Spike-timing-dependent Plasticity Model Research Articles

Reversed timing-dependent associative plasticity in the human brain through interhemispheric interactions

Spike timing-dependent plasticity (STDP) has been proposed as one of the key mechanisms underlying learning and memory. Repetitive median nerve stimulation, followed by transcranial magnetic stimulation (TMS) of the contralateral primary motor cortex (M1), defined as paired-associative stimulation (PAS), has been used as an in vivo model of STDP in humans. PAS-induced excitability changes in M1 have been repeatedly shown to be time-dependent in a STDP-like fashion, since synchronous arrival of inputs within M1 induces long-term potentiation-like effects, whereas an asynchronous arrival induces long-term depression (LTD)-like effects. Here, we show that interhemispheric inhibition of the sensorimotor network during PAS, with the peripheral stimulation over the hand ipsilateral to the motor cortex receiving TMS, results in a LTD-like effect, as opposed to the standard STDP-like effect seen for contralateral PAS. Furthermore, we could show that this reversed-associative plasticity critically depends on the timing interval between afferent and cortical stimulation. These results indicate that the outcome of associative stimulation in the human brain depends on functional network interactions (inhibition or facilitation) at a systems level and can either follow standard or reversed STDP-like mechanisms.

GABAA receptor-mediated feedforward and feedback inhibition differentially modulate hippocampal spike timing-dependent plasticity

Synaptic plasticity is believed to play an important role in hippocampal learning and memory. The precise and relative timing of pre- and postsynaptic activity has been shown to determine the sign and amplitude of hippocampal synaptic plasticity through spike timing-dependent plasticity (STDP). While most studies on STDP have mainly focused on excitatory synapses, neural networks are composed not only of excitatory synapses, but also of inhibitory synapses. Interneurons are known to make inhibitory synaptic connections with hippocampal CA1 pyramidal neurons through feedforward and feedback inhibitory networks. However, the roles of different inhibitory network structures on STDP remain unknown. Using a simplified hippocampal network model with a deterministic Ca2+ dynamics-dependent STDP model, we show that feedforward and feedback inhibitory networks differentially modulate STDP. Moreover, inhibitory synaptic weight and synaptic location influenced the STDP profile. Taken together, our results provide a computational role of inhibitory network in STDP and in memory processing of hippocampal circuits.

Interaction of inhibition and triplets of excitatory spikes modulates the NMDA-R-mediated synaptic plasticity in a computational model of spike timing-dependent plasticity

Spike timing-dependent plasticity (STDP) experiments have shown that a synapse is strengthened when a presynaptic spike precedes a postsynaptic one and depressed vice versa. The canonical form of STDP has been shown to have an asymmetric shape with the peak long-term potentiation at +6 ms and the peak long-term depression at -5 ms. Experiments in hippocampal cultures with more complex stimuli such as triplets (one presynaptic spike combined with two postsynaptic spikes or one postsynaptic spike with two presynaptic spikes) have shown that pre-post-pre spike triplets result in no change in synaptic strength, whereas post-pre-post spike triplets lead to significant potentiation. The sign and magnitude of STDP have also been experimentally hypothesized to be modulated by inhibition. Recently, a computational study showed that the asymmetrical form of STDP in the CA1 pyramidal cell dendrite when two spikes interact switches to a symmetrical one in the presence of inhibition under certain conditions. In the present study, I investigate computationally how inhibition modulates STDP in the CA1 pyramidal neuron dendrite when it is driven by triplets. The model uses calcium as the postsynaptic signaling agent for STDP and is shown to be consistent with the experimental triplet observations in the absence of inhibition: simulated pre-post-pre spike triplets result in no change in synaptic strength, whereas simulated post-pre-post spike triplets lead to significant potentiation. When inhibition is bounded by the onset and offset of the triplet stimulation, then the strength of the synapse is decreased as the strength of inhibition increases. When inhibition arrives either few milliseconds before or at the onset of the last spike in the pre-post-pre triplet stimulation, then the synapse is potentiated. Variability in the frequency of inhibition (50 vs. 100 Hz) produces no change in synaptic strength. Finally, a 5% variation in model's calcium parameters (calcium thresholds) proves that the model's performance is robust.

