical diagnosis. Recent insights into cortical dynamics highlighted a state of strongly reduced spike count correlations, termed the asynchronous state (AS). The AS has received considerable attention from experimenters and theorists alike, regarding its implications for cortical dynamics and coding of information. However, how reconcilable are these vanishing correlations in the AS with large-scale potentials such as M/EEG observed in most experiments? Typically the latter are assumed to be based on underlying correlations in activity, in particular between subthreshold potentials. We survey the occurrence of the AS across brain states, regions, and layers and argue for a reconciliation of this seeming disparity: large-scale potentials are either observed, first, at transitions between cortical activity states, which entail transient changes in population firing rate, as well as during the AS, and, second, on the basis of sufficiently large, asynchronous populations that only need to exhibit weak correlations in activity. Cells with no or little spiking activity can contribute to large-scale potentials via their subthreshold currents, while they do not contribute to the estimation of spiking correlations, defining the AS. Furthermore, third, the AS occurs only within particular cortical regions and layers associated with the currently selected modality, allowing for correlations at other times and between other areas and layers.

INTRODUCTION

The brain performs a wide range of functions across a variety of states of alertness, ranging from deep sleep to passive and active performance. These functions are enabled and constrained by the dynamics of the underlying networks. In recent years, theoretical and experimental studies have highlighted a cortical network state of strongly reduced spiking correlations, which has been termed the asynchronous state (AS) (Ecker et al. 2010, 2014; Renart et al. 2010; van Vreeswijk and Sompolinsky 1996).

The AS is predominantly present during awake or active sensation, suggesting a particular importance in relation to cognitive functions. While the detailed properties and computational significance of the AS are currently under intense investigation (Beaman et al. 2017; Doiron et al. 2016; Nandy et al. 2019; Ostojic 2014; Rosenbaum et al. 2017), we focus on a different question: How is the AS compatible with the potentials observed in large-scale recording methods, in particular in humans? (Fig. 1)

Fig. 1.

Electrical activity during the asynchronous state appears inconsistent between the local and the global level. When electrical activity is recorded both on the local, i.e., neural spiking, and the global level, e.g., EEG (left), substantial potentials are observed on the large scale (right top), while on the local scale cortex is in a state of low synchrony (right bottom), the asynchronous state (AS), in particular during stimulation. To understand how these concurrent electrical activities are consistent, one needs to detail the conditions under which an activity on the microlevel translates to a potential on the macrolevel.

Large-scale, electrical recording methods, i.e., electro- (EEG) and magnetoencephalography (MEG), allow noninvasive access to fast brain signals and have become indispensable tools in human cognitive research and medical diagnosis. Since the M/EEG sensors are placed distant from the neural sources, the interpretation of M/EEG signals is limited by mixing of different neural sources and noise. As a consequence, M/EEG potentials, e.g., event-related potentials (ERPs), large-scale scalp topographies, and interregional synchronization, correspond to sufficiently synchronous coactivations of relatively large neural groups. Many specific data analysis methods have been developed to interpret such data (Cohen 2014; Makeig et al. 2004).

The AS, on the other hand, has been investigated using mostly small-scale methods, i.e., local electrode recordings, which allow access to the correlations between neurons. Since there are only few studies that recorded simultaneously on the small scale and large scale (Crochet and Petersen 2006; Poulet and Petersen 2008; Whittingstall and Logothetis 2009), the correspondence between electrical signals on the small and large scale has remained incompletely understood.

Here, we focus on the particular question, whether the occurrence of the AS is compatible with the concurrent presence of large-scale potentials (Fig. 1). Addressing this question is highly relevant for both neuroscientists and clinicians interested in bridging levels of scale of brain activity. In particular, it would allow us to infer the underlying type of brain activity from noninvasive EEG recordings, which carries substantial diagnostic value for patients and neuropsychologists.

To resolve this, many important details about when, where, and how strongly the AS is expressed in cortex need to be addressed. The AS is defined as a state with very low noise correlation in the number of spikes (“spike count”) between neurons (as commonly done in the recent literature, e.g., Ostojic 2014; Renart et al. 2010; Tan et al. 2014). Spike count correlations are a way to quantify correlated trial-to-trial response variability between two neurons. Large-scale potentials are defined as those that can be reliably identified in EEG, in particular ERPs and narrowband activity (see large-scale electrical potentials in m/eeg), which both require some level of neuronal correlation to be visible on the EEG level. In particular, we hence ask if the AS and large-scale potentials cooccur [e.g., the presentation of a simple visual stimulus (Tan et al. 2014)], what are the specific conditions that make them compatible (e.g., that the AS is not completely void of correlations and would thus prevent any large-scale potentials). Because few studies have simultaneously recorded on local and global scales (Crochet and Petersen 2006; Poulet and Petersen 2008; Whittingstall and Logothetis 2009), the review is largely based on studies that have either recorded from one or the other level but under comparable conditions.

Our critical survey of the literature suggests a resolution for this question: we propose that classical M/EEG potentials correspond either to, first, transitions between states on the neural population level accompanied by transient changes in population firing rate (which often correspond to stimulation) or to, second, large-scale integration of weakly correlated synaptic currents. Third, the AS is a local property that only occurs under particular circumstances at the activated modality, potentially even restricted to a few layers, and hence does not prohibit correlations with or in other areas. After a brief introduction to large-scale recordings, we first review the current knowledge about the AS, recapitulate when and where it occurs, and arrive at the above hypotheses guided by recent work on relating small- and large-scale potentials.

