Pattern dynamics and stochasticity of the brain rhythms.

Our current understanding of brain rhythms is based on quantifying their instantaneous or time-averaged characteristics. What remains unexplored is the actual structure of the waves-their shapes and patterns over finite timescales. Here, we study brain wave patterning in different physiological contexts using two independent approaches: The first is based on quantifying stochasticity relative to the underlying mean behavior, and the second assesses "orderliness" of the waves' features. The corresponding measures capture the waves' characteristics and abnormal behaviors, such as atypical periodicity or excessive clustering, and demonstrate coupling between the patterns' dynamics and the animal's location, speed, and acceleration. Specifically, we studied patterns of θ, γ, and ripple waves recorded in mice hippocampi and observed speed-modulated changes of the wave's cadence, an antiphase relationship between orderliness and acceleration, as well as spatial selectiveness of patterns. Taken together, our results offer a complementary-mesoscale-perspective on brain wave structure, dynamics, and functionality.

Reliable detection of generalized convulsive seizures using an off-the-shelf digital watch: A multisite phase 2 study.

OBJECTIVE: The aim of this study was to develop a machine learning algorithm using an off-the-shelf digital watch, the Samsung watch (SM-R800), and evaluate its effectiveness for the detection of generalized convulsive seizures (GCS) in persons with epilepsy. METHODS: This multisite epilepsy monitoring unit (EMU) phase 2 study included 36 adult patients. Each patient wore a Samsung watch that contained accelerometer, gyroscope, and photoplethysmographic sensors. Sixty-eight time and frequency domain features were extracted from the sensor data and were used to train a random forest algorithm. A testing framework was developed that would better reflect the EMU setting, consisting of (1) leave-one-patient-out cross-validation (LOPO CV) on GCS patients, (2) false alarm rate (FAR) testing on nonseizure patients, and (3) "fixed-and-frozen" prospective testing on a prospective patient cohort. Balanced accuracy, precision, sensitivity, and FAR were used to quantify the performance of the algorithm. Seizure onsets and offsets were determined by using video-electroencephalographic (EEG) monitoring. Feature importance was calculated as the mean decrease in Gini impurity during the LOPO CV testing. RESULTS: LOPO CV results showed balanced accuracy of .93 (95% confidence interval [CI] = .8-.98), precision of .68 (95% CI = .46-.85), sensitivity of .87 (95% CI = .62-.96), and FAR of .21/24 h (interquartile range [IQR] = 0-.90). Testing the algorithm on patients without seizure resulted in an FAR of .28/24 h (IQR = 0-.61). During the "fixed-and-frozen" prospective testing, two patients had three GCS, which were detected by the algorithm, while generating an FAR of .25/24 h (IQR = 0-.89). Feature importance showed that heart rate-based features outperformed accelerometer/gyroscope-based features. SIGNIFICANCE: Commercially available wearable digital watches that reliably detect GCS, with minimum false alarm rates, may overcome usage adoption and other limitations of custom-built devices. Contingent on the outcomes of a prospective phase 3 study, such devices have the potential to provide non-EEG-based seizure surveillance and forecasting in the clinical setting.

Grid Cell Percolation.

Grid cells play a principal role in enabling cognitive representations of ambient environments. The key property of these cells-the regular arrangement of their firing fields-is commonly viewed as a means for establishing spatial scales or encoding specific locations. However, using grid cells' spiking outputs for deducing geometric orderliness proves to be a strenuous task due to fairly irregular activation patterns triggered by the animal's sporadic visits to the grid fields. This article addresses statistical mechanisms enabling emergent regularity of grid cell firing activity from the perspective of percolation theory. Using percolation phenomena for modeling the effect of the rat's moves through the lattices of firing fields sheds new light on the mechanisms of spatial information processing, spatial learning, path integration, and establishing spatial metrics. It is also shown that physiological parameters required for spiking percolation match the experimental range, including the characteristic 2/3 ratio between the grid fields' size and the grid spacing, pointing at a biological viability of the approach.

