Brain stimulation competes with ongoing oscillations for control of spike timing in the primate brain.

Transcranial alternating current stimulation (tACS) is a popular method for modulating brain activity noninvasively. In particular, tACS is often used as a targeted intervention that enhances a neural oscillation at a specific frequency to affect a particular behavior. However, these interventions often yield highly variable results. Here, we provide a potential explanation for this variability: tACS competes with the brain's ongoing oscillations. Using neural recordings from alert nonhuman primates, we find that when neural firing is independent of ongoing brain oscillations, tACS readily entrains spiking activity, but when neurons are strongly entrained to ongoing oscillations, tACS often causes a decrease in entrainment instead. Consequently, tACS can yield categorically different results on neural activity, even when the stimulation protocol is fixed. Mathematical analysis suggests that this competition is likely to occur under many experimental conditions. Attempting to impose an external rhythm on the brain may therefore often yield precisely the opposite effect.

A deep generative adversarial network capturing complex spiral waves in disinhibited circuits of the cerebral cortex.

BACKGROUND: In the cerebral cortex, disinhibited activity is characterized by propagating waves that spread across neural tissue. In this pathological state, a widely reported form of activity are spiral waves that travel in a circular pattern around a fixed spatial locus termed the center of mass. Spiral waves exhibit stereotypical activity and involve broad patterns of co-fluctuations, suggesting that they may be of lower complexity than healthy activity. RESULTS: To evaluate this hypothesis, we performed dense multi-electrode recordings of cortical networks where disinhibition was induced by perfusing a pro-epileptiform solution containing 4-Aminopyridine as well as increased potassium and decreased magnesium. Spiral waves were identified based on a spatially delimited center of mass and a broad distribution of instantaneous phases across electrodes. Individual waves were decomposed into "snapshots" that captured instantaneous neural activation across the entire network. The complexity of these snapshots was examined using a measure termed the participation ratio. Contrary to our expectations, an eigenspectrum analysis of these snapshots revealed a broad distribution of eigenvalues and an increase in complexity compared to baseline networks. A deep generative adversarial network was trained to generate novel exemplars of snapshots that closely captured cortical spiral waves. These synthetic waves replicated key features of experimental data including a tight center of mass, a broad eigenvalue distribution, spatially-dependent correlations, and a high complexity. By adjusting the input to the model, new samples were generated that deviated in systematic ways from the experimental data, thus allowing the exploration of a broad range of states from healthy to pathologically disinhibited neural networks. CONCLUSIONS: Together, results show that the complexity of population activity serves as a marker along a continuum from healthy to disinhibited brain states. The proposed generative adversarial network opens avenues for replicating the dynamics of cortical seizures and accelerating the design of optimal neurostimulation aimed at suppressing pathological brain activity.

Key role of neuronal diversity in structured reservoir computing.

Chaotic time series have been captured by reservoir computing models composed of a recurrent neural network whose output weights are trained in a supervised manner. These models, however, are typically limited to randomly connected networks of homogeneous units. Here, we propose a new class of structured reservoir models that incorporates a diversity of cell types and their known connections. In a first version of the model, the reservoir was composed of mean-rate units separated into pyramidal, parvalbumin, and somatostatin cells. Stability analysis of this model revealed two distinct dynamical regimes, namely, (i) an inhibition-stabilized network (ISN) where strong recurrent excitation is balanced by strong inhibition and (ii) a non-ISN network with weak excitation. These results were extended to a leaky integrate-and-fire model that captured different cell types along with their network architecture. ISN and non-ISN reservoir networks were trained to relay and generate a chaotic Lorenz attractor. Despite their increased performance, ISN networks operate in a regime of activity near the limits of stability where external perturbations yield a rapid divergence in output. The proposed framework of structured reservoir computing opens avenues for exploring how neural microcircuits can balance performance and stability when representing time series through distinct dynamical regimes.

Frequency-separated principal component analysis of cortical population activity.

