Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity

Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Here we present an adaptive model of a balanced neuronal network that combines two different types of plasticity, STDP and synaptic scaling. The plasticity rules yield both long-tailed distributions of synaptic weights and firing rates. Simultaneously, a highly connected subnetwork of driver neurons with strong synapses emerges. Coincident spiking activity of several driver cells can evoke population bursts and driver cells have similar dynamical properties as leader neurons found experimentally. Our model allows us to observe the delicate interplay between structural and dynamical properties of the emergent inhomogeneities. It is simple, robust to parameter changes and able to explain a multitude of different experimental findings in one basic network.     

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.     

Spike timing-dependent plasticity and memory

Spike timing-dependent plasticity (STDP) is a bidirectional form of synaptic plasticity discovered about 30 years ago and based on the relative timing of pre- and post-synaptic spiking activity with a millisecond precision. STDP is thought to be involved in the formation of memory but the millisecond-precision spike-timing required for STDP is difficult to reconcile with the much slower timescales of behavioral learning. This review therefore aims to expose and discuss recent findings about i) the multiple STDP learning rules at both excitatory and inhibitory synapses in vitro, ii) the contribution of STDP-like synaptic plasticity in the formation of memory in vivo and iii) the implementation of STDP rules in artificial neural networks and memristive devices.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Brain plasticity and ion channels

It is generally believed that spatio-temporal configurations of distributed activity in the brain contribute to the coding of neuronal information and that synaptic contacts between nerve cells could play a central role in the formation of privileged pathways of activity. Synaptic plasticity is not the only mode of regulation of information processing in the brain and persistent regulations of ionic conductances in some specialized neuronal areas such as the dendrites, the cell body and the axon could also modulate, in the short- and the long-term, the propagation of information in the brain. Persistent changes in intrinsic excitability have been reported in several brain areas in which activity is modified during a classical conditioning. The role of synaptic activity seems to be determinant in the induction but the learning rules and the underlying mechanisms remain to be defined. This review discusses the role of neuronal activity in the induction of intrinsic plasticity in cortical, hippocampal and cerebellar neurons. Activation and inactivation properties of ionic channels in the axon determine the short-term dynamics of axonal propagation and synaptic transmission. Activation of glutamate receptors initiates a long-term modification in neuronal excitability that may represent the substrate for the mnesic engram and for the stabilization of the epileptic state. Similarly to synaptic plasticity, long-lasting intrinsic plasticity appears to be reversible and to express a certain level of input or cellular specificity. These non-synaptic forms of plasticity affect the signal propagation in the axon, the dendrites and the soma. They not only share common learning rules and induction pathways with the better known synaptic plasticity such as NMDA receptor-dependent LTP and LTD but also contribute in synergy with these synaptic changes to the formation of a coherent mnesic engram.     

Homeostatic control of synaptic rewiring in recurrent networks induces the formation of stable memory engrams

Brain networks store new memories using functional and structural synaptic plasticity. Memory formation is generally attributed to Hebbian plasticity, while homeostatic plasticity is thought to have an ancillary role in stabilizing network dynamics. Here we report that homeostatic plasticity alone can also lead to the formation of stable memories. We analyze this phenomenon using a new theory of network remodeling, combined with numerical simulations of recurrent spiking neural networks that exhibit structural plasticity based on firing rate homeostasis. These networks are able to store repeatedly presented patterns and recall them upon the presentation of incomplete cues. Storage is fast, governed by the homeostatic drift. In contrast, forgetting is slow, driven by a diffusion process. Joint stimulation of neurons induces the growth of associative connections between them, leading to the formation of memory engrams. These memories are stored in a distributed fashion throughout connectivity matrix, and individual synaptic connections have only a small influence. Although memory-specific connections are increased in number, the total number of inputs and outputs of neurons undergo only small changes during stimulation. We find that homeostatic structural plasticity induces a specific type of “silent memories”, different from conventional attractor states.     

