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

Neurons show plasticity in neuronal and synaptic properties due to development and/or learning, affecting both the input levels to the neuron as well as the neural excitability. However, neurons have a limited dynamic range, i.e. the range over which they are sensitive to the input and are not in either a quiescent or a saturated activity state. This suggests neurons possess control mechanisms that match neural excitability and synaptic input levels. Recent experimental studies suggest that neurons indeed show a homeostatic scaling of excitability (HSE) by sensing activity levels and adapting the neural excitability via regulation of specific membrane conductance densities. The maintenance of sensitivity to synaptic input is also central to learning processes. In one form of learning it has been demonstrated that synaptic modification depends on the exact timing of presynaptic inputs and postsynaptic spikes. The performance of this spike timing dependent plasticity (STDP) is expected to be affected by a decrease in the sensitivity of the neuron to its input. At the one hand this suggests an important role for HSE in the functioning of STDP, at the other hand it leads to the question whether HSE could interfere with the learning of input patterns via STDP. Here, we address these issues by using both mathematical analysis and numerical simulations of a neuron that shows HSE and that receives input from synapses showing STDP. Based on experimental results, HSE is implemented as activity-dependent shifts of the input-output function. We use the multiplicative formulation of STDP in which the changes in synaptic strength depend on the synaptic strength itself. We show that while background input levels vary greatly, HSE keeps the neuron within its dynamic range and does not affect the synaptic weight distribution. HSE can also easily compensate for variations in the shape of the STDP learning window and maintain the sensitivity to correlations in the input. However, in neurons without HSE, the sensitivity to correlations in the input depends strongly on the various parameters. The effects of HSE are further explored by examining the neuron response to input patterns. We show that when neural excitability is controlled by HSE, STDP leads to changes of the synaptic weights as a function of the properties of the input pattern, i.e. the number of inputs forming the pattern and the strength of the correlation within the pattern. Learning of a pattern increases the probability of it generating a postsynaptic spike, depending on the properties of the pattern. HSE makes the effect of learning input patterns almost independent of the background levels. The results suggest HSE does not interfere with STDP and that HSE has a central role in maintaining the learning capabilities of the neuron in its highly plastic environment.

A fascinating property of the brain is its ability to continuously evolve and adapt to a constantly changing environment. This ability to change over time, called plasticity, is mainly implemented at the level of the connections between neurons (i.e. the synapses). So if we want to understand the ability of the brain to evolve and to store new memories, it is necessary to study the rules that govern synaptic plasticity. Among the large variety of factors which influence synaptic plasticity, we focus our study on the dependence upon the precise timing of the pre- and postsynaptic spikes. This form of plasticity, called Spike-Timing-Dependent Plasticity (STDP), works as follows: if a presynaptic spike is elicited before a postsynaptic one, the synapse is up-regulated (or potentiated) whereas if the opposite occurs, the synapse is down-regulated (or depressed). In this thesis, we propose several models of STDP which address the two following questions: (1) what is the functional role of a synapse which elicits STDP and (2) what is the most compact and accurate description of STDP? In the first two papers contained in this thesis, we show that in a supervised scenario, the best learning rule which enhances the precision of the postsynaptic spikes is consistent with STDP. In the three following papers, we show that the information transmission between the input and output spike trains is maximized if synaptic plasticity is governed by a rule similar to STDP. Moreover, we show that this infomax principle added to an homeostatic constraint leads to the well-known Bienenstock-Cooper-Munro (BCM) learning rule. Finally, in the last two papers, we propose a phenomenological model of STDP which considers not only pairs of pre- and postsynaptic spikes, but also triplets of spikes (e.g. 1 pre and 2 post or 1 post and 2 pre). This model can reproduce of lot of experimental results and can be mapped to the BCM learning rule.

