Attractor neural networks and spatial maps in hippocampus

Attractor neural network theory has been proposed as a theory for long-term memory. Recent studies of hippocampal place cells, including a study by Leutgeb et al. in this issue of Neuron, address the potential role of attractor dynamics in the formation of hippocampal representations of spatial maps.     

Oscillatory models of the hippocampus: A study of spatio-temporal patterns of neural activity

Spatial patterns of theta-rhythm activity in oscillatory models of the hippocampus are studied here using canonical models for both Hodgkin's class-1 and class-2 excitable neuronal systems. Dynamics of these models are studied in both the frequency domain, to determine phase-locking patterns, and in the time domain, to determine the amplitude responses resulting from phase-locking patterns. Computer simulations presented here demonstrate that phase deviations (timings) between inputs from the medial septum and the entorhinal cortex can create spatial patterns of theta-rhythm phase-locking. In this way, we show that the timing of inputs (not only their frequencies alone) can encode specific patterns of theta-rhythm activity. This study suggests new experiments to determine temporal and spatial synchronization. Received: 31 July 1998 /Accepted in revised form: 20 April 1999     

Interneuron networks in the hippocampus

The hippocampus has contributed enormously to our understanding of the operation of elemental brain circuits, not least through the classification of forebrain interneurons. Understanding the operation of interneuron networks however requires not only a wiring diagram that describes the innervation and postsynaptic targets of different GABAergic cells, but also an appreciation of the temporal dimension. Interneurons differ extensively in their intrinsic firing rates, their recruitment in different brain rhythms, and in their synaptic kinetics. Furthermore, in common with principal neurons, both the synapses innervating interneurons and the synapses made by these cells are highly modifiable, reflecting both their recent or remote use (short-term and long-term plasticity) and the action of extracellular messengers. This review examines recent progress in understanding how different hippocampal interneuron networks contribute to feedback and feed-forward inhibition at different timescales.     

Novel recurrent neural network for modelling biological networks: Oscillatory p53 interaction dynamics

Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system – a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.     

Frequency potentiation in the neonatal rabbit hippocampus

The formation of properties of frequency potentiation in the entorhinal afferent pathway of the hippocampus was studied in unanesthetized rabbits aged from 1 to 15 days. In areas CA₁ and CA₃ of the dorsal hippocampus in newborn rabbits repetitive (1–20 Hz) electrical stimulation of the perforant path led to an increase in amplitude of the slow wave of the field potential by 20–100% compared with the control and to an increase in the probability of response discharges from the neurons from 0–0.5 in the control to 0.8–1.0 during tetanization. In rabbits aged 2–3 days potentiation was more marked at a frequency of 4–6 Hz, whereas depression of the responses developed rapidly to a higher frequency of stimulation. The frequency optimum of 4–15 Hz was established on the 5th day. Potentiation of the first component of the field potential was observed starting from the 8th–10th day of life. The experimental results show that the property of frequency potentiation in the cortical afferent connections of the hippocampus is found in rabbits actually at birth, and it acquires the adult form at the beginning of the second week of life.Brain Institute, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 11, No. 6, pp. 533–539, November–December, 1979.     

Oscillatory synchronization in large-scale cortical networks predicts perception

Normal brain function requires the dynamic interaction of functionally specialized but widely distributed cortical regions. Long-range synchronization of oscillatory signals has been suggested to mediate these interactions within large-scale cortical networks, but direct evidence is sparse. Here we show that oscillatory synchronization is organized in such large-scale networks. We implemented an analysis approach that allows for imaging synchronized cortical networks and applied this technique to EEG recordings in humans. We identified two networks: beta-band synchronization (~20 Hz) in a fronto-parieto-occipital network and gamma-band synchronization (~80 Hz) in a centro-temporal network. Strong perceptual correlates support their functional relevance: the strength of synchronization within these networks predicted the subjects' perception of an ambiguous audiovisual stimulus as well as the integration of auditory and visual information. Our results provide evidence that oscillatory neuronal synchronization mediates neuronal communication within frequency-specific, large-scale cortical networks.     

