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Structure and dynamics of neural network oscillators.

Techniques are given to represent oscillating neural networks by asynchronous logical switching networks, and to analyze the oscillating networks using a directed graph called a state transition diagram. Consideration is restricted to network oscillators containing no rhythm determining pacemaker neurons, and no neurons exhibiting self-limiting properties such as post-inhibitory rebound or accumulating refractoriness. In the state transition diagrams, stable oscillations are associated with a particular geometric configuration called a cyclic attractor (the heavy cycle in Fig. 2). We show that given the network connectivity it is possible to predict autonomous dynamic behaviour, as well as behaviour following hyperpolarizing or depolarizing inputs to neurons of the network. Conversely, given information about patterns of firing activity during cycles and transients of neural networks, the network connectivity can be predicted. The theoretical techniques can be used to generate a census of network structures capable of generating stable oscillations. Several representative network oscillators are discussed in the context of previous theoretical and experimental studies of the structure of neural network oscillators. Although the number of theoretically possile network oscillators capable of generating sustained oscillations is very large, the techniques which are given should be useful in the design of experiments capable of distinguishing between equally plausible hypotheses.

Action Potentials↗

Intrinsic dynamics in neuronal networks. I. Theory.

Many networks in the mammalian nervous system remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How are these firing patterns generated? Specifically, how do dynamic interactions between excitatory and inhibitory neurons produce these firing patterns, and how do networks switch from one firing pattern to the other? We investigated these questions theoretically by examining the intrinsic dynamics of large networks of neurons. Using both a semianalytic model based on mean firing rate dynamics and simulations with large neuronal networks, we found that the dynamics, and thus the firing patterns, are controlled largely by one parameter, the fraction of endogenously active cells. When no endogenously active cells are present, networks are either silent or fire at a high rate; as the number of endogenously active cells increases, there is a transition to bursting; and, with a further increase, there is a second transition to steady firing at a low rate. A secondary role is played by network connectivity, which determines whether activity occurs at a constant mean firing rate or oscillates around that mean. These conclusions require only conventional assumptions: excitatory input to a neuron increases its firing rate, inhibitory input decreases it, and neurons exhibit spike-frequency adaptation. These conclusions also lead to two experimentally testable predictions: 1) isolated networks that fire at low rates must contain endogenously active cells and 2) a reduction in the fraction of endogenously active cells in such networks must lead to bursting.

Action Potentials↗

Collective dynamics of 'small-world' networks.

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

Animals↗

Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.

Action Potentials↗

Cholinergic modulation of cortical function: a hypothetical role in shifting the dynamics in cortical network.

Wide innervation of cholinergic projections throughout the cortex implies that acetylcholine (ACh) plays an essential role in information processing, but how it works is still enigmatic. Experimental as well as theoretical work in the olfactory cortex and hippocampus suggests that ACh, via the muscarinic receptors, serves to shift the dynamics of the cortical networks into a state where afferent influence predominates over intracortical influence. Recent experiments in the visual and somatosensory cortex suggested that this hypothesis could be extended to neocortex. In addition, participation of the nicotinic receptors in regulating the synaptic response in the somatosensory cortex further substantiates this hypothesis. This hypothesis, derived mainly from in vitro work, also seemed to account for results from in vivo experiments without any obvious inconsistencies.

Acetylcholine↗

Neural dynamics in cortical networks--precision of joint-spiking events.

Electrophysiological studies of cortical function on the basis of multiple single-neuron recordings reveal neuronal interactions which depend on stimulus context and behavioural events. These interactions exhibit dynamics on different time scales, with time constants down to the millisecond range. Mechanisms underlying such dynamic organization of the cortical network were investigated by experimental and theoretical approaches. We review some recent results from these studies, concentrating on the occurrence of precise joint-spiking events in cortical activity, both in physiological and in model neural networks. These findings suggest that a combinatorial neural code, based on rapid associations of groups of neurons co-ordinating their activity at the single spike level, is biologically feasible.

Action Potentials↗

A Cayley tree immune network model with antibody dynamics.

A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvist et al. (1989. Proc. natn. Acad. Sci. U.S.A. 86, 5074-5078), injection of Ab1 antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations of Ab1 and Ab2 antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvist et al. but not accounted for previously.

Animals↗

Sanguinarine as a multi-target therapeutic candidate for laryngeal cancer: insights from network pharmacology, molecular dynamics and in vitro validation.