Forecasting seizure clusters from chronic ambulatory electrocorticography.

Seizure clusters are seizures that occur in rapid succession during periods of heightened seizure risk and are associated with substantial morbidity and sudden unexpected death in epilepsy. The objective of this feasibility study was to evaluate the performance of a novel seizure cluster forecasting algorithm. Chronic ambulatory electrocorticography recorded over an average of 38 months in 10 subjects with drug-resistant epilepsies was analyzed pseudoprospectively by dividing data into training (first 85%) and validation periods. For each subject, the probability of seizure clustering, derived from the Kolmogorov-Smirnov statistic using a novel algorithm, was forecasted in the validation period using individualized autoregressive models that were optimized from training data. The primary outcome of this study was the mean absolute scaled error (MASE) of 1-day horizon forecasts. From 10 subjects, 394 ± 142 (mean ± SD) electrocorticography-based seizure events were extracted for analysis, representing a span of 38 ± 27 months of recording. MASE across all subjects was .74 ± .09, .78 ± .09, and .83 ± .07 at .5-, 1-, and 2-day horizons. The feasibility study demonstrates that seizure clusters are quasiperiodic and can be forecasted to clinically meaningful horizons. Pending validation in larger cohorts, the forecasting approach described herein may herald chronotherapy during imminent heightened seizure vulnerability.

Robust spatial memory maps encoded by networks with transient connections.

The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space-a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long period. However, the neuronal substrate that produces this map is transient: the synaptic connections in the hippocampus and in the downstream neuronal networks never cease to form and to deteriorate at a rapid rate. How can the brain maintain a robust, reliable representation of space using a network that constantly changes its architecture? We address this question using a computational framework that allows evaluating the effect produced by the decaying connections between simulated hippocampal neurons on the properties of the cognitive map. Using novel Algebraic Topology techniques, we demonstrate that emergence of stable cognitive maps produced by networks with transient architectures is a generic phenomenon. The model also points out that deterioration of the cognitive map caused by weakening or lost connections between neurons may be compensated by simulating the neuronal activity. Lastly, the model explicates the importance of the complementary learning systems for processing spatial information at different levels of spatiotemporal granularity.

Gamma Synchronization Influences Map Formation Time in a Topological Model of Spatial Learning.

The mammalian hippocampus plays a crucial role in producing a cognitive map of space-an internalized representation of the animal's environment. We have previously shown that it is possible to model this map formation using a topological framework, in which information about the environment is transmitted through the temporal organization of neuronal spiking activity, particularly those occasions in which the firing of different place cells overlaps. In this paper, we discuss how gamma rhythm, one of the main components of the extracellular electrical field potential affects the efficiency of place cell map formation. Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.

A model of topological mapping of space in bat hippocampus.

The mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal spatial maps in rats, assuming a topological perspective on spatial information processing. In this article, we use the topological approach to study the formation of a 3D spatial map in bats, which produces several insights into neurophysiological mechanisms of the hippocampal spatial leaning. First, we demonstrate that, in order to produce accurate maps of the environment, place cell should be organized into functional groups, which can be interpreted as cell assemblies. Second, the model suggests that the readout neurons in these cell assemblies should function as integrators of synaptic inputs, rather than detectors of place cells' coactivity, which allows estimating the integration time window. Lastly, the model suggests that, in contrast with relatively slow moving rats, suppressing θ-precession in bats improves the place cells capacity to encode spatial maps, which is consistent with the experimental observations. © 2016 Wiley Periodicals, Inc.

Genetic suppression of transgenic APP rescues Hypersynchronous network activity in a mouse model of Alzeimer's disease.

