Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity

Hyperpolarization-activated currents drive neuronal activation sequences in sleep

Sequential neuronal patterns are believed to support information processing in the cortex, yet their origin is still a matter of debate. We report that neuronal activity in the mouse postsubiculum (PoSub), where a majority of neurons are modulated by the animal's head direction, was sequentially activated along the dorsoventral axis during sleep at the transition from hyperpolarized "DOWN" to activated "UP" states, while representing a stable direction. Computational modeling suggested that these dynamics could be attributed to a spatial gradient of hyperpolarization-activated currents (Ih), which we confirmed in ex vivo slice experiments and corroborated in other cortical structures. These findings open up the possibility that varying amounts of Ih across cortical neurons could result in sequential neuronal patterns and that traveling activity upstream of the entorhinal-hippocampal circuit organizes large-scale neuronal activity supporting learning and memory during sleep.

Metastability in networks of nonlinear stochastic integrate-and-fire neurons

Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment of information. How these collective patterns of activity depend on single neuron properties is often unclear. Single-neuron recordings have shown that individual neural responses to inputs are nonlinear, which prevents a straightforward extrapolation from single neuron features to emergent collective states. In this work, we use a field theoretic formulation of a stochastic leaky integrate-and-fire model to study the impact of nonlinear intensity functions on macroscopic network activity. We show that the interplay between nonlinear spike emission and membrane potential resets can i) give rise to metastable transitions between active firing rate states, and ii) can enhance or suppress mean firing rates and membrane potentials in opposite directions.

Spontaneous persistent activity and inactivity in vivo reveals differential cortico-entorhinal functional connectivity

Understanding the functional connectivity between brain regions and its emergent dynamics is a central challenge. Here we present a theory-experiment hybrid approach involving iteration between a minimal computational model and in vivo electrophysiological measurements. Our model not only predicted spontaneous persistent activity (SPA) during Up-Down-State oscillations, but also inactivity (SPI), which has never been reported. These were confirmed in vivo in the membrane potential of neurons, especially from layer 3 of the medial and lateral entorhinal cortices. The data was then used to constrain two free parameters, yielding a unique, experimentally determined model for each neuron. Analytic and computational analysis of the model generated a dozen quantitative predictions about network dynamics, which were all confirmed in vivo to high accuracy. Our technique predicted functional connectivity; e. g. the recurrent excitation is stronger in the medial than lateral entorhinal cortex. This too was confirmed with connectomics data. This technique uncovers how differential cortico-entorhinal dialogue generates SPA and SPI, which could form an energetically efficient working-memory substrate and influence the consolidation of memories during sleep. More broadly, our procedure can reveal the functional connectivity of large networks and a theory of their emergent dynamics.

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.

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal replay, which is critical for memory consolidation. The sudden and repeated occurrences of these burst states during ongoing neural activity suggest metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to stochastic spiking and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesoscopic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie to obtain a "chemical Langevin equation", which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down-states dynamics) by means of phase-plane analysis. An extension of the Langevin equation for small network sizes is also presented. The stochastic neural mass model constitutes the basic component of our mesoscopic model for replay. We show that the mesoscopic model faithfully captures the statistical structure of individual replayed trajectories in microscopic simulations and in previously reported experimental data. Moreover, compared to the deterministic Romani-Tsodyks model of place-cell dynamics, it exhibits a higher level of variability regarding order, direction and timing of replayed trajectories, which seems biologically more plausible and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.

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.

Neural mechanisms underlying the temporal organization of naturalistic animal behavior

Naturalistic animal behavior exhibits a strikingly complex organization in the temporal domain, with variability arising from at least three sources: hierarchical, contextual, and stochastic. What neural mechanisms and computational principles underlie such intricate temporal features? In this review, we provide a critical assessment of the existing behavioral and neurophysiological evidence for these sources of temporal variability in naturalistic behavior. Recent research converges on an emergent mechanistic theory of temporal variability based on attractor neural networks and metastable dynamics, arising via coordinated interactions between mesoscopic neural circuits. We highlight the crucial role played by structural heterogeneities as well as noise from mesoscopic feedback loops in regulating flexible behavior. We assess the shortcomings and missing links in the current theoretical and experimental literature and propose new directions of investigation to fill these gaps.

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.

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Complexity of isoflurane-induced slow waves reliably determines anesthesia level

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In deep anesthesia, the propagation strictly alternates between front-back-front patterns

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In light anesthesia, there is a continuum of directions and faster propagation

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Local excitability underpins the cortical reorganization in fading anesthesia

Nonlinear collision between propagating waves in mouse somatosensory cortex

How does cellular organization shape the spatio-temporal patterns of activity in the cortex while processing sensory information? After measuring the propagation of activity in the mouse primary somatosensory cortex (S1) in response to single whisker deflections with Voltage Sensitive Dye (VSD) imaging, we developed a two dimensional model of S1. We designed an inference method to reconstruct model parameters from VSD data, revealing that a spatially heterogeneous organization of synaptic strengths between pyramidal neurons in S1 is likely to be responsible for the heterogeneous spatio-temporal patterns of activity measured experimentally. The model shows that, for strong enough excitatory cortical interactions, whisker deflections generate a propagating wave in S1. Finally, we report that two consecutive stimuli activating different spatial locations in S1 generate two waves which collide sub-linearly, giving rise to a suppressive wave. In the inferred model, the suppressive wave is explained by a lower sensitivity to external perturbations of neural networks during activated states.