Activity-dependent competition regulated by nonlinear interspike interaction in STDP: a model for visual cortical plasticity

The development of visual cortical circuits is strongly influenced by the sensory experience during a restricted critical period, as demonstrated by the loss of neural responses to the eye that has been briefly deprived of vision. It has been suggested that, to reflect the sensory experience into the synaptic pattern, the competition between different groups of correlated inputs to a postsynaptic cell is essential and that spike-timing-dependent plasticity (STDP) may provide the basis of this type of activity-dependent competition. To predict the consequences of competition by STDP in natural physiological conditions, I here investigate the effects of nonlinear interspike interactions in STDP which are experimentally observed in the visual cortical cells. The simulations using a biophysical STDP model show that the interspike interaction can prevent the induction of competition and counteract the effect of activity-dependent feedback (ADFB) modulation of STDP that facilitates competition. However, once the competition occurs, the level of competition is not affected by the interspike interaction. These results may suggest that the interspike interaction in STDP leads to a delay in the induction of experience-dependent plasticity through suppressing synaptic competition, thereby causing a delay in the onset of critical period in the visual cortex.

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.

Tracking a trajectory of a moving stimulus by spike timing dependent plasticity

The present study, we propose the recurrent network with spike timing dependent plasticity (STDP) that can track a trajectory of a moving stimulus. In STDP, synaptic efficiency is changed depending on the difference of firing time between pre- and postsynaptic neurons. There are many researches about temporal information processing. In the previous study, we have shown that the recurrent network with STDP can provide spatial filtering stimulating a static input [1]. Here we demonstrate the recurrent network with STDP can store spatiotemporal information of a stimulus. The structure of the proposed network is 2-dimension array. A neuron in the network connects with the neighbor neurons through synapses whose changes are subjected to STDP. The learning window of STDP is applied to that found in hippocampus. We used STDP model proposed by Song and Abbott [2]. The left figure in Figure ​Figure11 shows a schematic image of the input. The 2-dimensional input of the network consisted of a circle that moved straightly form left to right side. The white circle in the left figure indicates stronger inputs than the others. The diameter and the center of the circle is 20 and Y = 20, respectively. The right figure in Fig. ​Fig.11 indicates peri-stimulus time histogram (PSTH) of the network. Two white lines appeared on PSTH. The lines indicate higher firing rates of the neurons than those of the others. The lines correspond to edges of the moving circle (see dashed line in Fig. ​Fig.1.).1.). The lines that represented higher firing rate could be considered as the trajectory of the moving circle of the input. This result suggests that the trajectory of the moving circle is accumulated in the synaptic weights of the neurons in the network. In the other words, the network could provide storage of a trajectory of a stimulus. Figure 1 The input with a moving circle and the output of the network. The left figure is schematic image of the input. The right figure indicates the firing rate of the network. In the summary, the present study showed that the recurrent network with STDP could store a trajectory of a moving stimulus. STDP is also found in the midbrain of an electric fish. The electric fish can detect features of a moving object using electrosensory system. The object features present on the fish body surface as an electric image [3]. The function of the network shown in the present study helps explain how the electric fish can extract information from the features of an electric image generated by a moving object.

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.

Does Spike-Timing-Dependent Synaptic Plasticity Couple or Decouple Neurons Firing in Synchrony?

Spike synchronization is thought to have a constructive role for feature integration, attention, associative learning, and the formation of bidirectionally connected Hebbian cell assemblies. By contrast, theoretical studies on spike-timing-dependent plasticity (STDP) report an inherently decoupling influence of spike synchronization on synaptic connections of coactivated neurons. For example, bidirectional synaptic connections as found in cortical areas could be reproduced only by assuming realistic models of STDP and rate coding. We resolve this conflict by theoretical analysis and simulation of various simple and realistic STDP models that provide a more complete characterization of conditions when STDP leads to either coupling or decoupling of neurons firing in synchrony. In particular, we show that STDP consistently couples synchronized neurons if key model parameters are matched to physiological data: First, synaptic potentiation must be significantly stronger than synaptic depression for small (positive or negative) time lags between presynaptic and postsynaptic spikes. Second, spike synchronization must be sufficiently imprecise, for example, within a time window of 5–10 ms instead of 1 ms. Third, axonal propagation delays should not be much larger than dendritic delays. Under these assumptions synchronized neurons will be strongly coupled leading to a dominance of bidirectional synaptic connections even for simple STDP models and low mean firing rates at the level of spontaneous activity.