Alzheimer's disease (AD) is associated with an elevated risk for seizures that may be fundamentally connected to cognitive dysfunction. Supporting this link, many mouse models for AD exhibit abnormal electroencephalogram (EEG) activity in addition to the expected neuropathology and cognitive deficits. Here, we used a controllable transgenic system to investigate how network changes develop and are maintained in a model characterized by amyloid ß (Aß) overproduction and progressive amyloid pathology. EEG recordings in tet-off mice overexpressing amyloid precursor protein (APP) from birth display frequent sharp wave discharges (SWDs). Unexpectedly, we found that withholding APP overexpression until adulthood substantially delayed the appearance of epileptiform activity. Together, these findings suggest that juvenile APP overexpression altered cortical development to favor synchronized firing. Regardless of the age at which EEG abnormalities appeared, the phenotype was dependent on continued APP overexpression and abated over several weeks once transgene expression was suppressed. Abnormal EEG discharges were independent of plaque load and could be extinguished without altering deposited amyloid. Selective reduction of Aß with a γ-secretase inhibitor has no effect on the frequency of SWDs, indicating that another APP fragment or the full-length protein was likely responsible for maintaining EEG abnormalities. Moreover, transgene suppression normalized the ratio of excitatory to inhibitory innervation in the cortex, whereas secretase inhibition did not. Our results suggest that APP overexpression, and not Aß overproduction, is responsible for EEG abnormalities in our transgenic mice and can be rescued independently of pathology.

The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map.

Learning arises through the activity of large ensembles of cells, yet most of the data neuroscientists accumulate is at the level of individual neurons; we need models that can bridge this gap. We have taken spatial learning as our starting point, computationally modeling the activity of place cells using methods derived from algebraic topology, especially persistent homology. We previously showed that ensembles of hundreds of place cells could accurately encode topological information about different environments ("learn" the space) within certain values of place cell firing rate, place field size, and cell population; we called this parameter space the learning region. Here we advance the model both technically and conceptually. To make the model more physiological, we explored the effects of theta precession on spatial learning in our virtual ensembles. Theta precession, which is believed to influence learning and memory, did in fact enhance learning in our model, increasing both speed and the size of the learning region. Interestingly, theta precession also increased the number of spurious loops during simplicial complex formation. We next explored how downstream readout neurons might define co-firing by grouping together cells within different windows of time and thereby capturing different degrees of temporal overlap between spike trains. Our model's optimum coactivity window correlates well with experimental data, ranging from ∼150-200 msec. We further studied the relationship between learning time, window width, and theta precession. Our results validate our topological model for spatial learning and open new avenues for connecting data at the level of individual neurons to behavioral outcomes at the neuronal ensemble level. Finally, we analyzed the dynamics of simplicial complex formation and loop transience to propose that the simplicial complex provides a useful working description of the spatial learning process.

Grid cells, border cells, and discrete complex analysis.

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

Grid Cells, Border Cells and Discrete Complex Analysis.

We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity towards the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.

Rapid Spectral Dynamics in Hippocampal Oscillons.

Neurons in the brain are submerged into oscillating extracellular potential produced by synchronized synaptic currents. The dynamics of these oscillations is one of the principal characteristics of neurophysiological activity, broadly studied in basic neuroscience and used in applications. However, our interpretation of the brain waves' structure and hence our understanding of their functions depend on the mathematical and computational approaches used for data analysis. The oscillatory nature of the wave dynamics favors Fourier methods, which have dominated the field for several decades and currently constitute the only systematic approach to brain rhythms. In the following study, we outline an alternative framework for analyzing waves of local field potentials (LFPs) and discuss a set of new structures that it uncovers: a discrete set of frequency-modulated oscillatory processes-the brain wave oscillons and their transient spectral dynamics.

From Topological Analyses to Functional Modeling: The Case of Hippocampus.

Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus-a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition-the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

Through synapses to spatial memory maps via a topological model.

Various neurophysiological and cognitive functions are based on transferring information between spiking neurons via a complex system of synaptic connections. In particular, the capacity of presynaptic inputs to influence the postsynaptic outputs-the efficacy of the synapses-plays a principal role in all aspects of hippocampal neurophysiology. However, a direct link between the information processed at the level of individual synapses and the animal's ability to form memories at the organismal level has not yet been fully understood. Here, we investigate the effect of synaptic transmission probabilities on the ability of the hippocampal place cell ensembles to produce a cognitive map of the environment. Using methods from algebraic topology, we find that weakening synaptic connections increase spatial learning times, produce topological defects in the large-scale representation of the ambient space and restrict the range of parameters for which place cell ensembles are capable of producing a map with correct topological structure. On the other hand, the results indicate a possibility of compensatory phenomena, namely that spatial learning deficiencies may be mitigated through enhancement of neuronal activity.