OBJECTIVE: To identify the core targets and elucidate the potential molecular mechanisms of sanguinarine (SA) against laryngeal squamous cell carcinoma (LSCC), and to validate its antitumor effects in vitro. METHODS: Potential targets of SA were predicted using SwissTargetPrediction, TargetNet, and SuperPred and intersected with LSCC-related targets obtained from the GeneCards, OMIM, and DISEASES databases. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses were performed. A protein-protein interaction (PPI) network was constructed using the STRING database (combined score > 0.900), and topological parameters including degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), eigenvector centrality (EC), and local average connectivity (LAC) were calculated in Cytoscape to identify core genes based on median thresholds. Molecular docking and 100-ns molecular dynamics (MD) simulations were conducted for epidermal growth factor receptor (EGFR), Phosphatidylinositide-3-kinase catalytic subunit alpha (PIK3CA), phosphatidylinositol-4,5-biphosphate 3-kinase catalytic subunit β (PIK3CB), phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit delta (PIK3CD), and Non-Receptor Tyrosine Kinase (SRC). The effects of SA on LSCC were evaluated using CCK-8, colony formation, Transwell migration, and wound-healing assays in TU177 cells and TU212. RESULTS: A total of 213 common targets were identified, which were significantly enriched in PI3K-Akt signaling, EGFR tyrosine kinase inhibitor resistance, and adhesion- and migration-related pathways. The PPI network comprised 259 nodes and 259 edges, from which five core genes-PIK3CA, PIK3CB, PIK3CD, EGFR, and SRC-were identified. Molecular docking revealed strong binding affinities between SA and the PI3K family proteins (- 9.79 to - 10.96 kcal/mol), as well as EGFR (- 8.58 kcal/mol) and SRC (- 6.77 kcal/mol). MD simulations indicated greater stability of SA complexes with EGFR and PI3K family members compared with SRC. In vitro assays demonstrated that SA significantly inhibited TU177 cell and TU212 cell proliferation, colony formation, and migration. CONCLUSION: SA may exert anti-laryngeal cancer effects through synergistic multi-target inhibition centered on the EGFR/SRC/PI3K signaling axis, highlighting its potential as a promising therapeutic candidate for LSCC.

Humans↗

Reticular activation and the dynamics of neuronal networks.

It is postulated that during arousal the cortical system is driven by a spatially and temporally noisy signal arising from non-specific reticulo-cortical pathways. An elementary unit of cortical neuroanatomy is assumed, which permits non-linear dynamics to be represented by stochastic linear equations. Under these assumptions the resonant modes of the system of cortical dendrites approach thermodynamic equilibrium. Specific sensory signals perturb the dendritic system about equilibrium, generate low frequency, linear, non-dispersive waves corresponding to the EEG, which in turn regulate action potential sequences, and instantiate internal inputs to the dendritic field. A large and distributed memory capacity in axo-synaptic couplings, resistance to interference between functionally separate logical operations, and a very large next-state function set emerge as properties of the network. The model is able to explain the close association of the EEG with cognition, the channel of low capacity corresponding to the field of immediate attention, the low overall correlation of action potentials with EEG, and specificity of action potentials in some neurons during particular cognitive activity. Predictions made from hypothesis include features of thermal equilibrium in EEG (determinable by autoregression) and expectation that the cortical evoked response can be accounted for as the response to a sensory impulse of specific time characteristics.

Brain↗

Self-organized dynamics in plastic neural networks: bistability and coherence.

In this paper, we study the combined dynamics of the neural activity and the synaptic efficiency changes in a fully connected network of biologically realistic neurons with simple synaptic plasticity dynamics including both potentiation and depression. Using a mean-field of technique, we analyzed the equilibrium states of neural networks with dynamic synaptic connections and found a class of bistable networks. For this class of networks, one of the stable equilibrium states shows strong connectivity and coherent responses to external input. In the other stable equilibrium, the network is loosely connected and responds non coherently to external input. Transitions between the two states can be achieved by positively or negatively correlated external inputs. Such networks can therefore switch between their phases according to the statistical properties of the external input. Non-coherent input can only "rcad" the state of the network, while a correlated one can change its state. We speculate that this property, specific for plastic neural networks, can give a clue to understand fully unsupervised learning models.

Animals↗

Global dynamics of a network of stochastic neurons maximizes local mutual information.

We define a stochastic neuron as an element that increases its internal state with probability p until a threshold value is reached; after that its internal state is set back to the initial value. We study the local information of a stochastic neuron between the message arriving from the input neurons and the response of the neuron. We study the dependence of the local information on the firing probability alpha of the synaptic inputs in a network of such stochastic neurons. The values of alpha obtained in the simulations are the same as those obtained theoretically by maximization of local mutual information. We conclude that the global dynamics maximizes the local mutual information of single units, which means that the self-selected parameter value of the population dynamics is such that each neuron behaves as an optimal encoder.

Animals↗

Dynamical and complexity results for high order neural networks.

We present dynamical results concerning neural networks with high order arguments. More precisely, we study the family of block-sequential iteration of neural networks with polynomial arguments. In this context, we prove that, under a symmetric hypothesis, the sequential iteration is the only one of this family to converge to fixed points. The other iteration modes present a highly complex dynamical behavior: non-bounded cycles and simulation of arbitrary non-symmetric linear neural network. We also study a high order memory iteration scheme which accepts an energy functional and bounded cycles in the size of the memory steps.

Computer Simulation↗

Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity.

