Mechanisms of establishing long-term fluctuations in neuronal networks. II. Networks with pre- and postsynaptic inhibition

The role of pre- and postsynaptic inhibitory processes in establishing long-term activity measuring hundreds of milliseconds in neuronal networks was investigated on a simulated (mathematical) model. Additional factors appear in networks with pre- and postsynaptic inhibition which are responsible for terminating this long-term network activity, either owing to depolarization setting in at the neuronal terminals reaching a critical level together with marked suppression of the effects of synaptic excitation, or else due to activation of inhibitory neurons exerting a powerful hyperpolarizing action on other neurons of the network. It is deduced that introducing additional negative feedback circuits in the form of pre- or post-synaptic inhibition renders the workings of this mechanism for terminating activity within the neuronal network more reliable, less subject to disruptive action, and more accurate.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 18, No. 3, pp. 392–402, May–June, 1986.     

Response of de- and hyperpolarizing effects in neuronal networks with different mechanisms for terminating activity

The response of stochastically organized homogeneous neuronal networks and others reacting by pre- and postsynaptic inhibition to external de- and hyperpolarizing effects of different intensity and time course were compared using a simulated mathematical computer model. The area of lasting depolarizing effects extended in those with pre- and postsynaptic inhibition compared with heterogeneous neuronal networks. Effects of brief de- and hyperpolarizing effects in a network depended on fluctuations in the level of the activity it displays; depolarizing effects may shorten and hyperpolarizing influences prolong the activity period of networks. The effects of a shortened network activity stage due to brief depolarizing influences was also more marked in networks with preand postsynaptic inhibition. Findings from this research would lead to the deduction that the presence of additional negative feedback circuits in the form of presynaptic or postsynaptic inhibitory series promotes better control in the mechanisms terminating network activity.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 438–447, July–August, 1988.     

Self-stabilization of neuronal networks

Between the extreme views concerning ontogenesis (genetic vs. environmental determination), we use a moderate approach: a somehow pre-established neuronal model network reacts to activity deviations (reflecting input to be compensated), and stabilizes itself during a complex feed-back process. Morphogenesis is based on an algorithm formalizing the compensation theory of synaptogenesis (Wolff and Wagner 1983). This algorithm is applied to randomly connected McCulloch-Pitts networks that are able to maintain oscillations of their activity patterns over time. The algorithm can lead to networks which are morphogenetically stable but preserve self-maintained oscillations in activity. This is in contrast to most of the current models of synaptogenesis and synaptic modification based on Hebbian rules of plasticity. Hebbian networks are morphogenetically unstable without additional assumptions. The effects of compensation on structural and functional properties of the networks are described. It is concluded that the compensation theory of synaptogenesis can account for the development of morphogenetically stable neuronal networks out of randomly connected networks via selective stabilization and elimination of synapses.The logic of the compensation algorithm is based on experimental results. The present paper shows that the compensation theory can not only predict the behavior of synaptic populations (Wagner and Wolff, in preparation), but it can also describe the behavior of neurons interconnected in a network, with the resulting additional system properties. The neuronal interactions-leading to equilibrium in certain cases-are a self-organizing process in the sense that all decisions are performed on the individual cell level without knowing the overall network situation or goal.     

On the dynamics of the spontaneous activity in neuronal networks

Most neuronal networks, even in the absence of external stimuli, produce spontaneous bursts of spikes separated by periods of reduced activity. The origin and functional role of these neuronal events are still unclear. The present work shows that the spontaneous activity of two very different networks, intact leech ganglia and dissociated cultures of rat hippocampal neurons, share several features. Indeed, in both networks: i) the inter-spike intervals distribution of the spontaneous firing of single neurons is either regular or periodic or bursting, with the fraction of bursting neurons depending on the network activity; ii) bursts of spontaneous spikes have the same broad distributions of size and duration; iii) the degree of correlated activity increases with the bin width, and the power spectrum of the network firing rate has a 1/f behavior at low frequencies, indicating the existence of long-range temporal correlations; iv) the activity of excitatory synaptic pathways mediated by NMDA receptors is necessary for the onset of the long-range correlations and for the presence of large bursts; v) blockage of inhibitory synaptic pathways mediated by GABA(A) receptors causes instead an increase in the correlation among neurons and leads to a burst distribution composed only of very small and very large bursts. These results suggest that the spontaneous electrical activity in neuronal networks with different architectures and functions can have very similar properties and common dynamics.     

