Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

An experimental multiprocessor system for distributed parallel computations.

The availability of low-cost microprocessor chips with efficient instruction sets for specific numerical tasks (signal processors) has been exploited for building a versatile multiprocessor system, consisting of a host minicomputer augmented by a number of joint processors. The host provides a multiuser-multitasking environment and manages system resources and task scheduling. User applications can call upon one or more joint processors for parallel execution of adequately partitioned, computationally intensive numeric operations. Each joint processor has sufficient local memory for storing procedures and data and has access to regions in host memory for shared data. Kernel processes in the host and in the joint processors provide the necessary mechanism for initialization and synchronization of the distributed parallel execution of procedures

Role of nucleotide binding and GTPase domain dimerization in dynamin-like myxovirus resistance protein A for GTPase activation and antiviral activity

Myxovirus resistance (Mx) GTPases are induced by interferon and inhibit multiple viruses including influenza and human immunodeficiency viruses. They have the characteristic domain architecture of dynamin-related proteins with an amino-terminal GTPase (G) domain, a bundle signaling element, and a carboxy-terminal stalk responsible for self-assembly and effector functions. Human MxA (also called MX1) is expressed in the cytoplasm and is partly associated with membranes of the smooth endoplasmic reticulum (ER). It shows a protein concentration-dependent increase in GTPase activity, indicating regulation of GTP hydrolysis via G domain dimerization. Here, we characterized a panel of G domain mutants in MxA to clarify the role of GTP binding and the importance of the G domain interface for the catalytic and antiviral function of MxA. Residues in the catalytic center of MxA and the nucleotide itself were essential for G domain dimerization and catalytic activation. In pulldown experiments, MxA recognized Thogoto virus nucleocapsid proteins independently of nucleotide binding. However, both nucleotide binding and hydrolysis were required for the antiviral activity against Thogoto, influenza and La Crosse viruses. We further demonstrate that GTP binding facilitates formation of stable MxA assemblies associated with ER membranes, whereas nucleotide hydrolysis promotes dynamic redistribution of MxA from cellular membranes to viral targets. Our study highlights the role of nucleotide binding and hydrolysis for the intracellular dynamics of MxA during its antiviral action

Oscillator neural network model with distributed native frequencies

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to get entirely synchronized, long time behaviors of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. The oscillator network is shown to work as associative memory accompanied by synchronized oscillations. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations, confirming the validity of our theoretical treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.

Structural insights into crista junction formation by the Mic60-Mic19 complex

Mitochondrial cristae membranes are the oxidative phosphorylation sites in cells. Crista junctions (CJs) form the highly curved neck regions of cristae and are thought to function as selective entry gates into the cristae space. Little is known about how CJs are generated and maintained. We show that the central coiled-coil (CC) domain of the mitochondrial contact site and cristae organizing system subunit Mic60 forms an elongated, bow tie–shaped tetrameric assembly. Mic19 promotes Mic60 tetramerization via a conserved interface between the Mic60 mitofilin and Mic19 CHCH (CC-helix-CC-helix) domains. Dimerization of mitofilin domains exposes a crescent-shaped membrane-binding site with convex curvature tailored to interact with the curved CJ neck. Our study suggests that the Mic60-Mic19 subcomplex traverses CJs as a molecular strut, thereby controlling CJ architecture and function

Transmission of Information in Active Networks

Shannon's Capacity Theorem is the main concept behind the Theory of Communication. It says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication, it can be transmitted with arbitrarily small probability of error. This theorem is usually applicable to ideal channels of communication in which the information to be transmitted does not alter the passive characteristics of the channel that basically tries to reproduce the source of information. For an {\it active channel}, a network formed by elements that are dynamical systems (such as neurons, chaotic or periodic oscillators), it is unclear if such theorem is applicable, once an active channel can adapt to the input of a signal, altering its capacity. To shed light into this matter, we show, among other results, how to calculate the information capacity of an active channel of communication. Then, we show that the {\it channel capacity} depends on whether the active channel is self-excitable or not and that, contrary to a current belief, desynchronization can provide an environment in which large amounts of information can be transmitted in a channel that is self-excitable. An interesting case of a self-excitable active channel is a network of electrically connected Hindmarsh-Rose chaotic neurons.Comment: 15 pages, 5 figures. submitted for publication. to appear in Phys. Rev.

Analysis of Oscillator Neural Networks for Sparsely Coded Phase Patterns

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical neurodynamics to our model, we theoretically investigate the model's associative memory capability by evaluating its maximum storage capacities and deriving its basins of attraction. It is shown that, as in the Hopfield model, the storage capacity diverges as the activity level decreases. We consider various practically and theoretically important cases. For example, it is revealed that a dynamically adjusted threshold mechanism enhances the retrieval ability of the associative memory. It is also found that, under suitable conditions, the network can recall patterns even in the case that patterns with different activity levels are stored at the same time. In addition, we examine the robustness with respect to damage of the synaptic connections. The validity of these theoretical results is confirmed by reasonable agreement with numerical simulations.Comment: 23 pages, 11 figure

A comparison of two computer-based face identification systems with human perceptions of faces

The performance of two different computer systems for representing faces was compared with human ratings of similarity and distinctiveness, and human memory performance, on a specific set of face images. The systems compared were a graphmatching system (e.g. Lades et al., 1993) and coding based on Principal Components Analysis (PCA) of image pixels (e.g. Turk & Pentland, 1991). Replicating other work, the PCA-based system produced very much better performance at recognising faces, and higher correlations with human performance with the same images, when the images were initially standardised using a morphing procedure and separate analysis of "shape" and "shape-free" components then combined. Both the graph-matching and (shape + shape-free) PCA systems were equally able to recognise faces shown with changed expressions, both provided reasonable correlations with human ratings and memory data, and there were also correlations between the facial similarities recorded by each of the computer models. However, comparisons with human similarity ratings of faces with and without the hair visible, and prediction of memory performance with and without alteration in face expressions, suggested that the graph-matching system was better at capturing aspects of the appearance of the face, while the PCA-based system seemed better at capturing aspects of the appearance of specific images of faces

Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on $[0,2\pi)$ so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce the effective transfer function by assuming the fixed-point equation of the form of the TAP equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.Comment: published in Phys. Rev.

On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model

During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer's (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer's (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer's (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer