Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.     

Hebb and homeostasis in neuronal plasticity

The positive-feedback nature of Hebbian plasticity can destabilize the properties of neuronal networks. Recent work has demonstrated that this destabilizing influence is counteracted by a number of homeostatic plasticity mechanisms that stabilize neuronal activity. Such mechanisms include global changes in synaptic strengths, changes in neuronal excitability, and the regulation of synapse number. These recent studies suggest that Hebbian and homeostatic plasticity often target the same molecular substrates, and have opposing effects on synaptic or neuronal properties. These advances significantly broaden our framework for understanding the effects of activity on synaptic function and neuronal excitability.     

The role of neuronal death during the development of topographically ordered projections: a computational approach

At the time of synaptogenesis typically 50% of the neurons die. The biological role of this is still unclear, but there is evidence in the visual system that many neurons projecting to topographically inappropriate parts of their target are eliminated to improve the accuracy of the mapping. The signaling that determines neuronal survival involves electrical activity and trophic factors. Based on these observations, we have elaborated a computational model for the self-organization of a two-layered neural network. We observe changes in the topographical organization between the two layers. In layer 1, a traveling wave of electrical activity is used as input. Activity transmission to layer 2 can generate, according to a Hebbian rule, a retrograde death signal that is compensated by a trophic survival signal generated by the target cells. Approximately 50% of the neurons die, and we observe refinement in the topography between the two layers. In alternative versions of the model, we show that an equivalent reorganization can occur through Hebbian synaptic modification alone, but with less precision and efficiency. When the two mechanisms are combined, synaptic modification provides no further improvement over that produced by neuronal death alone. This computational study supports the hypothesis that neuronal death during development can play a role in the refinement of topographical projections in the nervous system. Received: 9 November 1998 / Accepted in revised form: 14 April 1999     

Communication between neurons and astrocytes: relevance to the modulation of synaptic and network activity

Neuromodulation is a fundamental process in the brain that regulates synaptic transmission, neuronal network activity and behavior. Emerging evidence demonstrates that astrocytes, a major population of glial cells in the brain, play previously unrecognized functions in neuronal modulation. Astrocytes can detect the level of neuronal activity and release chemical transmitters to influence neuronal function. For example, recent findings show that astrocytes play crucial roles in the control of Hebbian plasticity, the regulation of neuronal excitability and the induction of homeostatic plasticity. This review discusses the importance of astrocyte-to-neuron signaling in different aspects of neuronal function from the activity of single synapses to that of neuronal networks.     

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.     

Compensating for synaptic loss in Alzheimer’s disease

Confirming that synaptic loss is directly related to cognitive deficit in Alzheimer’s disease (AD) has been the focus of many studies. Compensation mechanisms counteract synaptic loss and prevent the catastrophic amnesia induced by synaptic loss via maintaining the activity levels of neural circuits. Here we investigate the interplay between various synaptic degeneration and compensation mechanisms, and abnormal cortical oscillations based on a large-scale network model consisting of 100,000 neurons exhibiting several cortical firing patterns, 8.5 million synapses, short-term plasticity, axonal delays and receptor kinetics. The structure of the model is inspired by the anatomy of the cerebral cortex. The results of the modelling study suggest that cortical oscillations respond differently to compensation mechanisms. Local compensation preserves the baseline activity of theta (5–7 Hz) and alpha (8–12 Hz) oscillations whereas delta (1–4 Hz) and beta (13–30 Hz) oscillations are maintained via global compensation. Applying compensation mechanisms independently shows greater effects than combining both compensation mechanisms in one model and applying them in parallel. Consequently, it can be speculated that enhancing local compensation might recover the neural processes and cognitive functions that are associated with theta and alpha oscillations whereas inducing global compensation might contribute to the repair of neural (cognitive) processes which are associated with delta and beta band activity. Compensation mechanisms may vary across cortical regions and the activation of inappropriate compensation mechanism in a particular region may fail to recover network dynamics and/or induce secondary pathological changes in the network.     

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.     

Communication through Resonance in Spiking Neuronal Networks

The cortex processes stimuli through a distributed network of specialized brain areas. This processing requires mechanisms that can route neuronal activity across weakly connected cortical regions. Routing models proposed thus far are either limited to propagation of spiking activity across strongly connected networks or require distinct mechanisms that create local oscillations and establish their coherence between distant cortical areas. Here, we propose a novel mechanism which explains how synchronous spiking activity propagates across weakly connected brain areas supported by oscillations. In our model, oscillatory activity unleashes network resonance that amplifies feeble synchronous signals and promotes their propagation along weak connections (“communication through resonance”). The emergence of coherent oscillations is a natural consequence of synchronous activity propagation and therefore the assumption of different mechanisms that create oscillations and provide coherence is not necessary. Moreover, the phase-locking of oscillations is a side effect of communication rather than its requirement. Finally, we show how the state of ongoing activity could affect the communication through resonance and propose that modulations of the ongoing activity state could influence information processing in distributed cortical networks.     

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.This work was partially supported by the National Science Foundation, under award DMS-0414023     

Adaptive synaptogenesis constructs networks that maintain information and reduce statistical dependence

This report demonstrates the effectiveness of two processes in constructing simple feedforward networks which perform good transformations on their inputs. Good transformations are characterized by the minimization of two information measures: the information loss incurred with the transformation and the statistical dependency of the output. The two processes build appropriate synaptic connections in initially unconnected networks. The first process, synaptogenesis, creates new synaptic connections; the second process, associative synaptic modification, adjusts the connection strength of existing synapses. Synaptogenesis produces additional innervation for each output neuron until each output neuron achieves a firing rate of approximately 0.50. Associative modification of existing synaptic connections lends robustness to network construction by adjusting suboptimal choices of initial synaptic weights. Networks constructed using synaptogenesis and synaptic modification successfully preserve the information content of a variety of inputs. By recording a high-dimensional input into an output of much smaller dimension, these networks drastically reduce the statistical dependence of neuronal representations. Networks constructed with synaptogenesis and associative modification perform good transformations over a wide range of neuron firing thresholds.     

Learning-Induced Synchronization and Plasticity of a Developing Neural Network

Learning-induced synchronization of a neural network at various developing stages is studied by computer simulations using a pulse-coupled neural network model in which the neuronal activity is simulated by a one-dimensional map. Two types of Hebbian plasticity rules are investigated and their differences are compared. For both models, our simulations show a logarithmic increase in the synchronous firing frequency of the network with the culturing time of the neural network. This result is consistent with recent experimental observations. To investigate how to control the synchronization behavior of a neural network after learning, we compare the occurrence of synchronization for four networks with different designed patterns under the influence of an external signal. The effect of such a signal on the network activity highly depends on the number of connections between neurons. We discuss the synaptic plasticity and enhancement effects for a random network after learning at various developing stages.     

Pharmacological Characterization of Cultivated Neuronal Networks: Relevance to Synaptogenesis and Synaptic Connectivity

Mental disorders, such as schizophrenia or Alzheimer’s disease, are associated with impaired synaptogenesis and/or synaptic communication. During development, neurons assemble into neuronal networks, the primary supracellular mediators of information processing. In addition to the orchestrated activation of genetic programs, spontaneous electrical activity and associated calcium signaling have been shown to be critically involved in the maturation of such neuronal networks. We established an in vitro model that recapitulates the maturation of neuronal networks, including spontaneous electrical activity. Upon plating, mouse primary hippocampal neurons grow neurites and interconnect via synapses to form a dish-wide neuronal network. Via live cell calcium imaging, we identified a limited period of time in which the spontaneous activity synchronizes across neurons, indicative of the formation of a functional network. After establishment of network activity, the neurons grow dendritic spines, the density of which was used as a morphological readout for neuronal maturity and connectivity. Hence, quantification of neurite outgrowth, synapse density, spontaneous neuronal activity, and dendritic spine density allowed to study neuronal network maturation from the day of plating until the presence of mature neuronal networks. Via acute pharmacological intervention, we show that synchronized network activity is mediated by the NMDA-R. The balance between kynurenic and quinolinic acid, both neuro-active intermediates in the tryptophan/kynurenine pathway, was shown to be decisive for the maintenance of network activity. Chronic modulation of the neurotrophic support influenced the network formation and revealed the extreme sensitivity of calcium imaging to detect subtle alterations in neuronal physiology. Given the reproducible cultivation in a 96-well setup in combination with fully automated analysis of the calcium recordings, this approach can be used to build a high-content screening assay usable for neurotoxicity screening, target identification/validation, or phenotypic drug screening.     

Bursting Reverberation as a Multiscale Neuronal Network Process Driven by Synaptic Depression-Facilitation

Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5–30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation: in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2–5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.     

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.     

Theta oscillations by synaptic excitation in a neocortical circuit model

Neocortical theta-band oscillatory activity is associated with cognitive tasks involving learning and memory. This oscillatory activity is proposed to originate from the synchronization of interconnected layer V intrinsic bursting (IB) neurons by recurrent excitation. To test this hypothesis, a sparsely connected spiking circuit model based on empirical data was simulated using Hodgkin-Huxley-type bursting neurons and use-dependent depressing synaptic connections. In response to a heterogeneous tonic current stimulus, the model generated coherent and robust oscillatory activity throughout the theta-band (4-12 Hz). These oscillations were not, however, self-sustaining without a driving current, and not dependent on N-methyl-D-aspartate receptor synaptic currents. At realistic connection strengths, synaptic depression was necessary to avoid instability and expanded the basin of attraction for theta oscillations by controlling the gain of recurrent excitation. These results support the hypothesis that IB neuron networks can generate robust and coherent theta-band oscillations in neocortex.     

