Dissection of Bidirectional Synaptic Plasticity Into Saturable Unidirectional Processes

Stability against fluctuations: a two-dimensional study of scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity

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.

Nonlinear slow-timescale mechanisms in synaptic plasticity

Learning and memory rely on synapses changing their strengths in response to neural activity. However, there is a substantial gap between the timescales of neural electrical dynamics (1-100 ms) and organism behaviour during learning (seconds-minutes). What mechanisms bridge this timescale gap? What are the implications for theories of brain learning? Here I first cover experimental evidence for slow-timescale factors in plasticity induction. Then I review possible underlying cellular and synaptic mechanisms, and insights from recent computational models that incorporate such slow-timescale variables. I conclude that future progress in understanding brain learning across timescales will require both experimental and computational modelling studies that map out the nonlinearities implemented by both fast and slow plasticity mechanisms at synapses, and crucially, their joint interactions.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Asymmetric Voltage Attenuation in Dendrites Can Enable Hierarchical Heterosynaptic Plasticity

Long-term synaptic plasticity is mediated via cytosolic calcium concentrations ([Ca2+]). Using a synaptic model that implements calcium-based long-term plasticity via two sources of Ca2+ - NMDA receptors and voltage-gated calcium channels (VGCCs) - we show in dendritic cable simulations that the interplay between these two calcium sources can result in a diverse array of heterosynaptic effects. When spatially clustered synaptic input produces a local NMDA spike, the resulting dendritic depolarization can activate VGCCs at nonactivated spines, resulting in heterosynaptic plasticity. NMDA spike activation at a given dendritic location will tend to depolarize dendritic regions that are located distally to the input site more than dendritic sites that are proximal to it. This asymmetry can produce a hierarchical effect in branching dendrites, where an NMDA spike at a proximal branch can induce heterosynaptic plasticity primarily at branches that are distal to it. We also explored how simultaneously activated synaptic clusters located at different dendritic locations synergistically affect the plasticity at the active synapses, as well as the heterosynaptic plasticity of an inactive synapse "sandwiched" between them. We conclude that the inherent electrical asymmetry of dendritic trees enables sophisticated schemes for spatially targeted supervision of heterosynaptic plasticity.

The Impact of Sparse Coding on Memory Lifetimes in Simple and Complex Models of Synaptic Plasticity

Models of associative memory with discrete state synapses learn new memories by forgetting old ones. In the simplest models, memories are forgotten exponentially quickly. Sparse population coding ameliorates this problem, as do complex models of synaptic plasticity that posit internal synaptic states, giving rise to synaptic metaplasticity. We examine memory lifetimes in both simple and complex models of synaptic plasticity with sparse coding. We consider our own integrative, filter-based model of synaptic plasticity, and examine the cascade and serial synapse models for comparison. We explore memory lifetimes at both the single-neuron and the population level, allowing for spontaneous activity. Memory lifetimes are defined using either a signal-to-noise ratio (SNR) approach or a first passage time (FPT) method, although we use the latter only for simple models at the single-neuron level. All studied models exhibit a decrease in the optimal single-neuron SNR memory lifetime, optimised with respect to sparseness, as the probability of synaptic updates decreases or, equivalently, as synaptic complexity increases. This holds regardless of spontaneous activity levels. In contrast, at the population level, even a low but nonzero level of spontaneous activity is critical in facilitating an increase in optimal SNR memory lifetimes with increasing synaptic complexity, but only in filter and serial models. However, SNR memory lifetimes are valid only in an asymptotic regime in which a mean field approximation is valid. By considering FPT memory lifetimes, we find that this asymptotic regime is not satisfied for very sparse coding, violating the conditions for the optimisation of single-perceptron SNR memory lifetimes with respect to sparseness. Similar violations are also expected for complex models of synaptic plasticity.

