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To understand the cortical neuronal dynamics behind movement generation and control, most studies have focused on tasks where actions were planned and then executed using different instances of visuomotor transformations. However, to fully understand the dynamics related to movement control, one must also study how movements are actively inhibited. Inhibition, indeed, represents the first level of control both when different alternatives are available and only one solution could be adopted and when it is necessary to maintain the current position. We recorded neuronal activity from a multielectrode array in the dorsal premotor cortex (PMd) of monkeys performing a countermanding reaching task that requires, in a subset of trials, them to cancel a planned movement before its onset. In the analysis of the neuronal state space of PMd, we found a subspace in which activities conveying temporal information were confined during active inhibition and position holding. Movement execution required activities to escape from this subspace toward an orthogonal subspace and, furthermore, surpass a threshold associated with the maturation of the motor plan. These results revealed further details in the neuronal dynamics underlying movement control, extending the hypothesis that neuronal computation confined in an “output-null” subspace does not produce movements.

Slow oscillations are an emergent activity of the cerebral cortex network consisting of alternating periods of activity (Up states) and silence (Down states). Up states are periods of persistent cortical activity that share properties with that of underlying wakefulness. However, the occurrence of Down states is almost invariably associated with unconsciousness, both in animal models and clinical studies. Down states have been attributed relevant functions, such as being a resetting mechanism or breaking causal interactions between cortical areas. But what do Down states consist of? Here, we explored in detail the network dynamics (e.g., synchronization and phase) during these silent periodsin vivo(male mice),in vitro(ferrets, either sex), andin silico, investigating various experimental conditions that modulate them: anesthesia levels, excitability (electric fields), and excitation/inhibition balance. We identified metastability as two complementary phases composing such quiescence states: a highly synchronized “deterministic” period followed by a low-synchronization “stochastic” period. The balance between these two phases determines the dynamical properties of the resulting rhythm, as well as the responsiveness to incoming inputs or refractoriness. We propose detailed Up and Down state cycle dynamics that bridge cortical properties emerging at the mesoscale with their underlying mechanisms at the microscale, providing a key to understanding unconscious states.SIGNIFICANCE STATEMENTThe cerebral cortex expresses slow oscillations consisting of Up (active) and Down (silent) states. Such activity emerges not only in slow wave sleep, but also under anesthesia and in brain lesions. Down states functionally disconnect the network, and are associated with unconsciousness. Based on a large collection of data, novel data analysis approaches and computational modeling, we thoroughly investigate the nature of Down states. We identify two phases: a highly synchronized “deterministic” period, followed by a low-synchronization “stochastic” period. The balance between these two phases determines the dynamic properties of the resulting rhythm and responsiveness to incoming inputs. This finding reconciles different theories of slow rhythm generation and provides clues about how the brain switches from conscious to unconscious brain states.

Human studies employing intracerebral and transcranial perturbations suggest that the input-output properties of cortical circuits are dramatically affected during sleep in healthy subjects as well as in awake patients with multifocal and focal brain injury. In all these conditions, cortical circuits react to direct stimulation with an initial activation followed by suppression of activity (Off-period) that disrupts the build-up of sustained causal interactions typically observed in healthy wakefulness. The transition to this stereotypical response is of clinical relevance, being associated with loss of consciousness or loss of function. Here, we provide a mechanistic explanation of these findings by means of mean-field theory and simulations of a cortical-like module endowed with activity-dependent adaptation. First, we show that fundamental aspects of the local responses elicited in humans by direct cortical stimulation can be replicated by systematically varying the relationships between adaptation strength and excitation level in the network. Then, we reveal a region in the adaptation-excitation parameter space of key relevance for both physiological and pathological conditions, where spontaneous activity and responses to perturbation diverge in their ability to reveal Off-periods. Finally, we substantiate through simulations of connected cortical-like modules the role of adaptation mechanisms in preventing cortical neurons from engaging in reciprocal causal interactions, as suggested by empirical studies. These modeling results provide a general theoretical framework and a mechanistic interpretation for a body of neurophysiological measurements that bears key relevance for physiological states as well as for the assessment and rehabilitation of brain-injured patients.Significance StatementSuppression of cortical activity following an initial activation is a defining feature of deep sleep in healthy subjects and wakefulness in patients affected by focal and multifocal brain injuries. Experimental findings suggest that these bimodal responses disrupt the emergence of complex interactions among cortical regions, leading to loss of consciousness or functional impairments. Given their practical implications, it is important to study the mechanisms involved within a general theoretical framework. Using a neuronal network model, we provide evidence for a key role of activity-dependent adaptation mechanisms in shaping the responses to perturbation and in affecting the build-up of complex cortical interactions. Overall, this work provides a mechanistic interpretation relevant for the stratification, follow-up, and rehabilitation of brain-injured patients.

Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies composing cortical columns is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing $\nu(t)$ scale with the size of the assembly and persist in isolated network, i.e., in absence of external source of noise. Although deterministic chaos due to the quenched disorder of the synaptic couplings likely underlies this seemingly stochastic dynamics, an effective theory for the network dynamics of a finite ensemble of spiking neurons is lacking. Here, we fill this gap by extending the so-called population density approach including an activity- and size-dependent stochastic source in the Fokker-Planck equation for the membrane potential density. The finite-size noise embedded in this stochastic partial derivative equation is analytically characterized leading to a self-consistent and non-perturbative description of $\nu(t)$ valid for a wide class of spiking neuron networks. Its power spectra of $\nu(t)$ are found in excellent agreement with those from detailed simulations both in the linear regime and across a synchronization phase transition, when a size-dependent smearing of the critical dynamics emerges., Comment: 6 pages, 4 figures

In ambiguous or conflicting sensory situations, perception is often ‘multistable’ in that it perpetually changes at irregular intervals, shifting abruptly between distinct alternatives. The interval statistics of these alternations exhibits quasi-universal characteristics, suggesting a general mechanism. Using binocular rivalry, we show that many aspects of this perceptual dynamics are reproduced by a hierarchical model operating out of equilibrium. The constitutive elements of this model idealize the metastability of cortical networks. Independent elements accumulate visual evidence at one level, while groups of coupled elements compete for dominance at another level. As soon as one group dominates perception, feedback inhibition suppresses supporting evidence. Previously unreported features in the serial dependencies of perceptual alternations compellingly corroborate this mechanism. Moreover, the proposed out-of-equilibrium dynamics satisfies normative constraints of continuous decision-making. Thus, multistable perception may reflect decision-making in a volatile world: integrating evidence over space and time, choosing categorically between hypotheses, while concurrently evaluating alternatives.

Cortical slow oscillations (≲ 1 Hz) are a hallmark of slow-wave sleep and deep anesthesia across animal species. They arise from spatiotemporal patterns of activity with low degree of complexity, eventually increasing as wakefulness is approached and cognitive functions emerge. The arousal process is then an open window on the widely unknown mechanisms underlying the emergence of the dynamical richness of awake cortical networks. Here, we investigated the changes in the network dynamics as anesthesia fades out and wakefulness is approached in layer 5 neuronal assemblies of the rat visual cortex. Far from being a continuum, this transition displays both gradual and abrupt activity changes. Starting from deep anesthesia, slow oscillations increase their frequency eventually expressing maximum regularity. This stage is followed by the abrupt onset of an infra-slow (~ 0.2 Hz) alternation between sleep-like oscillations and activated states. A population rate model reproduces this transition driven by an increased excitability that brings it to periodically cross a critical point. We conclude that dynamical richness emerges as a competition between two metastable attractor states whose existence is here experimentally confirmed.