A hallmark of neocortical activity is the presence of low-dimensional fluctuations in firing rate that are coordinated across neurons. However, the impact of these fluctuations on sensory processing remains unclear. Here, we examined fluctuations in populations of orientation-selective neurons from anesthetized macaque primary visual cortex (V1) during stimulus viewing as well as spontaneous activity. We introduce a novel approach termed frequency-separated principal component analysis (FS-PCA) to characterize these fluctuations. This method unveiled a distribution of components with a broad range of frequencies whose eigenvalues and variance followed an approximate power law. During stimulus viewing, subpopulations of V1 neurons correlated either positively or negatively with low-dimensional fluctuations. These two subpopulations displayed distinct activation properties and noise correlations in response to sensory input. Together, results suggest that slow, low-dimensional fluctuations in V1 population activity shape the response of individual neurons to oriented stimuli and may impact the transmission of sensory information to downstream regions of the primary visual system.NEW & NOTEWORTHY A method termed frequency-separated principal component analysis (FS-PCA) is introduced for analyzing populations of simultaneously recorded neurons. This framework extends standard principal component analysis by extracting components of activity delimited to specific frequency bands. FS-PCA revealed that circuits of the primary visual cortex generate a broad range of components dominated by low-frequency activity. Furthermore, low-dimensional fluctuations in population activity modulated the response of individual neurons to sensory input.

Optimal Readout of Correlated Neural Activity in a Decision-Making Circuit.

The neural correlates of decision making have been extensively studied with tasks involving a choice between two alternatives that is guided by visual cues. While a large body of work argues for a role of the lateral intraparietal (LIP) region of cortex in these tasks, this role may be confounded by the interaction between LIP and other regions, including medial temporal (MT) cortex. Here, we describe a simplified linear model of decision making that is adapted to two tasks: a motion discrimination and a categorization task. We show that the distinct contribution of MT and LIP may indeed be confounded in these tasks. In particular, we argue that the motion discrimination task relies on a straightforward visuomotor mapping, which leads to redundant information between MT and LIP. The categorization task requires a more complex mapping between visual information and decision behavior, and therefore does not lead to redundancy between MT and LIP. Going further, the model predicts that noise correlations within LIP should be greater in the categorization compared to the motion discrimination task due to the presence of shared inputs from MT. The impact of these correlations on task performance is examined by analytically deriving error estimates of an optimal linear readout for shared and unique inputs. Taken together, results clarify the contribution of MT and LIP to decision making and help characterize the role of noise correlations in these regions.

Non-monotonic accumulation of spike time variance during membrane potential oscillations.

A spike-phase neural code has been proposed as a mechanism to encode stimuli based on the precise timing of spikes relative to the phase of membrane potential oscillations. This form of coding has been reported in both in vivo and in vitro experiments across several regions of the brain, yet there are concerns that such precise timing may be compromised by an effect referred to as variance accumulation, wherein spike timing variance increases over the phase of an oscillation. Here, we provide a straightforward explanation of this effect based on the theoretical spike time variance. The proposed theory is consistent with recordings of mitral neurons. It shows that spike time variance can increase in a nonlinear fashion with spike number, in a way that is dependent upon the frequency and amplitude of the oscillation. Further, non-monotonic accumulation of variance can arise from different combinations of oscillation parameters. Nonlinear accumulation sometimes leads to lower variance than that of a mean rate-matched homogeneous Poisson process, particularly for spikes that occur in later phases of oscillation. However, such an advantage is limited to a narrow range of oscillation amplitudes and frequencies. These results suggest fundamental constraints on spike-phase coding, and reveal how certain spikes in a sequence may exhibit increased firing time precision relative to their neighbors.

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems.

Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences of chaos for how such networks encode streams of temporal stimuli? On the one hand, chaos is a strong source of randomness, suggesting that small changes in stimuli will be obscured by intrinsically generated variability. On the other hand, recent work shows that the type of chaos that occurs in spiking networks can have a surprisingly low-dimensional structure, suggesting that there may be room for fine stimulus features to be precisely resolved. Here we show that strongly chaotic networks produce patterned spikes that reliably encode time-dependent stimuli: using a decoder sensitive to spike times on timescales of 10's of ms, one can easily distinguish responses to very similar inputs. Moreover, recurrence serves to distribute signals throughout chaotic networks so that small groups of cells can encode substantial information about signals arriving elsewhere. A conclusion is that the presence of strong chaos in recurrent networks need not exclude precise encoding of temporal stimuli via spike patterns.

Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks.