Cephalopod neural networks

Cephalopods have arguably the largest and most complex nervous systems amongst the invertebrates; but despite the squid giant axon being one of the best studied nerve cells in neuroscience, and the availability of superb information on the morphology of some cephalopod brains, there is surprisingly little known about the operation of the neural networks that underlie the sophisticated range of behaviour these animals display. This review focuses on a few of the best studied neural networks: the giant fiber system, the chromatophore system, the statocyst system, the visual system and the learning and memory system, with a view to summarizing our current knowledge and stimulating new studies, particularly on the activities of identified central neurons, to provide a more complete understanding of networks within the cephalopod nervous system.     

Bayesian neural networks

A neural network that uses the basic Hebbian learning rule and the Bayesian combination function is defined. Analogously to Hopfield's neural network, the convergence for the Bayesian neural network that asynchronously updates its neurons' states is proved. The performance of the Bayesian neural network in four medical domains is compared with various classification methods. The Bayesian neural network uses more sophisticated combination function than Hopfield's neural network and uses more economically the available information. The naive Bayesian classifier typically outperforms the basic Bayesian neural network since iterations in network make too many mistakes. By restricting the number of iterations and increasing the number of fixed points the network performs better than the naive Bayesian classifier. The Bayesian neural network is designed to learn very quickly and incrementally.     

New experiences enhance coordinated neural activity in the hippocampus

The acquisition of new memories for places and events requires synaptic plasticity in the hippocampus, and plasticity depends on temporal coordination among neurons. Spatial activity in the hippocampus is relatively disorganized during the initial exploration of a novel environment, however, and it is unclear how neural activity during the initial stages of learning drives synaptic plasticity. Here we show that pairs of CA1 cells that represent overlapping novel locations are initially more coactive and more precisely coordinated than are cells representing overlapping familiar locations. This increased coordination occurs specifically during brief, high-frequency events (HFEs) in the local field potential that are similar to ripples and is not associated with better coordination of place-specific neural activity outside of HFEs. As novel locations become more familiar, correlations between cell pairs decrease. Thus, hippocampal neural activity during learning has a unique structure that is well suited to induce synaptic plasticity and to allow for rapid storage of new memories.     

Feeding neural networks in the mollusc Aplysia

Aplysia feeding is striking in that it is executed with a great deal of plasticity. At least in part, this flexibility is a result of the organization of the feeding neural network. To illustrate this, we primarily discuss motor programs triggered via stimulation of the command-like cerebral-buccal interneuron 2 (CBI-2). CBI-2 is interesting in that it can generate motor programs that serve opposing functions, i.e., programs can be ingestive or egestive. When programs are egestive, radula-closing motor neurons are activated during the protraction phase of the motor program. When programs are ingestive, radula-closing motor neurons are activated during retraction. When motor programs change in nature, activity in the radula-closing circuitry is altered. Thus, CBI-2 stimulation stereotypically activates the protraction and retraction circuitry, with protraction being generated first, and retraction immediately thereafter. In contrast, radula-closing motor neurons can be activated during either protraction or retraction. Which will occur is determined by whether other cerebral and buccal neurons are recruited, e.g. radula-closing motor neurons tend to be activated during retraction if a second CBI, CBI-3, is recruited. Fundamentally different motor programs are, therefore, generated because CBI-2 activates some interneurons in a stereotypic manner and other interneurons in a variable manner.     

Hypnosis modelling in neural networks

In the framework of the neural network theory effects similar to hypnotic displays are constructed. They are based on the associative paradigm involving non-linear interaction of excitatory and inhibitory channels with synaptic memory. The non-linearity of long-term memorizing processes may cause effects exhibited by blind spots, which are interpreted as the first stage of hypnosis. More complicated phenomena are discussed in terms of a two-layer network.     

Dynamic connections in neural networks

Massively parallel (neural-like) networks are receiving increasing attention as a mechanism for expressing information processing models. By exploiting powerful primitive units and stability-preserving construction rules, various workers have been able to construct and test quite complex models, particularly in vision research. But all of the detailed technical work was concerned with the structure and behavior offixed networks. The purpose of this paper is to extend the methodology to cover several aspects of change and memory.     