Slow oscillations in the sleeping and anesthetized brain invariantly emerge as an alternation between Up (high firing) and Down (almost quiescent) states. In cortex, they occur simultaneously in cell assemblies in different layers and propagate as traveling waves, a concerted activity at multiple scales whose interplay and role is still under debate. Slow oscillations have been reported to start in deep layers, more specifically in layer 5. Here, we studied the laminar organization of slow oscillations in the anesthetized rat cortex and we found that the activity leading to Up states actually initiates in layer 6, then spreads towards upper layers. Layer 5 cell assemblies have a threshold-like activation that can persist after layer 6 inactivation, giving rise to hysteresis loops like in “flip-flop” computational units. We found that such hysteresis is finely tuned by the columnar circuitry depending on the recent history of the local ongoing activity. Furthermore, thalamic inactivation reduced infragranular excitability without affecting the columnar activation pattern. We propose a role for layer 6 acting as a hub unraveling a hierarchy of cortical loops.

Slow oscillations are a pattern of synchronized network activity generated by the cerebral cortex. They consist of Up and Down states, which are periods of activity interspersed with periods of silence, respectively. However, even when this is a unique dynamic regime of transitions between Up and Down states, this pattern is not constant: there is a range of oscillatory frequencies (0.1–4 Hz), and the duration of Up vs. Down states during the cycles is variable. This opens many questions. Is there a constant relationship between the duration of Up and Down states? How much do they vary across conditions and oscillatory frequencies? Are there different sub regimes within the slow oscillations? To answer these questions, we aimed to explore a concrete aspect of slow oscillations, Up and Down state durations, across three conditions: deep anesthesia, light anesthesia, and slow-wave sleep (SWS), in the same chronically implanted rats. We found that light anesthesia and SWS have rather similar properties, occupying a small area of the Up and Down state duration space. Deeper levels of anesthesia occupy a larger region of this space, revealing that a large variety of Up and Down state durations can emerge within the slow oscillatory regime. In a network model, we investigated the network parameters that can explain the different points within our bifurcation diagram in which slow oscillations are expressed.

During sleep and anesthesia, large groups of neurons throughout the entire cortex activate rhythmically producing wavefronts of activity referred to as slow-wave activity (SWA). In the arousal process, the brain restores its integrative and complex activity. The network mechanisms underlying this global state transition remain however to be elucidated. Here we investigated the network features shaping the SWA under fading anesthesia. Using electrocorticographical recordings of wide cortical areas of the mouse brain, we developed a quantitative measure of the anesthesia level based on slow-wave frequency and complexity. At deep anesthesia, we document a stringent alternation of posterior-anterior-posterior modes of propagation. With fading anesthesia, SWA evolves to produce a plethora of metastable spatiotemporal patterns. A network model of spiking neurons reproduced the data using short-range connectivity, subcortical input and a local activity-dependent adaptation. The emergence from deep anesthesia does not require modifying the connectivity, but small changes in the local excitability of cortical cell assemblies, further supporting the hypothesis of a tight bound between scales in the brain.

In ambiguous or conflicting sensory situations, perception is often ‘multistable’ in that it changes abruptly at irregular intervals, shifting perpetually between distinct alternatives. Intriguingly, the interval statistics of these alternations exhibits quasi-universal characteristics, suggesting a general mechanism. Here we show that the stereotypical features of multistable perception, exemplified by binocular rivalry, are reproduced in detail by a hierarchical dynamics operating out of equilibrium. Its constitutive elements are discretely stochastic and idealize the metastability of cortical networks. Independent elements accumulate visual evidence at one level, while groups of coupled elements compete for dominance at another level. As soon as one group dominates perception, feedback inhibition suppresses supporting evidence. This mechanism is corroborated compellingly by unexpected serial dependencies of perceptual alternations. Moreover, it satisfies normative constraints of continuous decision-making. We conclude that multistable perception reflects decision-making in a volatile world: integrating evidence over space and time, choosing categorically between hypotheses, while concurrently evaluating alternatives.

Slow oscillations have been suggested as the default emergent activity of the cortical network. This is a low complexity state that integrates neuronal, synaptic, and connectivity properties of the cortex. Shaped by variations of physiological parameters, slow oscillations provide information about the underlying healthy or pathological network. We review how this default activity is shaped, how it acts as a powerful attractor, and how getting out of it is necessary for the brain to recover the levels of complexity associated with conscious states. We propose that slow oscillations provide a robust unifying paradigm for the study of cortical function.