General conditions for spiking neurons and plasticity rules to perform independent component analysis

Given the many different proposed spiking neuron and plasticity models, it is hard to assess what functional roles their behavior may entail. One possible purpose may be to implement independent component analysis (ICA), which directly relates to sparse coding and finding relevant projections in the input space. Based on the theory of ICA [1], we show how different possible implementations of spiking neurons and spike timing dependent plasticity (STDP) can give similar results. We demonstrate how, given a neuron’s characteristics such as activation rule, STDP model and homeostatic mechanisms, one can assess whether a feedforward two-layer network is able to perform ICA. In particular, we study the behavior of exponential integrate-and-fire neurons with voltage-dependent STDP, a non-linear Hebbian rule [2] that can be related to the BCM theory. Both firing rate and spike-time correlation codes can be used as input, illustrating the flexibility of the plasticity rule in terms of neural coding. When applied to natural image patches, we investigate the capacity of generating Gabor-like receptive fields, as found in the primary visual cortex [3], suggesting a biological implementation of ICA in the brain.

STDP, Hebbian cell assemblies, and temporal coding by spike synchronization

The question whether neural activity follows a rate code or a temporal code is still an unsolved issue in neuroscience. Recent theoretical works have suggested that realistic models of spike-timing-dependent-plasticity (STDP) in recurrent networks could resolve this issue because they observed a seemingly unique relation between the neural code and the resulting pattern of synaptic connections [1]. In particular, these works argue that temporal coding would be inconsistent with bidirectional synaptic connectivity as observed in visual cortex [2] and expected for Hebbian cell assemblies (“what fires together wires together”). This conclusion is based on two assumptions, first, that simple STDP based on spike doublets would be generally unable to produce bidirectional synaptic connectivity (see references in [1]) and, second, that realistic voltage-based STDP would be able to produce bidirectional synaptic connectivity only for rate coding where signals are coded by cell ensembles jointly elevating firing rates on a time scale of hundreds of milliseconds [1]. We have disproved both assumptions. In particular, here we show that already simple STDP models can easily grow bidirectional connections for a temporal code based on spike synchronization unless synchronization is extremely precise (see [3] for disproving the second assumption). To this end we present simulation results for various STDP models [4] including all-to-all (AA) doublet STDP, nearest-neighbor (NN) doublet STDP, and various triplet STDP model variants with parameters fitted to experimental data and including realistic propagation delays. It turns out that all model variants can grow functional cell assemblies as reflected by strong bidirectional connectivity and tested within an associative memory framework [5]. This requires coarsely synchronized inputs such that spikes of the neurons within a cell assembly get synchronized on a time scale of 5 to 50 milliseconds, whereas more precise synchronization leads to depression of synaptic weights and, thus, destruction of the cell assembly. For NN doublet STDP and triplet STDP synaptic potentiation is boosted by increasing the rate of synchronized inputs, whereas high rates destroy cell assemblies for AA doublet STDP. Thus, both rate coding and temporal coding based on coarse synaptic synchronization can account for the bidirectional connectivity observed, for example, in visual cortex [2]. However, we argue that the temporal code will be much more energy efficient for learning because it allows to grow and preserve cell assemblies at low mean firing rates at the level of spontaneous activity, whereas a rate code (based on uncorrelated Poissonian firing) can grow cell assemblies only by maintaining high firing rates over longer time intervals. Moreover, additional simulation experiments demonstrate how STDP can quickly grow multiple independent cell assemblies reflecting the spike timing relations of simultaneously active input neurons. We speculate that such a multiplexing mechanism may play a role both for working memory and long-range communication where “copies” or “indices” [6] of cell assemblies could easily be transmitted between cortical areas.

Different neural codes result in bidirectional connectivity formed by the same model of spike-timing-dependent plasticity

Recent studies on phenomenological models of spike-timing-dependent plasticity (STDP) extend the idea of a pure spike-based paradigm to the level of dendritic voltage [1]. In such models, the decision to induce early long-term potentiation (eLTP) or long-term depression (eLTD) not solely depends on the time difference between pre- and post-synaptic spikes but also on the precise dynamics of the post-synaptic potential. From simulations of small neural networks and different stimulation schemes corresponding to different neural codes, these studies have concluded that the pattern of synaptic connectivity would directly follow from the neural code and vice versa. For example, they have suggested that strong uni-directional connectivity would emerge through temporal coding, whereas bidirectional connectivity would be indicative for a rate code. Relying on results from earlier studies on first generation STDP models [2-4], synchronous temporal codes forming bidirectional connectivity patterns were considered unlikely in [1]. However, recent findings revise a general exclusion of this relationship [5] even for first generation STDP models. In particular, our work shows that realistic STDP models as proposed in [1] can actually not predict the neural code (temporal vs. rate coding) by looking at the pattern of synaptic connectivity within a specific brain area. With the same kind of simulations as in [1], but additionally considering stimulation conditions for synchronous temporal coding, we show that bidirectional connections are still possible. Furthermore we discuss the influence of synchronization precision and oscillatory activity.

