Neuronal population dynamics during motor plan cancellation in nonhuman primates.

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.

Deterministic and Stochastic Components of Cortical Down States: Dynamics and Modulation.

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 periods in vivo (male mice), in vitro (ferrets, either sex), and in 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 STATEMENT The 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.

Self-Consistent Stochastic Dynamics for Finite-Size Networks of Spiking Neurons.

Despite the huge number of neurons composing a brain network, ongoing activity of local cell assemblies is intrinsically stochastic. Fluctuations in their instantaneous rate of spike firing ν(t) scale with the size of the assembly and persist in isolated networks, i.e., in the absence of external sources of noise. Although deterministic chaos due to the quenched disorder of the synaptic couplings underlies this seemingly stochastic dynamics, an effective theory for the network dynamics of a finite assembly 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 nonperturbative description of ν(t) valid for a wide class of spiking neuron networks. Power spectra of ν(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.

Modulation of cortical slow oscillations and complexity across anesthesia levels.

The ability of different groups of cortical neurons to engage in causal interactions that are at once differentiated and integrated results in complex dynamic patterns. Complexity is low during periods of unconsciousness (deep sleep, anesthesia, unresponsive wakefulness syndrome) in which the brain tends to generate a stereotypical pattern consisting of alternating active and silent periods of neural activity-slow oscillations- and is high during wakefulness. But how is cortical complexity built up? Is it a continuum? An open question is whether cortical complexity can vary within the same brain state. Here we recorded with 32-channel multielectrode arrays from the cortical surface of the mouse and used both spontaneous dynamics (wave propagation entropy and functional complexity) and a perturbational approach (a variation of the perturbation complexity index) to measure complexity at different anesthesia levels. Variations in anesthesia level within the bistable regime of slow oscillations (0.1-1.5 Hz) resulted in a modulation of the slow oscillation frequency. Both perturbational and spontaneous complexity increased with decreasing anesthesia levels, in correlation with the decrease in coherence of the underlying network. Changes in complexity level are related to, but not dependent on, changes in excitability. We conclude that cortical complexity can vary within a single brain state dominated by slow oscillations, building up to the higher complexity associated with consciousness.

Dimensional reduction in networks of non-Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays.

Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity.

Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure.

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.

Collective Activity of Many Bistable Assemblies Reproduces Characteristic Dynamics of Multistable Perception.

UNLABELLED: The timing of perceptual decisions depends on both deterministic and stochastic factors, as the gradual accumulation of sensory evidence (deterministic) is contaminated by sensory and/or internal noise (stochastic). When human observers view multistable visual displays, successive episodes of stochastic accumulation culminate in repeated reversals of visual appearance. Treating reversal timing as a "first-passage time" problem, we ask how the observed timing densities constrain the underlying stochastic accumulation. Importantly, mean reversal times (i.e., deterministic factors) differ enormously between displays/observers/stimulation levels, whereas the variance and skewness of reversal times (i.e., stochastic factors) keep characteristic proportions of the mean. What sort of stochastic process could reproduce this highly consistent "scaling property?" Here we show that the collective activity of a finite population of bistable units (i.e., a generalized Ehrenfest process) quantitatively reproduces all aspects of the scaling property of multistable phenomena, in contrast to other processes under consideration (Poisson, Wiener, or Ornstein-Uhlenbeck process). The postulated units express the spontaneous dynamics of attractor assemblies transitioning between distinct activity states. Plausible candidates are cortical columns, or clusters of columns, as they are preferentially connected and spontaneously explore a restricted repertoire of activity states. Our findings suggests that perceptual representations are granular, probabilistic, and operate far from equilibrium, thereby offering a suitable substrate for statistical inference. SIGNIFICANCE STATEMENT: Spontaneous reversals of high-level perception, so-called multistable perception, conform to highly consistent and characteristic statistics, constraining plausible neural representations. We show that the observed perceptual dynamics would be reproduced quantitatively by a finite population of distinct neural assemblies, each with locally bistable activity, operating far from the collective equilibrium (generalized Ehrenfest process). Such a representation would be consistent with the intrinsic stochastic dynamics of neocortical activity, which is dominated by preferentially connected assemblies, such as cortical columns or clusters of columns. We predict that local neuron assemblies will express bistable dynamics, with spontaneous active-inactive transitions, whenever they contribute to high-level perception.

Overexpression of Dyrk1A, a Down Syndrome Candidate, Decreases Excitability and Impairs Gamma Oscillations in the Prefrontal Cortex.

