Spike-timing-dependent Plasticity Model Research Articles

Location-specific activity of signaling molecules underlying STDP in a model CA1 pyramidal neuron

Spike-timing-dependent plasticity (STDP) is a form of bidirectional change in synaptic strength that depends on the temporal order and temporal difference of the pre- and postsynaptic activity [1]. The synapse undergoes long-term potentiation (LTP) if the presynaptic spike precedes the postsynaptic spike, and exhibits long-term depression (LTD) if the temporal order is reversed. Recent physiological observations suggest that the form of plasticity at a synapse depends not only on the timing of the pre- and postsynaptic activity but also on the location of the synapse on the dendritic tree [2]. We proposed a biophysical model of STDP predicting that learning rules are location-dependent [3]. Numerous modeling studies investigate molecular mechanisms of synaptic plasticity (e.g. [4], [5]). However, the influence of the dendritic location of the synapse on the plasticity mechanisms has not been addressed in detailed models of STDP. It is known that calcium-activated CaMKII and calcineurin cause phosphorylation or dephosphorylation of AMPA-type glutamate receptors, and these changes are thought to underlie LTP and LTD. In this study, we model the trigger of the second messenger cascades, the calcium signal, by pairing the AMPA and NMDA receptor activation with a backpropagating action potential at a spine close to the soma and by pairing the AMPA and NMDA receptor activation with a dendritic spike at a spine in distal dendritic regions. We employ a detailed compartmental model of CA1 cell [6] and adjust the calcium handling mechanism following [7]. The resulting calcium signals are used in a bistable biochemical model of the CaMKII autophosphorylation and dephosphorylation system [5]. In this model, transition from a weakly phosphorylated state to a highly phosphorylated state corresponds to LTP, and transition into the opposite direction leads to LTD. We show that CaMKII is highly phosphorylated for the multiple pre-post spike pairing protocol and it is weakly phosphorylated if the temporal order is reversed in a proximal spine. These results are consistent with the rules for LTP/LTD induction observed experimentally. However, CaMKII stays highly phosphorylated for the pre-post and post-pre protocols in a distal spine and implies that synapses tend to avoid transitions to LTD neglecting the temporal order of the pre- and local postsynaptic events in distal dendritic regions. The results imply that synapse location is one of the critical factors for plasticity rules at a synapse.

Connectivity reflects coding: a model of voltage-based STDP with homeostasis

Electrophysiological connectivity patterns in cortex often have a few strong connections, which are sometimes bidirectional, among a lot of weak connections. To explain these connectivity patterns, we created a model of spike timing-dependent plasticity (STDP) in which synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential, filtered with two different time constants. Our model describes several nonlinear effects that are observed in STDP experiments, as well as the voltage dependence of plasticity. We found that, in a simulated recurrent network of spiking neurons, our plasticity rule led not only to development of localized receptive fields but also to connectivity patterns that reflect the neural code. For temporal coding procedures with spatio-temporal input correlations, strong connections were predominantly unidirectional, whereas they were bidirectional under rate-coded input with spatial correlations only. Thus, variable connectivity patterns in the brain could reflect different coding principles across brain areas; moreover, our simulations suggested that plasticity is fast.

Stability and competition in multi-spike models of spike-timing dependent plasticity

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STDP in Adaptive Neurons Gives Close-To-Optimal Information Transmission

Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for spike-timing-dependent plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, as does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons.