Reverberation of excitation in neuronal networks interconnected through voltage-gated gap junction channels

We combined Hodgkin–Huxley equations and gating models of gap junction (GJ) channels to simulate the spread of excitation in two-dimensional networks composed of neurons interconnected by voltage-gated GJs. Each GJ channel contains two fast and slow gates, each exhibiting current–voltage (I-V) rectification and gating properties that depend on transjunctional voltage (V_j). The data obtained show how junctional conductance (g_j), which is necessary for synchronization of the neuronal network, depends on its size and the intrinsic firing rate of neurons. A phase shift between action potentials (APs) of neighboring neurons creates bipolar, short-lasting V_j spikes of approximately ±100 mV that induce V_j gating, leading to a small decay of g_j, which can accumulate into larger decays during bursting activity of neurons. We show that I-V rectification of GJs in local regions of the two-dimensional network of neurons can lead to unidirectional AP transfer and consequently to reverberation of excitation. This reverberation can be initiated by a single electrical pulse and terminated by a low-amplitude pulse applied in a specific window of reverberation cycle. Thus, the model accounts for the influence of dynamically modulatable electrical synapses in shaping the function of a neuronal network and the formation of reverberation, which, as proposed earlier, may be important for the development of short-term memory and its consolidation into long-term memory.     

Network reconfiguration and neuronal plasticity in rhythm-generating networks

Neuronal networks are highly plastic and reconfigure in a state-dependent manner. The plasticity at the network level emerges through multiple intrinsic and synaptic membrane properties that imbue neurons and their interactions with numerous nonlinear properties. These properties are continuously regulated by neuromodulators and homeostatic mechanisms that are critical to maintain not only network stability and also adapt networks in a short- and long-term manner to changes in behavioral, developmental, metabolic, and environmental conditions. This review provides concrete examples from neuronal networks in invertebrates and vertebrates, and illustrates that the concepts and rules that govern neuronal networks and behaviors are universal.     

Effect of protein synthesis inhibitors on neuronal mechanisms of sensitization inHelix snail

A sensitizing treatment with 5–10% quinine solution causes short-term (lasting 50–70 min) and long-term (lasting several hours) changes in the activity of the command neurons for defensive behavior (LPl1 and PPl1) in the snailHelix lucorum. The short-term effects are characterized by a depolarizing shift in membrane potential, increased excitability, and an initial increase in the content of bound calcium (Ca-c) in the neurons. The long-term effects appear as facilitation of synaptic components of neuronal responses to sensory stimuli without any changes in excitability and in membrane potential, and also as a repeated increase of Ca-c content. Treatment with anisomycin or cycloheximide during sensitization acquirement prevents development of long-term sensitization.Translated from Neirofiziologiya, Vol. 25, No. 2, pp. 109–115, March–April, 1993.     

Characterization of synchronized bursts in cultured hippocampal neuronal networks with learning training on microelectrode arrays

Spontaneous synchronized bursts seem to play a key role in brain functions such as learning and memory. Still controversial is the characterization of spontaneous synchronized bursts in neuronal networks after learning training, whether depression or promotion. By taking advantages of the main features of the microelectrode array (MEA) technology (i.e. multisite recordings, stable and long-term coupling with the biological preparation), we analyzed changes of spontaneous synchronized bursts in cultured hippocampal neuronal networks after learning training. And for this purpose, a learning model at networking level on MEA system was constructed, and analysis of spontaneous synchronized burst activity modulation was presented. Preliminary results show that, the number of burst was increased by 154%, burst duration was increased by 35%, and the number of spikes per burst was increased by 124%, while interburst interval decreased by 44% with learning. In particular, correlation and synchrony of neuronal activities in networks were enhanced by 51% and 36%, respectively, with learning. In contrast, dynamic properties of neuronal networks were not changed much when the network was under “non-learning” condition. These results indicate that firing, association and synchrony of spontaneous bursts in neuronal networks were promoted by learning. Furthermore, from these observations, we are encouraged to think of a more engineered system based on in vitro hippocampal neurons, as a novel sensitive system for electrophysiological evaluations.     

Self-stabilization of neuronal networks

This study is concerned with synaptic reorganization in local neuronal networks. Within networks of 30 neurons, an initial disequilibrium in connectivity has to be compensated by reorganization of synapses. Such plasticity is not a genetically determined process, but depends on results of neuronal interaction. Neurobiological experiments have lead to a model of the behavior of individual neurons during neuroplastic reorganization, formalized as a synaptogenetic rule that governs changes in the amount of synaptic elements on each neuron. — When this synaptogenetic rule is applied to a system of neurons, there is some freedom left to the choice of further conditions. In this study it is examined, which assumptions additional to the synaptogenetic rule are essential in order to obtain morphogenetic stability. By explicating these assumptions, their plausibility can be tested. It is analysed, in which respect these conditions are important, in which part of the model they exert their influence, and what kind of instability and degeneration happens if the assumptions are violated. —Our essentials for reaching morphogenetic stability are: (1) A network structure that guarantees the possibility of oscillations, (2) a compensation algorithm that guarantees a smooth morphogenesis, (3) kinetic parameters that guarantee convergence in the synaptic elements' change, and (4) a synaptic modification rule that prohibits Hebb-like as well as anti-Hebb-like synaptic changes. — It is concluded that many structural features of the mammalian cerebral cortex are in accordance with the requirements of the model.     