The dual-specificity tyrosine phosphorylation-regulated kinase DYRK1A is a serine/threonine kinase involved in neuronal differentiation and synaptic plasticity and a major candidate of Down syndrome brain alterations and cognitive deficits. DYRK1A is strongly expressed in the cerebral cortex, and its overexpression leads to defective cortical pyramidal cell morphology, synaptic plasticity deficits, and altered excitation/inhibition balance. These previous observations, however, do not allow predicting how the behavior of the prefrontal cortex (PFC) network and the resulting properties of its emergent activity are affected. Here, we integrate functional, anatomical, and computational data describing the prefrontal network alterations in transgenic mice overexpressingDyrk1A(TgDyrk1A). Usingin vivoextracellular recordings, we show decreased firing rate and gamma frequency power in the prefrontal network of anesthetized and awakeTgDyrk1Amice. Immunohistochemical analysis identified a selective reduction of vesicular GABA transporter punctae on parvalbumin positive neurons, without changes in the number of cortical GABAergic neurons in the PFC ofTgDyrk1Amice, which suggests that selective disinhibition of parvalbumin interneurons would result in an overinhibited functional network. Using a conductance-based computational model, we quantitatively demonstrate that this alteration could explain the observed functional deficits including decreased gamma power and firing rate. Our results suggest that dysfunction of cortical fast-spiking interneurons might be central to the pathophysiology of Down syndrome. SIGNIFICANCE STATEMENT: DYRK1Ais a major candidate gene in Down syndrome. Its overexpression results into altered cognitive abilities, explained by defective cortical microarchitecture and excitation/inhibition imbalance. An open question is how these deficits impact the functionality of the prefrontal cortex network. Combining functional, anatomical, and computational approaches, we identified decreased neuronal firing rate and deficits in gamma frequency in the prefrontal cortices of transgenic mice overexpressingDyrk1A We also identified a reduction of vesicular GABA transporter punctae specifically on parvalbumin positive interneurons. Using a conductance-based computational model, we demonstrate that this decreased inhibition on interneurons recapitulates the observed functional deficits, including decreased gamma power and firing rate. Our results suggest that dysfunction of cortical fast-spiking interneurons might be central to the pathophysiology of Down syndrome.

Heterogeneous attractor cell assemblies for motor planning in premotor cortex.

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.

Stochastic accumulation by cortical columns may explain the scalar property of multistable perception.

The timing of certain mental events is thought to reflect random walks performed by underlying neural dynamics. One class of such events--stochastic reversals of multistable perceptions--exhibits a unique scalar property: even though timing densities vary widely, higher moments stay in particular proportions to the mean. We show that stochastic accumulation of activity in a finite number of idealized cortical columns--realizing a generalized Ehrenfest urn model--may explain these observations. Modeling stochastic reversals as the first-passage time of a threshold number of active columns, we obtain higher moments of the first-passage time density. We derive analytical expressions for noninteracting columns and generalize the results to interacting columns in simulations. The scalar property of multistable perception is reproduced by a dynamic regime with a fixed, low threshold, in which the activation of a few additional columns suffices for a reversal.

A modular and adaptable analysis pipeline to compare slow cerebral rhythms across heterogeneous datasets.

Neuroscience is moving toward a more integrative discipline where understanding brain function requires consolidating the accumulated evidence seen across experiments, species, and measurement techniques. A remaining challenge on that path is integrating such heterogeneous data into analysis workflows such that consistent and comparable conclusions can be distilled as an experimental basis for models and theories. Here, we propose a solution in the context of slow-wave activity (<1 Hz), which occurs during unconscious brain states like sleep and general anesthesia and is observed across diverse experimental approaches. We address the issue of integrating and comparing heterogeneous data by conceptualizing a general pipeline design that is adaptable to a variety of inputs and applications. Furthermore, we present the Collaborative Brain Wave Analysis Pipeline (Cobrawap) as a concrete, reusable software implementation to perform broad, detailed, and rigorous comparisons of slow-wave characteristics across multiple, openly available electrocorticography (ECoG) and calcium imaging datasets.

A novel network approach to multiscale biological regulation.

Modeling systems at multiple interacting scales is probably the most relevant task for pursuing a physically motivated explanation of biological regulation. In a new study, Smart and Zilman develop a convincing, albeit preliminary, model of the interplay between the cell microscale and the macroscopic tissue organization in biological systems.

Adaptation Shapes Local Cortical Reactivity: From Bifurcation Diagram and Simulations to Human Physiological and Pathological Responses.

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 has important clinical implications, being associated with loss of consciousness or loss of functions. Here, we provide a mechanistic explanation of these findings by means of simulations of a cortical-like module endowed with activity-dependent adaptation and mean-field theory. 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 crucial relevance for both physiological and pathologic 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 critical relevance for physiological states as well as for the assessment and rehabilitation of brain-injured patients.

Learning selective top-down control enhances performance in a visual categorization task.

We model the putative neuronal and synaptic mechanisms involved in learning a visual categorization task, taking inspiration from single-cell recordings in inferior temporal cortex (ITC). Our working hypothesis is that learning the categorization task involves both bottom-up, ITC to prefrontal cortex (PFC), and top-down (PFC to ITC) synaptic plasticity and that the latter enhances the selectivity of the ITC neurons encoding the task-relevant features of the stimuli, thereby improving the signal-to-noise ratio. We test this hypothesis by modeling both areas and their connections with spiking neurons and plastic synapses, ITC acting as a feature-selective layer and PFC as a category coding layer. This minimal model gives interesting clues as to properties and function of the selective feedback signal from PFC to ITC that help solving a categorization task. In particular, we show that, when the stimuli are very noisy because of a large number of nonrelevant features, the feedback structure helps getting better categorization performance and decreasing the reaction time. It also affects the speed and stability of the learning process and sharpens tuning curves of ITC neurons. Furthermore, the model predicts a modulation of neural activities during error trials, by which the differential selectivity of ITC neurons to task-relevant and task-irrelevant features diminishes or is even reversed, and modulations in the time course of neural activities that appear when, after learning, corrupted versions of the stimuli are input to the network.