Stability of complex spike timing-dependent plasticity in cerebellar learning

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.     

Cellular and molecular mechanisms of memory

There has been nearly a century of interest in the idea that information is encoded in the brain as specific spatio-temporal patterns of activity in distributed networks and stored as changes in the efficacy of synaptic connections on neurons that are activated during learning. The discovery and detailed report of the phenomenon generally known as long-term potentiation opened a new chapter in the study of synaptic plasticity in the vertebrate brain, and this form of synaptic plasticity has now become the dominant model in the search for the cellular bases of learning and memory. To date, the key events in the cellular and molecular mechanisms underlying synaptic plasticity are starting to be identified. They require the activation of specific receptors and of several molecular cascades to convert extracellular signals into persistent functional changes in neuronal connectivity. Accumulating evidence suggests that the rapid activation of the genetic machinery is a key mechanism underlying the enduring modification of neural networks required for the laying down of memory. The recent developments in the search for the cellular and molecular mechanisms of memory storage are reviewed.     

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.     

Myosin IIb-dependent Regulation of Actin Dynamics Is Required for N-Methyl-d-aspartate Receptor Trafficking during Synaptic Plasticity

N-Methyl-d-aspartate receptor (NMDAR) synaptic incorporation changes the number of NMDARs at synapses and is thus critical to various NMDAR-dependent brain functions. To date, the molecules involved in NMDAR trafficking and the underlying mechanisms are poorly understood. Here, we report that myosin IIb is an essential molecule in NMDAR synaptic incorporation during PKC- or θ burst stimulation-induced synaptic plasticity. Moreover, we demonstrate that myosin light chain kinase (MLCK)-dependent actin reorganization contributes to NMDAR trafficking. The findings from additional mutual occlusion experiments demonstrate that PKC and MLCK share a common signaling pathway in NMDAR-mediated synaptic regulation. Because myosin IIb is the primary substrate of MLCK and can regulate actin dynamics during synaptic plasticity, we propose that the MLCK- and myosin IIb-dependent regulation of actin dynamics is required for NMDAR trafficking during synaptic plasticity. This study provides important insights into a mechanical framework for understanding NMDAR trafficking associated with synaptic plasticity.     

Shaping embodied neural networks for adaptive goal-directed behavior

The acts of learning and memory are thought to emerge from the modifications of synaptic connections between neurons, as guided by sensory feedback during behavior. However, much is unknown about how such synaptic processes can sculpt and are sculpted by neuronal population dynamics and an interaction with the environment. Here, we embodied a simulated network, inspired by dissociated cortical neuronal cultures, with an artificial animal (an animat) through a sensory-motor loop consisting of structured stimuli, detailed activity metrics incorporating spatial information, and an adaptive training algorithm that takes advantage of spike timing dependent plasticity. By using our design, we demonstrated that the network was capable of learning associations between multiple sensory inputs and motor outputs, and the animat was able to adapt to a new sensory mapping to restore its goal behavior: move toward and stay within a user-defined area. We further showed that successful learning required proper selections of stimuli to encode sensory inputs and a variety of training stimuli with adaptive selection contingent on the animat's behavior. We also found that an individual network had the flexibility to achieve different multi-task goals, and the same goal behavior could be exhibited with different sets of network synaptic strengths. While lacking the characteristic layered structure of in vivo cortical tissue, the biologically inspired simulated networks could tune their activity in behaviorally relevant manners, demonstrating that leaky integrate-and-fire neural networks have an innate ability to process information. This closed-loop hybrid system is a useful tool to study the network properties intermediating synaptic plasticity and behavioral adaptation. The training algorithm provides a stepping stone towards designing future control systems, whether with artificial neural networks or biological animats themselves.     

