Synaptic modifications depend on synapse location and activity: a biophysical model of STDP

In spike-timing-dependent plasticity (STDP) the synapses are potentiated or depressed depending on the temporal order and temporal difference of the pre- and post-synaptic signals. We present a biophysical model of STDP which assumes that not only the timing, but also the shapes of these signals influence the synaptic modifications. The model is based on a Hebbian learning rule which correlates the NMDA synaptic conductance with the post-synaptic signal at synaptic location as the pre- and post-synaptic quantities. As compared to a previous paper [Saudargiene, A., Porr, B., Worgotter, F., 2004. How the shape of pre- and post-synaptic signals can influence stdp: a biophysical model. Neural Comp.], here we show that this rule reproduces the generic STDP weight change curve by using real neuronal input signals and combinations of more than two (pre- and post-synaptic) spikes. We demonstrate that the shape of the STDP curve strongly depends on the shape of the depolarising membrane potentials, which induces learning. As these potentials vary at different locations of the dendritic tree, model predicts that synaptic changes are location dependent. The model is extended to account for the patterns of more than two spikes of the pre- and post-synaptic cells. The results show that STDP weight change curve is also activity dependent.     

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.     

Computational consequences of experimentally derived spike-time and weight dependent plasticity rules

We present two weight- and spike-time dependent synaptic plasticity rules consistent with the physiological data of Bi and Poo (J Neurosci 18:10464–10472, 1998). One rule assumes synaptic saturation, while the other is scale free. We extend previous analyses of the asymptotic consequences of weight-dependent STDP to the case of strongly correlated pre- and post-synaptic spiking, more closely resembling associative learning. We further provide a general formula for the contribution of any number of spikes to synaptic drift. Asymptotic weights are shown to principally depend on the correlation and rate of pre- and post-synaptic activity, decreasing with increasing rate under correlated activity, and increasing with rate under uncorrelated activity. Spike train statistics reveal a quantitative effect only in the pre-asymptotic regime, and we provide a new interpretation of the relation between BCM and STDP data.     

Calcium-Dependent Calcium Decay Explains STDP in a Dynamic Model of Hippocampal Synapses

It is widely accepted that the direction and magnitude of synaptic plasticity depends on post-synaptic calcium flux, where high levels of calcium lead to long-term potentiation and moderate levels lead to long-term depression. At synapses onto neurons in region CA1 of the hippocampus (and many other synapses), NMDA receptors provide the relevant source of calcium. In this regard, post-synaptic calcium captures the coincidence of pre- and post-synaptic activity, due to the blockage of these receptors at low voltage. Previous studies show that under spike timing dependent plasticity (STDP) protocols, potentiation at CA1 synapses requires post-synaptic bursting and an inter-pairing frequency in the range of the hippocampal theta rhythm. We hypothesize that these requirements reflect the saturation of the mechanisms of calcium extrusion from the post-synaptic spine. We test this hypothesis with a minimal model of NMDA receptor-dependent plasticity, simulating slow extrusion with a calcium-dependent calcium time constant. In simulations of STDP experiments, the model accounts for latency-dependent depression with either post-synaptic bursting or theta-frequency pairing (or neither) and accounts for latency-dependent potentiation when both of these requirements are met. The model makes testable predictions for STDP experiments and our simple implementation is tractable at the network level, demonstrating associative learning in a biophysical network model with realistic synaptic dynamics.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity.     

Stability versus neuronal specialization for STDP: long-tail weight distributions solve the dilemma

Spike-timing-dependent plasticity (STDP) modifies the weight (or strength) of synaptic connections between neurons and is considered to be crucial for generating network structure. It has been observed in physiology that, in addition to spike timing, the weight update also depends on the current value of the weight. The functional implications of this feature are still largely unclear. Additive STDP gives rise to strong competition among synapses, but due to the absence of weight dependence, it requires hard boundaries to secure the stability of weight dynamics. Multiplicative STDP with linear weight dependence for depression ensures stability, but it lacks sufficiently strong competition required to obtain a clear synaptic specialization. A solution to this stability-versus-function dilemma can be found with an intermediate parametrization between additive and multiplicative STDP. Here we propose a novel solution to the dilemma, named log-STDP, whose key feature is a sublinear weight dependence for depression. Due to its specific weight dependence, this new model can produce significantly broad weight distributions with no hard upper bound, similar to those recently observed in experiments. Log-STDP induces graded competition between synapses, such that synapses receiving stronger input correlations are pushed further in the tail of (very) large weights. Strong weights are functionally important to enhance the neuronal response to synchronous spike volleys. Depending on the input configuration, multiple groups of correlated synaptic inputs exhibit either winner-share-all or winner-take-all behavior. When the configuration of input correlations changes, individual synapses quickly and robustly readapt to represent the new configuration. We also demonstrate the advantages of log-STDP for generating a stable structure of strong weights in a recurrently connected network. These properties of log-STDP are compared with those of previous models. Through long-tail weight distributions, log-STDP achieves both stable dynamics for and robust competition of synapses, which are crucial for spike-based information processing.     

Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits.     

Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity

Spike-timing dependent plasticity (STDP) is a form of associative synaptic modification which depends on the respective timing of pre- and post-synaptic spikes. The biophysical mechanisms underlying this form of plasticity are currently not known. We present here a biophysical model which captures the characteristics of STDP, such as its frequency dependency, and the effects of spike pair or spike triplet interactions. We also make links with other well-known plasticity rules. A simplified phenomenological model is also derived, which should be useful for fast numerical simulation and analytical investigation of the impact of STDP at the network level.     

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

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

Short-Term Synaptic Plasticity Orchestrates the Response of Pyramidal Cells and Interneurons to Population Bursts

The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the pre-synaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cell population bursts on post-synaptic pyramidal cells receiving depressing synapses, and on a class of interneuron that receives facilitating synapses. In experiment a significant shift of the order of one hundred milliseconds is seen between the response of these two cell classes to the same population burst. It is demonstrated here that such a temporal differentiation of the response can be explained by the synaptic and membrane properties without recourse to elaborate cortical wiring schemes. Experimental data is first used to construct models of the two types of dynamic synaptic response. A population-based approach is then followed to examine analytically the temporal synaptic filtering effects of the population burst for the two post-synaptic targets. The peak-to-peak delays seen in experiment can be captured by the model for experimentally realistic parameter ranges. It is further shown that the temporal separation of the response is communicated in the outgoing action potentials of the two post-synaptic cells: pyramidal cells fire at the beginning of the burst and the class of interneuron receiving facilitating synapses fires at the end of the burst. The functional role of such delays in the temporal organisation of activity in the cortical microcircuit is discussed.     

LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.     

Gephyrin expression and clustering affects the size of glutamatergic synaptic contacts

We have recently shown that disrupting the expression and post-synaptic clustering of gephyrin in cultured hippocampal pyramidal cells, by either gephyrin RNAi (RNA interference) or over-expression of a dominant negative gephyrin-enhanced green fluorescent protein (EGFP) fusion protein, leads to decreased number of post-synaptic gephyrin and GABA_A receptor clusters and to reduced GABAergic innervation of these cells. On the other hand, increasing gephyrin expression led to a small increase in the number of gephyrin and GABA_A receptor clusters and to little or no effect on GABAergic innervation. We are now reporting that altering gephyrin expression and clustering affects the size but not the density of glutamatergic synaptic contacts. Knocking down gephyrin with gephyrin RNAi, or preventing gephyrin clustering by over-expression of the dominant negative gephyrin-enhanced green fluorescent protein fusion protein, leads to larger post-synaptic PSD-95 clusters and larger pre-synaptic glutamatergic terminals. On the other hand, over-expression of gephyrin leads to slightly smaller PSD-95 clusters and pre-synaptic glutamatergic terminals. The change in size of PSD-95 clusters were accompanied by a parallel change in the size of NR2-NMDA receptor clusters. It is concluded that the levels of expression and clustering of gephyrin, a protein that concentrates at the post-synaptic complex of the inhibitory synapses, not only has homotypic effects on GABAergic synaptic contacts, but also has heterotypic effects on glutamatergic synaptic contacts. We are proposing that gephyrin is a counterpart of the post-synaptic glutamatergic scaffold protein PSD-95 in regulating the number and/or size of the excitatory and inhibitory synaptic contacts.     

Aromatase is pre-synaptic and sexually dimorphic in the adult zebra finch brain

Oestrogens organize and activate circuits within the vertebrate central nervous system. Oestrogen synthesis occurs via the expression of aromatase, a P450 enzyme detected in microsomes and more recently in pre-synaptic boutons. Synaptic aromatase has only been described in brain regions that express aromatase in many subcellular compartments, so its function remains poorly understood. To more thoroughly study the role of oestrogen synthesis at synaptic terminals, we examined the ultrastructural compartmentalization of aromatase in the zebra finch; a species in which high aromatase activity can be measured in brain areas that do not contain somal aromatase. Here, we report the presence of aromatase in pre-synaptic boutons in the hippocampus and the high vocal centre brain areas with low and undetectable somal aromatase, respectively, in addition to areas with abundant somal aromatase such as the preoptic area and caudomedial nidopallium. At these brain areas, males had more total synapses, more aromatase pre-synaptic boutons and importantly, the proportion of total synaptic profiles that expressed aromatase was significantly higher in males relative to females. Aromatase-positive pre-synaptic boutons were always observed innervating aromatase-negative post-synaptic elements. We conclude that oestrogen may be provided to discrete oestrogen-sensitive targets by synaptic aromatization. Further, some targets may be exposed to more oestrogen in males. The expression of aromatase in individual synapses of projection neurons represents a unique mechanism of neuroendocrine action. Neurons with steroidogenic capability may modulate distant targets with the specificity of axonal innervation.     