Neuromodulation to the Rescue: Compensation of Temperature-Induced Breakdown of Rhythmic Motor Patterns via Extrinsic Neuromodulatory Input

Stable rhythmic neural activity depends on the well-coordinated interplay of synaptic and cell-intrinsic conductances. Since all biophysical processes are temperature dependent, this interplay is challenged during temperature fluctuations. How the nervous system remains functional during temperature perturbations remains mostly unknown. We present a hitherto unknown mechanism of how temperature-induced changes in neural networks are compensated by changing their neuromodulatory state: activation of neuromodulatory pathways establishes a dynamic coregulation of synaptic and intrinsic conductances with opposing effects on neuronal activity when temperature changes, hence rescuing neuronal activity. Using the well-studied gastric mill pattern generator of the crab, we show that modest temperature increase can abolish rhythmic activity in isolated neural circuits due to increased leak currents in rhythm-generating neurons. Dynamic clamp-mediated addition of leak currents was sufficient to stop neuronal oscillations at low temperatures, and subtraction of additional leak currents at elevated temperatures was sufficient to rescue the rhythm. Despite the apparent sensitivity of the isolated nervous system to temperature fluctuations, the rhythm could be stabilized by activating extrinsic neuromodulatory inputs from descending projection neurons, a strategy that we indeed found to be implemented in intact animals. In the isolated nervous system, temperature compensation was achieved by stronger extrinsic neuromodulatory input from projection neurons or by augmenting projection neuron influence via bath application of the peptide cotransmitter Cancer borealis tachykinin-related peptide Ia (CabTRP Ia). CabTRP Ia activates the modulator-induced current I_MI (a nonlinear voltage-gated inward current) that effectively acted as a negative leak current and counterbalanced the temperature-induced leak to rescue neuronal oscillations. Computational modelling revealed the ability of I_MI to reduce detrimental leak-current influences on neuronal networks over a broad conductance range and indicated that leak and I_MI are closely coregulated in the biological system to enable stable motor patterns. In conclusion, these results show that temperature compensation does not need to be implemented within the network itself but can be conditionally provided by extrinsic neuromodulatory input that counterbalances temperature-induced modifications of circuit-intrinsic properties.     

Influence of noise on the function of a “physiological” neural network

A model neural network with stochastic elements in its millisecond dynamics is investigated. The network consists of neuronal units which are modelled in close analogy to physiological neurons. Dynamical variables of the network are the cellular potentials, axonic currents and synaptic efficacies. The dynamics of the synapses obeys a modified Hebbian rule and, as proposed by v. d. Malsburg (1981, 1985), develop on a time scale of a tenth of a second. In a previous publication (Buhmann and Schulten 1986) we have confirmed that the resulting noiseless autoassociative network is capable of the well-known computational tasks of formal associative networks (Cooper 1973; Kohonen et al. 1984, 1981; Hopfield 1982). In the present paper we demonstrate that random fluctuations of the membrane potential improve the performance of the network. In comparison to a deterministic network a noisy neural network can learn at lower input frequencies and with lower average neural firing rates. The electrical activity of a noisy network is very reminiscent of that observed by physiological recordings. We demonstrate furthermore that associative storage reduces the effective dimension of the phase space in which the electrical activity of the network develops.     

Bidirectional regulation of hippocampal mossy fiber filopodial motility by kainate receptors: a two-step model of synaptogenesis

The rapid motility of axonal filopodia and dendritic spines is prevalent throughout the developing CNS, although the function of this motility remains controversial. Using two-photon microscopy, we imaged hippocampal mossy fiber axons in slice cultures and discovered that filopodial extensions are highly motile. Axonal filopodial motility is actin based and is downregulated with development, although it remains in mature cultures. This motility is correlated with free extracellular space yet is inversely correlated with contact with postsynaptic targets, indicating a potential role in synaptogenesis. Filopodial motility is differentially regulated by kainate receptors: synaptic stimulation of kainate receptors enhances motility in younger slices, but it inhibits it in mature slices. We propose that neuronal activity controls filopodial motility in a developmentally regulated manner, in order to establish synaptic contacts in a two-step process. A two-step model of synaptogenesis can also explain the opposite effects of neuronal activity on the motility of dendritic protrusions.     

Inhibitory transmission, activity-dependent ionic changes and neuronal network oscillations

Oscillatory network activity arises from interactions between synaptic and intrinsic membrane properties of neurons. In this review, we summarize general mechanisms of synchronous neuronal oscillations. In addition, we focus on recent experimental and computational studies which suggest that activity-dependent changes of ionic environment can affect both the synaptic and intrinsic neuronal properties and influence the network behavior. GABA(A) receptor (GABA(A)R)-mediated signaling, that is based on Cl(-) and HCO(3)(-) permeability, is thought to be important for the oscillogenesis and synchronization in cortical networks. A remarkable feature of GABAergic synapses is that prolonged GABA(A)R activation may lead to switching from a hyperpolarizing to a depolarizing response. This is partly due to a positive shift of the GABA(A) R reversal potential (E(GABA)) that is generated by GABA-induced Cl(-) accumulation in neurons. Recent studies suggest that activity-dependent E(GABA) changes may have important implications for the mechanisms of gamma oscillations and seizure-like discharges. Thus, a better understanding of the impact of intracellular Cl(-) dynamics on network behavior may provide insights into the mechanisms of physiological and pathological brain rhythms. Combination of experiments and simulations is a promising approach for elucidating which properties of the time-varying ionic environment can shape the dynamics of a given circuit.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.