Pre- and postsynaptically expressed spike-timing-dependent plasticity contribute differentially to neuronal learning

A plethora of experimental studies have shown that long-term synaptic plasticity can be expressed pre- or postsynaptically depending on a range of factors such as developmental stage, synapse type, and activity patterns. The functional consequences of this diversity are not clear, although it is understood that whereas postsynaptic expression of plasticity predominantly affects synaptic response amplitude, presynaptic expression alters both synaptic response amplitude and short-term dynamics. In most models of neuronal learning, long-term synaptic plasticity is implemented as changes in connective weights. The consideration of long-term plasticity as a fixed change in amplitude corresponds more closely to post- than to presynaptic expression, which means theoretical outcomes based on this choice of implementation may have a postsynaptic bias. To explore the functional implications of the diversity of expression of long-term synaptic plasticity, we adapted a model of long-term plasticity, more specifically spike-timing-dependent plasticity (STDP), such that it was expressed either independently pre- or postsynaptically, or in a mixture of both ways. We compared pair-based standard STDP models and a biologically tuned triplet STDP model, and investigated the outcomes in a minimal setting, using two different learning schemes: in the first, inputs were triggered at different latencies, and in the second a subset of inputs were temporally correlated. We found that presynaptic changes adjusted the speed of learning, while postsynaptic expression was more efficient at regulating spike timing and frequency. When combining both expression loci, postsynaptic changes amplified the response range, while presynaptic plasticity allowed control over postsynaptic firing rates, potentially providing a form of activity homeostasis. Our findings highlight how the seemingly innocuous choice of implementing synaptic plasticity by single weight modification may unwittingly introduce a postsynaptic bias in modelling outcomes. We conclude that pre- and postsynaptically expressed plasticity are not interchangeable, but enable complimentary functions.     

Intrinsic stability of temporally shifted spike-timing dependent plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent "triplet" model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study.     

Maturation of GABAergic Inhibition Promotes Strengthening of Temporally Coherent Inputs among Convergent Pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.     

Spike-timing-dependent plasticity: common themes and divergent vistas

Recent experimental observations of spike-timing-dependent synaptic plasticity (STDP) have revitalized the study of synaptic learning rules. The most surprising aspect of these experiments lies in the observation that synapses activated shortly after the occurrence of a postsynaptic spike are weakened. Thus, synaptic plasticity is sensitive to the temporal ordering of pre- and postsynaptic activation. This temporal asymmetry has been suggested to underlie a range of learning tasks. In the first part of this review we highlight some of the common themes from a range of findings in the framework of predictive coding. As an example of how this principle can be used in a learning task, we discuss a recent model of cortical map formation. In the second part of the review, we point out some of the differences in STDP models and their functional consequences. We discuss how differences in the weight-dependence, the time-constants and the non-linear properties of learning rules give rise to distinct computational functions. In light of these computational issues raised, we review current experimental findings and suggest further experiments to resolve some controversies.     

Cortical development and remapping through spike timing-dependent plasticity.

Long-term modification of synaptic efficacy can depend on the timing of pre- and postsynaptic action potentials. In model studies, such spike timing-dependent plasticity (STDP) introduces the desirable features of competition among synapses and regulation of postsynaptic firing characteristics. STDP strengthens synapses that receive correlated input, which can lead to the formation of stimulus-selective columns and the development, refinement, and maintenance of selectivity maps in network models. The temporal asymmetry of STDP suppresses strong destabilizing self-excitatory loops and allows a group of neurons that become selective early in development to direct other neurons to become similarly selective. STDP, acting alone without further hypothetical global constraints or additional forms of plasticity, can also reproduce the remapping seen in adult cortex following afferent lesions.     

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)     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

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.     

