Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons

Recent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed light on how a population of neurones can follow arbitrary variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey.     

The expansion of information in ecological systems: Emergence as a quantifiable state

Although the term ‘emergence’ has received wide attention in the literature, most of this attention has been focused on epistemological discussions about the nature of what might be considered emergent behavior in self-organizing systems. For the concept of emergence to have any great utility for biologists, it must (1) be perceptible as a physical, quantitative property rather than just a philosophical one; (2) have a quantitative definition applicable to all levels of biological organization; and (3) be an essential component of biological system performance or evolution. Using an independent, cellular population model (running in the StarLogo system), we have developed a mutual information calculation to measure the information expansion when considering the interactions between a population of herbivores and an environment in comparison to the interactions between the individual herbivores and that environment. In self-organizing biological systems, the collective action of massively parallel units generates a greater potential complexity in the information processing capacity of the ‘whole’ system relative to the ‘individual’ parts, and as such, there is a demonstrable increase in mutual information content. From this perspective, we consider emergence to exist as a simple information expansion that is a default behavior of any system with multiple, component parts governed by a simple, probabilistic rule set. It is not a first principle of self-organizing biological systems, but rather a collective behavior that can be quantitatively described in practical terms for experimental biologists. With a quantitative formulation, the concept of emergence may become a useful information statistic in assessing the structure of biological systems.     

Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore consider that the neuron dynamics may occur at a (shorter) time scale than synaptic plasticity and consider the possibility of learning rules with passive forgetting. We show that the application of such Hebbian learning leads to drastic changes in the network dynamics and structure. In particular, the learning rule contracts the norm of the weight matrix and yields a rapid decay of the dynamics complexity and entropy. In other words, the network is rewired by Hebbian learning into a new synaptic structure that emerges with learning on the basis of the correlations that progressively build up between neurons. We also observe that, within this emerging structure, the strongest synapses organize as a small-world network. The second effect of the decay of the weight matrix spectral radius consists in a rapid contraction of the spectral radius of the Jacobian matrix. This drives the system through the "edge of chaos" where sensitivity to the input pattern is maximal. Taken together, this scenario is remarkably predicted by theoretical arguments derived from dynamical systems and graph theory.     

Responses of olfactory receptor neurons in the spiny lobster to binary mixtures are predictable using a noncompetitive model that incorporates excitatory and inhibitory transduction pathways

Coding of binary mixtures by a population of olfactory receptor neurons in the spiny lobster (Panulirus argus) was examined. Extracellular single-unit responses of 50 neurons to seven compounds and their binary mixtures were recorded. The ability of a noncompetitive model with correction for binding inhibition to predict responses to mixtures based on responses to their components was compared with the predictive abilities of other models. This model assumes that different compounds activate different transduction processes in the same neuron leading to excitation or inhibition, and it includes a term quantifying the degree to which binding of an odorant to its receptor sites is inhibited by other compounds. The model accurately predicted the absolute response magnitude of the population of neurons for 13 of 15 mixtures assessed, which is superior to the predictive power of any of the other models. The model also accurately predicted the across neuron patterns generated by the binary mixtures, as evaluated by multidimensional scaling analysis. The results suggest that there is no emergence of unique qualities for binary mixtures relative to components of these mixtures.Abbreviations AMP or A adenosine-5-monophosphate - ANP across neuron pattern - ARM absolute response magnitude - ASW artificial sea water - Bet or B betaine - Cys or C L-cysteine - Glu or G L-glutamate - MDS multidimensional scaling - MID mixture interaction distance - NC model noncompetitive model - NCBI model noncompetitive model with correction for binding inhibition - C model competitive model - CBI model competitive model with correction for binding inhibition - MEC more effective component - NH ₄ or N ammonium chloride - ORN olfactory receptor neuron - Suc or S DL-succinate - Tau or T taurine     

A compartmental approach in modeling a neuronal network. Role of inhibitory and excitatory processes]

The conception and main principles of the compartmental approach to the modeling of neuronal networks are presented. Excitatory and inhibitory ties are described, and reducible and nonreducible neuronal networks are considered. The periodical solution in models of neuronal networks is the model of normal rhythmic (e.g., respiratory) activity. The role of external (chemoreceptor drives) is discussed. The biological interpretation of the results of modeling is given. The observed biological phenomena are considered.     