LARGE-SCALE ELECTRICAL POTENTIALS IN M/EEG

There exists a long history of recording the electrical activity of the brain noninvasively using electrodes placed on the skull (Fig. 1, left, blue), known as electroencephalography (EEG). Early studies were already able to identify large-scale potentials with particular temporal/spatial structure, e.g., the slow α-rhythm in the occipital region during eye-closure, etc. (Cantero et al. 1999). These large-scale potentials reflect the composite activity of the underlying neuronal activity, both sub- and suprathreshold (which will be detailed below specifically in relation to the AS). Both nearby and distant brain areas contribute to the potential at each skull location due to spatial summation (Cohen 2014).

Modern EEG systems feature up to hundreds of electrodes and can thus provide a detailed sampling of the potential on the skull. The recorded signal is multidimensional and carries information about time, space, and frequency of activation. However, due to the summation mentioned above, the effective spatial precision of EEG remains low, also due to the distortion and attenuation of the tissues surrounding the brain. However, since EEG is a direct measure of the electric field, its temporal resolution is high.

Magnetoencephalography (MEG), measuring the brain's magnetic field from the skull, has been enabled by the advent of sensitive magnetometers (Cohen 1972). MEG provides advantages in spatial selectivity but otherwise shares a lot of characteristics with EEG in terms of signal content and temporal resolution.

Presently, we focus on the kind of large-scale potentials that have been at the center of attention of M/EEG research in the past decades, namely, 1) those evoked by stimulation or movement initiation, so-called event-related potentials (ERPs), and 2) narrowband activity, i.e., particular frequencies in the activity.

Our treatment ignores unsystematic/nuisance potentials of nonneural origins, such as muscular activity (e.g., from eye movements) or general noise.

We also do not go into details regarding local field potential (LFP), i.e., the summed electrical potential of neurons that can be measured locally inside the brain, since it can only be obtained using invasive techniques and should be considered medium-scale given a typical contribution range of 0.2–3 mm (Katzner et al. 2009; Kreiman et al. 2006; Lindén et al. 2011). Being a medium-scale measure of the neural activity, LFP carries more fine-grained information than M/EEG signals (Pesaran et al. 2018) but comes with its own set of limitations and complications that warrant a separate treatment (Hadjipapas et al. 2015; Haider et al. 2016; Herreras 2016; Musall et al. 2014; Poulet and Petersen 2008). Mainly, however, we wanted to keep the presentation concise and relevant for users of noninvasive measures.

While M/EEG potentials reflect the underlying neuronal activity, they can in principle also influence the neural activity in turn, often referred to as ephaptic coupling. However, recent studies have suggested that the expected effect would be an increase in entrainment/correlation (Anastassiou et al. 2011). Since the opposite is observed in the AS, ephaptic coupling does not appear to have a causal role in the generation of the AS and is thus not treated here.

THE ASYNCHRONOUS STATE: THEORY AND EXPERIMENTAL FINDINGS

Correlations in the activity between neurons have long been identified as a potential, powerful principle of neural information coding (Averbeck et al. 2006; Pouget et al. 2000). However, recent studies have found that, in particular during active processing, the activity of certain neurons in cortex decorrelates. More specifically, the average correlation between neurons can approach vanishingly low values on the order of ~0.01 (Ecker et al. 2010; Renart et al. 2010; Shadlen and Newsome 1998). This has been termed the “asynchronous state” (AS) of cortical population activity and has attracted considerable attention as a characteristic property of active, cortical processing. Importantly, the correlations addressed here are those that remain after accounting for the effects of activation by stimuli (“signal correlations”) or global modulations in firing rate (Ecker et al. 2014). Intuitively, these are usually thought of as “network correlations,” i.e., arising from the local connectivity. They can be modulated by bottom-up or top-down inputs and intrinsic network dynamics. The AS has been predicted in theoretical studies (Fig. 2, B and C) (Renart et al. 2010; van Vreeswijk and Sompolinsky 1996; Wang 2010; Ostojic 2014) and was confirmed in several experimental studies (Fig. 2C) in both cortical (Averbeck and Lee 2004; Downer et al. 2015; Ecker et al. 2010; Ly et al. 2012; Miura et al. 2012; Renart et al. 2010; Ruff and Cohen 2016; Vinck et al. 2015) and some subcortical areas (Nevet et al. 2007).

Fig. 2.

The asynchronous state in cortical networks A: cortical networks can desynchronize under different conditions, e.g., under sensory stimulation. Presentation of a stimulus (“A”) leads to a thalamic (black) activation, which in turn activates excitatory (red) and inhibitory (blue) cells in cortical areas such as, e.g., the visual cortex. The local decorrelation has been attributed to a recurrent interaction of excitatory and inhibitory populations of neurons, receiving common thalamic input. Right: principles that govern this decorrelation can be described by a feedback loop, driven by the thalamic input, with recurrent interactions that contribute to stabilizing the loop (modified from Renart et al. 2010). Thalamic inputs establish the (anti-)correlation between excitatory and inhibitory currents received by cells in the network. Tracking of excitation by inhibition leads to cancellation of currents, which decorrelates the overall currents in the network. The resulting asynchronous currents lead to even more decorrelated firing. Residual correlations in rate are amplified by synaptic integration and contribute to the current correlations but also depend on a neuron's particular connectivity. B: in the asynchronous state (AS), excitatory (E, red), and inhibitory (I, blue) synaptic currents closely track each other, with inhibition delayed by only a few milliseconds. Hence, excitatory and inhibitory currents largely cancel, keeping the membrane potential (V_m) close to threshold (top; adapted from Denève and Machens 2016). Precise spike times are determined by input fluctuations and differ between neurons (bottom, 2 sample traces from different neurons). C: the resulting correlation in firing rate between neuron pairs is distributed around a very low average value, as evidenced by theoretical and experimental findings [left, model (Renart et al. 2010); right, V1 (Ecker et al. 2010)].