Unsupervised learning of visual features through spike timing dependent plasticity

Spike timing dependent plasticity (STDP) is a learning rule that modifies synaptic strength as a function of the relative timing of pre- and postsynaptic spikes. When a neuron is repeatedly presented with similar inputs, STDP is known to have the effect of concentrating high synaptic weights on afferents that systematically fire early, while postsynaptic spike latencies decrease. Here we use this learning rule in an asynchronous feedforward spiking neural network that mimics the ventral visual pathway and shows that when the network is presented with natural images, selectivity to intermediate-complexity visual features emerges. Those features, which correspond to prototypical patterns that are both salient and consistently present in the images, are highly informative and enable robust object recognition, as demonstrated on various classification tasks. Taken together, these results show that temporal codes may be a key to understanding the phenomenal processing speed achieved by the visual system and that STDP can lead to fast and selective responses.     

Local learning rules: predicted influence of dendritic location on synaptic modification in spike-timing-dependent plasticity

Recent indirect experimental evidence suggests that synaptic plasticity changes along the dendrites of a neuron. Here we present a synaptic plasticity rule which is controlled by the properties of the pre- and postsynaptic signals. Using recorded membrane traces of back-propagating and dendritic spikes we demonstrate that LTP and LTD will depend specifically on the shape of the postsynaptic depolarization at a given dendritic site. We find that asymmetrical spike-timing-dependent plasticity (STDP) can be replaced by temporally symmetrical plasticity within physiologically relevant time windows if the postsynaptic depolarization rises shallow. Presynaptically the rule depends on the NMDA channel characteristic, and the model predicts that an increase in Mg²⁺ will attenuate the STDP curve without changing its shape. Furthermore, the model suggests that the profile of LTD should be governed by the postsynaptic signal while that of LTP mainly depends on the presynaptic signal shape.     

Spectral analysis of input spike trains by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron "sees" the input correlations. We thus denote this unsupervised learning scheme as 'kernel spectral component analysis' (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a "linear" response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.     

Bursts shape the NMDA-R mediated spike timing dependent plasticity curve: role of burst interspike interval and GABAergic inhibition

Spike timing dependent plasticity (STDP) is a synaptic learning rule where the relative timing between the presynaptic and postsynaptic action potentials determines the sign and strength of synaptic plasticity. In its basic form STDP has an asymmetric form which incorporates both persistent increases and persistent decreases in synaptic strength. The basic form of STDP, however, is not a fixed property and depends on the dendritic location. An asymmetric curve is observed in the distal dendrites, whereas a symmetrical one is observed in the proximal ones. A recent computational study has shown that the transition from the asymmetry to symmetry is due to inhibition under certain conditions. Synapses have also been observed to be unreliable at generating plasticity when excitatory postsynaptic potentials and single spikes are paired at low frequencies. Bursts of spikes, however, are reliably signaled because transmitter release is facilitated. This article presents a two-compartment model of the CA1 pyramidal cell. The model is neurophysiologically plausible with its dynamics resulting from the interplay of many ionic and synaptic currents. Plasticity is measured by a deterministic Ca²⁺ dynamics model which measures the instantaneous calcium level and its time course in the dendrite and change the strength of the synapse accordingly. The model is validated to match the asymmetrical form of STDP from the pairing of a presynaptic (dendritic) and postsynaptic (somatic) spikes as observed experimentally. With the parameter set unchanged the model investigates how pairing of bursts with single spikes and bursts in the presence or absence of inhibition shapes the STDP curve. The model predicts that inhibition strength and frequency are not the only factors of the asymmetry-to-symmetry switch of the STDP curve. Burst interspike interval is another factor. This study is an important first step towards understanding how STDP is affected under natural firing patterns in vivo.     

The spike-timing dependence of plasticity

In spike-timing-dependent plasticity (STDP), the order and precise temporal interval between presynaptic and postsynaptic spikes determine the sign and magnitude of long-term potentiation (LTP) or depression (LTD). STDP is widely utilized in models of circuit-level plasticity, development, and learning. However, spike timing is just one of several factors (including firing rate, synaptic cooperativity, and depolarization) that govern plasticity induction, and its relative importance varies across synapses and activity regimes. This review summarizes this broader view of plasticity, including the forms and cellular mechanisms for the spike-timing dependence of plasticity, and, the evidence that spike timing is an important determinant of plasticity in?vivo.     

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.     