Control of Brain State Transitions with a Photoswitchable Muscarinic Agonist

The ability to control neural activity is essential for research not only in basic neuroscience, as spatiotemporal control of activity is a fundamental experimental tool, but also in clinical neurology for therapeutic brain interventions. Transcranial-magnetic, ultrasound, and alternating/direct current (AC/DC) stimulation are some available means of spatiotemporal controlled neuromodulation. There is also light-mediated control, such as optogenetics, which has revolutionized neuroscience research, yet its clinical translation is hampered by the need for gene manipulation. As a drug-based light-mediated control, the effect of a photoswitchable muscarinic agonist (Phthalimide-Azo-Iper (PAI)) on a brain network is evaluated in this study. First, the conditions to manipulate M2 muscarinic receptors with light in the experimental setup are determined. Next, physiological synchronous emergent cortical activity consisting of slow oscillations-as in slow wave sleep-is transformed into a higher frequency pattern in the cerebral cortex, both in vitro and in vivo, as a consequence of PAI activation with light. These results open the way to study cholinergic neuromodulation and to control spatiotemporal patterns of activity in different brain states, their transitions, and their links to cognition and behavior. The approach can be applied to different organisms and does not require genetic manipulation, which would make it translational to humans.

Impact of GABAA and GABAB Inhibition on Cortical Dynamics and Perturbational Complexity during Synchronous and Desynchronized States

Quantitative estimations of spatiotemporal complexity of cortical activity patterns are used in the clinic as a measure of consciousness levels, but the cortical mechanisms involved are not fully understood. We used a version of the perturbational complexity index (PCI) adapted to multisite recordings from the ferret (either sex) cerebral cortex in vitro (sPCI) to investigate the role of GABAergic inhibition in cortical complexity. We studied two dynamical states: slow-wave activity (synchronous state) and desynchronized activity, that express low and high causal complexity respectively. Progressive blockade of GABAergic inhibition during both regimes revealed its impact on the emergent cortical activity and on sPCI. Gradual GABAA receptor blockade resulted in higher synchronization, being able to drive the network from a desynchronized to a synchronous state, with a progressive decrease of complexity (sPCI). Blocking GABAB receptors also resulted in a reduced sPCI, in particular when in a synchronous, slow wave state. Our findings demonstrate that physiological levels of inhibition contribute to the generation of dynamical richness and spatiotemporal complexity. However, if inhibition is diminished or enhanced, cortical complexity decreases. Using a computational model, we explored a larger parameter space in this relationship and demonstrate a link between excitatory/inhibitory balance and the complexity expressed by the cortical network.SIGNIFICANCE STATEMENT The spatiotemporal complexity of the activity expressed by the cerebral cortex is a highly revealing feature of the underlying network's state. Complexity varies with physiological brain states: it is higher during awake than during sleep states. But it also informs about pathologic states: in disorders of consciousness, complexity is lower in an unresponsive wakefulness syndrome than in a minimally conscious state. What are the network parameters that modulate complexity? Here we investigate how inhibition, mediated by either GABAA or GABAA receptors, influences cortical complexity. And we do this departing from two extreme functional states: a highly synchronous, slow-wave state, and a desynchronized one that mimics wakefulness. We find that there is an optimal level of inhibition in which complexity is highest.

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.

State-Dependent Regulation of Cortical Processing Speed via Gain Modulation

To thrive in dynamic environments, animals must be capable of rapidly and flexibly adapting behavioral responses to a changing context and internal state. Examples of behavioral flexibility include faster stimulus responses when attentive and slower responses when distracted. Contextual or state-dependent modulations may occur early in the cortical hierarchy and may be implemented via top-down projections from corticocortical or neuromodulatory pathways. However, the computational mechanisms mediating the effects of such projections are not known. Here, we introduce a theoretical framework to classify the effects of cell type-specific top-down perturbations on the information processing speed of cortical circuits. Our theory demonstrates that perturbation effects on stimulus processing can be predicted by intrinsic gain modulation, which controls the timescale of the circuit dynamics. Our theory leads to counterintuitive effects, such as improved performance with increased input variance. We tested the model predictions using large-scale electrophysiological recordings from the visual hierarchy in freely running mice, where we found that a decrease in single-cell intrinsic gain during locomotion led to an acceleration of visual processing. Our results establish a novel theory of cell type-specific perturbations, applicable to top-down modulation as well as optogenetic and pharmacological manipulations. Our theory links connectivity, dynamics, and information processing via gain modulation.SIGNIFICANCE STATEMENT To thrive in dynamic environments, animals adapt their behavior to changing circumstances and different internal states. Examples of behavioral flexibility include faster responses to sensory stimuli when attentive and slower responses when distracted. Previous work suggested that contextual modulations may be implemented via top-down inputs to sensory cortex coming from higher brain areas or neuromodulatory pathways. Here, we introduce a theory explaining how the speed at which sensory cortex processes incoming information is adjusted by changes in these top-down projections, which control the timescale of neural activity. We tested our model predictions in freely running mice, revealing that locomotion accelerates visual processing. Our theory is applicable to internal modulation as well as optogenetic and pharmacological manipulations and links circuit connectivity, dynamics, and information processing.