Clustering with neural networks

Partitioning a set ofN patterns in ad-dimensional metric space intoK clusters — in a way that those in a given cluster are more similar to each other than the rest — is a problem of interest in many fields, such as, image analysis, taxonomy, astrophysics, etc. As there are approximatelyK ^N/K! possible ways of partitioning the patterns amongK clusters, finding the best solution is beyond exhaustive search whenN is large. We show that this problem, in spite of its exponential complexity, can be formulated as an optimization problem for which very good, but not necessarily optimal, solutions can be found by using a Hopfield model of neural networks. To obtain a very good solution, the network must start from many randomly selected initial states. The network is simulated on the MPP, a 128 × 128 SIMD array machine, where we use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also in starting the network from many initial states at once thus obtaining many solutions in one run. We achieve speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of further speedups of three to six orders of magnitude.Supported by a National Research Council-NASA Research Associatship     

Potassium diffusive coupling in neural networks

Conventional neural networks are characterized by many neurons coupled together through synapses. The activity, synchronization, plasticity and excitability of the network are then controlled by its synaptic connectivity. Neurons are surrounded by an extracellular space whereby fluctuations in specific ionic concentration can modulate neuronal excitability. Extracellular concentrations of potassium ([K⁺]_o) can generate neuronal hyperexcitability. Yet, after many years of research, it is still unknown whether an elevation of potassium is the cause or the result of the generation, propagation and synchronization of epileptiform activity. An elevation of potassium in neural tissue can be characterized by dispersion (global elevation of potassium) and lateral diffusion (local spatial gradients). Both experimental and computational studies have shown that lateral diffusion is involved in the generation and the propagation of neural activity in diffusively coupled networks. Therefore, diffusion-based coupling by potassium can play an important role in neural networks and it is reviewed in four sections. Section 2 shows that potassium diffusion is responsible for the synchronization of activity across a mechanical cut in the tissue. A computer model of diffusive coupling shows that potassium diffusion can mediate communication between cells and generate abnormal and/or periodic activity in small (§3) and in large networks of cells (§4). Finally, in §5, a study of the role of extracellular potassium in the propagation of axonal signals shows that elevated potassium concentration can block the propagation of neural activity in axonal pathways. Taken together, these results indicate that potassium accumulation and diffusion can interfere with normal activity and generate abnormal activity in neural networks.     

Energy coding in biological neural networks

According to the experimental result of signal transmission and neuronal energetic demands being tightly coupled to information coding in the cerebral cortex, we present a brand new scientific theory that offers an unique mechanism for brain information processing. We demonstrate that the neural coding produced by the activity of the brain is well described by our theory of energy coding. Due to the energy coding model’s ability to reveal mechanisms of brain information processing based upon known biophysical properties, we can not only reproduce various experimental results of neuro-electrophysiology, but also quantitatively explain the recent experimental results from neuroscientists at Yale University by means of the principle of energy coding. Due to the theory of energy coding to bridge the gap between functional connections within a biological neural network and energetic consumption, we estimate that the theory has very important consequences for quantitative research of cognitive function.     

Causal networks in simulated neural systems

Neurons engage in causal interactions with one another and with the surrounding body and environment. Neural systems can therefore be analyzed in terms of causal networks, without assumptions about information processing, neural coding, and the like. Here, we review a series of studies analyzing causal networks in simulated neural systems using a combination of Granger causality analysis and graph theory. Analysis of a simple target-fixation model shows that causal networks provide intuitive representations of neural dynamics during behavior which can be validated by lesion experiments. Extension of the approach to a neurorobotic model of the hippocampus and surrounding areas identifies shifting causal pathways during learning of a spatial navigation task. Analysis of causal interactions at the population level in the model shows that behavioral learning is accompanied by selection of specific causal pathways—“causal cores”—from among large and variable repertoires of neuronal interactions. Finally, we argue that a causal network perspective may be useful for characterizing the complex neural dynamics underlying consciousness.