How do sensory systems optimize detection of behaviorally relevant stimuli when the sensory environment is constantly changing? We addressed the role of spike timing-dependent plasticity (STDP) in driving changes in synaptic strength in a sensory pathway and whether those changes in synaptic strength could alter sensory tuning. It is challenging to precisely control temporal patterns of synaptic activity in vivo and replicate those patterns in vitro in behaviorally relevant ways. This makes it difficult to make connections between STDP-induced changes in synaptic physiology and plasticity in sensory systems. Using the mormyrid species Brevimyrus niger and Brienomyrus brachyistius, which produce electric organ discharges for electrolocation and communication, we can precisely control the timing of synaptic input in vivo and replicate these same temporal patterns of synaptic input in vitro. In central electrosensory neurons in the electric communication pathway, using whole cell intracellular recordings in vitro, we paired presynaptic input with postsynaptic spiking at different delays. Using whole cell intracellular recordings in awake, behaving fish, we paired sensory stimulation with postsynaptic spiking using the same delays. We found that Hebbian STDP predictably alters sensory tuning in vitro and is mediated by NMDA receptors. However, the change in synaptic responses induced by sensory stimulation in vivo did not adhere to the direction predicted by the STDP observed in vitro. Further analysis suggests that this difference is influenced by polysynaptic activity, including inhibitory interneurons. Our findings suggest that STDP rules operating at identified synapses may not drive predictable changes in sensory responses at the circuit level.NEW & NOTEWORTHY We replicated behaviorally relevant temporal patterns of synaptic activity in vitro and used the same patterns during sensory stimulation in vivo. There was a Hebbian spike timing-dependent plasticity (STDP) pattern in vitro, but sensory responses in vivo did not shift according to STDP predictions. Analysis suggests that this disparity is influenced by differences in polysynaptic activity, including inhibitory interneurons. These results suggest that STDP rules at synapses in vitro do not necessarily apply to circuits in vivo.

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.

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.

Spike-Timing-Dependent Plasticity (STDP)

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.

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

Stochastic models of synaptic plasticity must confront the corrosive influence of fluctuations in synaptic strength on patterns of synaptic connectivity. To solve this problem, we have proposed that synapses act as filters, integrating plasticity induction signals and expressing changes in synaptic strength only upon reaching filter threshold. Our earlier analytical study calculated the lifetimes of quasi-stable patterns of synaptic connectivity with synaptic filtering. We showed that the plasticity step size in a stochastic model of spike-timing-dependent plasticity (STDP) acts as a temperature-like parameter, exhibiting a critical value below which neuronal structure formation occurs. The filter threshold scales this temperature-like parameter downwards, cooling the dynamics and enhancing stability. A key step in this calculation was a resetting approximation, essentially reducing the dynamics to one-dimensional processes. Here, we revisit our earlier study to examine this resetting approximation, with the aim of understanding in detail why it works so well by comparing it, and a simpler approximation, to the system’s full dynamics consisting of various embedded two-dimensional processes without resetting. Comparing the full system to the simpler approximation, to our original resetting approximation, and to a one-afferent system, we show that their equilibrium distributions of synaptic strengths and critical plasticity step sizes are all qualitatively similar, and increasingly quantitatively similar as the filter threshold increases. This increasing similarity is due to the decorrelation in changes in synaptic strength between different afferents caused by our STDP model, and the amplification of this decorrelation with larger synaptic filters.

Spike-timing dependent plasticity (STDP) is a form of synaptic modification, which depends on relative timings of presynaptic and postsynaptic spikes. In this paper, a novel calcium-based simple STDP model is presented, where the model is described by an ordinary differential equation having only two state variables: one represents intracellular calcium density and the other represents fraction of open state NMDARs. It is shown that, in spite of the simplicity of the model, it can reproduce STDP characteristics that are experimentally observed in various brain areas (e.g., layer 2/3, 5 visual cortical slices and hippocampal cultures) with respect to various patterns of presynaptic and postsynaptic spikes. In addition, comparisons to other STDP models are given, and advantages and significances of the presented model are clarified.

Various mathematical models have been formulated to describe the changes in synaptic strengths resulting from spike-timing-dependent plasticity (STDP). A subset of these models include a third factor, dopamine, which interacts with spike timing to contribute to plasticity at specific synapses, notably those from cortex to striatum at the input layer of the basal ganglia. Theoretical work to analyze these plasticity models has largely focused on abstract issues, such as the conditions under which they may promote synchronization and the weight distributions induced by inputs with simple correlation structures, rather than on scenarios associated with specific tasks, and has generally not considered dopamine-dependent forms of STDP. In this paper we introduce forms of dopamine-modulated STDP adapted from previously proposed plasticity rules. We then analyze, mathematically and with simulations, their performance in two biologically relevant scenarios. We test the ability of each of the three models to complete simple value estimation and action selection tasks, studying the learned weight distributions and corresponding task performance in each setting. Interestingly, we find that each plasticity rule is well suited to a subset of the scenarios studied but falls short in others. Different tasks may therefore require different forms of synaptic plasticity, yielding the prediction that the precise form of the STDP mechanism present may vary across regions of the striatum, and other brain areas impacted by dopamine, that are involved in distinct computational functions.