A large body of experimental and theoretical work on neural coding suggests that the information stored in brain circuits is represented by time-varying patterns of neural activity. Reservoir computing, where the activity of a recurrently connected pool of neurons is read by one or more units that provide an output response, successfully exploits this type of neural activity. However, the question of system robustness to small structural perturbations, such as failing neurons and synapses, has been largely overlooked. This contrasts with well-studied dynamical perturbations that lead to divergent network activity in the presence of chaos, as is the case for many reservoir networks. Here, we distinguish between two types of structural network perturbations, namely local (e.g., individual synaptic or neuronal failure) and global (e.g., network-wide fluctuations). Surprisingly, we show that while global perturbations have a limited impact on the ability of reservoir models to perform various tasks, local perturbations can produce drastic effects. To address this limitation, we introduce a new architecture where the reservoir is driven by a layer of oscillators that generate stable and repeatable trajectories. This model outperforms previous implementations while being resistant to relatively large local and global perturbations. This finding has implications for the design of reservoir models that capture the capacity of brain circuits to perform cognitively and behaviorally relevant tasks while remaining robust to various forms of perturbations. Further, our work proposes a novel role for neuronal oscillations found in cortical circuits, where they may serve as a collection of inputs from which a network can robustly generate complex dynamics and implement rich computations.

Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons.

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.

Estimating null and potent modes of feedforward communication in a computational model of cortical activity.

Communication across anatomical areas of the brain is key to both sensory and motor processes. Dimensionality reduction approaches have shown that the covariation of activity across cortical areas follows well-delimited patterns. Some of these patterns fall within the "potent space" of neural interactions and generate downstream responses; other patterns fall within the "null space" and prevent the feedforward propagation of synaptic inputs. Despite growing evidence for the role of null space activity in visual processing as well as preparatory motor control, a mechanistic understanding of its neural origins is lacking. Here, we developed a mean-rate model that allowed for the systematic control of feedforward propagation by potent and null modes of interaction. In this model, altering the number of null modes led to no systematic changes in firing rates, pairwise correlations, or mean synaptic strengths across areas, making it difficult to characterize feedforward communication with common measures of functional connectivity. A novel measure termed the null ratio captured the proportion of null modes relayed from one area to another. Applied to simultaneous recordings of primate cortical areas V1 and V2 during image viewing, the null ratio revealed that feedforward interactions have a broad null space that may reflect properties of visual stimuli.

Spiking neurons that keep the rhythm.

Detecting the temporal relationship among events in the environment is a fundamental goal of the brain. Following pulses of rhythmic stimuli, neurons of the retina and cortex produce activity that closely approximates the timing of an omitted pulse. This omitted stimulus response (OSR) is generally interpreted as a transient response to rhythmic input and is thought to form a basis of short-term perceptual memories. Despite its ubiquity across species and experimental protocols, the mechanisms underlying OSRs remain poorly understood. In particular, the highly transient nature of OSRs, typically limited to a single cycle after stimulation, cannot be explained by a simple mechanism that would remain locked to the frequency of stimulation. Here, we describe a set of realistic simulations that capture OSRs over a range of stimulation frequencies matching experimental work. The model does not require an explicit mechanism for learning temporal sequences. Instead, it relies on spike timing-dependent plasticity (STDP), a form of synaptic modification that is sensitive to the timing of pre- and post-synaptic action potentials. In the model, the transient nature of OSRs is attributed to the heterogeneous nature of neural properties and connections, creating intricate forms of activity that are continuously changing over time. Combined with STDP, neural heterogeneity enabled OSRs to complex rhythmic patterns as well as OSRs following a delay period. These results link the response of neurons to rhythmic patterns with the capacity of heterogeneous circuits to produce transient and highly flexible forms of neural activity.

Estimating Fisher discriminant error in a linear integrator model of neural population activity.

Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that lead to beneficial and detrimental effects of noise correlation on decoding. Further, the proposed framework sheds light on the contribution of neuronal noise, highlighting cases where, counter-intuitively, increased noise may lead to improved decoding performance. Finally, we examined the impact of dynamical parameters, including neuronal leak and integration time constant, on decoding. Overall, this work presents a fruitful approach to the study of decoding using a comprehensive theoretical framework that merges dynamical parameters with estimates of readout error.

Extreme neural machines.

Recurrent neural networks can solve a variety of computational tasks and produce patterns of activity that capture key properties of brain circuits. However, learning rules designed to train these models are time-consuming and prone to inaccuracies when tuning connection weights located deep within the network. Here, we describe a rapid one-shot learning rule to train recurrent networks composed of biologically-grounded neurons. First, inputs to the model are compressed onto a smaller number of recurrent neurons. Then, a non-iterative rule adjusts the output weights of these neurons based on a target signal. The model learned to reproduce natural images, sequential patterns, as well as a high-resolution movie scene. Together, results provide a novel avenue for one-shot learning in biologically realistic recurrent networks and open a path to solving complex tasks by merging brain-inspired models with rapid optimization rules.