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.

Modulation of cortical slow oscillatory rhythm by GABAB receptors: an in vitro experimental and computational study

KEY POINTS

We confirm that GABAB receptors (GABAB -Rs) are involved in the termination of Up-states; their blockade consistently elongates Up-states. GABAB -Rs also modulate Down-states and the oscillatory cycle, thus having an impact on slow oscillation rhythm and its regularity. The most frequent effect of GABAB -R blockade is elongation of Down-states and subsequent decrease of oscillatory frequency, with an increased regularity. In a quarter of cases, GABAB -R blockade shortened Down-states and increased oscillatory frequency, changes that are independent of firing rates in Up-states. Our computer model provides mechanisms for the experimentally observed dynamics following blockade of GABAB -Rs, for Up/Down durations, oscillatory frequency and regularity. The time course of excitation, inhibition and adaptation can explain the observed dynamics of the network. This study brings novel insights into the role of GABAB -R-mediated slow inhibition on the slow oscillatory activity, which is considered the default activity pattern of the cortical network.

ABSTRACT

Slow wave oscillations (SWOs) dominate cortical activity during deep sleep, anaesthesia and in some brain lesions. SWOs are composed of periods of activity (Up states) interspersed with periods of silence (Down states). The rhythmicity expressed during SWOs integrates neuronal and connectivity properties of the network and is often altered under pathological conditions. Adaptation mechanisms as well as synaptic inhibition mediated by GABAB receptors (GABAB -Rs) have been proposed as mechanisms governing the termination of Up states. The interplay between these two mechanisms is not well understood, and the role of GABAB -Rs controlling the whole cycle of the SWO has not been described. Here we contribute to its understanding by combining in vitro experiments on spontaneously active cortical slices and computational techniques. GABAB -R blockade modified the whole SWO cycle, not only elongating Up states, but also affecting the subsequent Down state duration. Furthermore, while adaptation tends to yield a rather regular behaviour, we demonstrate that GABAB -R activation desynchronizes the SWOs. Interestingly, variability changes could be accomplished in two different ways: by either shortening or lengthening the duration of Down states. Even when the most common observation following GABAB -Rs blocking is the lengthening of Down states, both changes are expressed experimentally and also in numerical simulations. Our simulations suggest that the sluggishness of GABAB -Rs to follow the excitatory fluctuations of the cortical network can explain these different network dynamics modulated by GABAB -Rs.

The (Un)Conscious Mouse as a Model for Human Brain Functions: Key Principles of Anesthesia and Their Impact on Translational Neuroimaging

In recent years, technical and procedural advances have brought functional magnetic resonance imaging (fMRI) to the field of murine neuroscience. Due to its unique capacity to measure functional activity non-invasively, across the entire brain, fMRI allows for the direct comparison of large-scale murine and human brain functions. This opens an avenue for bidirectional translational strategies to address fundamental questions ranging from neurological disorders to the nature of consciousness. The key challenges of murine fMRI are: (1) to generate and maintain functional brain states that approximate those of calm and relaxed human volunteers, while (2) preserving neurovascular coupling and physiological baseline conditions. Low-dose anesthetic protocols are commonly applied in murine functional brain studies to prevent stress and facilitate a calm and relaxed condition among animals. Yet, current mono-anesthesia has been shown to impair neural transmission and hemodynamic integrity. By linking the current state of murine electrophysiology, Ca2+ imaging and fMRI of anesthetic effects to findings from human studies, this systematic review proposes general principles to design, apply and monitor anesthetic protocols in a more sophisticated way. The further development of balanced multimodal anesthesia, combining two or more drugs with complementary modes of action helps to shape and maintain specific brain states and relevant aspects of murine physiology. Functional connectivity and its dynamic repertoire as assessed by fMRI can be used to make inferences about cortical states and provide additional information about whole-brain functional dynamics. Based on this, a simple and comprehensive functional neurosignature pattern can be determined for use in defining brain states and anesthetic depth in rest and in response to stimuli. Such a signature can be evaluated and shared between labs to indicate the brain state of a mouse during experiments, an important step toward translating findings across species.