Distinct roles for ephrinB3 in the formation and function of hippocampal synapses

The transmembrane ephrinB ligands and their Eph receptor tyrosine kinases are known to regulate excitatory synaptic functions in the hippocampus. In the CA3-CA1 synapse, ephrinB ligands are localized to the post-synaptic membrane, while their cognate Eph receptors are presumed to be pre-synaptic. Interaction of ephrinB molecules with Eph receptors leads to changes in long-term potentiation (LTP), which has been reported to be mediated by reverse signaling into the post-synaptic membrane. Here, we demonstrate that the cytoplasmic domain of ephrinB3 and hence reverse signaling is not required for ephrinB dependent learning and memory tasks or for LTP of these synapses. Consistent with previous reports, we find that ephrinB3(KO) null mutant mice exhibit a striking reduction in CA3-CA1 LTP that is associated with defective learning and memory tasks. We find the null mutants also show changes in both pre- and post-synaptic proteins including increased levels of synapsin and synaptobrevin and reduced levels of NMDA receptor subunits. These abnormalities are not observed in ephrinB3(lacZ) reverse signaling mutants that specifically delete the ephrinB3 intracellular region, supporting a cytoplasmic domain-independent forward signaling role for ephrinB3 in these processes. We also find that both ephrinB3(KO) and ephrinB3(lacZ) mice show an increased number of excitatory synapses, demonstrating a cytoplasmic-dependent reverse signaling role of ephrinB3 in regulating synapse number. Together, these data suggest that ephrinB3 may act like a receptor to transduce reverse signals to regulate the number of synapses formed in the hippocampus, and that it likely acts to stimulate forward signaling to modulate a number of other proteins involved in synaptic activity and learning/memory.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

The effects of ethanol on pre-synaptic components of synaptic transmission in a model glutamatergic synapse: the crayfish neuromuscular junction

We have elucidated some of the mechanisms by which ethanol (EtOH) reduces synaptic efficacy at model glutamatergic synapses. The crayfish phasic and tonic neuromuscular junctions are superb models for directly assessing the effects of EtOH on pre-synaptic components of synaptic transmission. The ability to perform quantal analysis of synaptic transmission has allowed us to assess pre-synaptic alterations of release. Using this system, we report that the application of EtOH, within a range observed in intoxicated humans (44 and 88 mM), resulted in a diminution of excitatory post-synaptic potentials (EPSP) amplitudes. Additionally, using focal macro-patch recordings, quantal synaptic currents were recorded to assess the pre-synaptic component as potential target sites for EtOH's action. At the tonic neuromuscular junctions, EtOH (88 mM) reduced the probability of release (p), and in some cases, reduced the number of the release sites (n), but did not alter facilitation index nor did it affect the latency of vesicular release. At the phasic neuromuscular junction, a reduction in synaptic charge occurred during the presence of EtOH. Thus, the observed decrease in synaptic strength is at least partially attributable to a pre-synaptic alteration, specifically the release of fewer vesicles.     

The Effect of STDP Temporal Kernel Structure on the Learning Dynamics of Single Excitatory and Inhibitory Synapses

Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.     

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.     

A feature-based neurocomputational model of semantic memory

According with a featural organization of semantic memory, this work is aimed at investigating, through an attractor network, the role of different kinds of features in the representation of concepts, both in normal and neurodegenerative conditions. We implemented new synaptic learning rules in order to take into account the role of partially shared features and of distinctive features with different saliency. The model includes semantic and lexical layers, coding, respectively for object features and word-forms. Connections among nodes are strongly asymmetrical. To account for the feature saliency, asymmetrical synapses were created using Hebbian rules of potentiation and depotentiation, setting different pre-synaptic and post-synaptic thresholds. A variable post-synaptic threshold, which automatically changed to reflect the feature frequency in different concepts (i.e., how many concepts share a feature), was used to account for partially shared features. The trained network solved naming tasks and word recognition tasks very well, exploiting the different role of salient versus marginal features in concept identification. In the case of damage, superordinate concepts were preserved better than the subordinate ones. Interestingly, the degradation of salient features, but not of marginal ones, prevented object identification. The model suggests that Hebbian rules, with adjustable post-synaptic thresholds, can provide a reliable semantic representation of objects exploiting the statistics of input features.