Resilience of network activity in preconditioned neurons exposed to 'stroke-in-a-dish' insults.

Exposing cultured cortical neurons to stimulatory agents - the K+ channel blocker 4-aminopyridine (4-ap), and the GABAA receptor antagonist bicuculline (bic) - for 48 h induces down-regulated synaptic scaling, and preconditions neurons to withstand subsequent otherwise lethal 'stroke-in-a-dish' insults; however, the degree to which usual neuronal function remains is unknown. As a result, multi-electrode array and patch-clamp electrophysiological techniques were employed to characterize hallmarks of spontaneous synaptic activity over a 12-day preconditioning/insult experiment. Spiking frequency increased 8-fold immediately upon 4-ap/bic treatment but declined within the 48 h treatment window to sub-baseline levels that persisted long after washout. Preconditioning resulted in key markers of network activity - spiking frequency, bursting and avalanches - being impervious to an insult. Surprisingly, preconditioning resulted in higher peak NMDA mEPSC amplitudes, resulting in a decrease in the ratio of AMPA:NMDA mEPSC currents, suggesting a relative increase in synaptic NMDA receptors. An investigation of a broad mRNA panel of excitatory and inhibitory signaling mediators indicated preconditioning rapidly up-regulated GABA synthesis (GAD67) and BDNF, followed by up-regulation of neuronal activity-regulated pentraxin and down-regulation of presynaptic glutamate release (VGLUT1). Preconditioning also enhanced surface expression of GLT-1, which persisted following an insult. Overall, preconditioning resulted in a reduced spiking frequency which was impervious to subsequent exposure to 'stroke-in-a-dish' insults, a phenotype initiated predominantly by up-regulation of inhibitory neurotransmission, a lower neuronal postsynaptic AMPA: NMDA receptor ratio, and trafficking of GLT-1 to astrocyte plasma membranes.

Can structure predict function in the human brain?

Over the past decade, scientific interest in the properties of large-scale spontaneous neural dynamics has intensified. Concurrently, novel technologies have been developed for characterizing the connective anatomy of intra-regional circuits and inter-regional fiber pathways. It will soon be possible to build computational models that incorporate these newly detailed structural network measurements to make predictions of neural dynamics at multiple scales. Here, we review the practicality and the value of these efforts, while at the same time considering in which cases and to what extent structure does determine neural function. Studies of the healthy brain, of neural development, and of pathology all yield examples of direct correspondences between structural linkage and dynamical correlation. Theoretical arguments further support the notion that brain network topology and spatial embedding should strongly influence network dynamics. Although future models will need to be tested more quantitatively and against a wider range of empirical neurodynamic features, our present large-scale models can already predict the macroscopic pattern of dynamic correlation across the brain. We conclude that as neuroscience grapples with datasets of increasing completeness and complexity, and attempts to relate the structural and functional architectures discovered at different neural scales, the value of computational modeling will continue to grow.

Learning Long Temporal Sequences in Spiking Networks by Multiplexing Neural Oscillations.

Many cognitive and behavioral tasks-such as interval timing, spatial navigation, motor control, and speech-require the execution of precisely-timed sequences of neural activation that cannot be fully explained by a succession of external stimuli. We show how repeatable and reliable patterns of spatiotemporal activity can be generated in chaotic and noisy spiking recurrent neural networks. We propose a general solution for networks to autonomously produce rich patterns of activity by providing a multi-periodic oscillatory signal as input. We show that the model accurately learns a variety of tasks, including speech generation, motor control, and spatial navigation. Further, the model performs temporal rescaling of natural spoken words and exhibits sequential neural activity commonly found in experimental data involving temporal processing. In the context of spatial navigation, the model learns and replays compressed sequences of place cells and captures features of neural activity such as the emergence of ripples and theta phase precession. Together, our findings suggest that combining oscillatory neuronal inputs with different frequencies provides a key mechanism to generate precisely timed sequences of activity in recurrent circuits of the brain.

Nonperiodic synchronization in heterogeneous networks of spiking neurons.