Several interpretations have been provided for the usefulness of this decorrelation, ranging from unbiased decoding (Abbott and Dayan 1999) and rapid tracking (van Vreeswijk and Sompolinsky 1996) to efficient coding (Denève and Machens 2016). While the functional relevance of the AS is a current and exciting research topic, the focus here is on the question of how the AS relates to large-scale potentials, which can be measured simultaneously in M/EEG.

Over the past decades, experimental research has provided insights into the neural basis of the AS, guided by multiple theoretical studies: cortical processing, regardless of brain and behavioral state, is regulated by a dynamic interplay between excitatory and inhibitory neurons (Shadlen and Newsome 1994). On a basic level, recurrent inhibition can prevent an escalation of activity in a network. In fact, excitation and inhibition are attuned more finely, often balancing each other quantitatively at the millisecond time scale (Crochet and Petersen 2006; Gentet et al. 2010; Poulet and Petersen 2008; Renart et al. 2010; Wehr and Zador 2003) across brain states (Dehghani et al. 2016) (Fig. 2). This has been termed the “E/I balance” [note, however, that both excitatory (Abbott and van Vreeswijk 1993) and inhibitory (Brunel and Hakim 1999) networks are themselves capable of rich dynamics under certain assumptions]. Recent theoretical work suggests that the precision of the E/I balance is less crucial than originally assumed and inhibitory feedback can be sufficient to achieve decorrelation (Tetzlaff et al. 2012).

The mechanism by which the E/I balance leads to decorrelation can be sketched as follows: excitatory and inhibitory neurons are driven by their common input (e.g., from the thalamus, Fig. 2A, left/middle) to covary in their response rate. On average, both neural populations thus coactivate on a fine time scale. The resulting excitatory-inhibitory input onto other neurons therefore cancels on average, leading to a membrane potential near the neuron's threshold (Poulet et al. 2012; Tan et al. 2014). This is a consequence of a high synaptic conductance with an average reversal potential close to the neuron's threshold. Spikes are mostly elicited based on input current fluctuations, which differ across neurons and therefore occur decorrelated (steps illustrated in Fig. 2A, right) (Renart et al. 2010). “Decorrelation” refers here to a reduction in coactivation of pairs or ensembles of neurons. Hence, this process of decorrelation is not externally enforced but only triggered (e.g., by a change in the stimulus) and reflects a dynamical process intrinsic to the network.

In conclusion, cortical networks appear to have a built-in mechanism to decorrelate their activity, in particular during active processing. On the other hand, the existence of large-scale potentials requires some level of neuronal synchronization. It hence comes, at first sight, as a surprise that human M/EEG research, typically conducted in the awake/active state, regularly finds evoked and oscillatory potentials. To gain insight into their coexistence, we first review how general the AS is across cortex and across time in prevalence of the asynchronous state in cortex and neural population activity and the organism's state.

PREVALENCE OF THE ASYNCHRONOUS STATE IN CORTEX

The recent emphasis on the AS in cortical research is warranted given the hypothesized implications for neural coding and the general understanding of cortical dynamics. However, as often the case in biology, the situation is less unified than it initially appears. Here, we first detail some limitations on how prevalent the AS actually is in cortex and how closely the AS, in its pure form, matches the experimental data. In neural population activity and the organism's state, we then focus on when, i.e., in which states of activity, it occurs.

First, the term asynchronous state may be considered slightly misleading: while there is general consensus about a local decorrelation in the AS, the level of residual correlation appears to be influenced by the preparation and the task, ranging from 0.01 to 0.25 (see table in Cohen and Kohn 2011).

Second, the amount of correlation varies with both cortical depth and location. As a function of the depth, neurons in the granular layer (layer 4) appear to be least correlated, while supra (layer 2/3)- and infragranular layers (layer 5 and 6) exhibit relatively larger covariation during the anesthetized [~0.05 (Hansen et al. 2012; Smith et al. 2013)] and awake state [~0.25, (Hansen et al. 2012; Smith et al. 2013)]. Cortical location also has an important influence: most studies of the AS have been conducted in lower and higher sensory cortexes, hence, the picture is not complete. AS seems to be most prominent in areas associated with the current task, e.g., in barrel cortex during whisking (Poulet and Petersen 2008), in visual cortex during visual presentation (Ecker et al. 2010), and in auditory cortex during acoustic presentation (Renart et al. 2010). While a recent, unpublished study (Jacobs et al. 2018) suggests that the decorrelation does not remain very local, it also indicates that is does not become completely global either.

Third, the degree of decorrelation may depend on the tuning properties of coactivated cells under certain conditions. While previous studies (Ecker et al. 2010; Poulet and Petersen 2008 suggested that both similarly and differently tuned cells show low correlation during activation (stimulation/whisking), a recent study (Verhoef and Maunsell 2017) showed that for unattended, competitive stimulus presentations, decorrelation occurs for oppositely tuned cells but not for similarly tuned cells. This suggests that the current models are not complete regarding their description of the conditions leading to the AS in relation to cellular tuning.

Fourth, correlations during the AS (i.e., arising from intrinsic network dynamics) may be minimal, while concurrently spike count correlations from shared, global variations in activity may persist. This possibility was raised by Ecker et al. (2014), using a low-dimensional process to account for shared fluctuations between all recorded neurons. The remaining activity is then left nearly asynchronous, which aligns with previous results (Ecker et al. 2010; Renart et al. 2010). This suggests that the correlations observed in multiple previous studies (Cohen and Kohn 2011) could at least be partially explainable by global variations in firing rate. This raises the important. and to our knowledge unresolved. question of how cortex selects which correlations to remove and which ones to maintain. Given the implications of correlations for coding of information, maintaining certain correlations may be essential (see Averbeck et al. 2006 for details on the effect of positive and negative correlations on coding capacity). Relating to the topic of this review, the potentially different sources of correlation indicate that even for studies that reported decorrelation (after accounting for shared fluctuations), certain shared fluctuations may have been concurrently present, which can be the source for large-scale potentials.