Spike timing dependent plasticity: a consequence of more fundamental learning rules

Spike timing dependent plasticity (STDP) is a phenomenon in which the precise timing of spikes affects the sign and magnitude of changes in synaptic strength. STDP is often interpreted as the comprehensive learning rule for a synapse – the “first law” of synaptic plasticity. This interpretation is made explicit in theoretical models in which the total plasticity produced by complex spike patterns results from a superposition of the effects of all spike pairs. Although such models are appealing for their simplicity, they can fail dramatically. For example, the measured single-spike learning rule between hippocampal CA3 and CA1 pyramidal neurons does not predict the existence of long-term potentiation one of the best-known forms of synaptic plasticity. Layers of complexity have been added to the basic STDP model to repair predictive failures, but they have been outstripped by experimental data. We propose an alternate first law: neural activity triggers changes in key biochemical intermediates, which act as a more direct trigger of plasticity mechanisms. One particularly successful model uses intracellular calcium as the intermediate and can account for many observed properties of bidirectional plasticity. In this formulation, STDP is not itself the basis for explaining other forms of plasticity, but is instead a consequence of changes in the biochemical intermediate, calcium. Eventually a mechanism-based framework for learning rules should include other messengers, discrete change at individual synapses, spread of plasticity among neighboring synapses, and priming of hidden processes that change a synapse's susceptibility to future change. Mechanism-based models provide a rich framework for the computational representation of synaptic plasticity.

A Model of Spike-Timing-Dependent Plasticity

It has been shown that postsynaptic calcium dynamics plays an important role in spike timing-dependent plasticity (STDP), a process in which changes in synaptic strength are determined by the relative timing of pre- and postsynaptic activity. It has been suggested 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 of this network between these states is driven by the postsynaptic Ca2+ concentration, but the manner in which the Ca2+ dynamics causes the switching to depend on the relative timing of pre- and postsynaptic activity remains unclear. We describe a 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). Following Shouval and coworkers, we assume that a portion of the influx of postsynaptic Ca2+ is controlled by NMDA receptors that allow an inward Ca2+ current in response to both glutamate binding and a back propagating action potential (BPAP). To this we add a contribution from voltage dependent calcium channels (VDCCs). We show that this model is able to reproduce the observed time dependence of STDP when a single presynaptic pulse is either followed or preceded by a single BPAP. The behavior of the model with triplet pulse protocols, e.g., two presynaptic pulses separated by a BPAP, or two BPAPs separated by a presynaptic pulse, and the incorporation of more sophisticated models of AMPA trafficking are also described.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.

Modeling the effects of GABA-A inhibition on the spike timing-dependent plasticity of a CA1 pyramidal cell

A detailed CA1 microcircuit (MC) model of the hippocampus has been recently advanced to investigate the biophysical mechanisms by which hetero-association of spatio-temporal input patterns is achieved in the hippocampus [1,2]. The network model consisted of pyramidal (P) cells, basket (B) cells, axo-axonic (AA) cells, bistratified (BS) cells and oriens lacunosum-molecurale (OLM) cells. Inputs to the network came from the entorhinal cortex (EC), the CA3 Schaffer collaterals and medial septum (MS). The EC input provided the sensory information, whereas all other inputs provided context and timing information. The MS input paced the network theta rhythm activity. Storage and recall of memories were separated into different functional theta half-cycles. Storage was accomplished via a local spike timing-dependent plasticity (STDP) rule mediating hetero-association of the postsynaptic PC response due to the incoming EC input and the CA3 input spike pattern on the pyramidal cell stratum radiatum (SR) AMPA synapses. The model simulated the timing of firing of different hippocampal cell types relative to the theta rhythm and proposed functional roles for the different classes of inhibitory interneurons in the storage and recall cycles of input patterns. Memory capacity and recall performance of the MC model were quantitatively studied. Particular emphasis was given as to how the temporal patterning of the inputs interacted with the STDP learning to either promote or inhibit pattern storage and hence ultimately pattern recall. In this work, we extend the STDP rule applied to the PCSR AMPA synapses of the CA1 MC model with a Ca2+ dynamics STDP model applied to the PC-SR NMDA synapses in order to study how GABA inhibition affects the detailed CA2+ dynamics underlying synaptic plasticity on the NMDA synapses of the CA1 pyramidal cells. Experimental studies has shown that GABAergic inhibition in the proximal stratum radiatum (SR) dendrite of the hippocampal CA1 pyramidal neuron is probably responsible for the observed symmetry-to-asymmetry transition of the STDP curve [5]. Recent computational works from our group [3,4] predicted that symmetry-to-asymmetry transition is strongly dependent on the frequency band (theta vs. gamma), the conductance value of GABAA inhibition and the relative timing between the GABAergic spike train and the preand post-synaptic excitation. Two distinct long-term depression (LTD) tails of the symmetrical STDP curve were shown to be centered at +10 ms, +40 ms and 10 ms, respectively. The largest LTP value and the two distinct LTD tails were inversely proportional to the increase of GABA conductance. With this work we continue to investigate the effects of the GABA inhibition on the STDP learning curve in the presence of more complex excitatory inputs such as triplets, quadruplets and bursts. We explore in more detail the effects on the STDP curve of various gamma frequency sub-bands (40 Hz, 75 Hz and 100 Hz), the GABAA conductance value and the relative timing of the GABA inhibition with the complex excitatory inputs. An important implication of these results is that they raise the possibility that GABArgic interneurons can be trained to fire at specific times and frequencies, and confrom Eighteenth Annual Computational Neuroscience Meeting: CNS*2009 Berlin, Germany. 18–23 July 2009