A Nonlinear Cable Framework for Bidirectional Synaptic Plasticity

Finding the rules underlying how axons of cortical neurons form neural circuits and modify their corresponding synaptic strength is the still subject of intense research. Experiments have shown that internal calcium concentration, and both the precise timing and temporal order of pre and postsynaptic action potentials, are important constituents governing whether the strength of a synapse located on the dendrite is increased or decreased. In particular, previous investigations focusing on spike timing-dependent plasticity (STDP) have typically observed an asymmetric temporal window governing changes in synaptic efficacy. Such a temporal window emphasizes that if a presynaptic spike, arriving at the synaptic terminal, precedes the generation of a postsynaptic action potential, then the synapse is potentiated; however if the temporal order is reversed, then depression occurs. Furthermore, recent experimental studies have now demonstrated that the temporal window also depends on the dendritic location of the synapse. Specifically, it was shown that in distal regions of the apical dendrite, the magnitude of potentiation was smaller and the window for depression was broader, when compared to observations from the proximal region of the dendrite. To date, the underlying mechanism(s) for such a distance-dependent effect is (are) currently unknown. Here, using the ionic cable theory framework in conjunction with the standard calcium based plasticity model, we show for the first time that such distance-dependent inhomogeneities in the temporal learning window for STDP can be largely explained by both the spatial and active properties of the dendrite.     

Network Evolution Induced by Asynchronous Stimuli through Spike-Timing-Dependent Plasticity

In sensory neural system, external asynchronous stimuli play an important role in perceptual learning, associative memory and map development. However, the organization of structure and dynamics of neural networks induced by external asynchronous stimuli are not well understood. Spike-timing-dependent plasticity (STDP) is a typical synaptic plasticity that has been extensively found in the sensory systems and that has received much theoretical attention. This synaptic plasticity is highly sensitive to correlations between pre- and postsynaptic firings. Thus, STDP is expected to play an important role in response to external asynchronous stimuli, which can induce segregative pre- and postsynaptic firings. In this paper, we study the impact of external asynchronous stimuli on the organization of structure and dynamics of neural networks through STDP. We construct a two-dimensional spatial neural network model with local connectivity and sparseness, and use external currents to stimulate alternately on different spatial layers. The adopted external currents imposed alternately on spatial layers can be here regarded as external asynchronous stimuli. Through extensive numerical simulations, we focus on the effects of stimulus number and inter-stimulus timing on synaptic connecting weights and the property of propagation dynamics in the resulting network structure. Interestingly, the resulting feedforward structure induced by stimulus-dependent asynchronous firings and its propagation dynamics reflect both the underlying property of STDP. The results imply a possible important role of STDP in generating feedforward structure and collective propagation activity required for experience-dependent map plasticity in developing in vivo sensory pathways and cortices. The relevance of the results to cue-triggered recall of learned temporal sequences, an important cognitive function, is briefly discussed as well. Furthermore, this finding suggests a potential application for examining STDP by measuring neural population activity in a cultured neural network.     

Neuromodulation of STDP through short-term changes in firing causality

Spike timing dependent plasticity (STDP) likely plays an important role in forming and changing connectivity patterns between neurons in our brain. In a unidirectional synaptic connection between two neurons, it uses the causal relation between spiking activity of a presynaptic input neuron and a postsynaptic output neuron to change the strength of this connection. While the nature of STDP benefits unsupervised learning of correlated inputs, any incorporation of value into the learning process needs some form of reinforcement. Chemical neuromodulators such as Dopamine or Acetylcholine are thought to signal changes between external reward and internal expectation to many brain regions, including the basal ganglia. This effect is often modelled through a direct inclusion of the level of Dopamine as a third factor into the STDP rule. While this gives the benefit of direct control over synaptic modification, it does not account for observed instantaneous effects in neuronal activity on application of Dopamine agonists. Specifically, an instant facilitation of neuronal excitability in the striatum can not be explained by the only indirect effect that dopamine-modulated STDP has on a neuron’s firing pattern. We therefore propose a model for synaptic transmission where the level of neuromodulator does not directly influence synaptic plasticity, but instead alters the relative firing causality between pre- and postsynaptic neurons. Through the direct effect on postsynaptic activity, our rule allows indirect modulation of the learning outcome even with unmodulated, two-factor STDP. However, it also does not prohibit joint operation together with three-factor STDP rules.     