Fifth, most theoretical studies have assumed a simplified model of cortex, usually with just a single excitatory and inhibitory population, no spatial dependence of connectivity, simplified neuronal dynamics, and random connectivity. While these models are important in highlighting general, sufficient boundary conditions for the AS, they may fall short in accounting for the details. Recent work has started to address these problems by introducing spatial and layer differences (Rosenbaum et al. 2017) and specific connectivity structures (Litwin-Kumar and Doiron 2012; Mastrogiuseppe and Ostojic 2018). A study of particular interest recently indicated that the global, shared variability (see previous paragraph) can be created from inside the network and may thus not always constitute top-down modulation (Huang et al. 2019).

Sixth, decorrelation on the local level does not necessitate the disappearance of all correlated activity for larger populations: for example, oscillations are measured in large-scale potentials in several frequency bands, during sensory stimulation, of special interest is the γ-frequency range (30–80 Hz, for review, see Fries 2009). Theoretically these γ-oscillations can coexist with the AS: large E/I networks can exhibit γ-band oscillatory activity, while small groups of neurons may appear to discharge irregularly (Brunel 2000; Brunel and Wang 2003). However, the exact relation between the AS and the occurrence of oscillations remains unresolved (Harris and Thiele 2011), especially in empirical studies, which find contradictory results depending on the stimulated region and species. Based on the number of neurons recorded and the length of the time window used for computing correlations, these oscillations may have been missed in empirical studies. Partial, rather weak relations have been established between population activity and large scale potentials, e.g., between firing rate and δ-phase and γ-amplitude (Mazzoni et al. 2010; Whittingstall and Logothetis 2009).

Lastly, fine differences in analysis between studies can lead to diverging values, e.g., the time scale over which this covariation is experimentally assessed can influence the observed absolute level of correlation (Cohen and Kohn 2011).

In summary, the AS is not as general as parts of the literature may suggest, being limited spatially and in relation to the neurons tuning as well as being overlaid with global variations in activity. These observations and considerations constrain and further specify our proposals to link phenomena such as and large scales that are present at different levels of organization.

NEURAL POPULATION ACTIVITY AND THE ORGANISM'S STATE

In approaching the central question of how the AS is related to the large-scale potentials, it is useful to survey different organismal states where neural activity is routinely measured across different scales. Cortical populations exhibit many patterns of coactivation depending on the organism's cognitive state (Steriade et al. 2001), ranging from transient synchrony to nearly asynchronous firing in the AS. As the cognitive state changes frequently under both experimental and real-world conditions, cortical activity regularly transitions into and out of the AS.

Recent studies have shown that changes in brain state are accompanied by changes in the E/I balance and generate different modes of activity in the brain (Bennett et al. 2013; Zhou et al. 2014). In particular the spatiotemporal firing patterns of interneuron subtypes are highly brain state dependent (Kepecs and Fishell 2014; Klausberger et al. 2003). The shift in E/I balance has also been suggested to control the AS (Treviño 2016) and thereby the transitions.

As detailed below, the AS is mainly observed during stimulated and active states, which are the most typical states in experiments, in particular as a consequence of stimulus presentation. In this section, we first describe the observed relationship between the cognitive and cortical states. In the neural basis for large-scale potentials in the asynchronous state, we then propose several accounts of how the AS and large-scale potentials can coexist.

Sleep

The most synchronous end of the network activity spectrum is observed during sleep (Fig. 3A), in particular during non-REM, slow-wave sleep, which is classically characterized by slow (0.5 to 4.0 Hz), synchronized, oscillatory neocortical activity (Greene and Frank 2010). The most notable aspect of slow-wave sleep is the <1 Hz slow-wave (SW) oscillation. The SW has been proposed to coordinate other oscillations (Poulet and Petersen 2008; Steriade et al. 1993a, 1993c). The SW oscillation creates a bistable situation where neurons collectively switch between a relatively depolarized Up state and a hyperpolarized, low-spiking Down state (Haider and McCormick 2009; Harris and Thiele 2011; McCormick et al. 2015; Neske 2016; Poulet and Petersen 2008; Sanchez-Vives and McCormick 2000).

Fig. 3.

Different activity states induce patterns of neural population activity reflected in large-scale potentials. A: during sleep the population activity (A3) frequently cycles through Up and Down states causing large fluctuations in spiking activity. A2: in EEG this leads to strong rhythmic waves, between 0.1 and 12 Hz representing spindles, k-complexes, and δ-waves. A4: on a local network level, relatively high spike count correlations are measured. In this schematic, the depicted gray scale indicates the level of local correlation, i.e., between closely neurons, across the cortex: while there is variability in the level of local correlation, the overall level is higher than in the cases of quiet wakefulness and activity/stimulation. B3: during quiet wakefulness, synchronized and desynchronized activity alternate more frequently. B2: in EEG, this leads to the occurrence of intermittent large scale potentials, e.g., δ-activity increases during eye closure. B4: the local spike count correlations will hence be lower on average, i.e., indicated here by a lighter gray. C: curing active behavior and stimulus processing, the activated areas in cortex desynchronize locally. C2 and C3: this is signified by a decrease in EEG variance (note that on single trials the stimulus-evoked EEG response may be difficult to disentangle from noise) (C2) as well as by continued, desynchronized spiking between cells in the local population (C3). The desynchronization occurs predominantly in areas associated with the current processing (indicated in white), e.g., here visual areas, while the correlation level within other areas may stay similar as in the inactive/unstimulated case. ERP, event-related potential. C4: furthermore, interarea correlations (arrows) within the modality between coactivated regions can in fact increase [e.g., V1 and MT during motion processing (Ruff and Cohen 2016)]. Data in A2, B2, and C2 were provided by U. Gorska. Population activity (A3, B3, and C3) was modified from Mochol et al. (2015). Noise correlation plots (A4, B4, and C4) are cartoons and do not depict actual recordings.