Up and Down States and Memory Consolidation Across Somatosensory, Entorhinal, and Hippocampal Cortices

In the course of a day, brain states fluctuate, from conscious awake information-acquiring states to sleep states, during which previously acquired information is further processed and stored as memories. One hypothesis is that memories are consolidated and stored during "offline" states such as sleep, a process thought to involve transfer of information from the hippocampus to other cortical areas. Up and Down states (UDS), patterns of activity that occur under anesthesia and sleep states, are likely to play a role in this process, although the nature of this role remains unclear. Here we review what is currently known about these mechanisms in three anatomically distinct but interconnected cortical areas: somatosensory cortex, entorhinal cortex, and the hippocampus. In doing so, we consider the role of this activity in the coordination of "replay" during sleep states, particularly during hippocampal sharp-wave ripples. We conclude that understanding the generation and propagation of UDS may provide key insights into the cortico-hippocampal dialogue linking archi- and neocortical areas during memory formation.

Cortical state transitions and stimulus response evolve along stiff and sloppy parameter dimensions, respectively

Previous research showed that spontaneous neuronal activity presents sloppiness: the collective behavior is strongly determined by a small number of parameter combinations, defined as ‘stiff’ dimensions, while it is insensitive to many others (‘sloppy’ dimensions). Here, we analyzed neural population activity from the auditory cortex of anesthetized rats while the brain spontaneously transited through different synchronized and desynchronized states and intermittently received sensory inputs. We showed that cortical state transitions were determined by changes in stiff parameters associated with the activity of a core of neurons with low responses to stimuli and high centrality within the observed network. In contrast, stimulus-evoked responses evolved along sloppy dimensions associated with the activity of neurons with low centrality and displaying large ongoing and stimulus-evoked fluctuations without affecting the integrity of the network. Our results shed light on the interplay among stability, flexibility, and responsiveness of neuronal collective dynamics during intrinsic and induced activity.

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.

Cholinergic Switch between Two Types of Slow Waves in Cerebral Cortex

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory versus excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

Analysis Pipeline for Extracting Features of Cortical Slow Oscillations

Cortical slow oscillations (≲1 Hz) are an emergent property of the cortical network that integrate connectivity and physiological features. This rhythm, highly revealing of the characteristics of the underlying dynamics, is a hallmark of low complexity brain states like sleep, and represents a default activity pattern. Here, we present a methodological approach for quantifying the spatial and temporal properties of this emergent activity. We improved and enriched a robust analysis procedure that has already been successfully applied to both in vitro and in vivo data acquisitions. We tested the new tools of the methodology by analyzing the electrocorticography (ECoG) traces recorded from a custom 32-channel multi-electrode array in wild-type isoflurane-anesthetized mice. The enhanced analysis pipeline, named SWAP (Slow Wave Analysis Pipeline), detects Up and Down states, enables the characterization of the spatial dependency of their statistical properties, and supports the comparison of different subjects. The SWAP is implemented in a data-independent way, allowing its application to other data sets (acquired from different subjects, or with different recording tools), as well as to the outcome of numerical simulations. By using the SWAP, we report statistically significant differences in the observed slow oscillations (SO) across cortical areas and cortical sites. Computing cortical maps by interpolating the features of SO acquired at the electrode positions, we give evidence of gradients at the global scale along an oblique axis directed from fronto-lateral toward occipito-medial regions, further highlighting some heterogeneity within cortical areas. The results obtained using the SWAP will be essential for producing data-driven brain simulations. A spatial characterization of slow oscillations will also trigger a discussion on the role of, and the interplay between, the different regions in the cortex, improving our understanding of the mechanisms of generation and propagation of delta rhythms and, more generally, of cortical properties.

Bistability, Causality, and Complexity in Cortical Networks: An In Vitro Perturbational Study

Measuring the spatiotemporal complexity of cortical responses to direct perturbations provides a reliable index of the brain's capacity for consciousness in humans under both physiological and pathological conditions. Upon loss of consciousness, the complex pattern of causal interactions observed during wakefulness collapses into a stereotypical slow wave, suggesting that cortical bistability may play a role. Bistability is mainly expressed in the form of slow oscillations, a default pattern of activity that emerges from cortical networks in conditions of functional or anatomical disconnection. Here, we employ an in vitro model to understand the relationship between bistability and complexity in cortical circuits. We adapted the perturbational complexity index applied in humans to electrically stimulated cortical slices under different neuromodulatory conditions. At this microscale level, we demonstrate that perturbational complexity can be effectively modulated by pharmacological reduction of bistability and, albeit to a lesser extent, by enhancement of excitability, providing mechanistic insights into the macroscale measurements performed in humans.

