In vivo like states in cortical networks
This project begun with Fabian Alvarez (postdoc in my group at UNIC)  and has been continued by Sami El Boustani [2,3] (PhD student in my group), Pierre Yger  (PhD student in Fregnac's group) and Lyle Muller  (PhD student in my group), and consists of finding self-generated network states compatible with intracellular recordings during ``active states'' (desynchronized EEG) in neocortex. These states will then be used later for various computing paradigms. A first approach was to obtain all possible network configurations that are compatible with given conductance measurements (excitatory and inhibitory) by studying self-consistency between inputs and output (firing rate, variability) in single cells. The predicted network configurations were then tested numerically to verify that active states are stable .
In a second approach, a macroscopic model of asynchronous irregular (AI) states was built. A mean-field approach was derived specifically for networks of excitatory and inhibitory spiking neurons in AI states. This approach successfully reproduced the complex state diagrams calculated numerically in networks of excitatory and inhibitory neurons . This approach is presently pursued to analyze voltage-sensitive dye recordings in vivo (work in progress).
In a third approach, we considered networks of adaptative exponential integrate-and-fire neurons, which can simulate the diversity of intrinsic firing properties in neocortex . Cortical and thalamocortical networks were considered, with network sizes ranging from small networks up to large networks. These networks reproduced many different in vivo like states, such as desynchronized states (AI states), or slow-wave oscillations with Up and Down states. Modulating spike frequency adaptation enabled the transition between these states. Both networks were simulated on hardware ASIC neurons [4,10].
More recently, we considered networks of integrate-and-fire neurons with more realistic connectivity integrating the probability of connection found in cortical tissue . These ``topological networks'' displayed different activity states very similar to random networks. The main finding is that such properties, when they are averaged at a macroscopic scale, are invariant with respect to the different connectivity patterns, provided the excitatory-inhibitory balance is the same. In particular, the same correlation structure holds for different connectivity profiles. This study suggests that the ``mean-field'' statistics of such networks does not depend on the details of the connectivity at a microscopic scale, suggesting that the mean-field formalism should apply to networks with realistic connectivity.
The state of activity of the network can also be determinant to determine large-scale features such as propagating waves. In a recent paper , we reviewed experiments on propagating activity in thalamus and neocortex across various levels of anesthesia and stimulation conditions, as well as computational models. Some discrepancies between experiments can be explained by the "network state", which differs vastly between anesthetized and awake conditions. This hypothesis was investigated in a network model displaying different states and investigate their effect on the spatial structure of self-sustained and externally driven activity. Indeed, the models showed that the occurence of propagation very sensitively depends on network state .
The presence of propagating waves in the awake and aroused brain was investigated more recently , in collaboration with Frederic Chavane (INT, Marseille). By combining voltage-sensitive dye (VSD) recordings of neuronal activity in awake monkey visual cortex, with a novel detection method based on the phase latency maps, we could show that not only propagating waves are present in the visual cortex, but nearly all visual stimuli evoke a propagating wave. There are also waves occurring spontaneously, and the interaction between these noisy spontaneous waves with those evoked by sensory stimuli constitute a fascinating perspective for future research.
Another feature of active states is the conductance interplay underlying spiking activity. We have shown previously that such an interplay can be observed in intracellular recordings using conductance-based analyses [7,8] (see Section 4.2). In particular, it was shown that in awake cats, spikes are always correlated to opposite variations of excitatory and inhibitory conductances . In a recent review article , we showed that such opposite variations betray the fact that most spikes are due to recurrent activity in the network, or in other words by its "internal state".
In collaboration with Mavi Sanchez (University of Barcelona), we have studied the properties of "gain modulation" during active states in vivo . Our main finding is that some stimuli are amplified by the network activity, while other stimuli are attenuated. This dual effect can be explained by the gain modulation provided by background activity, as we showed using a computational model. We could explain quantitatively the neural responses observed by either cortical stimulation, thalamic stimulation or auditory inputs with such a formalism.