Interplay between dendritic non-linearities and STDP

Recent results about dendritic computation of responses to presynaptic stimulations have raised a lot of interest. In particular, the integration of postsynaptic potentials (PSPs) exhibits non-linearities depending on their location on dendrites, even before it reaches the soma [1]. This implies important implications for spike processing at the scale of the whole neuron, when stimulated by many input spike trains via distributed synapses. Here we examine a specific aspect of dendritic non-linearities related to spike-timing-dependent plasticity (STDP). Under STDP, synapses are strengthened or weakened depending on the relative timing of pre- and postsynaptic spikes at the scale of milliseconds. The resulting learning dynamics can dramatically shape the distribution of synaptic weights, which in turn modifies the neuronal response to its inputs [2]. We investigate the interplay between dendritic non-linearities, weight distributions and STDP-based learning, in order to evaluate whether their combined effects can be useful in terms of spiking computation. We develop a mathematical analysis using the Poisson neuron model (spiking neuron) and a phenomenological model of STDP that describes the weight update using a learning window function [3]. The synaptic competition depends on properties of the STDP learning window, non-linear PSP integration, and stimulating inputs (in particular, the input spike-time correlations). As a first step, we constrain the present study to a configuration where pools of input spike trains with (narrow) temporal correlations excite certain groups of synapses. In addition, we assume linearity in the summation of PSPs for proximal (basal) synapses, whereas PSPs on distal (apical) synapses experience a supralinear summation when they belong to the same branch [1]. Using our mathematical framework, we show how distinct STDP rules applied to proximal and distal synapses can “match” their different PSP properties. Because of the corresponding supralinearity, a small increase of the weights for distal synapses will be felt stronger at the soma, as compared to proximal synapses. In this sense, a Gaussian-like distribution for the former is equivalent to a long-tail weight distribution for the latter. For linear PSP summation, such distributions can be produced by multiplicative STDP [2] and a new weight-dependent STDP model that we proposed recently (submitted work), respectively. Here we discuss how these distributions are affected by the dendritic non-linearities. Then we investigate how some synapses are potentiated at the expense of others for various input configurations, in particular, the possibility of jointly selecting correlated inputs even though they excite different dendritic sites. A previous study [4] used additive (weight-independent) STDP with a realistic neuron model in order to examine the competition between basal and apical synapses. It was found in this configuration that, in most cases, either basal or apical synapses take over, and a balance between them is difficult to obtain. Our results suggest that non-additive STDP models can partly solve this problem by adjusting their weight dependence to the dendritic non-linearity, and realize a “fair” synaptic competition. This means that the emerging connectivity can reflect the stimulating input properties despite the constraint of being located on different dendritic branches. A future step consists in incorporating more physiological details in our model (e.g., compartmental neuron model as in [4]) to verify that our results still hold. Eventually, we aim to understand how the diversity of STDP and PSP properties observed in the biology contributes to the computational power of neurons in terms of spike processing.

Stochastic gradient ascent learning with spike timing dependent plasticity

Stochastic gradient ascent learning exploits correlations of parameter variations with overall success of a system. This algorithmic idea has been related to neuronal network learning by postulating eligibility traces at synapses, which make them selectable for synaptic changes depending on later reward signals ([1] and [2]). Formalizations of the synaptic and neuronal dynamics supporting gradient ascent learning in terms of differential equations exhibit strong similarities with a recent formulation of spike timing dependent plasticity (STDP) [3] when it is combined with a reward signal. Here we present conditions under which reward modulated STDP is in fact guaranteed to maximize expected reward. We present numerical simulations underlining the relevance of realistic STDP models for reward dependent learning. In particular, we find that the nonlinear adaptation to pre- and post-synaptic activities of STDP [3] contributes to stable learning. Figure 1 Learning the XOR function with a reward modulated STDP rule. Left: Output activity versus training episode in a feed forward network with Poisson-like neurons (2 input nodes, 10 hidden nodes and 1 output node). The output activity for the [true, false] ...

