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.     

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.     

Cellular and molecular mechanisms of neuronal migration in neocortical development

The complicated mammalian brain structure arises from accurate movements of neurons from their birthplace to their final locations. Detailed observation of this migration process by various methods revealed that neuronal migration is highly motile and that there are different modes of migration. Moreover, mouse mutants or human disorders that disrupt normal migration have provided significant insights into molecular pathways that control the neuronal migration. Although our knowledge is still fragmentary, it is becoming clear that various molecules are participating in this process. In this review, we outline about the cellular and molecular mechanisms of neuronal migration in the cerebral cortex.     

Subdural grid recordings of distributed neocortical networks involved with somatosensory discrimination

Previous studies suggest that evidence for the sub-second activation of distributed neural networks can be obtained by computing the covariance between segments of the scalp-recorded evoked potential. However, the cortical representation of such potentials is not known. Here we report a case study where the evoked potential covariance (EPC) measure was applied to data recorded from a 58-channel subdural grid implanted in an epilepsy patient. Recordings were made while the patient performed a task that required judging the somatosensory intensities of electrical stimuli and executing precise finger flexion responses in response to a subset of those stimuli. Post-stimulus EPC patterns involved covariances between somatosensory, motor, and temporal regions. Pre-stimulus EPC patterns involved these same regions, but only when it could be anticipated that the upcoming stimulus would likely require a response. The majority of the observed EPCs occurred with non-zero time-lags, and these EPCs often involved non-adjacent electrode pairs. Thus, the observed EPCs were unlikely to arise solely from volume conduction. Rather, they appeared to reflect the transient integration of activity across distinct cortical processing nodes.     

CRE-mediated gene transcription in neocortical neuronal plasticity during the developmental critical period

Neuronal activity-dependent processes are believed to mediate the formation of synaptic connections during neocortical development, but the underlying intracellular mechanisms are not known. In the visual system, altering the pattern of visually driven neuronal activity by monocular deprivation induces cortical synaptic rearrangement during a postnatal developmental window, the critical period. Here, using transgenic mice carrying a CRE-lacZ reporter, we demonstrate that a calcium- and cAMP-regulated signaling pathway is activated following monocular deprivation. We find that monocular deprivation leads to an induction of CRE-mediated lacZ expression in the visual cortex preceding the onset of physiologic plasticity, and this induction is dramatically downregulated following the end of the critical period. These results suggest that CRE-dependent coordinate regulation of a network of genes may control physiologic plasticity during postnatal neocortical development.     

Excitatory neuronal CHD8 in the regulation of neocortical development and sensory-motor behaviors

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Cross-correlation analysis of background neuronal activity in guinea pig neocortical slices in vitro

Interaction between the background activity of adjoining neurons was investigated using simultaneous recording in surviving slices from the guinea pig sensory motor cortex by means of cross-correlation analysis. A numerical connection was found between the timing of successive discharges in sixteen of the twenty six neuronal pairs investigated. Significant discrepancies were observed in correlation tables, mainly in the range of time shifts of ±100 msec from zero point. These emerged as symmetrical or asymmetrical peaks of up to 150 msec in duration and negative shifts measuring up to 200 msec. More complex positive-negative cross-correlation patterns were also encountered. These findings may be compared with those obtained in the cortex of the intact brain. The subject of the contribution made by intrinsic cortical neuronal interaction and that of external afferents to firing correlation is discussed.Institute of Biological Physics, Academy of Sciences of the USSR, Pushchino, Moscow. Translated from Neirofiziologiya, Vol. 23, No. 4, pp. 392–399, July–August, 1991.     

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.     

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.     

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.     

Organization of actin networks in intact filopodia

Filopodia are finger-like extensions of the cell surface that are involved in sensing the environment, in attachment of particles for phagocytosis, in anchorage of cells on a substratum, and in the response to chemoattractants or other guidance cues. Filopodia present an excellent model for actin-driven membrane protrusion. They grow at their tips by the assembly of actin and are stabilized along their length by a core of bundled actin filaments. To visualize actin networks in their native membrane-anchored state, filopodia of Dictyostelium cells were subjected to cryo-electron tomography. At the site of actin polymerization, a peculiar structure, the "terminal cone," is built of short filaments fixed with their distal end to the filopod's tip and with their proximal end to the flank of the filopod. The backbone of the filopodia consists of actin filaments that are shorter than the entire filopod and aligned in parallel or obliquely to the filopod's axis. We hypothesize that growth of the highly dynamic filopodia of Dictyostelium is accompanied by repetitive nucleation of actin polymerization at the filopod tip, followed by the rearrangement of filaments within the shaft.     

NudC is required for interkinetic nuclear migration and neuronal migration during neocortical development

NudC is a highly conserved protein necessary for cytoplasmic dynein-mediated nuclear migration in Aspergillus nidulans. NudC interacts genetically with Aspergillus NudF and physically with its mammalian orthologue Lis1, which is crucial for nuclear and neuronal migration during brain development. To test for related roles for NudC, we performed in utero electroporation into embryonic rat brain of cDNAs encoding shRNAs as well as wild-type and mutant forms of NudC. We show here that NudC, like Lis1, is required for neuronal migration during neocorticogenesis and we identify a specific role in apical nuclear migration in radial glial progenitor cells. These results identify a novel neuronal migration gene with a specific role in interkinetic nuclear migration, consistent with cytoplasmic dynein regulation.     

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.     

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.     

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".     

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.     

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.