Slow waves form expanding, memory-rich mesostates steered by local excitability in fading anesthesia.

In the arousal process, the brain restores its integrative activity from the synchronized state of slow wave activity (SWA). The mechanisms underpinning this state transition remain, however, to be elucidated. Here we simultaneously probed neuronal assemblies throughout the whole cortex with micro-electrocorticographic recordings in mice. We investigated the progressive shaping of propagating SWA at different levels of isoflurane. We found a form of memory of the wavefront shapes at deep anesthesia, tightly alternating posterior-anterior-posterior patterns. At low isoflurane, metastable patterns propagated in more directions, reflecting an increased complexity. The wandering across these mesostates progressively increased its randomness, as predicted by simulations of a network of spiking neurons, and confirmed in our experimental data. The complexity increase is explained by the elevated excitability of local assemblies with no modifications of the network connectivity. These results shed new light on the functional reorganization of the cortical network as anesthesia fades out.

Slow and fast rhythms generated in the cerebral cortex of the anesthetized mouse.

A characterization of the oscillatory activity in the cerebral cortex of the mouse was realized under ketamine anesthesia. Bilateral recordings were obtained from deep layers of primary visual, somatosensory, motor, and medial prefrontal cortex. A slow oscillatory activity consisting of up and down states was detected, the average frequency being 0.97 Hz in all areas. Different parameters of the oscillation were estimated across cortical areas, including duration of up and down states and their variability, speed of state transitions, and population firing rate. Similar values were obtained for all areas except for prefrontal cortex, which showed significant faster down-to-up state transitions, higher firing rate during up states, and more regular cycles. The wave propagation patterns in the anteroposterior axis in motor cortex and the mediolateral axis in visual cortex were studied with multielectrode recordings, yielding speed values between 8 and 93 mm/s. The firing of single units was analyzed with respect to the population activity. The most common pattern was that of neurons firing in >90% of the up states with 1-6 spikes. Finally, fast rhythms (beta, low gamma, and high gamma) were analyzed, all of them showing significantly larger power during up states than in down states. Prefrontal cortex exhibited significantly larger power in both beta and gamma bands (up to 1 order of magnitude larger in the case of high gamma) than the rest of the cortical areas. This study allows us to carry out interareal comparisons and provides a baseline to compare against cortical emerging activity from genetically altered animals.

Energy-Based Hierarchical Clustering of Cortical Slow Waves in Multi-Electrode Recordings.

The recent development of novel multi-electrode recording technologies has revealed the existence of traveling patterns of cortical activity in many species and under different states of awareness. Among these, slow activation waves occurring under sleep and anesthesia have been widely investigated as they provide unique insights into network features such as excitability, connectivity, structure, and dynamics of the cerebral cortex. Such characterization is usually based on clustering methods which are constrained by a priori assumptions as to the number of clusters to be used or rely on wave-by-wave pattern reconstruction. Here, we introduce a new computational tool based on modal analysis of fluid flows which is robustly applied to multivariate electrophysiological data from cortical networks, namely the Energy-based Hierarchical Waves Clustering method (EHWC). EHWC is composed of three main steps: (1) detecting the occurrence of global waves; (2) reducing the data dimensionality via singular value decomposition; (3) clustering hierarchically the singled-out waves. The analysis does not require the single-channel contribution to the waves, which is a typical bottleneck in this kind of analysis due to the unavoidable intrinsic variability of locally recorded activity. For testing and validation, here we used in vivo extracellular recordings from mice cortex under three different levels of anesthesia. As a result, we found slow waves with an increasing number of propagation modes as the anesthesia level decreases, giving an estimate of the increasing complexity of network dynamics. This and other wave's features replicate and extend the findings from previous literature, paving the way to extend the same approach to non-invasive electrophysiological recordings like EEG and fMRI used clinically for the characterization of brain dynamics and clinical stratification in brain lesions.

Attractor competition enriches cortical dynamics during awakening from anesthesia.

Slow oscillations (≲ 1 Hz), a hallmark of slow-wave sleep and deep anesthesia across species, arise from spatiotemporal patterns of activity whose complexity increases as wakefulness is approached and cognitive functions emerge. The arousal process constitutes an open window to the unknown mechanisms underlying the emergence of such dynamical richness in awake cortical networks. Here, we investigate the changes in network dynamics as anesthesia fades out in the rat visual cortex. Starting from deep anesthesia, slow oscillations gradually 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. Based on our model, dynamical richness emerges as a competition between two metastable attractor states, a conclusion strongly supported by the data.

Binocular rivalry reveals an out-of-equilibrium neural dynamics suited for decision-making.

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.

Up and Down States During Slow Oscillations in Slow-Wave Sleep and Different Levels of Anesthesia.

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.