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Computational simulation: astrocyte-induced depolarization of neighboring neurons mediates synchronous UP states in a neural network

Although recent reports have suggested that synchronous neuronal UP states are mediated by astrocytic activity, the mechanism responsible for this remains unknown. Astrocytic glutamate release synchronously depolarizes adjacent neurons, while synaptic transmissions are blocked. The purpose of this study was to confirm that astrocytic depolarization, propagated through synaptic connections, can lead to synchronous neuronal UP states. We applied astrocytic currents to local neurons in a neural network consisting of model cortical neurons. Our results show that astrocytic depolarization may generate synchronous UP states for hundreds of milliseconds in neurons even if they do not directly receive glutamate release from the activated astrocyte.     

Coarse-grained reduction and analysis of a network model of cortical response: I. Drifting grating stimuli

We present a reduction of a large-scale network model of visual cortex developed by McLaughlin, Shapley, Shelley, and Wielaard. The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations. It accounts explicitly for spatially varying architecture, ordered cortical maps (such as orientation preference) that vary regularly across the cortical layer, and disordered cortical maps (such as spatial phase preference or stochastic input conductances) that may vary widely from cortical neuron to cortical neuron. The result of the reduction is a set of nonlinear spatiotemporal integral equations for phase-averaged firing rates of neuronal subpopulations across the model cortex, derived asymptotically from the full model without the addition of any extra phenomological constants. This reduced system is used to study the response of the model to drifting grating stimuli—where it is shown to be useful for numerical investigations that reproduce, at far less computational cost, the salient features of the point-neuron network and for analytical investigations that unveil cortical mechanisms behind the responses observed in the simulations of the large-scale computational model. For example, the reduced equations clearly show (1) phase averaging as the source of the time-invariance of cortico-cortical conductances, (2) the mechanisms in the model for higher firing rates and better orientation selectivity of simple cells which are near pinwheel centers, (3) the effects of the length-scales of cortico-cortical coupling, and (4) the role of noise in improving the contrast invariance of orientation selectivity.     

Application of chaotic dynamics in a recurrent neural network to control: hardware implementation into a novel autonomous roving robot

Originating from a viewpoint that complex/chaotic dynamics would play an important role in biological system including brains, chaotic dynamics introduced in a recurrent neural network was applied to control. The results of computer experiment was successfully implemented into a novel autonomous roving robot, which can only catch rough target information with uncertainty by a few sensors. It was employed to solve practical two-dimensional mazes using adaptive neural dynamics generated by the recurrent neural network in which four prototype simple motions are embedded. Adaptive switching of a system parameter in the neural network results in stationary motion or chaotic motion depending on dynamical situations. The results of hardware implementation and practical experiment using it show that, in given two-dimensional mazes, the robot can successfully avoid obstacles and reach the target. Therefore, we believe that chaotic dynamics has novel potential capability in controlling, and could be utilized to practical engineering application.     

Observation and control in a model of a cell population affected by radiation

The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction.     

Autocatalysis in cultural ecology: model ecosystems and the dynamics of biocultural evolution

Using a well-known mathematical model frequently applied in theoretical population dynamics, certain ecological mechanisms are investigated that are inherent in the organic evolution of cultural capacities in man. Culture is argued to involve ecological interactions exhibiting analogies to the interaction of chemical species in autocatalytic biomolecular reactions. In the model, biocultural evolution proceeds by more and more broadening ecological niches and, thus, releasing competitive selection pressure on the populations involved. This, in turn, facilitates the maintenance of polymorphism in these populations as well as the individual acquisition of organic traits through learning and cultural transmission. The result is that the genetic variance in phenotypic expressions decreases at an accelerated rate.     

The population dynamics of Ostertagia gruehneri in reindeer: a model for the seasonal and intensity dependent variation in nematode fecundity

The gastrointestinal nematode Ostertagia gruehneri is a parasite of reindeer that can have a significant impact on host population dynamics. To gain a better understanding of the population dynamics of O. gruehneri, we parameterise a model for its fecundity that describes the observed seasonal and intensity dependent pattern of faecal egg counts well. The faecal egg count model is combined with a model for the seasonal faecal production rate of Svalbard reindeer to obtain quantitative estimates of the fecundity of O. gruehneri. The model is used to evaluate the relative contribution to pasture contamination of variation in the abundance of O. gruehneri and variation in reindeer densities. It is concluded that due to the intensity dependence in nematode fecundity, variation in reindeer population densities is likely to be the most important of these factors for pasture contamination.     