Model of theta frequency perturbations and contextual fear memory

Theta oscillations in the hippocampal local field potential (LFP) appear during translational movement and arousal, modulate the activity of principal cells, and are associated with spatial cognition and episodic memory function. All known anxiolytics slightly but consistently reduce hippocampal theta frequency. However, whether this electrophysiological effect is mechanistically related to the decreased behavioral expression of anxiety is currently unclear. Here, we propose that a reduction in theta frequency affects synaptic plasticity and mnemonic function and that this can explain the reduction in anxiety behavior. We test this hypothesis in a biophysical model of contextual fear conditioning. First, we confirm that our model reproduces previous empirical results regarding the dependence of synaptic plasticity on presynaptic firing rate. Next, we investigate how theta frequency during contextual conditioning impacts learning. These simulations demonstrate that learned associations between threat and context are attenuated when learning takes place under reduced theta frequency. Additionally, our simulations demonstrate that learned associations result in increased theta activity in the amygdala, consistent with empirical data. In summary, we propose a mechanism that can account for the behavioral effect of anxiolytics by impairing the integration of threat attributes of an environment into the cognitive map due to reduced synaptic potentiation.

Memory consolidation and improvement by synaptic tagging and capture in recurrent neural networks

The synaptic-tagging-and-capture (STC) hypothesis formulates that at each synapse the concurrence of a tag with protein synthesis yields the maintenance of changes induced by synaptic plasticity. This hypothesis provides a biological principle underlying the synaptic consolidation of memories that is not verified for recurrent neural circuits. We developed a theoretical model integrating the mechanisms underlying the STC hypothesis with calcium-based synaptic plasticity in a recurrent spiking neural network. In the model, calcium-based synaptic plasticity yields the formation of strongly interconnected cell assemblies encoding memories, followed by consolidation through the STC mechanisms. Furthermore, we show for the first time that STC mechanisms modify the storage of memories such that after several hours memory recall is significantly improved. We identify two contributing processes: a merely time-dependent passive improvement, and an active improvement during recall. The described characteristics can provide a new principle for storing information in biological and artificial neural circuits.

Dendritic Voltage Recordings Explain Paradoxical Synaptic Plasticity: A Modeling Study

Experiments have shown that the same stimulation pattern that causes Long-Term Potentiation in proximal synapses, will induce Long-Term Depression in distal ones. In order to understand these, and other, surprising observations we use a phenomenological model of Hebbian plasticity at the location of the synapse. Our model describes the Hebbian condition of joint activity of pre- and postsynaptic neurons in a compact form as the interaction of the glutamate trace left by a presynaptic spike with the time course of the postsynaptic voltage. Instead of simulating the voltage, we test the model using experimentally recorded dendritic voltage traces in hippocampus and neocortex. We find that the time course of the voltage in the neighborhood of a stimulated synapse is a reliable predictor of whether a stimulated synapse undergoes potentiation, depression, or no change. Our computational model can explain the existence of different -at first glance seemingly paradoxical- outcomes of synaptic potentiation and depression experiments depending on the dendritic location of the synapse and the frequency or timing of the stimulation.

Short-term depression and long-term plasticity together tune sensitive range of synaptic plasticity

Synaptic efficacy is subjected to activity-dependent changes on short- and long time scales. While short-term changes decay over minutes, long-term modifications last from hours up to a lifetime and are thought to constitute the basis of learning and memory. Both plasticity mechanisms have been studied extensively but how their interaction shapes synaptic dynamics is little known. To investigate how both short- and long-term plasticity together control the induction of synaptic depression and potentiation, we used numerical simulations and mathematical analysis of a calcium-based model, where pre- and postsynaptic activity induces calcium transients driving synaptic long-term plasticity. We found that the model implementing known synaptic short-term dynamics in the calcium transients can be successfully fitted to long-term plasticity data obtained in visual- and somatosensory cortex. Interestingly, the impact of spike-timing and firing rate changes on plasticity occurs in the prevalent firing rate range, which is different in both cortical areas considered here. Our findings suggest that short- and long-term plasticity are together tuned to adapt plasticity to area-specific activity statistics such as firing rates.

Synaptic long-term plasticity, the long-lasting change in efficacy of connections between neurons, is believed to underlie learning and memory. Synapses furthermore change their efficacy reversibly in an activity-dependent manner on the subsecond time scale, referred to as short-term plasticity. It is not known how both synaptic plasticity mechanisms—long- and short-term—interact during activity epochs. To address this question, we used a biologically-inspired plasticity model in which calcium drives changes in synaptic efficacy. We applied the model to plasticity data from visual- and somatosensory cortex and found that synaptic changes occur in very different firing rate ranges, which correspond to the prevalent firing rates in both structures. Our results suggest that short- and long-term plasticity act in a well concerted fashion.