Efficient Partitioning of Memory Systems and Its Importance for Memory Consolidation

Long-term memories are likely stored in the synaptic weights of neuronal networks in the brain. The storage capacity of such networks depends on the degree of plasticity of their synapses. Highly plastic synapses allow for strong memories, but these are quickly overwritten. On the other hand, less labile synapses result in long-lasting but weak memories. Here we show that the trade-off between memory strength and memory lifetime can be overcome by partitioning the memory system into multiple regions characterized by different levels of synaptic plasticity and transferring memory information from the more to less plastic region. The improvement in memory lifetime is proportional to the number of memory regions, and the initial memory strength can be orders of magnitude larger than in a non-partitioned memory system. This model provides a fundamental computational reason for memory consolidation processes at the systems level.     

Dynamics of functional connectivity in visual cortical networks: An overview

The aim of the Royaumont Symposium was to review various dynamic aspects of adaptive changes in functional connectivity, expressed in cortical networks during development, learning, and possibly during recognition and cognitive processing. The link between the various experimental and theoretical models was the comparison of cellular and molecular mechanisms that could be involved in the up- and down-regulation of functional connectivity, over different time scales. These processes have been investigated using several approaches in parallel: 1) at the molecular/subcellular level, to identify postsynaptic receptors (NMDA, mGluR) and second messengers (calcium, protein kinases and phosphatases) involved in the induction of synaptic potentiation and depression, and to characterize diffusible factors (NO), released pre- or postsynaptically, involved in the spatial generalization of local changes to neighboring synapses; 2) at the level of integrating networks, to develop electrophysiological (single and multiple recording), pharmacological and optical imaging techniques in order to compare the dynamics of adaptive processes put into play during the natural development of cortical specificity and connectivity, versus those triggered during forced regimes of temporal correlations between pre- and post synaptic activities. Both in vitro and in vivo approaches have been combined in the primary visual cortex of the developing and adult vertebrate (rat, guinea-pig, ferret, cat and monkey). The various forms of ‘slow’ synaptic plasticity, demonstrated during epigenesis and selective phases of learning in the adult, can be compared with ‘fast’ forms of functional coupling (or synchronous firing) shown to develop during the time span required for perception and cognitive processing. Phenomenology of the dynamics in functional connectivity and their relative dependence on temporal correlation in neuronal activity have been analyzed in each of these situations. Experimental results have been compared at different levels of neuronal integration (synapse, column, map and cell assembly) in order to gain a better understanding of functional grouping within cortical networks.     

Nonlinear Dynamics Analysis of a Self-Organizing Recurrent Neural Network: Chaos Waning

Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs) have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks'' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-)continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.     

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.     

Pentylenetetrazol-Induced Epileptiform Activity Affects Basal Synaptic Transmission and Short-Term Plasticity in Monosynaptic Connections

Epileptic activity is generally induced in experimental models by local application of epileptogenic drugs, including pentylenetetrazol (PTZ), widely used on both vertebrate and invertebrate neurons. Despite the high prevalence of this neurological disorder and the extensive research on it, the cellular and molecular mechanisms underlying epileptogenesis still remain unclear. In this work, we examined PTZ-induced neuronal changes in Helix monosynaptic circuits formed in vitro, as a simpler experimental model to investigate the effects of epileptiform activity on both basal release and post-tetanic potentiation (PTP), a form of short-term plasticity. We observed a significant enhancement of basal synaptic strength, with kinetics resembling those of previously described use-dependent forms of plasticity, determined by changes in estimated quantal parameters, such as the readily releasable pool and the release probability. Moreover, these neurons exhibited a strong reduction in PTP expression and in its decay time constant, suggesting an impairment in the dynamic reorganization of synaptic vesicle pools following prolonged stimulation of synaptic transmission. In order to explain this imbalance, we determined whether epileptic activity is related to the phosphorylation level of synapsin, which is known to modulate synaptic plasticity. Using western blot and immunocytochemical staining we found a PTZ-dependent increase in synapsin phosphorylation at both PKA/CaMKI/IV and MAPK/Erk sites, both of which are important for modulating synaptic plasticity. Taken together, our findings suggest that prolonged epileptiform activity leads to an increase in the synapsin phosphorylation status, thereby contributing to an alteration of synaptic strength in both basal condition and tetanus-induced potentiation.     