Scaling of a Large-Scale Simulation of Synchronous Slow-Wave and Asynchronous Awake-Like Activity of a Cortical Model With Long-Range Interconnections

Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during wakefulness (AW). Such dynamic diversity poses a challenge for producing efficient large-scale simulations that embody realistic metaphors of short- and long-range synaptic connectivity. In fact, during SWA and AW different spatial extents of the cortical tissue are active in a given timespan and at different firing rates, which implies a wide variety of loads of local computation and communication. A balanced evaluation of simulation performance and robustness should therefore include tests of a variety of cortical dynamic states. Here, we demonstrate performance scaling of our proprietary Distributed and Plastic Spiking Neural Networks (DPSNN) simulation engine in both SWA and AW for bidimensional grids of neural populations, which reflects the modular organization of the cortex. We explored networks up to 192 × 192 modules, each composed of 1,250 integrate-and-fire neurons with spike-frequency adaptation, and exponentially decaying inter-modular synaptic connectivity with varying spatial decay constant. For the largest networks the total number of synapses was over 70 billion. The execution platform included up to 64 dual-socket nodes, each socket mounting 8 Intel Xeon Haswell processor cores @ 2.40 GHz clock rate. Network initialization time, memory usage, and execution time showed good scaling performances from 1 to 1,024 processes, implemented using the standard Message Passing Interface (MPI) protocol. We achieved simulation speeds of between 2.3 × 109 and 4.1 × 109 synaptic events per second for both cortical states in the explored range of inter-modular interconnections.

NREM sleep in the rodent neocortex and hippocampus reflects excitable dynamics

During non-rapid eye movement (NREM) sleep, neuronal populations in the mammalian forebrain alternate between periods of spiking and inactivity. Termed the slow oscillation in the neocortex and sharp wave-ripples in the hippocampus, these alternations are often considered separately but are both crucial for NREM functions. By directly comparing experimental observations of naturally-sleeping rats with a mean field model of an adapting, recurrent neuronal population, we find that the neocortical alternations reflect a dynamical regime in which a stable active state is interrupted by transient inactive states (slow waves) while the hippocampal alternations reflect a stable inactive state interrupted by transient active states (sharp waves). We propose that during NREM sleep in the rodent, hippocampal and neocortical populations are excitable: each in a stable state from which internal fluctuations or external perturbation can evoke the stereotyped population events that mediate NREM functions.

Quantification of Signal-to-Noise Ratio in Cerebral Cortex Recordings Using Flexible MEAs With Co-localized Platinum Black, Carbon Nanotubes, and Gold Electrodes

Developing new standardized tools to characterize brain recording devices is critical to evaluate neural probes and for translation to clinical use. The signal-to-noise ratio (SNR) measurement is the gold standard for quantifying the performance of brain recording devices. Given the drawbacks with the SNR measure, our first objective was to devise a new method to calculate the SNR of neural signals to distinguish signal from noise. Our second objective was to apply this new SNR method to evaluate electrodes of three different materials (platinum black, Pt; carbon nanotubes, CNTs; and gold, Au) co-localized in tritrodes to record from the same cortical area using specifically designed multielectrode arrays. Hence, we devised an approach to calculate SNR at different frequencies based on the features of cortical slow oscillations (SO). Since SO consist in the alternation of silent periods (Down states) and active periods (Up states) of neuronal activity, we used these as noise and signal, respectively. The spectral SNR was computed as the power spectral density (PSD) of Up states (signal) divided by the PSD of Down states (noise). We found that Pt and CNTs electrodes have better recording performance than Au electrodes for the explored frequency range (5–1500 Hz). Together with two proposed SNR estimators for the lower and upper frequency limits, these results substantiate our SNR calculation at different frequency bands. Our results provide a new validated SNR measure that provides rich information of the performance of recording devices at different brain activity frequency bands (<1500 Hz).

Sleep-like cortical OFF-periods disrupt causality and complexity in the brain of unresponsive wakefulness syndrome patients

Unresponsive wakefulness syndrome (UWS) patients may retain intact portions of the thalamocortical system that are spontaneously active and reactive to sensory stimuli but fail to engage in complex causal interactions, resulting in loss of consciousness. Here, we show that loss of brain complexity after severe injuries is due to a pathological tendency of cortical circuits to fall into silence (OFF-period) upon receiving an input, a behavior typically observed during sleep. Spectral and phase domain analysis of EEG responses to transcranial magnetic stimulation reveals the occurrence of OFF-periods in the cortex of UWS patients (N = 16); these events never occur in healthy awake individuals (N = 20) but are similar to those detected in healthy sleeping subjects (N = 8). Crucially, OFF-periods impair local causal interactions, and prevent the build-up of global complexity in UWS. Our findings link potentially reversible local events to global brain dynamics that are relevant for pathological loss and recovery of consciousness.