Up states are primarily initiated in L5 of the cortex (Sanchez-Vives and McCormick 2000); however, L2/3 also contributes (Hughes and Crunelli 2013; McCormick et al. 2015). Furthermore, sleep spindles initiated during thalamic down states contribute to the Up state (Mak-McCully et al. 2017). Spatially, the Up state either propagates through cortex as a wave or remains localized, e.g., in a column of barrel cortex (Petersen et al. 2003).

Down states have also been hypothesized to be initiated in cortex. Initially, this was thought to be due to local disfacilitation periods in cortex (Steriade et al. 1993b), denoted as k-complexes in the EEG literature (Mak-McCully et al. 2015). During the Down states early work indicated that both inhibitory and excitatory neurons are silent (Timofeev et al. 2001). However, more recently it was shown that parvalbumin (PV) interneurons can be active during the Down state (Ushimaru and Kawaguchi 2015; Zucca et al. 2017) and play a role in controlling the duration of the Down state. Furthermore, there is strong evidence that the thalamus controls SW activity through careful modulation of the E/I balance (Gent et al. 2018; McCormick et al. 2015; Steriade et al. 1993a; Urbain et al. 2019), e.g., the PV interneurons (which control the duration of the Down state) are controlled by neurons in the ventral posteromedial nucleus (Zucca et al. 2019).

The collective switching between the Up and Down states leads to an elevated spike count correlation under anesthesia (Cohen and Kohn 2011) and during naturally occurring slow-wave sleep (Issa and Wang 2013). High spike count correlations (~0.1, compared with ~0.01 during the active state) have been shown to extend multiple (~3.6) millimeters in sleeping humans (Peyrache et al. 2012). To our knowledge no corresponding studies are available in awake/active humans.

On the EEG level, these periods of cortical synchronization translate to well-studied, large-scale scalp-level activations. During the N3 phase of non-REM sleep, predominant δ-waves can be measured on the scalp (Silber et al. 2007), resulting from alternating Up and Down states (Steriade 2003). During the N2 stage of non-REM sleep, a characteristic EEG structure is the K-complex, which has been shown to correspond to an isolated Down state (Cash et al. 2009) (Fig. 3A3). Another characteristic feature of N2 sleep is the presence of sleep spindles, brief bursts of oscillatory activity at ~12–16 Hz with waxing and waning amplitude (Andrillon et al. 2011; Fogel et al. 2007; Zeithofer et al. 1997) (Fig. 3A3). By contrast, the classical EEG profile of REM sleep is similar to that of the awake state, exhibiting cortical activation and desynchronization (Platt and Riedel 2011).

Hence, the high degree of neural synchronization during certain sleep phases translates to the expectable large-scale potentials with conserved frequency content, while a state similar to the AS has only been reported known for REM sleep.

Quiet Wakefulness

Cortical function has traditionally been studied using either stimulation or during active behavior. However, the activity during the resting state is also spatially and temporally structured at multiple scales (Fig. 3B). M/EEG recordings from awake, resting subjects are dominated by low frequency signals (~10 Hz). With eyes closed or without task engagement, α-oscillations are prominent and indicative of internally generated inhibition of sensory areas during mental operations (Cooper et al. 2003; Klimesch et al. 2007). At the whole brain level, functional (f)MRI studies identified a set of networks that are temporally correlated at slow timescales (<0.1 Hz) in passively resting macaques (Schölvinck et al. 2010). The synchronized states generate distinct topographies on the EEG level, which are not locked to external events and can therefore be missed due to the overall noise. EEG microstates have been identified, which may be signatures of recurring, stereotypic synchronization patterns (Khanna et al. 2015). However, the state of quiet wakefulness is not uniform and can exhibit different dynamics. Eye opening or task preparation can result in global desynchronization of α-rhythms, reminiscent of the stimulated state (see Stimulated and Active States), accompanied by more local changes in other frequency bands (Barry et al. 2007, 2009).

At the single cell level, the quiet awake state is characterized by strong correlations between nearby neurons at frequencies <10 Hz. Over time, cortical regions fluctuate between relatively synchronized and desynchronized states, suggesting ongoing top-down processes that control arousal (Reimer et al. 2014) (Fig. 3B4). Collective transitions into quiescence have recently been identified to underlie synchronizing events (Mochol et al. 2015). This suggests that neural activity during quiet wakefulness varies from relatively synchronized to desynchronized states depending on the current cognitive state.

Stimulated and Active States

If an awake animal receives a stimulus or starts to move, certain cortical networks desynchronize (Fig. 3C), as demonstrated both extracellularly (Ecker et al. 2010; Pfurtscheller and Lopes da Silva 1999) and intracellularly (Poulet and Petersen 2008; Tan et al. 2014). Depending on the paradigm, passive (Ecker et al. 2010) or active (Downer et al. 2015) stimulus processing or just a shift in attention under constant stimulation (Mitchell et al. 2009) is sufficient for desynchronization. Furthermore, arousal alone can drive cortical activity toward the AS (Vinck et al. 2015). As indicated in Quiet Wakefulness, this desynchronization may be restricted to the granular layers (Hansen et al. 2012; Smith et al. 2013). Hence, cortical networks desynchronize when processing is related to their modality (Fig. 3C2), which has been hypothesized to improve the signal-to-noise ratio for decoding (Abbott and Dayan 1999; Averbeck et al. 2006). During this active AS, adaptation can be low, e.g., repetitive, similar tactile stimuli during active exploration continued to elicit responses (Crochet and Petersen 2006).