Mechanisms Underlying Long-Term Synaptic Zinc Plasticity at Mouse Dorsal Cochlear Nucleus Glutamatergic Synapses

In many brain areas, such as the neocortex, limbic structures, and auditory brainstem, synaptic zinc is released from presynaptic terminals to modulate neurotransmission. As such, synaptic zinc signaling modulates sensory processing and enhances acuity for discrimination of different sensory stimuli. Whereas sensory experience causes long-term changes in synaptic zinc signaling, the mechanisms underlying this long-term synaptic zinc plasticity remain unknown. To study these mechanisms in male and female mice, we used in vitro and in vivo models of zinc plasticity observed at the zinc-rich glutamatergic dorsal cochlear nucleus (DCN) parallel fiber synapses onto cartwheel cells. High-frequency stimulation of DCN parallel fiber synapses induced LTD of synaptic zinc signaling (Z-LTD), evidenced by reduced zinc-mediated inhibition of EPSCs. Low-frequency stimulation induced LTP of synaptic zinc signaling (Z-LTP), evidenced by enhanced zinc-mediated inhibition of EPSCs. Pharmacological manipulations of Group 1 metabotropic glutamate receptors (G1 mGluRs) demonstrated that G1 mGluR activation is necessary and sufficient for inducing Z-LTD and Z-LTP. Pharmacological manipulations of Ca²⁺ dynamics indicated that rises in postsynaptic Ca²⁺ are necessary and sufficient for Z-LTD induction. Electrophysiological measurements assessing postsynaptic expression mechanisms, and imaging studies with a ratiometric extracellular zinc sensor probing zinc release, supported that Z-LTD is expressed, at least in part, via reductions in presynaptic zinc release. Finally, exposure of mice to loud sound caused G1 mGluR-dependent Z-LTD at DCN parallel fiber synapses, thus validating our in vitro results. Together, our results reveal a novel mechanism underlying activity- and experience-dependent plasticity of synaptic zinc signaling.SIGNIFICANCE STATEMENT In the neocortex, limbic structures, and auditory brainstem, glutamatergic nerve terminals corelease zinc to modulate excitatory neurotransmission and sensory responses. Moreover, sensory experience causes bidirectional, long-term changes in synaptic zinc signaling. However, the mechanisms of this long-term synaptic zinc plasticity remain unknown. Here, we identified a novel Group 1 mGluR-dependent mechanism that causes bidirectional, long-term changes in synaptic zinc signaling. Our results highlight new mechanisms of brain adaptation during sensory processing, and potentially point to mechanisms of disorders associated with pathologic adaptation, such as tinnitus.

First Passage Time Memory Lifetimes for Simple, Multistate Synapses: Beyond the Eigenvector Requirement

Models of associative memory with discrete-strength synapses are palimpsests, learning new memories by forgetting old ones. Memory lifetimes can be defined by the mean first passage time (MFPT) for a perceptron's activation to fall below firing threshold. By imposing the condition that the vector of possible strengths available to a synapse is a left eigenvector of the stochastic matrix governing transitions in strength, we previously derived results for MFPTs and first passage time (FPT) distributions in models with simple, multistate synapses. This condition permits jump moments to be computed via a 1-dimensional Fokker-Planck approach. Here, we study memory lifetimes in the absence of this condition. To do so, we must introduce additional variables, including the perceptron activation, that parameterize synaptic configurations, permitting Markovian dynamics in these variables to be formulated. FPT problems in these variables require solving multidimensional partial differential or integral equations. However, the FPT dynamics can be analytically well approximated by focusing on the slowest eigenmode in this higher-dimensional space. We may also obtain a much better approximation by restricting to the two dominant variables in this space, the restriction making numerical methods tractable. Analytical and numerical methods are in excellent agreement with simulation data, validating our methods. These methods prepare the ground for the study of FPT memory lifetimes with complex rather than simple, multistate synapses.