Functional connectivity for somatosensory and motor cortex in spastic diplegia

Functional connectivity (fcMRI) was analyzed in individuals with spastic diplegia and age-matched controls. Pearson correlations (r-values) were computed between resting state spontaneous activity in selected seed regions (sROI) and each voxel throughout the brain. Seed ROI were centered on foci activated by tactile stimulation of the second fingertip in somatosensory and parietal dorsal attention regions. The group with diplegia showed significantly expanded networks for the somatomotor but not dorsal attention areas. These expanded networks overran nearly all topological representations in somatosensory and motor areas despite a sROI in a fingertip focus. A possible underlying cause for altered fcMRI in the group with dipegia, and generally sensorimotor deficits in spastic diplegia, is that prenatal third trimester white-matter injury leads to localized damage to subplate neurons. We hypothesize that intracortical connections become dominant in spastic diplegia through successful competition with diminished or absent thalamocortical inputs. Similar to the effects of subplate ablations on ocular dominance columns (Kanold and Shatz, Neuron 2006;51:627–638), a spike timing-dependent plasticity model is proposed to explain a shift towards intracortical inputs.

Frequency selectivity using spike-timing-dependent plasticity

Event Abstract Back to Event Frequency selectivity using spike-timing-dependent plasticity Learning in neuronal networks is believed to rely on mechanisms at the molecular level that modify the strength (or weight) of synaptic connections between neurons. Spike-timing-dependent plasticity (STDP) is a candidate synaptic mechanism, which determines the evolution of the weights according to the precise timing of pre- and post-synaptic spikes. In turn, this weight evolution slowly modifies the neuronal activity, which can lead to the emergence of functional pathways in neuronal networks. In the present paper we investigate a special case where STDP fine-tunes through synaptic competition the input selectivity for a single neuron stimulated by a periodic input signal. We show how STDP can potentiate or depress synapses in a pool depending on their post-synaptic response parameters (e.g. time constants and delays) and on the input frequency. Moreover, the quality of the resulting filter can be enhanced when the neuron also receives inhibition from the same input signal; in this case STDP can lead, at the same time, to a homeostatic equilibrium in the average weight, which results in excitation balancing the inhibition at low frequencies. This unsupervised learning can be performed by training either excitatory or inhibitory synapses; we constrain the present study to the case of plasticity on only the excitatory synapses. We use a theoretical framework based on additive STDP and Poisson neuron models in order to analyze the neuronal response to periodic inputs and the resulting evolution of the synaptic weights over time. Our analysis focuses on “steady”oscillatory inputs that have fixed frequency and amplitude. The weight change can be exactly calculated for each synapse in this case, which predicts the pattern of potentiation versus depression for the whole pool of synapses. Our results suggest that among a large pool of synapses with sufficient diversity of parameter values, the application of a periodic input signal can select the synapses that have appropriate post-synaptic response parameters. Consequently the response of the neuron will be strengthened for oscillatory synaptic inputs in the range of the stimulating frequency and weakened for other frequencies. These results are supported by numerical simulation. The mechanism presented in this paper can be considered as a first step in the larger process whereby STDP can give rise in a neuronal network to a frequency map encoding sensory periodic signals, such as arise in auditory processing. In order to obtain such a map, neurons are trained by presenting many frequencies and each neuron becomes selective to a portion of the stimulus spectrum. A second necessary step consists in obtaining a continuous representation of the frequencies in the map, such that neighboring neurons are selective to similar frequencies. In this way, the sensory map behaves as an estimator for the frequency component of its stimulating inputs. This second step will be the subject of a subsequent study. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Frequency selectivity using spike-timing-dependent plasticity. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.330 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 04 Feb 2009; Published Online: 04 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

