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Percentage change in peak synaptic amplitude after performing the Bi and Poo spike pairing protocol as a function of initial synaptic amplitude. Data from Bi and Poo Fitted additive potentiation update, gray dashed curve ; fitted multiplicative potentiation update, solid gray curve ; fitted power law update slopes 0. Figure adapted from Morrison et al.

Instead of plotting the percentage weight change, Fig. The exponent of the weight dependence can now be determined from the slope of a linear fit to the data, see Morrison et al. The upper two histograms show the behavior of a single synapse. In the top panel the presynaptic neuron is repeatedly stimulated before the postsynaptic neuron.

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Spike timing; mechanisms and function.

In the middle panel the timing relation is reversed. Adapted from Rubin et al. A bimodal distribution is only produced by rules with a very weak weight dependence i. Because of the high connectivity of the cortex, we may expect that the effective population size in vivo would be an order of magnitude greater, and so the region of bimodal stability would be vanishingly small according to this analysis. In contrast to a purely additive rule, the peaks of the distributions are not at the extrema of the permitted weight range.

Moreover, the bimodal distribution does not persist if the correlations in the input are removed after learning. Model parameters chosen for visual clarity as only the qualitative behavior is relevant. Note that the existence of a fixed point and its stability does not crucially depend on the presence of soft or hard bounds on the weight. Equations 18 and 19 can equate to zero for hard-bounded or or unbounded rules. Results on the consequences of STDP in large-scale networks are few and far between, and tend to contradict each other.

Part of the reason for the lack of simulation papers on this important subject is the fact that simulating such networks consumes huge amounts of memory, is computationally expensive, and potentially requires extremely long simulation times to overcome transients in the weight dynamics which can be of the order of hundreds of seconds of biological time. A lack of theoretical papers on the subject can be explained by the complexity of the interactions between the activity dynamics of the network and the weight dynamics, although some progress is being made in this area Burkitt et al.

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It was recently shown that power law STDP is compatible with balanced random networks in the asynchronousirregular regime Morrison et al. Although it has not yet been possible to perform systematic tests, it seems likely that all the formulations of STDP with the fixed point structure discussed in Sect. The results for additive STDP seem to be more contradictory. Izhikevich et al. In the former case, it is the existence of many strong synapses which defines the network, in the latter, the presence of many weak ones. This discrepancy may be attributable to different choices for the effective stabilized firing rates 20 in combination with different choices of delays in the network, see Sect.

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Examples of nearest neighbor spike pairing schemes for a presynaptic neuron j and a postsynaptic neuron i. In each case, the dark gray indicate which pairings contribute toward depression of a synapse, and light gray indicate which pairings contribute toward potentiation. It is sometimes assumed that the scheme used makes no difference, as the ISI of cortical network models is typically an order of magnitude larger than the time constant of the STDP window. However, this is not generally true Kempter et al.

For a review of a wide variety of schemes and their consequences, particularly with respect to selectivity of higher-frequency inputs, see Burkitt et al. Experimental results on this issue suggest limited interaction between pairs of spikes. Sjostrom et al. However, this result may also be due to the limitations of pair-based STDP models to explain the experimentally observed frequency dependence, see Sect.

More recently, Froemke et al. However, the amount of LTP was negatively correlated with the number of presynaptic spikes preceding a postsynaptic spike. This suggests that multiple spike pairings contribute to LTP, but not in the linear fashion of the all-to-all scheme, which would predict a positive correlation between the number of spikes and the amount of LTP.

Again, these results are good evidence for the limitations of pair-based STDP rules. Different partitions of synaptic delays and the resulting shift of the raw cross-correlation function as perceived at the synapse black curves with respect to the raw cross-correlation function as perceived at the soma gray curves. The cross-correlation functions shown are purely illustrative and do not result from a specific network model. The synaptic raw cross-correlation function is shifted to the left by d. The synaptic raw cross-correlation function is identical to the somatic raw cross-correlation function.

The synaptic raw cross-correlation function is shifted to the right by d. See Senn et al. There is considerable evidence that the pair-based rules discussed above cannot give a full account of STDP. Specifically, they reproduce neither the dependence of plasticity on the repetition frequency of pairs of spikes in an experimental protocol, nor the results of recent triplet and quadruplet experiments.