To understand the cortical neuronal dynamics behind movement generation and control most studies focused on tasks where actions were planned and then executed, using different instances of visuomotor transformations. However, to fully understand the dynamics related to movement control one must also study how movements are actively inhibited. Inhibition, indeed, represents the first level of control both when different alternatives are available and only one solution could be adopted, and when it is necessary to maintain the current position. We recorded neuronal activity from a multielectrode array in the dorsal premotor (PMd) cortex of monkeys performing a countermanding reaching task that requires, in a subset of trials, to cancel a planned movement before its onset. In the analysis of the neuronal state-space of PMd we found a subspace in which activities conveying temporal information were confined during active inhibition and position holding. Movement execution required activities to escape from this subspace toward an orthogonal subspace and, furthermore, surpass a threshold associated with the maturation of the motor plan. These results revealed further details in the neuronal dynamics underlying movement control, extending the hypothesis that neuronal computation confined in an -output-null- subspace does not produce movements.

Higher and higher interest has been shown in the recent years to large scale spiking simulations of cerebral neuronal networks, coming both from the presence of high performance computers and increasing details in the experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, that is the question addressed by mean field theories. Despite analytic solutions for the mean field dynamics has already been proposed generally for current based neurons (CUBA), the same for more realistic neural properties, such as conductance based (COBA) network of adaptive exponential neurons (AdEx), a complete analytic model has not been achieved yet. Here, we propose a novel principled approach to map a COBA on a CUBA. Such approach provides a state-dependent approximation capable to reliably predict the firing rate properties of an AdEx neuron with non-instantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular (AI) and synchronous irregular (SI) (slow oscillations, SO).This results show that a state-dependent approximation can be successfully introduced in order to take into account the subtle effects of COBA integration and to deal with a theory capable to correctly predicts the activity in regimes of alternating states like slow oscillations.

The intricate web of connections among the neurons composing the cerebral cortex is the seed of the complexity that our brain is capable to express. Such complexity is organized as it results from a hierarchical and modular organization of the network in which the roles of different cortical areas are distinct. Here, we speculate that such differentiation can be obtained by relying on the granular nature of the cortical surface tiled with ‘canonic’ modules which in turn can be flexibly tuned to compose diverse mesoscopic networks. The remarkable versatility of these cortical modules is governed by few key parameters like the excitability level and the sensitivity to the accumulated activity-dependent fatigue. These modules are naturally endowed with a rich repertoire of activity regimes which range from quasi-stable dynamics, possibly exploited to store information or provide persistent input to other modules, to collective oscillations reminiscent of the Up/Down activity cycle observed during sleep and deep anesthesia. Finally, we conclude showing that such slow oscillations, spontaneously expressed by the isolated cortex, can provide an ideal experimental framework to infer the dynamical properties of these cortical modules which in turn can inform also on cortical function in other brain states, such as during wakefulness.

Non-invasive brain stimulation techniques, such as transcranial direct current stimulation (tDCS), play a growing role in the treatment of neurological disorders. However, the mechanisms by which electric fields modulate cortical network activity are only partially understood. To explore the spatiotemporal modulation of cortical activity by electric fields (DC fields), we exposed neocortical slices to constant fields of varying intensity and direction and we measured their effect on the low (Significance statementActing on the brain through electrical stimulation in order to correct dysfunctions or to induce functional recovery is a relatively common technique nowadays used in the clinical realm. In spite of the existence of previous studies on the effect of electric fields on neuronal and network physiology, questions regarding the mechanisms underlying exogenous electrical modulation of cortical dynamics still remain open. We demonstrate that continuous electric fields between -6 and +6 V/m induce a precise modulation of slow and fast cortical rhythms. Based on both experimental evidence and theoretical analysis, we describe some of the mechanistic underpinnings at play and provide useful information for the development of tools with better spatiotemporal control of cortical activity.