Long-term action of camphor on "audio-sensitive" rats: Electrophysiological study and mathematical modeling of properties of neuronal networks

Krushinskii-Molodkina (KM) strain rats genetically predisposed to audiogenic convulsive reaction were given repeated camphor injections in gradually increasing doses (starting at the minimum threshold level required for seizures to occur) over a 4–5 month period. Animals were able to tolerate camphor at doses 3/2–3 times convulsion threshold level without seizure occurring once habituation to the action of this convulsant had been developed. At the same time, the cortical motor zone of strain KM rats acquired properties typical of an epileptic focus: spontaneous epileptiform firing peaks were noted in the background electrical activity of this zone. A decline in the parameter reflecting efficacy of the mechanisms underlying recurrent inhibition emerged in the cortical motor zone of strain KM rats receiving camphor from calculating the parameters of neuronal network from spectra of summated potentials (using the model of a neuronal network). It is suggested that the development of compensatory processes making it possible to avoid generalized seizure following administration of camphor in large doses is associated with intensification of inhibitory caudate function and attenuated hippocampal excitation.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 22, No. 2, pp. 193–200, March–April, 1990.     

Organization of neocortical neuronal networks

Multiple unit activity in deep layers of the frontal and motor cortices was recorded by chronically implanted semimicroelectrodes in waking cats with different levels of food motivation. From four to seven neuronal spike trains were selected from the recorded multiunit activity. Interactions between neighbouring neurons in the motor and frontal areas of the neocortex (within the local neuronal networks) and between the neurons of these areas (distributed neuronal networks) were estimated by means of statistical crosscorrelation analysis of spike trains within the range of delays from 0 to 100 ms. Neurons in the local networks were divided in two subgroups: the neurons with higher spike amplitudes with the dominance of divergent connections and neurons with lower spike amplitudes with the dominance of convergent connections. Strong monosynaptic connections (discharges with a delay of less than 2 ms) between the neurons with high- and low-amplitude spikes formed the background of the local networks. Connections between low-amplitude neurons in the frontal cortex and high-amplitude neurons in the motor cortex dominated in the distributed networks. A 24-hour food deprivation predominantly altered the late interneuronal crosscorrelations with time delays within the range of 2-100 ms in both local and distributed networks.     

Manifestation of function-follow-form in cultured neuronal networks

We expose hidden function-follow-form schemata in the recorded activity of cultured neuronal networks by comparing the activity with simulation results of a new modeling approach. Cultured networks grown from an arbitrary mixture of neuron and glia cells in the absence of external stimulations and chemical cues spontaneously form networks of different sizes (from 50 to several millions of neurons) that exhibit non-arbitrary complex spatio-temporal patterns of activity. The latter is marked by formation of a sequence of synchronized bursting events (SBEs)--short time windows (approximately 200 ms) of rapid neuron firing, separated by longer time intervals (seconds) of sporadic neuron firing. The new dynamical synapse and soma (DSS) model, used here, has been successful in generating sequences of SBEs with the same statistical scaling properties (over six time decades) as those of the small networks. Large networks generate statistically distinct sub-groups of SBEs, each with its own characteristic pattern of neuronal firing ('fingerprint'). This special function (activity) motif has been proposed to emanate from a structural (form) motif--self-organization of the large networks into a fabric of overlapping sub-networks of about 1 mm in size. Here we test this function-follow-form idea by investigating the influence of the connectivity architecture of a model network (form) on the structure of its spontaneous activity (function). We show that a repertoire of possible activity states similar to the observed ones can be generated by networks with proper underlying architecture. For example, networks composed of two overlapping sub-networks exhibit distinct types of SBEs, each with its own characteristic pattern of neuron activity that starts at a specific sub-network. We further show that it is possible to regulate the temporal appearance of the different sub-groups of SBEs by an additional non-synaptic current fed into the soma of the modeled neurons. The ability to regulate the relative temporal ordering of different SBEs might endow the networks with higher plasticity and complexity. These findings call for additional mechanisms yet to be discovered. Recent experimental observations indicate that glia cells coupled to neuronal soma might generate such non-synaptic regulating currents.     

The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics’ Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.     

Selective self-synchronization of pulses in neuronal networks of the visual system

In the present study we have checked the hypothesis that the degree of pulse synchrony in neuronal pools is determined by the level of excitation of the neuronal network or its loci and that this relationship does not depend on the factor that causes the excitation. Pulse reactions of neurons in pools (2–4 cells) of cat lateral geniculate nucleus and visual cortex were registered. Neurons were excited using either visual stimuli or glutamic acid microinjections into neuronal pools. The increase of neural pool excitation level (No) regardless of the type of stimulus was shown to increase the pulse synchrony (Ns), with a correlation coefficient of 0.716 ± 0.217. One may suppose that the level of neuronal network excitation “governs” the synchrony of pulses generated by the network, i.e., neuronal networks function in compliance with the principle of self-synchronization.     