Gradation (approx. 10 size states) of synaptic strength by quantal addition of structural modules

Memory storage involves activity-dependent strengthening of synaptic transmission, a process termed long-term potentiation (LTP). The late phase of LTP is thought to encode long-term memory and involves structural processes that enlarge the synapse. Hence, understanding how synapse size is graded provides fundamental information about the information storage capability of synapses. Recent work using electron microscopy (EM) to quantify synapse dimensions has suggested that synapses may structurally encode as many as 26 functionally distinct states, which correspond to a series of proportionally spaced synapse sizes. Other recent evidence using super-resolution microscopy has revealed that synapses are composed of stereotyped nanoclusters of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors and scaffolding proteins; furthermore, synapse size varies linearly with the number of nanoclusters. Here we have sought to develop a model of synapse structure and growth that is consistent with both the EM and super-resolution data. We argue that synapses are composed of modules consisting of matrix material and potentially one nanocluster. LTP induction can add a trans-synaptic nanocluster to a module, thereby converting a silent module to an AMPA functional module. LTP can also add modules by a linear process, thereby producing an approximately 10-fold gradation in synapse size and strength.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity'.

Mean First Passage Memory Lifetimes by Reducing Complex Synapses to Simple Synapses

Memory models that store new memories by forgetting old ones have memory lifetimes that are rather short and grow only logarithmically in the number of synapses. Attempts to overcome these deficits include "complex" models of synaptic plasticity in which synapses possess internal states governing the expression of synaptic plasticity. Integrate-and-express, filter-based models of synaptic plasticity propose that synapses act as low-pass filters, integrating plasticity induction signals before expressing synaptic plasticity. Such mechanisms enhance memory lifetimes, leading to an initial rise in the memory signal that is in radical contrast to other related, but nonintegrative, memory models. Because of the complexity of models with internal synaptic states, however, their dynamics can be more difficult to extract compared to "simple" models that lack internal states. Here, we show that by focusing only on processes that lead to changes in synaptic strength, we can integrate out internal synaptic states and effectively reduce complex synapses to simple synapses. For binary-strength synapses, these simplified dynamics then allow us to work directly in the transitions in perceptron activation induced by memory storage rather than in the underlying transitions in synaptic configurations. This permits us to write down master and Fokker-Planck equations that may be simplified under certain, well-defined approximations. These methods allow us to see that memory based on synaptic filters can be viewed as an initial transient that leads to memory signal rise, followed by the emergence of Ornstein-Uhlenbeck-like dynamics that return the system to equilibrium. We may use this approach to compute mean first passage time-defined memory lifetimes for complex models of memory storage.

The Enhanced Rise and Delayed Fall of Memory in a Model of Synaptic Integration: Extension to Discrete State Synapses

Integrate-and-express models of synaptic plasticity propose that synapses may act as low-pass filters, integrating synaptic plasticity induction signals in order to discern trends before expressing synaptic plasticity. We have previously shown that synaptic filtering strongly controls destabilizing fluctuations in developmental models. When applied to palimpsest memory systems that learn new memories by forgetting old ones, we have also shown that with binary-strength synapses, integrative synapses lead to an initial memory signal rise before its fall back to equilibrium. Such an initial rise is in dramatic contrast to nonintegrative synapses, in which the memory signal falls monotonically. We now extend our earlier analysis of palimpsest memories with synaptic filters to consider the more general case of discrete state, multilevel synapses. We derive exact results for the memory signal dynamics and then consider various simplifying approximations. We show that multilevel synapses enhance the initial rise in the memory signal and then delay its subsequent fall by inducing a plateau-like region in the memory signal. Such dynamics significantly increase memory lifetimes, defined by a signal-to-noise ratio (SNR). We derive expressions for optimal choices of synaptic parameters (filter size, number of strength states, number of synapses) that maximize SNR memory lifetimes. However, we find that with memory lifetimes defined via mean-first-passage times, such optimality conditions do not exist, suggesting that optimality may be an artifact of SNRs.

A nonlinear cable framework for bidirectional synaptic plasticity

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

Memory nearly on a spring: a mean first passage time approach to memory lifetimes

