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.     

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.     

Self-organized criticality in developing neuronal networks

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.     

Imaging neuronal networks in behaving animals

Neuronal activity has recently been imaged with single-cell resolution in behaving vertebrates. This was accomplished by using fluorescent calcium indicators in conjunction with confocal or two-photon microscopy. These optical techniques, along with other new approaches for imaging synaptic activity, second messengers, and neurotransmitters and their receptors offer great promise for the study of neuronal networks at high resolution in vivo.     

Mechanisms of establishing long-term fluctuations in the activity of neuronal networks. I. Stochastic uniform neuronal networks

The possibility of generating long-term self-terminating activity lasting some hundreds of milliseconds in neuronal networks with positive (excitatory) feedback was investigated using a computerized mathematical simulation model. This auto-termination is compounded of several factors: stochasticity of the neuronal network, mediating fluctuations in activity level; neuronal interaction, leading either to synchronized discharges and hence of postactivational inhibitory processes, or else to a reorganization of the microstructure underlying neuronal network activity mainly conducive to excitation of neurons with tenuous connections. The likely contribution of these mechanisms to establishing long-term self-terminating activity in the cerebral neuronal networks responsible for different types of programmed rhythmic activity (or generators) is discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 18, No. 3, pp. 382–391, May–June, 1986.     

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.     

A stimulus-dependent connectivity analysis of neuronal networks

We present an analysis of interactions among neurons in stimulus-driven networks that is designed to control for effects from unmeasured neurons. This work builds on previous connectivity analyses that assumed connectivity strength to be constant with respect to the stimulus. Since unmeasured neuron activity can modulate with the stimulus, the effective strength of common input connections from such hidden neurons can also modulate with the stimulus. By explicitly accounting for the resulting stimulus-dependence of effective interactions among measured neurons, we are able to remove ambiguity in the classification of causal interactions that resulted from classification errors in the previous analyses. In this way, we can more reliably distinguish causal connections among measured neurons from common input connections that arise from hidden network nodes. The approach is derived in a general mathematical framework that can be applied to other types of networks. We illustrate the effects of stimulus-dependent connectivity estimates with simulations of neurons responding to a visual stimulus. This research was supported by the National Science Foundation grants DMS-0415409 and DMS-0748417.     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Local and distributed neuronal networks and individuality

To estimate stable behavioural peculiarities, an individual varying choice of greater or better appetite reinforcement depending on the time of instrumental motor response was used with cats. A decisive role in realisation of the response choice is played by the influence of motivational structures of hypothalamus and amygdala on formal areas of neocortex typical for "impulsive" (fast reacting) cats, and interaction of the frontal cortex--hippocampus system for the animals with delayed pressing of the lever to obtain their preferred food, i.e. manifesting the ability of "self-control".     

Coping with variability in small neuronal networks

Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Parallel processing for associative and neuronal networks

We present a parallel processing network, consisting of nine microcomputers, for neuron-network simulations and for the realization of an associative computer memory. We add some remarks on the present possibilities to implement larger associative networks and on parallel processing strategies in general.     

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.     

Colloid-guided assembly of oriented 3D neuronal networks

A central challenge in neuroscience is to understand the formation and function of three-dimensional (3D) neuronal networks. In vitro studies have been mainly limited to measurements of small numbers of neurons connected in two dimensions. Here we demonstrate the use of colloids as moveable supports for neuronal growth, maturation, transfection and manipulation, where the colloids serve as guides for the assembly of controlled 3D, millimeter-sized neuronal networks. Process growth can be guided into layered connectivity with a density similar to what is found in vivo. The colloidal superstructures are optically transparent, enabling remote stimulation and recording of neuronal activity using layer-specific expression of light-activated channels and indicator dyes. The modular approach toward in vitro circuit construction provides a stepping stone for applications ranging from basic neuroscience to neuron-based screening of targeted drugs.     