A Biophysical Model of Synaptic Plasticity and Metaplasticity Can Account for the Dynamics of the Backward Shift of Hippocampal Place Fields

Hippocampal place cells in the rat undergo experience-dependent changes when the rat runs stereotyped routes. One such change, the backward shift of the place field center of mass, has been linked by previous modeling efforts to spike-timing-dependent plasticity (STDP). However, these models did not account for the termination of the place field shift and they were based on an abstract implementation of STDP that ignores many of the features found in cortical plasticity. Here, instead of the abstract STDP model, we use a calcium-dependent plasticity (CaDP) learning rule that can account for many of the observed properties of cortical plasticity. We use the CaDP learning rule in combination with a model of metaplasticity to simulate place field dynamics. Without any major changes to the parameters of the original model, the present simulations account both for the initial rapid place field shift and for the subsequent slowing down of this shift. These results suggest that the CaDP model captures the essence of a general cortical mechanism of synaptic plasticity, which may underlie numerous forms of synaptic plasticity observed both in vivo and in vitro.

Reinforcement Learning Through Modulation of Spike-Timing-Dependent Synaptic Plasticity

The persistent modification of synaptic efficacy as a function of the relative timing of pre- and postsynaptic spikes is a phenomenon known as spike-timing-dependent plasticity (STDP). Here we show that the modulation of STDP by a global reward signal leads to reinforcement learning. We first derive analytically learning rules involving reward-modulated spike-timing-dependent synaptic and intrinsic plasticity, by applying a reinforcement learning algorithm to the stochastic spike response model of spiking neurons. These rules have several features common to plasticity mechanisms experimentally found in the brain. We then demonstrate in simulations of networks of integrate-and-fire neurons the efficacy of two simple learning rules involving modulated STDP. One rule is a direct extension of the standard STDP model (modulated STDP), and the other one involves an eligibility trace stored at each synapse that keeps a decaying memory of the relationships between the recent pairs of pre- and postsynaptic spike pairs (modulated STDP with eligibility trace). This latter rule permits learning even if the reward signal is delayed. The proposed rules are able to solve the XOR problem with both rate coded and temporally coded input and to learn a target output firing-rate pattern. These learning rules are biologically plausible, may be used for training generic artificial spiking neural networks, regardless of the neural model used, and suggest the experimental investigation in animals of the existence of reward-modulated STDP.

Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations

Spike-timing dependent plasticity (STDP) is a type of synaptic modification found relatively recently, but the underlying biophysical mechanisms are still unclear. Several models of STDP have been proposed, and differ by their implementation, and in particular how synaptic weights saturate to their minimal and maximal values. We analyze here kinetic models of transmitter-receptor interaction and derive a series of STDP models. In general, such kinetic models predict progressive saturation of the weights. Various forms can be obtained depending on the hypotheses made in the kinetic model, and these include a simple linear dependence on the value of the weight ("soft bounds"), mixed soft and abrupt saturation ("hard bound"), or more complex forms. We analyze in more detail simple soft-bound models of Hebbian and anti-Hebbian STDPs, in which nonlinear spike interactions (triplets) are taken into account. We show that Hebbian STDPs can be used to selectively potentiate synapses that are correlated in time, while anti-Hebbian STDPs depress correlated synapses, despite the presence of nonlinear spike interactions. This correlation detection enables neurons to develop a selectivity to correlated inputs. We also examine different versions of kinetics-based STDP models and compare their sensitivity to correlations. We conclude that kinetic models generally predict soft-bound dynamics, and that such models seem ideal for detecting correlations among large numbers of inputs.

Triplets of Spikes in a Model of Spike Timing-Dependent Plasticity

Classical experiments on spike timing-dependent plasticity (STDP) use a protocol based on pairs of presynaptic and postsynaptic spikes repeated at a given frequency to induce synaptic potentiation or depression. Therefore, standard STDP models have expressed the weight change as a function of pairs of presynaptic and postsynaptic spike. Unfortunately, those paired-based STDP models cannot account for the dependence on the repetition frequency of the pairs of spike. Moreover, those STDP models cannot reproduce recent triplet and quadruplet experiments. Here, we examine a triplet rule (i.e., a rule which considers sets of three spikes, i.e., two pre and one post or one pre and two post) and compare it to classical pair-based STDP learning rules. With such a triplet rule, it is possible to fit experimental data from visual cortical slices as well as from hippocampal cultures. Moreover, when assuming stochastic spike trains, the triplet learning rule can be mapped to a Bienenstock-Cooper-Munro learning rule.

A model of STDP based on spatially and temporally local information: Derivation and combination with gated decay

Temporal relationships between neuronal firing and plasticity have received significant attention in recent decades. Neurophysiological studies have shown the phenomenon of spike-timing-dependent plasticity (STDP). Various models were suggested to implement an STDP-like learning rule in artificial networks based on spiking neuronal representations. The rule presented here was developed under three constraints. First, it only depends on the information that is available at the synapse at the time of synaptic modification. Second, it naturally follows from neurophysiological and psychological research starting with Hebb's postulate [D. Hebb. (1949). The organization of behavior. Wiley, New York]. Third, it is simple, computationally cheap and its parameters are straightforward to determine. This rule is further extended by addition of four different types of gating derived from conventionally used types of gated decay in learning rules for continuous firing rate neural networks. The results show that the advantages of using these gatings are transferred to the new rule without sacrificing its dependency on spike-timing.

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.

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.

A model of spike-timing dependent plasticity: one or two coincidence detectors?

In spike-timing dependent plasticity (STDP), synapses exhibit LTD or LTP depending on the order of activity in the presynaptic and postsynaptic cells. LTP occurs when a single presynaptic spike precedes a postsynaptic one (a positive interspike interval, or ISI), while the reverse order of activity (a negative ISI) produces LTD. A fundamental question is whether the "standard model" of plasticity in which moderate increases in Ca(2+) influx through the N-methyl-D-aspartate (NMDA) channels induce LTD and large increases induce LTP, can account for the order and interval sensitivity of STDP. To examine this issue we developed a model that captures postsynaptic Ca(2+) influx dynamics and the associativity of the NMDA receptors. While this model can generate both LTD and LTP, it predicts that LTD will be observed at both negative and positive ISIs. This is because longer and longer positive ISIs induce monotonically decreasing levels of Ca(2+), which eventually fall into the same range that produced LTD at negative ISIs. A second model that incorporated a second coincidence detector in addition to the NMDA receptor generated LTP at positive intervals and LTD only at negative ones. Our findings suggest that a single coincidence detector model based on the standard model of plasticity cannot account for order-specific STDP, and we predict that STDP requires two coincidence detectors.