We study memory lifetimes in a perceptron-based framework with binary synapses, using the mean first passage time for the perceptron's total input to fall below firing threshold to define memory lifetimes. Working with the simplest memory-related model of synaptic plasticity, we may obtain exact results for memory lifetimes or, working in the continuum limit, good analytical approximations that afford either much qualitative insight or extremely good quantitative agreement. In one particular limit, we find that memory dynamics reduce to the well-understood Ornstein-Uhlenbeck process. We show that asymptotically, the lifetimes of memories grow logarithmically in the number of synapses when the perceptron's firing threshold is zero, reproducing standard results from signal-to-noise ratio analyses. However, this is only an asymptotically valid result, and we show that extending its application outside the range of its validity leads to a massive overestimate of the minimum number of synapses required for successful memory encoding. In the case that the perceptron's firing threshold is positive, we find the remarkable result that memory lifetimes are strictly bounded from above. Asymptotically, the dependence of memory lifetimes on the number of synapses drops out entirely, and this asymptotic result provides a strict upper bound on memory lifetimes away from this asymptotic regime. The classic logarithmic growth of memory lifetimes in the simplest, palimpsest memories is therefore untypical and nongeneric: memory lifetimes are typically strictly bounded from above.

MHC class I immune proteins are critical for hippocampus-dependent memory and gate NMDAR-dependent hippocampal long-term depression

Memory impairment is a common feature of conditions that involve changes in inflammatory signaling in the brain, including traumatic brain injury, infection, neurodegenerative disorders, and normal aging. However, the causal importance of inflammatory mediators in cognitive impairments in these conditions remains unclear. Here we show that specific immune proteins, members of the major histocompatibility complex class I (MHC class I), are essential for normal hippocampus-dependent memory, and are specifically required for NMDAR-dependent forms of long-term depression (LTD) in the healthy adult hippocampus. In β2m^−/−TAP^−/−mice, which lack stable cell-surface expression of most MHC class I proteins, NMDAR-dependent LTD in area CA1 of adult hippocampus is abolished, while NMDAR-independent forms of potentiation, facilitation, and depression are unaffected. Altered NMDAR-dependent synaptic plasticity in the hippocampus of β2m^−/−TAP^−/−mice is accompanied by pervasive deficits in hippocampus-dependent memory, including contextual fear memory, object recognition memory, and social recognition memory. Thus normal MHC class I expression is essential for NMDAR-dependent hippocampal synaptic depression and hippocampus-dependent memory. These results suggest that changes in MHC class I expression could be an unexpected cause of disrupted synaptic plasticity and cognitive deficits in the aging, damaged, and diseased brain.

The emergence of functional microcircuits in visual cortex

Sensory processing occurs in neocortical microcircuits in which synaptic connectivity is highly structured and excitatory neurons form subnetworks that process related sensory information. However, the developmental mechanisms underlying the formation of functionally organized connectivity in cortical microcircuits remain unknown. Here we directly relate patterns of excitatory synaptic connectivity to visual response properties of neighbouring layer 2/3 pyramidal neurons in mouse visual cortex at different postnatal ages, using two-photon calcium imaging in vivo and multiple whole-cell recordings in vitro. Although neural responses were already highly selective for visual stimuli at eye opening, neurons responding to similar visual features were not yet preferentially connected, indicating that the emergence of feature selectivity does not depend on the precise arrangement of local synaptic connections. After eye opening, local connectivity reorganized extensively: more connections formed selectively between neurons with similar visual responses and connections were eliminated between visually unresponsive neurons, but the overall connectivity rate did not change. We propose a sequential model of cortical microcircuit development based on activity-dependent mechanisms of plasticity whereby neurons first acquire feature preference by selecting feedforward inputs before the onset of sensory experience--a process that may be facilitated by early electrical coupling between neuronal subsets--and then patterned input drives the formation of functional subnetworks through a redistribution of recurrent synaptic connections.

On the dynamics of cortical development: synchrony and synaptic self-organization

We describe a model for cortical development that resolves long-standing difficulties of earlier models. It is proposed that, during embryonic development, synchronous firing of neurons and their competition for limited metabolic resources leads to selection of an array of neurons with ultra-small-world characteristics. Consequently, in the visual cortex, macrocolumns linked by superficial patchy connections emerge in anatomically realistic patterns, with an ante-natal arrangement which projects signals from the surrounding cortex onto each macrocolumn in a form analogous to the projection of a Euclidean plane onto a Möbius strip. This configuration reproduces typical cortical response maps, and simulations of signal flow explain cortical responses to moving lines as functions of stimulus velocity, length, and orientation. With the introduction of direct visual inputs, under the operation of Hebbian learning, development of mature selective response “tuning” to stimuli of given orientation, spatial frequency, and temporal frequency would then take place, overwriting the earlier ante-natal configuration. The model is provisionally extended to hierarchical interactions of the visual cortex with higher centers, and a general principle for cortical processing of spatio-temporal images is sketched.