Coactivation of pre- and postsynaptic signaling mechanisms determines cell-specific spike-timing-dependent plasticity

Synapses may undergo long-term increases or decreases in synaptic strength dependent on critical differences in the timing between pre-and postsynaptic activity. Such spike-timing-dependent plasticity (STDP) follows rules that govern how patterns of neural activity induce changes in synaptic strength. Synaptic plasticity in the dorsal cochlear nucleus (DCN) follows Hebbian and anti-Hebbian patterns in a cell-specific manner. Here we show that these opposing responses to synaptic activity result from differential expression of two signaling pathways. Ca2+/calmodulin-dependent protein kinase II (CaMKII) signaling underlies Hebbian postsynaptic LTP in principal cells. By contrast, in interneurons, a temporally precise anti-Hebbian synaptic spike-timing rule results from the combined effects of postsynaptic CaMKII-dependent LTP and endocannabinoid-dependent presynaptic LTD. Cell specificity in the circuit arises from selective targeting of presynaptic CB1 receptors in different axonal terminals. Hence, pre- and postsynaptic sites of expression determine both the sign and timing requirements of long-term plasticity in interneurons.     

Interplay of the magnitude and time-course of postsynaptic Ca<Superscript>2 + </Superscript> concentration in producing spike timing-dependent plasticity

Synaptic strength can be modified by the relative timing of pre- and postsynaptic activity, a phenomenon termed spike timing-dependent plasticity (STDP). Studies of neurons in the hippocampus and in other regions have found that when presynaptic activity occurs within a narrow time window, typically 10 or 20 ms, before postsynaptic activity, long-term potentiation (LTP) is induced, while if presynaptic activity occurs within a similar time window after postsynaptic activity, long-term depression (LTD) results. The mechanisms underlying these modifications are not completely understood, although there is strong evidence that the postsynaptic Ca ^2 + concentration plays a central role. Some previous modeling of STDP has focused on the dynamics of the postsynaptic Ca ^2 + concentration, while other work has studied biophysical mechanisms of how a synapse can exist in, and switch between, different states corresponding to LTP and LTD. Building on previous work in these two areas we have developed the first low level STDP model of a tristable biochemical system that incorporates induction and maintenance of both LTP and LTD. Our model is able to explain the STDP observed in hippocampal neurons in response to pre- and postsynaptic pulse pairs, using only parameters derived from previous work and without the need for parameter fine-tuning. Our results also give insight into how and why the time course of the postsynaptic Ca ^2 + concentration can lead to either LTP or LTD, and suggest that voltage dependent calcium channels play a key role.     

Mechanisms and significance of spike-timing dependent plasticity

Hebb's original postulate left two important issues unaddressed: (i) what is the effective time window between pre- and postsynaptic activity that will result in potentiation? and (ii) what is the learning rule that underlies decreases in synaptic strength? While research over the past 2 decades has addressed these questions, several studies within the past 5 years have shown that synapses undergo long-term depression (LTD) or long-term potentiation (LTP) depending on the order of activity in the pre- and postsynaptic cells. This process has been referred to as spike-timing dependent plasticity (STDP). Here we discuss the experimental data on STDP, and develop models of the mechanisms that may underlie it. Specifically, we examine whether the standard model of LTP and LTD in which high and low levels of Ca(2+) produce LTP and LTD, respectively, can also account for STDP. We conclude that the standard model can account for a type of STDP in which, counterintuitively, LTD will be observed at some intervals in which the presynaptic cell fires before the postsynaptic cell. This form of STDP will also be sensitive to parameters such as the presence of an after depolarization following an action potential. Indeed, the sensitivity of this type of STDP to experimental parameters suggests that it may not play an important physiological role in vivo. We suggest that more robust forms of STDP, which do not exhibit LTD at pre-before-post intervals, are not accounted for by the standard model, and are likely to rely on a second coincidence detector in addition to the NMDA receptor.