Pacemaker neurons and neuronal networks: an integrative view

Rhythmically active neuronal networks give rise to rhythmic motor activities but also to seemingly non-rhythmic behaviors such as sleep, arousal, addiction, memory and cognition. Many of these networks contain pacemaker neurons. The ability of these neurons to generate bursts of activity intrinsically lies in voltage- and time-dependent ion fluxes resulting from a dynamic interplay among ion channels, second messenger pathways and intracellular Ca2+ concentrations, and is influenced by neuromodulators and synaptic inputs. This complex intrinsic and extrinsic modulation of pacemaker activity exerts a dynamic effect on network activity. The nonlinearity of bursting activity might enable pacemaker neurons to facilitate the onset of excitatory states or to synchronize neuronal ensembles--an interactive process that is intimately regulated by synaptic and modulatory processes.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.     

Signal propagation in feedforward neuronal networks with unreliable synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.     

Growth rules for the repair of Asynchronous Irregular neuronal networks after peripheral lesions

Several homeostatic mechanisms enable the brain to maintain desired levels of neuronal activity. One of these, homeostatic structural plasticity, has been reported to restore activity in networks disrupted by peripheral lesions by altering their neuronal connectivity. While multiple lesion experiments have studied the changes in neurite morphology that underlie modifications of synapses in these networks, the underlying mechanisms that drive these changes are yet to be explained. Evidence suggests that neuronal activity modulates neurite morphology and may stimulate neurites to selective sprout or retract to restore network activity levels. We developed a new spiking network model of peripheral lesioning and accurately reproduced the characteristics of network repair after deafferentation that are reported in experiments to study the activity dependent growth regimes of neurites. To ensure that our simulations closely resemble the behaviour of networks in the brain, we model deafferentation in a biologically realistic balanced network model that exhibits low frequency Asynchronous Irregular (AI) activity as observed in cerebral cortex. Our simulation results indicate that the re-establishment of activity in neurons both within and outside the deprived region, the Lesion Projection Zone (LPZ), requires opposite activity dependent growth rules for excitatory and inhibitory post-synaptic elements. Analysis of these growth regimes indicates that they also contribute to the maintenance of activity levels in individual neurons. Furthermore, in our model, the directional formation of synapses that is observed in experiments requires that pre-synaptic excitatory and inhibitory elements also follow opposite growth rules. Lastly, we observe that our proposed structural plasticity growth rules and the inhibitory synaptic plasticity mechanism that also balances our AI network both contribute to the restoration of the network to pre-deafferentation stable activity levels.     

Emergence and fragmentation of the alpha-band driven by neuronal network dynamics

Rhythmic neuronal network activity underlies brain oscillations. To investigate how connected neuronal networks contribute to the emergence of the α-band and to the regulation of Up and Down states, we study a model based on synaptic short-term depression-facilitation with afterhyperpolarization (AHP). We found that the α-band is generated by the network behavior near the attractor of the Up-state. Coupling inhibitory and excitatory networks by reciprocal connections leads to the emergence of a stable α-band during the Up states, as reflected in the spectrogram. To better characterize the emergence and stability of thalamocortical oscillations containing α and δ rhythms during anesthesia, we model the interaction of two excitatory networks with one inhibitory network, showing that this minimal topology underlies the generation of a persistent α-band in the neuronal voltage characterized by dominant Up over Down states. Finally, we show that the emergence of the α-band appears when external inputs are suppressed, while fragmentation occurs at small synaptic noise or with increasing inhibitory inputs. To conclude, α-oscillations could result from the synaptic dynamics of interacting excitatory neuronal networks with and without AHP, a principle that could apply to other rhythms.     

Measuring synchronization in neuronal networks for biosensor applications

Cultures of neurons can be grown on microelectrode arrays (MEAs), so that their spike and burst activity can be monitored. These activity patterns are quite sensitive to changes in the environment, such as chemical exposure, and hence the cultures can be used as biosensors. One key issue in analyzing the data from neuronal networks is how to quantify the level of synchronization among different units, which represent different neurons in the network. In this paper, we propose a synchronization metric, based on the statistical distribution of unit-to-unit correlation coefficients. We show that this synchronization metric changes significantly when the networks are exposed to bicuculline, strychnine, or 2,3-dioxo-6-nitro-l,2,3,4-tetrahydrobenzoquinoxaline-7-sulphonamide (NBQX). For that reason, this metric can be used to characterize pharmacologically induced changes in a network, either for research or for biosensor applications.