Experimental investigation of the dynamics of biological networks is a fundamental step towards understanding how the nervous system works. Spontaneous activity in cultured networks of cortical neurons has been investigated by using a multisite recording technique with planar electrode arrays. In these networks, the spatiotemporal firing patterns were studied in the presence of different extracellular solutions. Transitions from asynchronous firing dynamics to synchronous firing dynamics were observed when the extracellular Ca2+ concentration was increased from 0.1 mM to 1 mM. Addition of extracellular Mg2+ reduced the spontaneous activity at any Ca2+ concentration, and an increase in the extracellular K+ concentration enhanced the frequency of periodical synchronous bursts. N-methyl-D-aspartate (NMDA) and non-NMDA glutamate receptor antagonists inhibited synchronous activity. A spatiotemporal analysis of the data has been performed, and the properties of the network such as the synchronization and the periodicity have been quantified in order to clarify how variations of intrinsic parameters of the network can induce structural transitions in the neural dynamics. This experimental study is a possible approach to investigate the computational properties of a neuronal network.

Animals↗

Dynamic localization of rop GTPases to the tonoplast during vacuole development.

Vacuoles are essential pleomorphic organelles that undergo dynamic changes during cell growth and differentiation in plants. How developmental signals are linked to vacuole biogenesis and development is poorly understood. In this report, we show that a Rop GTPase is localized to developing vacuoles in pea (Pisum sativum cv Extra Early Alaska). Rop belongs to the RHO family of Ras-related small GTP-binding proteins that are key molecular switches in a wide variety of eukaryotic signal transduction pathways. Using indirect immunofluorescence and an anti-Rop antibody, we showed that Rop proteins accumulate to high levels in rapidly growing tapetal cells of pea anthers. In these cells, Rop is localized to an endomembrane system that exists as dynamic pleomorphic networks: a perinuclear fine network decorated with punctate dots, a network composed of small spheres and tubules, and interconnected chambers. Colocalization with a tonoplast annexin VCaB42 shows that these dynamic networks represent the tonoplast. Our results suggest that the dynamic Rop-containing tonoplast networks represent a unique stage of vacuole development. The specific localization of Rop to developing vacuoles supports a role for Rop in signal transduction that mediates vacuole development in plants.

Endoplasmic Reticulum↗

Laws for the dynamics of regulatory networks.

We start our analysis from historical but too seldom quoted papers by Delbrück, Noveck & Weiner, Cohn & Horibata and Monod & Jacob. We try to show how it became possible to draw a line coupling cell differentiation to the physical concept of multistationarity, and the latter to the concept of positive feedback circuits. Two laws give the minimal logical ingredients required for differentiative and homeostatic regulations. It is briefly shown how they can be used to treat such complex dynamics as deterministaic chaos, which, admittedly, does not yet belong to the corpus of developmental biology. It was taken as a challenge to express our ideas here in purely verbal terms, avoiding any formal treatment.

Animals↗

Fluorescently-labeled fimbrin decorates a dynamic actin filament network in live plant cells.

Recently it has been established, through a detailed biochemical analysis, that recombinant Arabidopsis thaliana fimbrin 1 (AtFim1) is a member of the fimbrin/plastin family of actin filament bundling or cross-linking proteins [D.R. Kovar et al. (2000) Plant J 24:625-636]. To determine whether AtFim1 can function as an F-actin-binding protein in the complex environment of the plant cell cytoplasm, we created a fluorescent protein analog and introduced it by microinjection into live Tradescantia virginiana L. stamen hair cells. AtFim1 derivatized with Oregon Green 488 had biochemical properties similar to unlabeled fimbrin, including the Kd value for binding to plant F-actin and the ability to cross-link filaments into higher-order structures. Fluorescent-fimbrin decorated an array of fine actin filaments in the cortical cytoplasm of stamen hair cells, which were shown with time-course studies to be highly dynamic. These data establish AtFim1 as a bona fide member of the fimbrin/plastin family, and represent the first use of a plant actin-binding protein as a powerful cytological tool for tracking the spatial and temporal redistribution of actin filaments in individual cells.

Actin Cytoskeleton↗

Emergence of clusters in the hidden layer of a dynamic recurrent neural network.

The neural integrator of the oculomotor system is a privileged field for artificial neural network simulation. In this paper, we were interested in an improvement of the biologically plausible features of the Arnold-Robinson network. This improvement was done by fixing the sign of the connection weights in the network (in order to respect the biological Dale's Law). We also introduced a notion of distance in the network in the form of transmission delays between its units. These modifications necessitated the introduction of a general supervisor in order to train the network to act as a leaky integrator. When examining the lateral connection weights of the hidden layer, the distribution of the weights values was found to exhibit a conspicuous structure: the high-value weights were grouped in what we call clusters. Other zones are quite flat and characterized by low-value weights. Clusters are defined as particular groups of adjoining neurons which have strong and privileged connections with another neighborhood of neurons. The clusters of the trained network are reminiscent of the small clusters or patches that have been found experimentally in the nucleus prepositus hypoglossi, where the neural integrator is located. A study was conducted to determine the conditions of emergence of these clusters in our network: they include the fixation of the weight sign, the introduction of a distance, and a convergence of the information from the hidden layer to the motoneurons. We conclude that this spontaneous emergence of clusters in artificial neural networks; performing a temporal integration, is due to computational constraints, with a restricted space of solutions. Thus, information processing could induce the emergence of iterated patterns in biological neural networks.

Animals↗