The Rise and Fall of Memory in a Model of Synaptic Integration

Plasticity-inducing stimuli must typically be presented many times before synaptic plasticity is expressed, perhaps because induction signals gradually accumulate before overt strength changes occur. We consider memory dynamics in a mathematical model with synapses that integrate plasticity induction signals before expressing plasticity. We find that the memory trace initially rises before reaching a maximum and then falling. The memory signal dissociates into separate oblivescence and reminiscence components, with reminiscence initially dominating recall. In radical contrast, related but nonintegrative models exhibit only a highly problematic oblivescence. Synaptic integration mechanisms possess natural timescales, depending on the statistics of the induction signals. Together with neuromodulation, these timescales may therefore also begin to provide a natural account of the well-known spacing effect in the transition to late-phase plasticity. Finally, we propose experiments that could distinguish between integrative and nonintegrative synapses. Such experiments should further elucidate the synaptic signal processing mechanisms postulated by our model.

Calcium input frequency, duration and amplitude differentially modulate the relative activation of calcineurin and CaMKII

NMDA receptor dependent long-term potentiation (LTP) and long-term depression (LTD) are two prominent forms of synaptic plasticity, both of which are triggered by post-synaptic calcium elevation. To understand how calcium selectively stimulates two opposing processes, we developed a detailed computational model and performed simulations with different calcium input frequencies, amplitudes, and durations. We show that with a total amount of calcium ions kept constant, high frequencies of calcium pulses stimulate calmodulin more efficiently. Calcium input activates both calcineurin and Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) at all frequencies, but increased frequencies shift the relative activation from calcineurin to CaMKII. Irrespective of amplitude and duration of the inputs, the total amount of calcium ions injected adjusts the sensitivity of the system to calcium input frequencies. At a given frequency, the quantity of CaMKII activated is proportional to the total amount of calcium. Thus, an input of a small amount of calcium at high frequencies can induce the same activation of CaMKII as a larger amount, at lower frequencies. Finally, the extent of activation of CaMKII signals with high calcium frequency is further controlled by other factors, including the availability of calmodulin, and by the potency of phosphatase inhibitors.

Dendritic mechanisms controlling the threshold and timing requirement of synaptic plasticity

Active conductances located and operating on neuronal dendrites are expected to regulate synaptic integration and plasticity. We investigate how Kv4.2-mediated A-type K(+) channels and Ca(2+) -activated K(+) channels are involved in the induction process of Hebbian-type plasticity that requires correlated pre- and postsynaptic activities. In CA1 pyramidal neurons, robust long-term potentiation (LTP) induced by a theta burst pairing protocol usually occurred within a narrow window during which incoming synaptic potentials coincided with postsynaptic depolarization. Elimination of dendritic A-type K(+) currents in Kv4.2(-/-) mice, however, resulted in an expanded time window, making the induction of synaptic potentiation less dependent on the temporal relation of pre- and postsynaptic activity. For the other type of synaptic plasticity, long-term depression, the threshold was significantly increased in Kv4.2(-/-) mice. This shift in depression threshold was restored to normal when the appropriate amount of internal free calcium was chelated during induction. In concert with A-type channels, Ca(2+) -activated K(+) channels also exerted a sliding effect on synaptic plasticity. Blocking these channels in Kv4.2(-/-) mice resulted in an even larger potentiation while by contrast, the depression threshold was shifted further. In conclusion, dendritic A-type and Ca(2+) -activated K(+) channels dually regulate the timing-dependence and thresholds of synaptic plasticity in an additive way.

Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location

Multiple stimulation protocols have been found to be effective in changing synaptic efficacy by inducing long-term potentiation or depression. In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. However, it is still unclear whether and how the dynamics of the postsynaptic calcium alone determine the outcome of synaptic plasticity. Here, we propose a calcium-based model of a synapse in which potentiation and depression are activated above calcium thresholds. We show that this model gives rise to a large diversity of spike timing-dependent plasticity curves, most of which have been observed experimentally in different systems. It accounts quantitatively for plasticity outcomes evoked by protocols involving patterns with variable spike timing and firing rate in hippocampus and neocortex. Furthermore, it allows us to predict that differences in plasticity outcomes in different studies are due to differences in parameters defining the calcium dynamics. The model provides a mechanistic understanding of how various stimulation protocols provoke specific synaptic changes through the dynamics of calcium concentration and thresholds implementing in simplified fashion protein signaling cascades, leading to long-term potentiation and long-term depression. The combination of biophysical realism and analytical tractability makes it the ideal candidate to study plasticity at the synapse, neuron, and network levels.