STDP experiments are usually carried out with about 60 pairs of spikes.


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The temporal distance of the spikes in the pair is of the order of a few to tens of milliseconds, whereas the temporal distance between the pairs is of the order of hundreds of milliseconds to seconds. In the case of a facilitation protocol i.


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This prediction is independent of whether the spike pairing scheme is all-to-all or nearest neighbor see Sect. However, experiments show that increasing the repetition frequency leads to an increase in potentiation Sjostrom et al. Other recent experiments employed multiple-spike protocols, such as repeated presentations of symmetric triplets of the form pre-post-pre and post-pre-post Bi and Wang ; Froemke and Dan ; Wang et al. Standard pair-based models predict that the two sequences should give essentially the same results, as they each contain one pre-post pair and one post-pre pair.

Experimentally, quite different results are observed. Here we review two examples of simple models which account for these experimental findings. For other models which also reproduce frequency dependence or multiple-spike protocol results, see Abarbanel et al. Implementation of the triplet rule by local variables. The spikes of presynaptic neuron j contribute to a trace x j t , the spikes of postsynaptic neuron i contribute to a fast trace y i 1 t and a slow trace y i 2 t.

The update of the weight w ij at the moment of a presynaptic spike is proportional to the momentary value of the fast trace y i 1 t unfilled circles , as in the pair-based model see Fig. The update of the weight w ij at the moment of a postsynaptic spike is proportional to the momentary value of the trace x j t black filled circles and the value of the slow trace y i 2 t just before the spike gray filled circles.

The triplet rule reproduces the finding that increased frequency of pair repetition leads to increased potentiation in visual cortex pyramidal neurons. Data from Sjostrom et al. This model gives a good fit to triplet and quadruplet protocols in visual cortex slice, and also gives a much better prediction for synaptic modification due to natural spike trains Froemke and Dan However, it does not predict the increase of LTP with the repetition frequency observed by Sjostrom et al.

A revised version of the model Froemke et al. Often a presynaptic pathway is stimulated extracellularly, so that several presynaptic neurons are activated.

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Depending on the level of the postsynaptic membrane potential, the activated synapses increase their efficacy while other non-activated synapses do not change their weight Artola et al. More recently, depolarization has also been combined with STDP experiments. In particular, Sjostrom et al. There is an ongoing discussion whether the voltage dependence is more fundamental than the dependence on postsynaptic spiking. Alternatively, a dependence on the slope of the postsynaptic membrane potential has also been shown to reproduce the characteristic STDP weight change curve Saudargiene et al.

The voltage effects caused by back-propagating spikes is implicitly contained in the mechanistic formulation of STDP models outlined above.

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In particular, the fast postsynaptic trace y 1 in the above triplet model could be seen as an approximation of a back-propagating action potential. However, the converse is not true: a pure STDP rule does not automatically generate a voltage dependence. Moreover, synaptic effects caused by subthreshold depolarization in the absence of postsynaptic firing cannot be modeled by standard STDP or triplet models.

We stress that all the above models concern induction of potentiation and depression, but not their maintenance. The induction of LTP may take only a few seconds: for example, stimulation with 50 pairs of pre- and postsynaptic spikes given at 20Hz takes less than 3 s. However, afterwards the synapse takes 60 min or more to consolidate these changes, and this process may also be interrupted Frey and Morris Consolidation is thought to rely on a different molecular mechanism than that of induction.

Simply speaking, gene transcription is necessary to trigger the building of new proteins that increase the synaptic efficacy. Long-term stability of synapses is necessary to retain memories that have been learned, despite ongoing activity of presynaptic neurons.


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  7. A simple possibility used in many models is that plasticity is simply switched off once the neuron has learned what it should. This approach makes sense in the context of reward-based learning: the learning rate goes to zero once the actual reward equals the expected reward and learning stops automatically see Sect. It also makes sense in the framework of supervised learning see Sect.

    Learning is normally driven by the difference between desired output and actual output. However, in the context of unsupervised learning it is inconsistent to switch off the dynamics. Nevertheless, receptive field properties should be retained for a fairly long time even if the stimulation characteristic changes.

    Whether single synapses themselves are binary or continuous is a matter of intense debate. Some experiments have suggested that synapses are binary Petersen et al.