On the M/EEG level, early processing of a stimulus is marked by ERP/event-related field). These commonly studied and relatively stable potentials occur locked to the stimulus (onset) and have a modality-specific shape. ERPs appear at first sight paradoxical with the AS, since the decorrelation in this state should not lead to large global potentials. However, the AS is not established immediately on the population level but only after a brief, correlated increase in firing rate (see Fig. 4, D and E, and the neural basis for large-scale potentials in the asynchronous state), which forms the basis of the ERP.

Fig. 4.

Large-scale signals in the asynchronous state. A: only certain neuronal morphologies produce detectable large-scale potentials, e.g., cells with elongated, aligned dendrites generate dipoles that sum constructively at distant electrodes. B: cells with less elongated, nonaligned dendrites create weak potentials, since their contributions mostly cancel. C: both subthreshold and spiking currents of spatially aligned neurons sum to generate large-scale potentials, accessible by M/EEG recordings. The effective size of this potential (vertical axis) increases with network size and the level of correlation between the cells (Hagen et al. 2016; Renart et al. 2010; see text for mathematical details). In the asynchronous state (AS), the correlation of spiking and currents are a function of the network size, shown as lines in the (correlation × network size) plane (based on Hagen et al. 2016; Renart et al. 2010) (Fig. 2C). In the AS, the level of correlation of subthreshold currents (maroon) exceeds that of spiking (orange) for all network sizes. Correspondingly, subthreshold currents make a relatively larger contribution to the overall potential, in particular for large network sizes. D: when global (M/EEG, black solid line) and local (spikes/rate, red solid line) activities are directly compared, strong variations in firing rate due to stimulation are reflected in transient potentials in the EEG, but additional large-scale potentials exist after the onsets (orange, added based on the stimulus timing). After the onsets, the activity appears to desynchronize (blue overlay), until the next change in the stimulus. E: large-scale potentials arise based on different types of low-level coactivation: outside the AS, spike synchronization leads to well-correlated synaptic currents. As cortex transitions into the AS, e.g., as the behavioral state changes from passive-awake to passive-stimulated and/or active, firing rates are initially correlated before desynchronizing. During the AS, weakly correlated currents translate to large-scale potentials due to their scaling with population-size (C). Since the AS is local, correlations with or in other areas also contribute to large-scale potentials in colocalized M/EEG sensors.

During continued, constant stimulus presentation, strong phase-locked potentials are mostly absent in the local EEG, consistent with the underlying local desynchronization (Crone et al. 1998; Pfurtscheller and Lopes da Silva 1999) (Fig. 3C3). Depending on the area, an increase in γ-power is observed (Bauer et al. 2006; Fries 2009; Harris and Thiele 2011), which could reflect a combination of local, temporal coordination, and nonlocal correlations between different cortical areas (Ruff and Cohen 2016; Womelsdorf and Fries 2007). Due to the prominent involvement of top-down processes, β-band oscillations seem to dominate (Engel and Fries 2010; Freeman 2004; Kühn et al. 2004). They are assumed to mediate long-range synchronization (Freeman 2004) but also desynchronize with the initialization of movements (Kühn et al. 2004). As mentioned above, global correlations can remain, which are not completely removed by the intracortical dynamics, which recent studies are only starting to address (Huang et al. 2019; see the Prevalence of the AS in Cortex).

Despite its prevalence in the engaged state, the AS is not the only brain state present during active processing (see Poulet and Crochet 2019 for a detailed review). Originally, cortical activation was thought to drive a single active state marked by a decrease in low-frequency EEG. However, recent studies show a spectrum of states of brain activity whose properties are context dependent (Crochet et al. 2019; Shimaoka et al. 2018). Cortical states seem to be goal-modulated and differ for particular tasks and stimuli. In particular, locomotion (Ayaz et al. 2019; Fernandez et al. 2017; Shimaoka et al. 2018) and arousal (Reimer et al. 2014; Vinck et al. 2015) seem to be distinct, driving modulators of the active state throughout the cortex. Furthermore, brain states are not always expressed globally but can also arise locally (Fernandez et al. 2017; Vyazovskiy et al. 2011).

In summary, during the active state, local and active desynchronization coexists with increased synchronization between different cortical areas. The net effect on the local EEG is an initial ERP followed by a reduction in variance, consistent with a local desynchronization when the AS is reached. Across all behavioral states, the AS is most prominently attained during stimulated, active or at least attending conditions, while it is rare during the sleep and only intermittent during quiet wakefulness.

THE NEURAL BASIS FOR LARGE-SCALE POTENTIALS IN THE ASYNCHRONOUS STATE

The relation between neural population activity and large-scale potentials, M/EEG, is physically governed by the laws of electromagnetism. However, due to the neural system's complexity, this relation is far from straightforward in practice. In particular, neuronal morphology, neural architecture, and activity dynamics shape the resulting, composite potentials.

Typically, elongated, asymmetric cells can create electric dipoles, which, if arranged in parallel, create joint potentials that can be measured on the skull (Fig. 4, A and B). Synaptic currents are generally considered to be the main source of large-scale extracellular electrical potentials (but see Reimann et al. 2013; however, multiple sources contribute, e.g., calcium spikes, intrinsic currents, and also spiking activity itself (for review, see Buzsáki et al. 2012; Herreras 2016). Whether these individual contributions are observable in the M/EEG is unclear but is likely to depend on temporal coactivation. In the AS, the correlation in activation has been found to be near zero.