The Formation of Multi-synaptic Connections by the Interaction of Synaptic and Structural Plasticity and Their Functional Consequences

Cortical connectivity emerges from the permanent interaction between neuronal activity and synaptic as well as structural plasticity. An important experimentally observed feature of this connectivity is the distribution of the number of synapses from one neuron to another, which has been measured in several cortical layers. All of these distributions are bimodal with one peak at zero and a second one at a small number (3–8) of synapses.In this study, using a probabilistic model of structural plasticity, which depends on the synaptic weights, we explore how these distributions can emerge and which functional consequences they have.We find that bimodal distributions arise generically from the interaction of structural plasticity with synaptic plasticity rules that fulfill the following biological realistic constraints: First, the synaptic weights have to grow with the postsynaptic activity. Second, this growth curve and/or the input-output relation of the postsynaptic neuron have to change sub-linearly (negative curvature). As most neurons show such input-output-relations, these constraints can be fulfilled by many biological reasonable systems.Given such a system, we show that the different activities, which can explain the layer-specific distributions, correspond to experimentally observed activities.Considering these activities as working point of the system and varying the pre- or postsynaptic stimulation reveals a hysteresis in the number of synapses. As a consequence of this, the connectivity between two neurons can be controlled by activity but is also safeguarded against overly fast changes.These results indicate that the complex dynamics between activity and plasticity will, already between a pair of neurons, induce a variety of possible stable synaptic distributions, which could support memory mechanisms.     

Efficacité de la mémoire associative inhérente à la potentiation post-tétanique

An associative memory is modeled in networks of cells that are assumed to have the short-term plasticity of the neuromuscular junction of the frog. The data relating synaptic transmission efficiency and stimulation frequency for post-tetanic potentiation of the neuromuscular junction are represented by polynomial expansions. Simulation of storage and retrieval demonstrates that functional associative memory is feasible based on this particular synaptic plasticity. Retrieval reaches a maximum efficiency at a delay of three minutes after storage and is lost after about 9 min. The signal to noise ratio of the retrieved pattern drops steadily as additional associations are stored in memory but retrieval appears to be possible with up to four stored associations. Although the data are derived from synapses not normally proposed as a basis for memory functions, the results here will generalize to other synaptic junctions located more centrally that have similar characteristics. This simulation technique allows the efficiency of associative memory based on various types of synaptic plasticity to be evaluated.     

Spike-timing dependent synaptic plasticity: a phenomenological framework

 In this paper a phenomenological model of spike-timing dependent synaptic plasticity (STDP) is developed that is based on a Volterra series-like expansion. Synaptic weight changes as a function of the relative timing of pre- and postsynaptic spikes are described by integral kernels that can easily be inferred from experimental data. The resulting weight dynamics can be stated in terms of statistical properties of pre- and postsynaptic spike trains. Generalizations to neurons that fire two different types of action potentials, such as cerebellar Purkinje cells where synaptic plasticity depends on correlations in two distinct presynaptic fibers, are discussed. We show that synaptic plasticity, together with strictly local bounds for the weights, can result in synaptic competition that is required for any form of pattern formation. This is illustrated by a concrete example where a single neuron equipped with STDP can selectively strengthen those synapses with presynaptic neurons that reliably deliver precisely timed spikes at the expense of other synapses which transmit spikes with a broad temporal distribution. Such a mechanism may be of vital importance for any neuronal system where information is coded in the timing of individual action potentials. Received: 23 January 2002 / Accepted: 28 March 2002 Correspondence to: W.M. Kistler (e-mail: kistler@anat.fgg.eur.nl Fax: +31 10 408 5459)     

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.