Neural synchronization is of wide interest in neuroscience and has been argued to form the substrate for conscious attention to stimuli, movement preparation, and the maintenance of task-relevant representations in active memory. Despite a wealth of possible functions, the mechanisms underlying synchrony are still poorly understood. In particular, in vitro preparations have demonstrated synchronization with no apparent periodicity, which cannot be explained by simple oscillatory mechanisms. Here, we investigate the possible origins of nonperiodic synchronization through biophysical simulations. We show that such aperiodic synchronization arises naturally under a simple set of plausible assumptions, depending crucially on heterogeneous cell properties. In addition, nonperiodicity occurs even in the absence of stochastic fluctuation in membrane potential, suggesting that it may represent an intrinsic property of interconnected networks. Simulations capture some of the key aspects of population-level synchronization in spontaneous network spikes (NSs) and suggest that the intrinsic nonperiodicity of NSs observed in reduced cell preparations is a phenomenon that is highly robust and can be reproduced in simulations that involve a minimal set of realistic assumptions. In addition, a model with spike timing-dependent plasticity can overcome a natural tendency to exhibit nonperiodic behavior. After rhythmic stimulation, the model does not automatically fall back to a state of nonperiodic behavior, but keeps replaying the pattern of evoked NSs for a few cycles. A cluster analysis of synaptic strengths highlights the importance of population-wide interactions in generating this result and describes a possible route for encoding temporal patterns in networks of neurons.

The topographic brain: from neural connectivity to cognition.

A hallmark feature of vertebrate brain organization is ordered topography, wherein sets of neuronal connections preserve the relative organization of cells between two regions. Although topography is often found in projections from peripheral sense organs to the brain, it also seems to participate in the anatomical and functional organization of higher brain centers, for reasons that are poorly understood. We propose that a key function of topography might be to provide computational underpinnings for precise one-to-one correspondences between abstract cognitive representations. This perspective offers a novel conceptualization of how the brain approaches difficult problems, such as reasoning and analogy making, and suggests that a broader understanding of topographic maps could be pivotal in fostering strong links between genetics, neurophysiology and cognition.

Getting into shape: optimal ligand gradients for axonal guidance.

During neural development, neurons from downstream, presynaptic regions of the nervous system (such as the retina) send spatially patterned axonal projections to upstream, target regions (the tectum or superior colliculus). A servomechanism model has been proposed to explain the pattern and time-course of axonal growth between these two regions [Honda, H., 1998. Topographic mapping in the retinotectal projection by means of complementary ligand and receptor gradients: a computer simulation study. J. Theor. Biol., 192, 235-246]. Here, we show that a modification of this model incorporating a different criterion for axonal decision-making, called the local optimum rule, is guaranteed to converge to a topographic map under a wide range of conditions encountered during neural development. A theoretical investigation of these conditions leads to new hypotheses regarding map formation.

Statistical Evaluation of Waveform Collapse Reveals Scale-Free Properties of Neuronal Avalanches.

Neural avalanches are a prominent form of brain activity characterized by network-wide bursts whose statistics follow a power-law distribution with a slope near 3/2. Recent work suggests that avalanches of different durations can be rescaled and thus collapsed together. This collapse mirrors work in statistical physics where it is proposed to form a signature of systems evolving in a critical state. However, no rigorous statistical test has been proposed to examine the degree to which neuronal avalanches collapse together. Here, we describe a statistical test based on functional data analysis, where raw avalanches are first smoothed with a Fourier basis, then rescaled using a time-warping function. Finally, an F ratio test combined with a bootstrap permutation is employed to determine if avalanches collapse together in a statistically reliable fashion. To illustrate this approach, we recorded avalanches from cortical cultures on multielectrode arrays as in previous work. Analyses show that avalanches of various durations can be collapsed together in a statistically robust fashion. However, a principal components analysis revealed that the offset of avalanches resulted in marked variance in the time-warping function, thus arguing for limitations to the strict fractal nature of avalanche dynamics. We compared these results with those obtained from cultures treated with an AMPA/NMDA receptor antagonist (APV/DNQX), which yield a power-law of avalanche durations with a slope greater than 3/2. When collapsed together, these avalanches showed marked misalignments both at onset and offset time-points. In sum, the proposed statistical evaluation suggests the presence of scale-free avalanche waveforms and constitutes an avenue for examining critical dynamics in neuronal systems.