While there are not sufficiently many multiscale studies to conclusively settle this seeming inconsistency with the observed large-scale potentials during the AS, we propose a combination of the following three explanations, based on our analysis of the literature.

Transient Phase of Correlated Spiking Can Lead to Large-Scale Potentials, Even Without the Presence of Noise Correlations

For the creation of a large-scale potential, it is irrelevant whether the correlation between cells is stemming from noise- or signal correlations. Hence, if many neurons transiently modulate their rate, e.g., in response to a stimulus (Fig. 4E, left), even if this modulation is the same for repeated stimulation (i.e., which would be signal correlations; suggested also by the dominant reduction in network/noise variance at stimulus onset, see Fig. 6 in Churchland et al. 2010), then the individual potentials can add to potentials observable on the large scale. This has recently been demonstrated experimentally for tactile ERPs, with excitatory input currents underlying the P1 (and initial N1) wave, while inhibitory input currents constituting the N1 wave (Bruyns-Haylett et al. 2017). Combining parallel micro- and macroscale recordings, this was also suggested by the relative timing between the spatial scales in Whittingstall and Logothetis (2009). Similarly, large-scale cortical simulations also exhibit a transient rate modulation after stimulus onset, before the network settles into the AS (Hagen et al. 2016, their Fig. 1). Aside from external stimulation, population rates can also be modulated by low-dimensional top-down processes [which can be consistent with asynchronous activity after accounting for these rate modulations (Ecker et al. 2014)].

It is also noteworthy that the AS is not established immediately, e.g., in the auditory cortex Mochol et al. (2015) found this process to complete after ~50 ms (their Fig. 2D). While noise correlations thus continue to exist in this time window, these dynamics are unlikely to explain large-scale potentials, since the noise correlations do not increase beyond their prestimulation levels.

For static stimuli, the cortical firing rates may settle to a less-variable level with asynchronous firing, which leads to the absence of ERPs in the EEG. Dynamic stimuli can be considered as a repeated stimulus presentation, and therefore, transients in firing rate may again lead to observable large-scale potentials.

While the AS Is Identified in Terms of Near-Zero Spiking Correlations, Subthreshold Correlations Remain Relatively Strong and May Contribute to Large-Scale Potentials for Sufficiently Large Populations

Generally, large-scale potentials are more strongly determined by correlated than by uncorrelated activity, since uncorrelated activity will generate field potentials that cancel at the aggregate scale. During the AS the average correlation between neurons decreases to a very low level, whose concrete value has been predicted to depend on the population size (spikes: r ~ N⁻¹; subthreshold currents: r ~ N^−0.25; N: population size, r: correlation, see Renart et al. 2010, their Fig. 1C, replotted in our Fig. 4C, red). In a real, finite network, the average correlation hence should stay >0, surrounded by a wide distribution of positive and negative correlations.

On the other hand, correlations contribute to the large-scale potentials as ~ N² (Hagen et al. 2016; Fig. 4C, gray: effective potential). Hence, the predicted residual correlations in the AS remain strong enough to be detectable on the population level. In addition, the subthreshold currents decorrelate less strongly than spikes as a function of N (as predicted by their relative exponents), which supports the classical hypothesis that synaptic currents are the dominant contributors to large-scale potentials [although this has partially been challenged (Reimann et al. 2013)]. A study by Hagen et al. (2016) presented an analytical account for this relationship, which follows on previous work on asynchronous activity of cortical networks (Renart et al. 2010; Shadlen and Newsome 1998).

Generally, multiple experimental studies had already documented that correlations are typically stronger for subthreshold currents than for spiking, as a consequence of the correlation-transfer at the spiking threshold (de la Rocha et al. 2007; Dorn and Ringach 2003). However, the reasoning above rests largely on simulation results (e.g., Renart et al. 2010), since the dependence of correlations on population size is hard to verify experimentally. These simulations include multiple homogeneity assumptions regarding connectivity and cellular dynamics, and these assumptions may not hold except at the local level. Additional research is thus required to verify how well this generalizes to larger populations or cortical areas with their particular cellular composition and connectivity.

Another factor adds to the dominant contribution of subthreshold potentials in the AS: the vast majority of studies investigating the AS have been performed using extracellular electrodes. Only the spiking of active cells can be accessed reliably with this method, which introduces a sampling bias for cell types displaying high firing rates. While the “invisible,” nonspiking cells cannot be meaningfully included in the analysis of spiking activity (and thus the definition of the AS), this substantial set of cells may thus contribute to large-scale potentials via their (possibly correlated) subthreshold currents. As cells in the supragranular layers exhibit lower firing rates (de Kock et al. 2007), this bias may also help explain why it was only later realized that the AS is mainly restricted to L4 (Hansen et al. 2012; Smith et al. 2013).

Recently, a nonmonotonic, U-shaped relation was observed between spike count correlation and the corresponding oscillations in different EEG bands (Snyder et al. 2015), which suggests the existence of an intermediate range of correlation with substantial large-scale potentials, whose origin is unclear.

Hence, even small levels of correlation between currents and spikes present during the AS should remain observable in the M/EEG power spectrum, given a sufficiently large network.