Distributed processing and temporal codes in neuronal networks

The cerebral cortex presents itself as a distributed dynamical system with the characteristics of a small world network. The neuronal correlates of cognitive and executive processes often appear to consist of the coordinated activity of large assemblies of widely distributed neurons. These features require mechanisms for the selective routing of signals across densely interconnected networks, the flexible and context dependent binding of neuronal groups into functionally coherent assemblies and the task and attention dependent integration of subsystems. In order to implement these mechanisms, it is proposed that neuronal responses should convey two orthogonal messages in parallel. They should indicate (1) the presence of the feature to which they are tuned and (2) with which other neurons (specific target cells or members of a coherent assembly) they are communicating. The first message is encoded in the discharge frequency of the neurons (rate code) and it is proposed that the second message is contained in the precise timing relationships between individual spikes of distributed neurons (temporal code). It is further proposed that these precise timing relations are established either by the timing of external events (stimulus locking) or by internal timing mechanisms. The latter are assumed to consist of an oscillatory modulation of neuronal responses in different frequency bands that cover a broad frequency range from <2 Hz (delta) to >40 Hz (gamma) and ripples. These oscillations limit the communication of cells to short temporal windows whereby the duration of these windows decreases with oscillation frequency. Thus, by varying the phase relationship between oscillating groups, networks of functionally cooperating neurons can be flexibly configurated within hard wired networks. Moreover, by synchronizing the spikes emitted by neuronal populations, the saliency of their responses can be enhanced due to the coincidence sensitivity of receiving neurons in very much the same way as can be achieved by increasing the discharge rate. Experimental evidence will be reviewed in support of the coexistence of rate and temporal codes. Evidence will also be provided that disturbances of temporal coding mechanisms are likely to be one of the pathophysiological mechanisms in schizophrenia. This article was part of LNCS 5286 (2008), Maria Marinaro, Silvia Scarpetta, Yoko Yamaguchi (eds.), “Dynamic Brain—from Neural Spikes to Behaviors, 12th International Summer School on Neural Networks Erice, Italy, December 2007 Revised Lectures” and summarized some of the putative functions of temporal codes resulting either from the timing of external events (feed forward/bottom up) or from internal timing mechanisms (top down). For comprehensive reviews of the theoretical prerequisites of synchronization in these processes see Yamaguchi and Shimizu (1994) and Shimizu et al. (1985).     

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.     

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.     

Paradoxical REM sleep promoting and permitting neuronal networks

Since its electrophysiological identification in the 1950's, the state of REMS or PS has been shown through multiple lines of evidence to be generated by neurons in the oral pontine tegmentum. The perpetration of this paradoxical state that combines cortical activation with the most profound behavioral sleep occurs through interplay between PS-promoting (On) and PS-permitting (Off) cell groups in the pons. Cholinergic cells in the LDTg and PPTg promote PS by initiating processes of both forebrain activation and peripheral muscle atonia. Bearing alpha1-adrenergic receptors, cholinergic cells, which likely project to the forebrain, are excited by NA and active during both W and PS (W/PS-On), when they promote cortical activation. Bearing alpha2-adrenergic receptors, other cholinergic cells, which likely project to the brainstem, are inhibited by NA and thus active selectively during PS (PS-On), when they promote muscle atonia. Noradrenergic, together with serotonergic, neurons, as PS-Off neurons, thus permit PS in part by lifting their inhibition upon the cholinergic PS-On cells. The noradrenergic/serotonergic neurons are inhibited in turn by local GABAergic PS-promoting neurons that may be excited by ACh. Other similarly modulated GABAergic neurons located through the brainstem reticular formation become active to participate in the inhibition of reticulo-spinal and raphe-spinal neurons as well as in the direct inhibition of motor neurons. In contrast, a select group of GABAergic neurons located in the oral pontine reticular formation and possibly inhibited by ACh turn off during PS. These GABAergic PS-permitting neurons release from inhibition the neighboring large glutamatergic neurons of the oral pontine reticular formation, which are likely concomitantly excited by ACh. In tandem with the cholinergic neurons, these glutamatergic reticular neurons propagate the paradoxical forebrain activation and peripheral inactivation that characterize PS.     

Behavioral choices: how neuronal networks make decisions

To survive, animals must constantly make behavioral choices. The analysis of simple, almost binary, behavioral choices in invertebrate animals with restricted nervous systems is beginning to yield insight into how neuronal networks make such decisions.