A simulation study on different STDP models concerning localized gamma oscillations

AbstractGamma oscillations are a prominent feature in experimental as well as theoretical descriptions of brain activity. One of the network models which has the capability to generate such oscillations is what we call a local cell assembly (CA), i.e. a group of neighboring neurons which are strongly interconnected in an excitatory manner. Postulated by experimenters and extensively used in theoretical studies, these local networks seem to be a good candidate for investigating the impact of biological constraints given by models of spike-timing-dependent plasticity (STDP) on local gamma oscillating structures in the mammalian brain. Therefore we fi*tted a two-compartment neuron model with AMPA- and NMDA-receptor mediated synaptic currents to desired properties of a local CA, meaning pattern completion and after-activity. We simulated 100 recurrently connected neurons with fi*xed axonal transmission delays. In addition, every neuron receives Poissonian spikes from 1000 input cells *firing at low background rate. During simulation the network is stimulated every second by increasing the input rate 10-fold for 35 msec. As a quality measure for keeping or even enhancing the properties of the network, we counted the relative amount of synapses with increased synaptic strengths with reference to the initial values. Three phenomenological STDP models (Song et al., Nature Neuroscience, 3, 2000; Pfi*ster and Gerstner, The J. of Neuroscience, 26, 2006; Clopath et al., Nature Neuroscience, 13, 2010) were implemented. Model-specifi*c parameters were varied in ranges determined by experimental measurements. We conclude that more recent STDP models which take into account frequency-dependent terms lead to a higher probability of strengthening synapses in a local CA (larger LTP region). This corresponds to experimental observations that long-term potentiation (LTP) outweighs long-term depression (LTD) in high-frequency pairing protocols. Furthermore, our simulations show that short axonal transmission delays clearly enlarge the LTP region of STDP parameter space.

Modeling of Spike Timing-Dependent Plasticity in the Presence of Complex Spike Protocols

Spike timing-dependent plasticity (STDP) is a process in which changes in synaptic strength are determined by the relative timing of pre- and post-synaptic activity. STDP can result in either long term potentiation (LTP) or long term depression (LTD), and there is strong experimental evidence that these changes are driven by the postsynaptic Ca2+ concentration. Previously we examined a computational model of STDP that combines the chemical network model of Pi and Lisman (2008), with a model of Ca2+ dynamics that builds on the work of Shouval and coworkers (2002) to explain experimental studies of STDP in response to pre- and post-synaptic spike pair protocols (Carlson and Giordano, 2010). Wang et al. (2005) have also explored more complex spike timing protocols such as triplets and quadruplets, and the results in some cases cannot be explained simply in terms of the STDP behavior found in response to spike pairs. For example, a spike pair triplet can be viewed as a combination of one spike pair (spikes 1 and 2) followed by a second spike pair (spikes 2 and 3), and in some cases the resulting STDP is not the simple sum of that found for the two spike pairs. We have extended our model of STDP to explore the multi-spike cases studied by Wang et al. and careful examination of the Ca2+ dynamics shows how such “non-additivity” can occur. Carlson, K. D. and Giordano, N. J. (2010) to be published. Pi, H. J., and Lisman, J. E. (2008) J. Neurosci. 28: 13132–13138. Shouval, H. Z., Bear, M. F., and Cooper, L. N. (2002) Proc. Natl. Acad. Sci. USA 99: 10831–10836. Wang, H. X., Gerkin, R. C., Nauen, D. W., and Bi, G. Q. (2005) Nat. Neurosci. 8: 187–194.

Analysis of Development of Direction Selectivity in Retinotectum by a Neural Circuit Model with Spike Timing-Dependent Plasticity