Various mathematical models have been formulated to describe the changes in synaptic strengths resulting from spike-timing-dependent plasticity (STDP). A subset of these models include a third factor, dopamine, which interacts with spike timing to contribute to plasticity at specific synapses, notably those from cortex to striatum at the input layer of the basal ganglia. Theoretical work to analyze these plasticity models has largely focused on abstract issues, such as the conditions under which they may promote synchronization and the weight distributions induced by inputs with simple correlation structures, rather than on scenarios associated with specific tasks, and has generally not considered dopamine-dependent forms of STDP. In this paper we introduce forms of dopamine-modulated STDP adapted from previously proposed plasticity rules. We then analyze, mathematically and with simulations, their performance in two biologically relevant scenarios. We test the ability of each of the three models to complete simple value estimation and action selection tasks, studying the learned weight distributions and corresponding task performance in each setting. Interestingly, we find that each plasticity rule is well suited to a subset of the scenarios studied but falls short in others. Different tasks may therefore require different forms of synaptic plasticity, yielding the prediction that the precise form of the STDP mechanism present may vary across regions of the striatum, and other brain areas impacted by dopamine, that are involved in distinct computational functions.

Various mathematical models have been formulated to describe the changes in synaptic strengths resulting from spike-timing-dependent plasticity (STDP). A subset of these models include a third factor, dopamine, which interacts with spike timing to contribute to plasticity at specific synapses, notably those from cortex to striatum at the input layer of the basal ganglia. Theoretical work to analyze these plasticity models has largely focused on abstract issues, such as the conditions under which they may promote synchronization and the weight distributions induced by inputs with simple correlation structures, rather than on scenarios associated with specific tasks, and has generally not considered dopamine-dependent forms of STDP. In this paper we introduce forms of dopamine-modulated STDP adapted from previously proposed plasticity rules. We then analyze, mathematically and with simulations, their performance in two biologically relevant scenarios. We test the ability of each of the three models to complete simple value estimation and action selection tasks, studying the learned weight distributions and corresponding task performance in each setting. Interestingly, we find that each plasticity rule is well suited to a subset of the scenarios studied but falls short in others. Different tasks may therefore require different forms of synaptic plasticity, yielding the prediction that the precise form of the STDP mechanism present may vary across regions of the striatum, and other brain areas impacted by dopamine, that are involved in distinct computational functions.

Spike timing is an important factor in the modification of synaptic strength. Various forms of spike timing-dependent plasticity (STDP) occur in the brains of diverse species, from insects to humans. In unimodal STDP, only LTP or LTD occurs at the synapse, regardless of which neuron spikes first; the magnitude of potentiation or depression increases as the time between presynaptic and postsynaptic spikes decreases. This from of STDP may promote developmental strengthening or weakening of early projections. In bidirectional Hebbian STDP, the magnitude and the sign (potentiation or depression) of plasticity depend, respectively, on the timing and the order of presynaptic and postsynaptic spikes. In the rodent barrel cortex, multiple forms of STDP appear sequentially during development, and they contribute to network formation, retraction, or fine-scale functional reorganization. Hebbian STDP appears at L4-L2/3 synapses starting at postnatal day (P) 15; the synapses exhibit unimodal "all-LTP STDP" before that age. The appearance of Hebbian STDP at L4-L2/3 synapses coincides with the maturation of parvalbumin-containing GABA interneurons in L4, which contributes to the generation of L4-before-L2/3 spiking in response to thalamic input by producing fast feedforward suppression of both L4 and L2/3 cells. After P15, L4-L2/3 STDP mediates fine-scale circuit refinement, essential for the critical period in the barrel cortex. In this review, we first briefly describe the relevance of STDP to map plasticity in the barrel cortex, then look over roles of distinct forms of STDP during development. Finally, we propose a hypothesis that explains the transition from network formation to the initiation of the critical period in the barrel cortex.

The idea that synaptic plasticity holds the key to the neural basis of learning and memory is now widely accepted in neuroscience. The precise mechanism of changes in synaptic strength has, however, remained elusive. Neurobiological research has led to the postulation of many models of plasticity, and among the most contemporary are spike-timing dependent plasticity (STDP) and long-term potentiation (LTP). The STDP model is based on the observation of single, distinct pairs of pre- and post- synaptic spikes, but it is less clear how it evolves dynamically under the input of long trains of spikes, which characterise normal brain activity. This research explores the emergent properties of a spiking artificial neural network which incorporates both STDP and LTP. Previous findings are replicated in most instances, and some interesting additional observations are made. These highlight the profound influence which initial conditions and synaptic input have on the evolution of synaptic weights.KeywordsFiring RateSpike TrainPlasticity ModelSynaptic WeightSynaptic StrengthThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.