We have recently investigated active states in the human and monkey brain, based on multielectrode data provided by Syd Cash (Harvard University) and Nicho Hatsopoulos (University of Chicago). A main finding was that the activity of excitatory and inhibitory neurons are almost perfectly balanced during all brain states of the wake-sleep cycle, but this balance breaks down during epileptic seizures . This type of analysis also revealed that these features are seen at multiple temporal scales, suggesting some scale invariance in the normal brain activity. Another finding was that fast oscillations (at beta and gamma frequencies) usually characteristic of wake states, are also found during sleep, but with higher coherence . Interestingly, these oscillations mostly involve inhibitory neurons.
 Alvarez, F.P. and Destexhe, A. Simulating cortical network activity states constrained by intracellular recordings. Neurocomputing 58: 285-290, 2004 (see abstract)
 El Boustani, S. and Destexhe, A. A master equation formalism for macroscopic modeling of asynchronous irregular activity states. Neural Computation 21: 46-100, 2009 (see abstract)
 Destexhe, A. Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons. J. Computational Neurosci. 27: 493-506, 2009 (see abstract)
 Bruderle D, Petrovici MA, Vogginger B, Matthias Ehrlich M, Pfeil T, Millner S, Grubl A, Wendt K, Muller E, Schwartz M-O, Husmann de Oliveira D, Jeltsch S, Fieres J, Schilling M, Muller P, Breitwieser O, Petkov V, Muller L, Davison AP, Krishnamurthy P, Kremkow J, Lundqvist M, Muller E, Partzsch J, Scholze S, Zuhl L, Mayr C, Destexhe A, Diesmann M, Potjans TC, Lansner A, Schuffny R, Schemmel J and Meier K. A comprehensive workflow for general-purpose neural modeling with highly configurable neuromorphic hardware systems. Biol. Cybernetics 104: 263-296, 2011 (see abstract)
 Yger, P., El Boustani, S., Destexhe, A. and Frégnac, Y. Invariant macroscopic statistics in topologically-connected balanced networks of conductance-based integrate-and-fire neurons. J. Computational Neurosci. 31: 229-245, 2011 (see abstract)
 Muller, L.E. and Destexhe, A. Propagating waves in thalamus, cortex and the thalamocortical system: experiments and models. J. Physiol. Paris 106: 222-238, 2012 (see abstract)
 Pospischil, M., Piwkowska, Z., Rudolph, M., Bal, T. and Destexhe, A. Calculating event-triggered average synaptic conductances from the membrane potential. Journal of Neurophysiology 97: 2544-2552, 2007 (see abstract)
 Rudolph, M., Pospischil, M., Timofeev, I. and Destexhe, A. Inhibition determines membrane potential dynamics and controls action potential generation in awake and sleeping cat cortex. Journal of Neuroscience 27: 5280-5290, 2007 (see abstract)
 Destexhe, A. Intracellular and computational evidence for a dominant role of internal network activity in cortical computations. Curr Opinion Neurobiol. 21: 717-725, 2011 (see abstract)
 Petrovici, M.A., Vogginger, B., Muller, P., Breitwieser, O., Lundqvist, M., Muller, L., Ehrlich, M., Destexhe, A., Lansner, A., Schuffny, R., Schemmel, J. and Meier, K. Characterization and compensation of network-level anomalies in mixed-signal neuromorphic modeling platforms. PLoS One 9: e108590, 2014 (see abstract)
 Muller, L.E., Reynaud, A., Chavane, F. and Destexhe, A. The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave. Nature Communications 5: 3675, 2014 (see abstract)
 Reig, R., Zerlaut, Y., Vergara, R., Destexhe, A. and Sanchez-Vives, M. Gain modulation of synaptic inputs by network state in auditory cortex in vivo. Journal of Neuroscience 35: 2689-2702, 2015 (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)
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