The development of direction selectivity in the visual system depends on visual experience. In the developing Xenopus retinotectal system, tectal neurons (TNs) become direction selective through spike timing-dependent plasticity (STDP) after repetitive retinal exposure to a moving bar in a specific direction. We investigated the mechanism responsible for the development of direction selectivity in the Xenopus retinotectal system using a neural circuit model with STDP. In this retinotectal circuit model, a moving bar stimulated the retinal ganglion cells (RGCs), which provided feedforward excitation to the TNs and interneurons (INs). The INs provided delayed feedforward inhibition to the TNs. The TNs also received feedback excitation from neighboring TNs. As a synaptic learning rule, a molecular STDP model was used for synapses between the RGCs and TNs. The retinotectal circuit model reproduced experimentally observed features of the development of direction selectivity, such as increase in input to the TN. The peak of feedforward excitation from RGCs to TNs shifted earlier as a result of STDP. Together with the delayed feedforward inhibition, a stronger earlier transient feedforward signal was generated, which exceeded the threshold of the feedback excitation from the neighboring TNs and resulted in amplification of input to the TN. The suppression of the delayed feedforward inhibition resulted in the development of orientation selectivity rather than direction selectivity, indicating the pivotal role of the delayed feedforward inhibition in direction selectivity. We propose a mechanism for the development of direction selectivity involving a delayed feedforward inhibition with STDP and the amplification of feedback excitation.

Interplay of the magnitude and time-course of postsynaptic Ca2 + 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.

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.

Reconciling the STDP and BCM Models of Synaptic Plasticity in a Spiking Recurrent Neural Network

Rate-coded Hebbian learning, as characterized by the BCM formulation, is an established computational model of synaptic plasticity. Recently it has been demonstrated that changes in the strength of synapses in vivo can also depend explicitly on the relative timing of pre- and postsynaptic firing. Computational modeling of this spike-timing-dependent plasticity (STDP) has demonstrated that it can provide inherent stability or competition based on local synaptic variables. However, it has also been demonstrated that these properties rely on synaptic weights being either depressed or unchanged by an increase in mean stochastic firing rates, which directly contradicts empirical data. Several analytical studies have addressed this apparent dichotomy and identified conditions under which distinct and disparate STDP rules can be reconciled with rate-coded Hebbian learning. The aim of this research is to verify, unify, and expand on these previous findings by manipulating each element of a standard computational STDP model in turn. This allows us to identify the conditions under which this plasticity rule can replicate experimental data obtained using both rate and temporal stimulation protocols in a spiking recurrent neural network. Our results describe how the relative scale of mean synaptic weights and their dependence on stochastic pre- or postsynaptic firing rates can be manipulated by adjusting the exact profile of the asymmetric learning window and temporal restrictions on spike pair interactions respectively. These findings imply that previously disparate models of rate-coded autoassociative learning and temporally coded heteroassociative learning, mediated by symmetric and asymmetric connections respectively, can be implemented in a single network using a single plasticity rule. However, we also demonstrate that forms of STDP that can be reconciled with rate-coded Hebbian learning do not generate inherent synaptic competition, and thus some additional mechanism is required to guarantee long-term input-output selectivity.

Model for the induction of spike timing-dependent plasticity by pre- and postsynaptic spike trains

Spike timing-dependent plasticity (STDP), a process in which changes in synaptic strength are determined by the relative timing of pre- and postsynaptic activity, has been studied and modeled by a number of researchers, but many questions still remain. It has been suggested that STDP involves a postsynaptic chemical network with stable states corresponding to long term potentiation (LTP) and long term depression (LTD). It is believed that the switching between these states is driven by the postsynaptic Ca2+ concentration, but the manner in which the Ca2+ dynamics is able to trigger either LTP or LTD, depending on the relative timing of pre- and postsynaptic activity remains unclear. We have investigated a model of STDP that combines (1) the tristable chemical network involving CaMKII and PP2A studied by Pi and Lisman [1], with (2) compartmental modeling of backpropagating action potentials (BPAPs), N-methyl D-aspartate receptors (NMDARs), and voltage-dependent calcium channels (VDCCs). In previous work we have studied how this model responds when a presynaptic pulse arrives either shortly before or shortly after a postsynaptic pulse (a BPAP), and shown how this model leads naturally to LTP when the presynaptic pulse arrives first, or LTD when the postsynaptic pulse arrives first, in agreement as found in experimental studies (e.g., [2] and [3]). The response to spike triplets and other more complex pre- and postsynaptic spike trains are also of interest. Experiments [4] have shown that the response to such multispike trains is not simply the sum of the responses to the component spike pairs. For example, the response to a spike triplet consisting of pre-post-presynaptic spikes is often not explained by the simple addition of the responses to a pre-post spike pair followed by a post-pre spike pair. Previous work has proposed only heuristic rules for such multispike responses. In this paper we describe the application of our model of STDP to multispike situations. Our model exhibits a non-additive response similar to that observed by Wang et al. [4], and gives insight into how this non-additivity arises from properties of the CaMKII/PP2A network.