Cortical slow oscillations (SO) of neural activity spontaneously emerge and propagate during deep sleep and anesthesia and are also expressed in isolated brain slices and cortical slabs. We lack full understanding of how SO integrate the different structural levels underlying local excitability of cell assemblies and their mutual interaction. Here, we focus on ongoing slow waves (SWs) in cortical slices reconstructed from a 16-electrode array designed to probe the neuronal activity at multiple spatial scales. In spite of the variable propagation patterns observed, we reproducibly found a smooth strip of loci leading the SW fronts, overlapping cortical layers 4 and 5, along which Up states were the longest and displayed the highest firing rate. Propagation modes were uncorrelated in time, signaling a memoryless generation of SWs. All these features could be modeled by a multimodular large-scale network of spiking neurons with a specific balance between local and intermodular connectivity. Modules work as relaxation oscillators with a weakly stable Down state and a peak of local excitability to model layers 4 and 5. These conditions allow for both optimal sensitivity to the network structure and richness of propagation modes, both of which are potential substrates for dynamic flexibility in more general contexts.

Cognitive functions like motor planning rely on the concerted activity of multiple neuronal assemblies underlying still elusive computational strategies. During reaching tasks, we observed stereotyped sudden transitions (STs) between low and high multiunit activity of monkey dorsal premotor cortex (PMd) predicting forthcoming actions on a single-trial basis. Occurrence of STs was observed even when movement was delayed or successfully canceled after a stop signal, excluding a mere substrate of the motor execution. An attractor model accounts for upward STs and high-frequency modulations of field potentials, indicative of local synaptic reverberation. We found in vivo compelling evidence that motor plans in PMd emerge from the coactivation of such attractor modules, heterogeneous in the strength of local synaptic self-excitation. Modules with strong coupling early reacted with variable times to weak inputs, priming a chain reaction of both upward and downward STs in other modules. Such web of "flip-flops" rapidly converged to a stereotyped distributed representation of the motor program, as prescribed by the long-standing theory of associative networks.

Neuronal spontaneous activity can provide valuable information on the functional structure of the underlying neuronal network. We focused on the spontaneous slow-wave activity that is generated and propagated in cortical slices, aiming at relating their spatio-temporal organization with the laminar structure of the tissue. We extracted multi-unit activities from simultaneous recordings obtained by means of an array of 16 electrodes covering the slice. Although each site displayed alternation between high-firing (Up) and almost quiescent (Down) states, slow oscillations (SO) were not spatially homogeneous, showing layer-dependent state durations and maximum firing rates. A distribution of time lags between electrodes in the onset and offset of Up states reflected a propagating activity wave. We found different propagation modes in terms of velocity, direction, wavefront shape (see Figure 1A), spatial extension and site of origin. Despite such variability, at the level of single waves, we consistently found that the head of the wavefront had a spatial distribution forming a strip almost parallel to the cortical surface (see Figure 1B black line), at a depth compatible with layer 4 and 5 (L4 and L5). Moreover, this strip widely overlapped with the region where Up states had the maximum duration and magnitude (see Figure 1B respectively green and blue line), a region possibly corresponding to the most excitable part of the network. To test such hypothesis, we tried to reproduce the properties of this strip using a large scale simulation of a slice model, with oscillating cortical modules of spiking neurons arranged in a 2D lattice with nearest neighbor connectivity. In this homogeneous medium we implemented a non-monotonic gradient in the connectivity level (see Figure 1C), aiming to embody the physiological differences in layer excitability, and setting an overexcited strip (dark circles). We found that the connectivity level increase was not trivially related to an increase of the speed of wave propagation, rather this parameter has to be chosen in an optimal range (see Figure 1C-D) in order to reproduce propagating patterns compatible with the experiments. Optimal networks were those having a metastable Down state in which finite-size fluctuations were capable to prime Down-to-Up transitions. In addition to this, we further predicted that SO features like maximum firing rate and longest Up state durations should be found at the same excitable strip. Conclusions As the model predicted, we found that strips of early wave propagation reliably overlapped with the regions where maximum Up state duration and firing activity occurred, strengthening the duality between spontaneous activity and network structure. Finally, we matched the excitable strips with the slice cortical layers as identified by histology, finding a reliable overlap between such strips and L4 and L5 (see Figure 1E). Figure 1. A. Wavefronts for 2 modes of propagation. B. Average strips where wavefronts propagate earlier (black), and where Up states have maximum duration (green) and magnitude (blue). C. Modulation of the connectivity parameter in the model. D. Nullclines under mean-field approximation varying levels of connectivity.  and C are average firing rate and fatigue level, respectively. Circles, fixed points. Dark to light gray, different excitability levels as in C, respectively. E. Example match between strip of early wave propagation and slice’s layers.