Many brain-injured patients retain large cortical islands that are intact, active and reactive but blocked in a state of low complexity, leading to unconsciousness. Here, the authors show that this loss of complexity is due to the pathological engagement of sleep-like neuronal mechanisms.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise : Spontaneous activity in networks with synaptic noise

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Milliseconds of Sensory Input Abruptly Modulate the Dynamics of Cortical States for Seconds

Spontaneous internal activity plays a major role in higher brain functions. The question of how it modulates sensory evoked activity and behavior has been explored in anesthetized rodents, cats, monkeys and in behaving human subjects. However, the complementary question of how a brief sensory input modulates the internally generated activity in vivo remains unresolved, and high-resolution mapping of these bidirectional interactions was never performed. Integrating complementary methodologies, at population and single cells levels, we explored this question. Voltage-sensitive dye imaging of population activity in anesthetized rats' somatosensory cortex revealed that spontaneous up-states were largely diminished for ~2 s, even after a single weak whisker deflection. This effect was maximal at the stimulated barrel but spread across several cortical areas. A higher velocity whisker deflection evoked activity at ~15Hz. Two-photon calcium imaging activity and cell-attached recordings confirmed the VSD results and revealed that for several seconds most single cells decreased their firing, but a small number increased firing. Comparing single deflection with long train stimulation, we found a dominant effect of the first population spike. We suggest that, at the onset of a sensory input, some internal messages are silenced to prevent overloading of the processing of relevant incoming sensory information.

Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Understanding the origin, nature, and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in neuroscience. Such patterns include collective oscillations emerging out of neural synchronization as well as highly heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches." Much debate has been generated about the possible scale invariance or criticality of such avalanches and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but crucially, includes stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-state, synchronous, asynchronous, and up-state phases and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition as usually assumed in theoretical approaches but to a synchronization phase transition, at which incipient oscillations and scale-free avalanches coexist. Furthermore, our model also accounts for up and down states as they occur (e.g., during deep sleep). This approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping to shed light on basic aspects of brain functioning from a very broad perspective.

Bistability and up/down state alternations in inhibition-dominated randomly connected networks of LIF neurons

Electrophysiological recordings in cortex in vivo have revealed a rich variety of dynamical regimes ranging from irregular asynchronous states to a diversity of synchronized states, depending on species, anesthesia, and external stimulation. The average population firing rate in these states is typically low. We study analytically and numerically a network of sparsely connected excitatory and inhibitory integrate-and-fire neurons in the inhibition-dominated, low firing rate regime. For sufficiently high values of the external input, the network exhibits an asynchronous low firing frequency state (L). Depending on synaptic time constants, we show that two scenarios may occur when external inputs are decreased: (1) the L state can destabilize through a Hopf bifucation as the external input is decreased, leading to synchronized oscillations spanning d δ to β frequencies; (2) the network can reach a bistable region, between the low firing frequency network state (L) and a quiescent one (Q). Adding an adaptation current to excitatory neurons leads to spontaneous alternations between L and Q states, similar to experimental observations on UP and DOWN states alternations.

UP-DOWN cortical dynamics reflect state transitions in a bistable network

In the idling brain, neuronal circuits transition between periods of sustained firing (UP state) and quiescence (DOWN state), a pattern the mechanisms of which remain unclear. Here we analyzed spontaneous cortical population activity from anesthetized rats and found that UP and DOWN durations were highly variable and that population rates showed no significant decay during UP periods. We built a network rate model with excitatory (E) and inhibitory (I) populations exhibiting a novel bistable regime between a quiescent and an inhibition-stabilized state of arbitrarily low rate. Fluctuations triggered state transitions, while adaptation in E cells paradoxically caused a marginal decay of E-rate but a marked decay of I-rate in UP periods, a prediction that we validated experimentally. A spiking network implementation further predicted that DOWN-to-UP transitions must be caused by synchronous high-amplitude events. Our findings provide evidence of bistable cortical networks that exhibit non-rhythmic state transitions when the brain rests.

Shaping the Default Activity Pattern of the Cortical Network

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.

Review: How do spontaneous and sensory-evoked activities interact?

Twenty years ago, the seminal work of Grinvald et al. revolutionized the view cast on spontaneous cortical activity by showing how, instead of being a mere measure of noise, it profoundly impacts cortical responses to a sensory input and therefore could play a role in sensory processing. This paved the way for a number of studies on the interactions between spontaneous and sensory-evoked activities. Spontaneous activity has subsequently been found to be highly structured and to participate in high cognitive functions, such as influencing conscious perception in humans. However, its functional role remains poorly understood, and only a few speculations exist, from the maintenance of the cortical network to the internal representation of an a priori knowledge of the environment. Furthermore, elucidation of this functional role could stem from studying the opposite relationship between spontaneous and sensory-evoked activities, namely, how a sensory input influences subsequent internal activities. Indeed, this question has remained largely unexplored, but a recent study by the Grinvald laboratory shows that a brief sensory input largely dampens spontaneous rhythms, suggesting a more sophisticated view where some spontaneous rhythms might relate to sensory processing and some others not.

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.

Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis

Two, partially interwoven, hot topics in the analysis and statistical modeling of neural data, are the development of efficient and informative representations of the time series derived from multiple neural recordings, and the extraction of information about the connectivity structure of the underlying neural network from the recorded neural activities. In the present paper we show that state-space clustering can provide an easy and effective option for reducing the dimensionality of multiple neural time series, that it can improve inference of synaptic couplings from neural activities, and that it can also allow the construction of a compact representation of the multi-dimensional dynamics, that easily lends itself to complexity measures. We apply a variant of the ‘mean-shift’ algorithm to perform state-space clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are largely uncorrelated from memories embedded in the synaptic matrix. In this context, we show that the neural states identified as clusters’ centroids offer a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from the neural activities. Moving to the more realistic case of a multi-modular spiking network, with spike-frequency adaptation inducing history-dependent effects, we propose a procedure inspired by Boltzmann learning, but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations; we then illustrate, in the spiking network, how clustering is effective in extracting relevant features of the network’s state-space landscape. Finally, we show that the knowledge of the cluster structure allows casting the multi-dimensional neural dynamics in the form of a symbolic dynamics of transitions between clusters; as an illustration of the potential of such reduction, we define and analyze a measure of complexity of the neural time series.

Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity

Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.

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.

Impact of sub and supra-threshold adaptation currents in networks of spiking neurons

Neuronal adaptation is the intrinsic capacity of the brain to change, by various mechanisms, its dynamical responses as a function of the context. Such a phenomena, widely observed in vivo and in vitro, is known to be crucial in homeostatic regulation of the activity and gain control. The effects of adaptation have already been studied at the single-cell level, resulting from either voltage or calcium gated channels both activated by the spiking activity and modulating the dynamical responses of the neurons. In this study, by disentangling those effects into a linear (sub-threshold) and a non-linear (supra-threshold) part, we focus on the the functional role of those two distinct components of adaptation onto the neuronal activity at various scales, starting from single-cell responses up to recurrent networks dynamics, and under stationary or non-stationary stimulations. The effects of slow currents on collective dynamics, like modulation of population oscillation and reliability of spike patterns, is quantified for various types of adaptation in sparse recurrent networks.

Dynamics of multistable states during ongoing and evoked cortical activity

Single-trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory, and decision-making. Yet, very little is known about the network mechanisms responsible for its genesis. It is often assumed that the onset of state sequences is triggered by an external stimulus. Here we show that state sequences can be observed also in the absence of overt sensory stimulation. Analysis of multielectrode recordings from the gustatory cortex of alert rats revealed ongoing sequences of states, where single neurons spontaneously attain several firing rates across different states. This single-neuron multistability represents a challenge to existing spiking network models, where typically each neuron is at most bistable. We present a recurrent spiking network model that accounts for both the spontaneous generation of state sequences and the multistability in single-neuron firing rates. Each state results from the activation of neural clusters with potentiated intracluster connections, with the firing rate in each cluster depending on the number of active clusters. Simulations show that the model's ensemble activity hops among the different states, reproducing the ongoing dynamics observed in the data. When probed with external stimuli, the model predicts the quenching of single-neuron multistability into bistability and the reduction of trial-by-trial variability. Both predictions were confirmed in the data. Together, these results provide a theoretical framework that captures both ongoing and evoked network dynamics in a single mechanistic model.

Stochastic transitions into silence cause noise correlations in cortical circuits

The spiking activity of cortical neurons is highly variable. This variability is generally correlated among nearby neurons, an effect commonly interpreted to reflect the coactivation of neurons due to anatomically shared inputs. Recent findings, however, indicate that correlations can be dynamically modulated, suggesting that the underlying mechanisms are not well understood. Here, we investigate the hypothesis that correlations are dominated by neuronal coinactivation: the occurrence of brief silent periods during which all neurons in the local network stop firing. We recorded spiking activity from large populations of neurons in the auditory cortex of anesthetized rats across different brain states. During spontaneous activity, the reduction of correlation accompanying brain state desynchronization was largely explained by a decrease in the density of the silent periods. The presentation of a stimulus caused an initial drop of correlations followed by a rebound, a time course that was mimicked by the instantaneous silence density. We built a rate network model with fluctuation-driven transitions between a silent and an active attractor and assumed that neurons fired Poisson spike trains with a rate following the model dynamics. Variations of the network external input altered the transition rate into the silent attractor and reproduced the relation between correlation and silence density found in the data, both in spontaneous and evoked conditions. This suggests that the observed changes in correlation, occurring gradually with brain state variations or abruptly with sensory stimulation, are due to changes in the likeliness of the microcircuit to transiently cease firing.