Replays of spatial memories suppress topological fluctuations in cognitive map.

The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space-a cognitive map. These cells do not only exhibit location-specific spiking during navigation, but also may rapidly replay the navigated routs through endogenous dynamics of the hippocampal network. Physiologically, such reactivations are viewed as manifestations of "memory replays" that help to learn new information and to consolidate previously acquired memories by reinforcing synapses in the parahippocampal networks. Below we propose a computational model of these processes that allows assessing the effect of replays on acquiring a robust topological map of the environment and demonstrate that replays may play a key role in stabilizing the hippocampal representation of space.

Topological Schemas of Memory Spaces.

Hippocampal cognitive map-a neuronal representation of the spatial environment-is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework-the memory space-that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as "networks of interconnections among the representations of events," have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature-a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

Transient cell assembly networks encode stable spatial memories.

One of the mysteries of memory is that it can last despite changes in the underlying synaptic architecture. How can we, for example, maintain an internal spatial map of an environment over months or years when the underlying network is full of transient connections? In the following, we propose a computational model for describing the emergence of the hippocampal cognitive map in a network of transient place cell assemblies and demonstrate, using methods of algebraic topology, how such a network can maintain spatial memory over time.

Topological Schemas of Cognitive Maps and Spatial Learning.

Spatial navigation in mammals is based on building a mental representation of their environment-a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key difficulty is that these maps are collective, emergent phenomena that cannot be reduced to a simple combination of inputs provided by individual neurons. In this paper we suggest computational frameworks for integrating the spiking signals of individual cells into a spatial map, which we call schemas. We provide examples of four schemas defined by different types of topological relations that may be neurophysiologically encoded in the brain and demonstrate that each schema provides its own large-scale characteristics of the environment-the schema integrals. Moreover, we find that, in all cases, these integrals are learned at a rate which is faster than the rate of complete training of neural networks. Thus, the proposed schema framework differentiates between the cognitive aspect of spatial learning and the physiological aspect at the neural network level.

A Topological Model of the Hippocampal Cell Assembly Network.

It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed that the place cells exhibiting frequent coactivity form functionally interconnected groups-place cell assemblies-that drive readout neurons in the downstream networks. However, the sheer number of coactive combinations is extremely large, which implies that only a small fraction of them actually gives rise to cell assemblies. The physiological processes responsible for selecting the winning combinations are highly complex and are usually modeled via detailed synaptic and structural plasticity mechanisms. Here we propose an alternative approach that allows modeling the cell assembly network directly, based on a small number of phenomenological selection rules. We then demonstrate that the selected population of place cell assemblies correctly encodes the topology of the environment in biologically plausible time, and may serve as a schematic model of the hippocampal network.

Levetiracetam mitigates doxorubicin-induced DNA and synaptic damage in neurons.

Neurotoxicity may occur in cancer patients and survivors during or after chemotherapy. Cognitive deficits associated with neurotoxicity can be subtle or disabling and frequently include disturbances in memory, attention, executive function and processing speed. Searching for pathways altered by anti-cancer treatments in cultured primary neurons, we discovered that doxorubicin, a commonly used anti-neoplastic drug, significantly decreased neuronal survival. The drug promoted the formation of DNA double-strand breaks in primary neurons and reduced synaptic and neurite density. Pretreatment of neurons with levetiracetam, an FDA-approved anti-epileptic drug, enhanced survival of chemotherapy drug-treated neurons, reduced doxorubicin-induced formation of DNA double-strand breaks, and mitigated synaptic and neurite loss. Thus, levetiracetam might be part of a valuable new approach for mitigating synaptic damage and, perhaps, for treating cognitive disturbances in cancer patients and survivors.