Role of the actin-binding protein profilin1 in radial migration and glial cell adhesion of granule neurons in the cerebellum

Profilins are small G-actin-binding proteins essential for cytoskeletal dynamics. Of the four mammalian profilin isoforms, profilin1 shows a broad expression pattern, profilin2 is abundant in the brain, and profilin3 and profilin4 are restricted to the testis. In vitro studies on cancer and epithelial cell lines suggested a role for profilins in cell migration and cell-cell adhesion. Genetic studies in mice revealed the importance of profilin1 in neuronal migration, while profilin2 has apparently acquired a specific function in synaptic physiology. We recently reported a mouse mutant line lacking profilin1 in the brain; animals display morphological defects that are typical for impaired neuronal migration. We found that during cerebellar development, profilin1 is specifically required for radial migration and glial cell adhesion of granule neurons. Profilin1 mutants showed cerebellar hypoplasia and aberrant organization of cerebellar cortex layers, with ectopically arranged granule neurons. In this commentary, we briefly introduce the profilin family and summarize the current knowledge on profilin activity in cell migration and adhesion. Employing cerebellar granule cells as a model, we shed some light on the mechanisms by which profilin1 may control radial migration and glial cell adhesion. Finally, a potential implication of profilin1 in human developmental neuropathies is discussed.     

Vertical signal flow and oscillations in a three-layer model of the cortex

A model of vertical signal flow across a layered cortical structure is presented and analyzed. Neurons communicate through spikes, which evoke an excitatory or inhibitory postsynaptic potential (spike response model). The layers incorporate two anatomical features - dendritic and axonal arborization patterns and distance-dependent time delays. The vertical signal flow through the network is discussed for various stimulus conditions using two different, but typical, axonal arborization patterns. We find stationary as well as oscillatory response, but the oscillatory response may be restricted to a single layer. Confronted with conflicting stimuli the network separates the patterns through phase-shifted oscillations. We also discuss two hypothetical animals, to be called cat and mouse. These have different axonal arborizations, which give rise to a different oscillatory response (if any) of the various layers.     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r² (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r² are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.     

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.     

Neuroplasticity and neuroprotection in enteric neurons: Role of epithelial cells

Neurons of enteric nervous system (ENS) regulate intestinal epithelial cells (IEC) functions but whether IEC can impact upon the neurochemical coding and survival of enteric neurons remain unknown. Neuro-epithelial interactions were studied using a coculture model composed of IEC lines and primary culture of rat ENS or human neuroblastoma cells (SH-SY5Y). Neurochemical coding of enteric neurons was analysed by immunohistochemistry and quantitative PCR. Neuroprotective effects of IEC were tested by measuring neuron specific enolase (NSE) release or cell permeability to 7-amino-actinomycin D (7-AAD). Following coculture with IEC, the percentage of VIP-immunoreactive (IR) neurons but not NOS-IR and VIP mRNA expression were significantly increased. IEC significantly reduced dopamine-induced NSE release and 7-AAD permeability in culture of ENS and SH-SY5Y, respectively. Finally, we showed that NGF had neuroprotective effects but reduced VIP expression in enteric neurons. In conclusion, our study identified a novel role for IEC in the regulation of enteric neuronal properties.     

Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations

We have examined the effects of current and conductance noise in a single-neuron model which can generate a variety of physiologically important impulse patterns. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Additive Gaussian white noise which is implemented as conductance noise appears in the voltage equations as an additive and a multiplicative term. Moreover, the originally white noise is turned into colored noise. The noise correlation time is a function of the system's control parameters which may explain the different effects of current and conductance noise in different dynamic states. We have found the most significant, qualitative differences between different noise implementations in a pacemaker-like, tonic firing regime at the transition to chaotic burst discharges. This reflects a dynamic state of high physiological relevance.     

Trend,signal and noise in the ecology of Ostracoda: information from rare species in low-diversity assemblages

Samples of Ostracoda from nearshore marine environments, where the water is more likely to be brackish or hypersaline, typically have low species diversity and are dominated by such species as Cyprideis torosa. In high-diversity samples from normal-marine environments, rare species are likely to contribute to environmental noise. Evaluation of low-diversity samples from Lake Manzala, Egypt, however, shows that the environmental signal provided by rare species can be masked by the overwhelmingly dominant species, C. torosa. In such instances, the dominant species should be removed from the data set and studies based on a large sample of the rare species.