Analysis of multi-electrode and ensemble recordings
Multi-electrode techniques are becoming every day more and more sophisticate, allowing the simultaneous recording of a large number of units, also called "ensemble recordings". Computational methods are needed not only to extract the single units from the extracellular signals recorded, but also to analyze the activity of such simultaneously-recorded ensembles of neurons. A first approach is to correlate the unit activity with other variables such as the local field potential (LFP). This approach was followed in collaboration with Diego Contreras and Mircea Steriade, we characterized the spatiotemporal distribution of oscillatory activity from multisite field potential recordings in cat cerebral cortex during natural wake and sleep states . The spatiotemporal pattern of activity was markedly different for slow-wave events and fast oscillations: slow waves in LFPs were characterized by a generalized silence in all cell types and were of remarkable spatiotemporal coherence, whereas during LFP fast oscillations the activity was less coherent and correlations were local within a millimeter range . Although fast oscillations are present during wake and REM sleep, brief periods of fast oscillations with identical spatiotemporal characteristics were also present during slow-wave sleep. These results suggest that slow-wave sleep in cats consists in brief periods of activity ("up states") with low spatiotemporal coherence, similar to wakefulness, interleaved with slow-wave complexes coherent over large cortical territories. We recently wrote a review article that summarizes the evidence that these "up" states represents fragments of wakefulness that are replayed during sleep .
Another type of computational analysis of ensemble recordings is to search for self-organisation or collective phenomena. The simplest type of interaction is to consider pairwise correlations between neurons. Here, the simplest paradigm is inspired from the Ising model, well-known in statistical physics. We examined Ising type models to predict the occurrence of population patterns in distributed spiking activity . Using a maximum entropy principle with a Markovian assumption, we elaborated a model that accounts for both spatial and temporal pairwise correlations among neurons. This model was tested on model data as well as on experimental data (multisite recordings), and it was shown that this approach correctly predicts the occurrence probabilities of spatio-temporal patterns of spikes, significantly better than Ising type models only based on pairwise correlations. The same approach can be used to generate surrogates that reproduce the spatial and temporal correlations of a given data set.
Another approach in the search for signs of self-organized activity is to determine if the system is operating close to a critical point. These so-called "self-organized critical" (SOC) states are characterized by long-range correlations and power-law relations. With Claude Bedard and Helmut Kröger, we investigated the presence of SOC states from LFP and multiple unit activity in cerebral cortex in vivo . Many complex systems display SOC states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of SOC states in neuronal activity. By analyzing simultaneous recordings of global and neuronal activities, we confirmed the 1/f scaling of global variables (such as LFPs) for selected frequency bands. However, by analyzing neuronal activities, we did not find the typical power-law scaling of SOC states ("avalanche analysis"), which suggests that neuronal activity does not stem from SOC states. The 1/f scaling of LFPs can be explained by a model which does not rely on critical states, but is rather due to a filtering process from extracellular space (see Section 1.3).
This approach was further investigated with Jonathan Touboul. We investigated whether the LFP signal can show evidence for SOC states , as found by other authors in awake monkeys. By using the same techniques, we could show that indeed, the statistics of negative LFP peaks (which are related to increase of firing), can show power-law scaling which could be taken as evidence for SOC. However, we did the same analysis for positive LFP peaks, which are unrelated to firing activity, and found the same results. Moreover, shuffled peaks also demonstrated apparent power-law scaling, suggesting that power-law scaling may be a generic property of thresholded stochastic processes. We next showed that, indeed, spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, but does not resist to more severe analysis such as the Kolmogorov-Smirnoff test. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon, and should be demonstrated by more stringent statistical tests (see details in ).
These conclusions were recently confirmed by an avalanche analysis from cat, monkey and human cerebral cortex, in wake and sleep states . This analysis made use of recently acquired unit and LFP recordings in humans  (see below). The avalanche analysis of such data, as well as from similar high-density recordings in cat and monkey (from 96 to 160 electrodes), all pointed to the absence of power-law distributions, in both units, and LFP recordings . In accordance with above, these data and analyses suggest that the awake and sleeping brain display dynamical states more complex than SOC.
A highlight of our recent research is the successful separation of excitatory and inhibitory neurons from unit recordings in humans . We have used high-density intracranial recordings from human temporal cortex (Neuroport probes, 96 electrodes), which lead typically to 80 to 100 discriminated single units. Based on spike shape, autocorrelation and firing rate, we could separate the units between regular-spiking (RS) and fast-spiking (FS) cells. The high density of the array allowed to directly see the postsynaptic effect of cells on their targets, as well as monosynaptic connections. In all cases, FS cells had an inhibitory influence on their targets, while RS cells were always excitatory. This separation allowed us to track for spatiotemporal correlation profiles between cell types. This analysis showed that as expected, correlations between excitatory cells decayed with distance. However, unexpectedly, correlations between inhibitory cells stayed high over distances up to 4~mm. This shows that the inhibitory network maintains correlated activity over large distances (see details in ). The reliable extraction of excitatory and inhibitory neurons constitutes a unique opportunity to understand their role in the different aspects of human brain activity, such as rhythmical activity or the different stages of sleep (work in progress).
In another study , we used tetrode recordings in rat prefrontal cortex (PFC), together with extracellular recordings in the hippocampus (which connects monosynaptically to PFC). In this case too, the units could be separated into RS and FS cells. We showed that during natural sleep spindles, oscillatory responses of cortical cells are different for different cell types and cortical layers. FS interneurons were always more modulated than RS pyramidal cells, both in firing rate and phase, suggesting that the dynamics are dominated by inhibition. In the deep layers, where most of the hippocampal fibers make contacts, pyramidal cells respond phasically to SPWRs, but not during spindles. These results demonstrate that during sleep spindles, the cortex is functionnaly "de-afferented" from its hippocampal inputs, based on processes of cortical origin, and presumably mediated by the strong recruitment of inhibitory interneurons. The interplay between hippocampal and thalamic inputs may underlie a global mechanism involved in the consolidation of recently formed memory traces (see details in ).
More recently, we collaborated with Dan Shulz laboratory at the UNIC into a mixed experimental-computational study of multisite recordings in rat barrel cortex in vivo . In that study, the goal was to determine, using a model-based analysis, how correlations in the stimulus were encoded by neuronal populations. The main finding is that when inputs are uncorrelated, barrel cortex neurons show features similar to the "simple" and "complex" cells of primary visual cortex. However, when correlations are present, the responses dramatically change, some cells detect global correlations, while some cells are sensitive to local correlated patterns.
We also compared human and monkey wake and sleep recordings . This analysis showed that for both species, the excitatory and inhibitory neuron populations are tighlty balanced. The only moments when this balance breaks down is during epileptic seizures, suggesting that balanced activity is a feature of the normally functioning brain.
Using the same type of recordings, we investigated how fast oscillations (beta and gamma frequencies) are organized in the units and LFP recordings in human and monkey . We found that mostly inhibitory neurons are active during these oscillations, in wake and sleep states. Surprisingly, the largest spatiotemporal coherence was found in slow-wave sleep. These results suggest that inhibitory cells, not only are dominantly involved in the genesis of beta and gamma oscillations, but also in the organization of their large-scale coherence in the awake and sleeping brain. These results set important constraints for the future models of wake and sleep states.
We also used human and monkey Utah-array recordings to investigate the relation between units and LFPs . This analysis led to the discovery that this relation was much more powerful for inhibitory neurons than for excitatory cells. This finding, if confirmed, can fundamentally change our interpretation of LFPs and possibly of the EEG. We are presently using realistic models to investigate this relation, and search for possible biophysical origins of this inhibitory participation to LFPs (work in progress).
Finally, we showed that maximum entropy models, similar to those studied previously , can be designed specifically for the case of recordings where excitatory and inhibitory neurons are discriminated . This approach can shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep. In addition, maximum entropy models can also unveil novel features of neuronal interactions, which were found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep .
 Destexhe, A., Contreras, D. and Steriade, M. Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states. J. Neurosci. 19: 4595-4608, 1999 (see abstract)
 Destexhe, A., Hughes, S.W., Rudolph, M. and Crunelli, V. Are corticothalamic `up' states fragments of wakefulness? Trends Neurosci. 30: 334-342, 2007 (see abstract)
 Marre, O., El Boustani, S., Frégnac, Y. and Destexhe, A. Prediction of spatio-temporal patterns of neural activity from pairwise correlations. Physical Review Letters 102: 138101, 2009 (see abstract).
 Bedard, C., Kröger, H. and Destexhe, A. Does the 1/f frequency-scaling of brain signals reflect self-organized critical states ? Physical Review Letters 97: 118102, 2006 (see abstract).
 Touboul, J. and Destexhe, A. Can power-law scaling and neuronal avalanches arise from stochastic dynamics? PLoS-One 5: e8982, 2010 (see abstract).
 Dehghani, N., Hatsopoulos, N.G., Haga, Z.D., Parker, R.A., Greger, B., Halgren, E., Cash, S.S., and Destexhe, A. Avalanche analysis from multi-electrode ensemble recordings in cat, monkey and human cerebral cortex during wakefulness and sleep. Frontiers Physiol. 3: 302, 2012 (see abstract).
 Peyrache, A., Dehghani, N., Eskandar, E.N., Madsen, J.R., Anderson, W.S., Donoghue, J.S., Hochberg, L.R., Halgren, E., Cash, S.S., and Destexhe, A. Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep. Proc. Natl. Acad. Sci. USA 109: 1731-1736, 2012 (see abstract)
 Peyrache, A., Battaglia, F. and Destexhe, A. Inhibition recruitment in prefrontal cortex during sleep spindles and gating of hippocampal inputs. Proc. Natl. Acad. Sci. USA 108: 17207-17212, 2011 (see abstract)
 Estebanez, L., El Boustani, S., Destexhe, A. and Shulz, D. Correlated input reveals coexisting coding schemes in a sensory cortex. Nature Neurosci. 15: 1691-1699, 2012 (see abstract)
 Dehghani, N., Peyrache, A., Telenczuk, B., Le Van Quyen, M., Halgren, E., Cash, S.S., Hatsopoulos, N.G. and Destexhe, A. Dynamic balance of excitation and inhibition in human and monkey neocortex. Nature Scientific Reports 6: 23176, 2016 (see abstract)
 Le Van Quyen, M., Muller, L., Telenczuk, B., Cash, S.S., Halgren, E., Hatsopoulos, N.G., Dehghani, N. and Destexhe, A. High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle. Proc. Natl. Acad. Sci. USA 113: 9363-9368, 2016 (see abstract)
 Telenczuk, B., Dehghani, N., Le Van Quyen, M., Cash, S., Halgren, E., Hatsopoulos, N.G. and Destexhe, A. Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex. Nature Scientific Reports 7: 40211, 2017 (see abstract)
 Nghiem, T-A., Telenczuk, B., Marre, O., Destexhe, A. and Ferrari, U. Maximum entropy models reveal the excitatory and inhibitory correlation structures in cortical neural activity. Physical Review E 98: 012402, 2018 (see abstract)
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