Rhythms at slow (

Perceptual decisions are made not only during goal-directed behavior such as choice tasks, but also occur spontaneously while multistable stimuli are being viewed. In both contexts, the formation of a perceptual decision is best captured by noisy attractor dynamics. Noise-driven attractor transitions can accommodate a wide range of timescales and a hierarchical arrangement with “nested attractors” harbors even more dynamical possibilities. The attractor framework seems particularly promising for understanding higher-level mental states that combine heterogeneous information from a distributed set of brain areas.

Reig R, Mattia M, Compte A, Belmonte C, Sanchez-Vives MV. Temperature modulation of slow and fast cortical rhythms. J Neurophysiol 103: 1253-1261, 2010. First published December 23, 2009; doi: 10.1152/jn.00890.2009. In the local cortical network, spontaneous emergent activity self-organizes in rhythmic patterns. These rhythms include a slow one (, This work was supported by the Ministry of Science and Innovation of Spain to M. V. Sanchez-Vives and A. Compte.

The function of sleep remained one of largest enigmas of neuroscience for most of the 20th century. However in recent years different evidence has accumulated in support of a critical role of sleep on functions such as replay and memory consolidation. In particular slow wave sleep, and its underlying corticothalamocortical activity, slow oscillations, could be critical not only for memory but also for the maintenance of the brain's structural and func- tional connectivity. In this article we ask: why slow oscillations? To answer this question we put forward the idea that slow oscillations are the default activity of the cortical network based on both experimental and theoretical evidence. We go on to discuss why slow oscillations emerge from the cortical circuits and what are the dynamic advantages of this activity pattern, such as the resilience to perturbances and the facilitation of transitions between a disconnected (e.g. deep sleep) brain and a connected, awake brain.

In this work we study the basic competitive and cooperative mechanisms of neural activity in the context of a two-alternative free-choice eye-movement task, as a function of the expectation of reward. We use a simplified version of the protocol followed by Platt and Glimcher [Neural correlates of decision variables in parietal cortex, Nature 400 (1999) 233-238], in which each choice is associated with independent underlying reward schedules, and explicitly model it using a biophysically realistic network of integrate-and-fire neurons that forms a categorical choice from the expected gain contingencies, via a simple bias mechanism. The model accounts for several experimental findings, such as the gain-modulated firing activity observed by Platt and Glimcher and the matching law.

Recent experiments on behaving monkeys have shown that learning a visual categorization task makes the neurons in infero-temporal cortex (ITC) more selective to the task-relevant features of the stimuli (Sigala and Logothetis in Nature 415 318-320, 2002). We hypothesize that such a selectivity modulation emerges from the interaction between ITC and other cortical area, presumably the prefrontal cortex (PFC), where the previously learned stimulus categories are encoded. We propose a biologically inspired model of excitatory and inhibitory spiking neurons with plastic synapses, modified according to a reward based Hebbian learning rule, to explain the experimental results and test the validity of our hypothesis. We assume that the ITC neurons, receiving feature selective inputs, form stronger connections with the category specific neurons to which they are consistently associated in rewarded trials. After learning, the top-down influence of PFC neurons enhances the selectivity of the ITC neurons encoding the behaviorally relevant features of the stimuli, as observed in the experiments. We conclude that the perceptual representation in visual areas like ITC can be strongly affected by the interaction with other areas which are devoted to higher cognitive functions.