Examination of rhythmicity of extracellularly recorded neurons in the entorhinal cortex

A number of studies have examined the theta-rhythmic modulation of neuronal firing in the hippocampal circuit. For extracellular recordings, this is often done by examining spectral properties of the spike-time autocorrelogram, most significantly, for validating the presence or absence of theta modulation across species. These techniques can show significant rhythmicity for high firing rate, highly rhythmic neurons; however, they are substantially biased by several factors including the peak firing rate of the neuron, the amount of time spent in the neuron's receptive field, and other temporal properties of the rhythmicity such as cycle-skipping. These limitations make it difficult to examine rhythmic modulation in neurons with low firing rates or when an animal has short dwell times within the firing field and difficult to compare rhythmicity under disparate experimental conditions when these factors frequently differ. Here, we describe in detail the challenges that researchers face when using these techniques and apply our findings to recent recordings from bat entorhinal grid cells, suggesting that they may have lacked enough data to examine theta rhythmicity robustly. We describe a more sensitive and statistically rigorous method using maximum likelihood estimation (MLE) of a parametric model of the lags within the autocorrelation window, which helps to alleviate some of the problems of traditional methods and was also unable to detect rhythmicity in bat grid cells. Using large batteries of simulated data, we explored the boundaries for which the MLE technique and the theta index can detect rhythmicity. The MLE technique is less sensitive to many features of the autocorrelogram and provides a framework for statistical testing to detect rhythmicity as well as changes in rhythmicity in individual sessions providing a substantial improvement over previous methods.

Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics

Short-term synaptic plasticity strongly affects the neural dynamics of cortical networks. The Tsodyks and Markram (TM) model for short-term synaptic plasticity accurately accounts for a wide range of physiological responses at different types of cortical synapses. Here, we report a route to chaotic behavior via a Shilnikov homoclinic bifurcation that dynamically organizes some of the responses in the TM model. In particular, the presence of such a homoclinic bifurcation strongly affects the shape of the trajectories in the phase space and induces highly irregular transient dynamics; indeed, in the vicinity of the Shilnikov homoclinic bifurcation, the number of population spikes and their precise timing are unpredictable and highly sensitive to the initial conditions. Such an irregular deterministic dynamics has its counterpart in stochastic/network versions of the TM model: The existence of the Shilnikov homoclinic bifurcation generates complex and irregular spiking patterns and--acting as a sort of springboard--facilitates transitions between the down-state and unstable periodic orbits. The interplay between the (deterministic) homoclinic bifurcation and stochastic effects may give rise to some of the complex dynamics observed in neural systems.

Sleep, neuroengineering and dynamics

Modeling of consciousness-related phenomena and neuroengineering are fields that are rapidly growing together. We review recent approaches and developments and point out some promising directions of future research: Understanding the dynamics of consciousness states and associated oscillations, pathological oscillations as well as their treatment by stimulation, neuroprosthetics and brain-computer-interface approaches, and stimulation approaches that probe, influence and strengthen memory consolidation. In all these fields, computational models connect theory, neurophysiology and neuroengineering research and pave a way towards medical applications.

Alteration of phase-phase coupling between theta and gamma rhythms in a depression-model of rats

Alterations in oscillatory brain activity are strongly correlated with cognitive performance in various physiological rhythms, especially the theta and gamma rhythms. In this study, we investigated the coupling relationship of neural activities between thalamus and medial prefrontal cortex (mPFC) by measuring the phase interactions between theta and gamma oscillations in a depression model of rats. The phase synchronization analysis showed that the phase locking at theta rhythm was weakened in depression. Furthermore, theta-gamma phase locking at n:m (1:6) ratio was found between thalamus and mPFC, while it was diminished in depression state. In addition, the analysis of coupling direction based on phase dynamics showed that the unidirectional influence from thalamus to mPFC was diminished in depression state only in theta rhythm, while it was partly recovered after the memantine treatment in a depression model of rats. The results suggest that the effects of depression on cognitive deficits are modulated via profound alterations in phase information transformation of theta rhythm and theta-gamma phase coupling.

The phase response of the cortical slow oscillation

Cortical slow oscillations occur in the mammalian brain during deep sleep and have been shown to contribute to memory consolidation, an effect that can be enhanced by electrical stimulation. As the precise underlying working mechanisms are not known it is desired to develop and analyze computational models of slow oscillations and to study the response to electrical stimuli. In this paper we employ the conductance based model of Compte et al. (J Neurophysiol 89:2707-2725, 2003) to study the effect of electrical stimulation. The population response to electrical stimulation depends on the timing of the stimulus with respect to the state of the slow oscillation. First, we reproduce the experimental results of electrical stimulation in ferret brain slices by Shu et al. (Nature 423:288-293, 2003) from the conductance based model. We then numerically obtain the phase response curve for the conductance based network model to quantify the network's response to weak stimuli. Our results agree with experiments in vivo and in vitro that show that sensitivity to stimulation is weaker in the up than in the down state. However, we also find that within the up state stimulation leads to a shortening of the up state, or phase advance, whereas during the up-down transition a prolongation of up states is possible, resulting in a phase delay. Finally, we compute the phase response curve for the simple mean-field model by Ngo et al. (EPL Europhys Lett 89:68002, 2010) and find that the qualitative shape of the PRC is preserved, despite its different mechanism for the generation of slow oscillations.