Dendritic spine dynamics regulate the long-term stability of synaptic plasticity

Long-term synaptic plasticity requires postsynaptic influx of Ca²⁺ and is accompanied by changes in dendritic spine size. Unless Ca²⁺ influx mechanisms and spine volume scale proportionally, changes in spine size will modify spine Ca²⁺ concentrations during subsequent synaptic activation. We show that the relationship between Ca²⁺ influx and spine volume is a fundamental determinant of synaptic stability. If Ca²⁺ influx is undercompensated for increases in spine size, then strong synapses are stabilized and synaptic strength distributions have a single peak. In contrast, overcompensation of Ca²⁺ influx leads to binary, persistent synaptic strengths with double-peaked distributions. Biophysical simulations predict that CA1 pyramidal neuron spines are undercompensating. This unifies experimental findings that weak synapses are more plastic than strong synapses, that synaptic strengths are unimodally distributed, and that potentiation saturates for a given stimulus strength. We conclude that structural plasticity provides a simple, local, and general mechanism that allows dendritic spines to foster both rapid memory formation and persistent memory storage.

Physiological activation of cholinergic inputs controls associative synaptic plasticity via modulation of endocannabinoid signaling

Cholinergic neuromodulation controls long-term synaptic plasticity underlying memory, learning, and adaptive sensory processing. However, the mechanistic interaction of cholinergic, neuromodulatory inputs with signaling pathways underlying long-term potentiation (LTP) and long-term depression (LTD) remains poorly understood. Here, we show that physiological activation of muscarinic acetylcholine receptors (mAChRs) controls the size and sign of associative long-term synaptic plasticity via interaction with endocannabinoid signaling. Our findings indicate that synaptic or pharmacological activation of postsynaptic M1/M3 converts postsynaptic Hebbian LTP to presynaptic anti-Hebbian LTD in principal neurons of the dorsal cochlear nucleus (DCN). This conversion is also dependent on NMDA receptor (NMDAR) activation and rises in postsynaptic Ca(2+). While NMDAR activation and Ca(2+) elevation lead to LTP, when these events are coordinated with simultaneous activation of M1/M3 mAChRs, anti-Hebbian LTD is induced. Anti-Hebbian LTD is mediated by a postsynaptic G-protein-coupled receptor intracellular signaling cascade that activates phospholipase C and that leads to enhanced endocannabinoid signaling. Moreover, the interaction between postsynaptic M1/M3 mAChRs and endocannabinoid signaling is input specific, as it occurs only in the parallel fiber inputs, but not in the auditory nerve inputs innervating the same DCN principal neurons. Based on the extensive distribution of cholinergic and endocannabinoid signaling, we suggest that their interaction may provide a general mechanism for dynamic, context-dependent modulation of associative synaptic plasticity.

The Mean Time to Express Synaptic Plasticity in Integrate-and-Express, Stochastic Models of Synaptic Plasticity Induction

Stochastic models of synaptic plasticity propose that single synapses perform a directed random walk of fixed step sizes in synaptic strength, thereby embracing the view that the mechanisms of synaptic plasticity constitute a stochastic dynamical system. However, fluctuations in synaptic strength present a formidable challenge to such an approach. We have previously proposed that single synapses must interpose an integration and filtering mechanism between the induction of synaptic plasticity and the expression of synaptic plasticity in order to control fluctuations. We analyze a class of three such mechanisms in the presence of possibly non-Markovian plasticity induction processes, deriving expressions for the mean expression time in these models. One of these filtering mechanisms constitutes a discrete low-pass filter that could be implemented on a small collection of molecules at single synapses, such as CaMKII, and we analyze this discrete filter in some detail. After considering Markov induction processes, we examine our own stochastic model of spike-timing-dependent plasticity, for which the probability density functions of the induction of plasticity steps have previously been derived. We determine the dependence of the mean time to express a plasticity step on pre- and postsynaptic firing rates in this model, and we also consider, numerically, the long-term stability against fluctuations of patterns of neuronal connectivity that typically emerge during neuronal development.