Correlated Activity with or in Other Areas

The AS in cortex is not a global, but a local, phenomenon, restricted to the stimulated/activated modality [e.g., different sensory areas (Smith and Kohn 2008; Solomon et al. 2015)] and even particular layers (Smith et al. 2013), hence, allowing for correlations with or in other brain areas (Rosenbaum et al. 2017; Ruff and Cohen 2016) (Fig. 4E, right). As locally measured M/EEG potentials depend on a wide spatial range of sources, reaching over centimeters (Nunez and Srinivasan 2006), these nonlocal correlations can directly influence the local large-scale potential. Correlated activity arising from distant sources can provide another explanation for the difference between the levels of noise correlations across cortical layers (Hansen et al. 2012; Smith et al. 2013). Layers that have long-range projections tend to exhibit larger noise correlations, whereas cortical input layer 4, which has more local connectivity exhibits smaller noise correlation. Such a difference across layers at a local level might be translated into strong EEG signals distant from the source (Herreras 2016). Additionally, each neural source is registered simultaneously by multiple M/EEG sensors; thus on the scalp level local activity can appear as global correlations [which is known as an inverse problem and can be partially addressed by neural source analysis (Grech et al. 2008)].

In summary, transient variations in rate before the AS, large-scale integration of weak correlations and correlations with/in other areas could explain why microscale decorrelation does not translate into vanishing large-scale potentials in matched recording locations. While the large-scale integration of residually correlated synaptic currents may be considered as the most general explanation, the others highlight two essential properties of the AS, its locality and nonimmediate onset.

CONCLUSIONS

We argued that neural firing asynchrony observed during active processing can be reconciled with cooccurring large-scale potentials via 1) transient changes in population firing rate that occur at the transition between states, e.g., as a consequence of a stimulus presentation or internal, top-down triggered change in state; 2) the scaling properties of integration of correlated activity, which allow even small correlations in currents to amount for large populations; and 3) desynchronization as a rather local phenomenon does not preclude correlations in or with other areas. These three sources of large-scale potentials typically coexist and thus jointly contribute, while their respective timing will differ, e.g., source 1 will dominate at transitions between states, while sources 2 and 3 are most relevant during the AS. Generally, the AS is not the default state of cortex but is realized only under particular circumstances and in particular cortical regions and layers. Current work is further addressing the conditions and the degree to which the AS is realized (e.g., Baker et al. 2019).

While the exact relation between the scales is not fully understood, this provides more consistency between the scales outside and inside the AS and allows limited inference of underlying brain states and their transitions on the basis of large-scale signals. As mentioned after the introduction, LFPs were not covered here, to keep the presentation concise and relevant for clinical practitioners and neuroscientists working with M/EEG. However, LFPs clearly deserve their own treatment (e.g., Buzsáki et al. 2012; Herreras 2016), as their relation to the local spiking activity as well as the EEG is also interesting but nontrivial in itself. For instance, the local geometry of current sources has been proposed to contribute more to the LFP signal than the synchronization of those sources (Herreras 2016). Furthermore, even though LFP signals are more correlated with synaptic currents in the local neural populations, this correlation can change in a complex manner depending on the state of the animal (Haider et al. 2016) and does not translate into a linear relationship between spiking activity and LFP amplitude (Poulet and Petersen 2008). In addition, the relationship between LFP and M/EEG signals can be nonlinear (Hadjipapas et al. 2015), with M/EEG signal depending on the synchronization of current sources across large patches of cortex (Musall et al. 2014). This makes it harder to make general claims that apply to both M/EEG and LFP signals at the same time, which is why we choose to focus on the M/EEG literature.

Future experiments combining simultaneous, large-scale recordings on both the neuronal and scalp level could address these questions more directly, e.g., high-density laminar electrode arrays combined with scalp-wide EEG scalp recordings can be used to address the relative contributions of different cortical layers and subcortical structures both at the site of the local recordings but also across the scalp (extending previous work, e.g., Whittingstall and Logothetis 2009). In particular, the relation between large, weakly correlated populations and the spatial extent of the AS, and its relation to scalp-level potentials could be resolved using this combined recording technique. With the use of optogenetically identified neurons, the contribution of different cell types could be studied systematically (Beltramo et al. 2013). In particular, optogenetic activation would directly quantify the sub- and suprathreshold contributions of local activity at different degrees of correlation to the large-scale potentials across the scalp. Finally, local optogenetic stimulation of identified cell types could illuminate their respective contributions to the M/EEG potentials, similar to previous approaches addressing the basis of fMRI (Lee et al. 2010). Lastly, most of the studies conducted so far have used extracellular electrode recordings, which biases the sample toward more active neurons. Future experiments should expand toward optical recordings at multiple layers, to estimate the neuronal contributions in an unbiased way.

The suggested approaches would complement the recent surge in precise modeling accounts and their diverse predictions on the local (Markram et al. 2015; Reimann et al. 2013) and the global level (Deco et al. 2014; Rosenbaum et al. 2017). These models may lead to more accurate inverse models, which allow inference of dynamical properties of the underlying neural networks and their functional relevance (Downer et al. 2017). With these tools in hand, the diagnostic value of M/EEG recordings could be substantially increased even for single subjects.

GRANTS

We acknowledge funding from the European Commission Starting Grant 638589 (to M. X. Cohen) and the Nederlande Wetenschap Organisatie ALW Open Grant ALWOP.346 (to B. Englitz). A. Alishbayli was supported by a Study Abroad Scholarship from the Ministry of Education of Azerbaijan and European Research Council Advanced Grant CONCEPT (http://erc.europa.eu; Project No. 294498). U. Gorska was supported by the Polish National Science Centre Award UMO-2015/17/N/HS6/02760 and UMO-2016/20/T/HS6/00.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

A.A., J.G.T., and B.E. prepared figures; A.A., J.G.T., U.G., M.X.C., and B.E. drafted manuscript; A.A., J.G.T., U.G., M.X.C., and B.E. edited and revised manuscript; A.A., J.G.T., U.G., M.X.C., and B.E. approved final version of manuscript.