Stability against fluctuations: scaling, bifurcations, and spontaneous symmetry breaking in stochastic models of synaptic plasticity

In stochastic models of synaptic plasticity based on a random walk, the control of fluctuations is imperative. We have argued that synapses could act as low-pass filters, filtering plasticity induction steps before expressing a step change in synaptic strength. Earlier work showed, in simulation, that such a synaptic filter tames fluctuations very well, leading to patterns of synaptic connectivity that are stable for long periods of time. Here, we approach this problem analytically. We explicitly calculate the lifetime of meta-stable states of synaptic connectivity using a Fokker-Planck formalism in order to understand the dependence of this lifetime on both the plasticity step size and the filtering mechanism. We find that our analytical results agree very well with simulation results, despite having to make two approximations. Our analysis reveals, however, a deeper significance to the filtering mechanism and the plasticity step size. We show that a filter scales the step size into a smaller, effective step size. This scaling suggests that the step size may itself play the role of a temperature parameter, so that a filter cools the dynamics, thereby reducing the influence of fluctuations. Using the master equation, we explicitly demonstrate a bifurcation at a critical step size, confirming this interpretation. At this critical point, spontaneous symmetry breaking occurs in the class of stochastic models of synaptic plasticity that we consider.

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.

Mechanisms of induction and maintenance of spike-timing dependent plasticity in biophysical synapse models

We review biophysical models of synaptic plasticity, with a focus on spike-timing dependent plasticity (STDP). The common property of the discussed models is that synaptic changes depend on the dynamics of the intracellular calcium concentration, which itself depends on pre- and postsynaptic activity. We start by discussing simple models in which plasticity changes are based directly on calcium amplitude and dynamics. We then consider models in which dynamic intracellular signaling cascades form the link between the calcium dynamics and the plasticity changes. Both mechanisms of induction of STDP (through the ability of pre/postsynaptic spikes to evoke changes in the state of the synapse) and of maintenance of the evoked changes (through bistability) are discussed.

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 Non-Markovian Random Walk Underlies a Stochastic Model of Spike-Timing-Dependent Plasticity

A stochastic model of spike-timing-dependent plasticity (STDP) proposes that spike timing influences the probability but not the amplitude of synaptic strength change at single synapses. The classic, biphasic STDP profile emerges as a spatial average over many synapses presented with a single spike pair or as a temporal average over a single synapse presented with many spike pairs. We have previously shown that the model accounts for a variety of experimental data, including spike triplet results, and has a number of desirable theoretical properties, including being entirely self-stabilizing in all regions of parameter space. Our earlier analyses of the model have employed cumbersome spike-to-spike averaging arguments to derive results. Here, we show that the model can be reformulated as a non-Markovian random walk in synaptic strength, the step sizes being fixed as postulated. This change of perspective greatly simplifies earlier calculations by integrating out the proposed switch mechanism by which changes in strength are driven and instead concentrating on the changes in strength themselves. Moreover, this change of viewpoint is generative, facilitating further calculations that would be intractable, if not impossible, with earlier approaches. We prepare the machinery here for these later calculations but also briefly indicate how this machinery may be used by considering two particular applications.

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.

Discrete States of Synaptic Strength in a Stochastic Model of Spike-Timing-Dependent Plasticity

A stochastic model of spike-timing-dependent plasticity (STDP) postulates that single synapses presented with a single spike pair exhibit all-or-none quantal jumps in synaptic strength. The amplitudes of the jumps are independent of spiking timing, but their probabilities do depend on spiking timing. By making the amplitudes of both upward and downward transitions equal, synapses then occupy only a discrete set of states of synaptic strength. We explore the impact of a finite, discrete set of strength states on our model, finding three principal results. First, a finite set of strength states limits the capacity of a single synapse to express the standard, exponential STDP curve. We derive the expression for the expected change in synaptic strength in response to a standard, experimental spike pair protocol, finding a deviation from exponential behavior. We fit our prediction to recent data from single dendritic spine heads, finding results that are somewhat better than exponential fits. Second, we show that the fixed-point dynamics of our model regulate the upward and downward transition probabilities so that these are on average equal, leading to a uniform distribution of synaptic strength states. However, third, under long-term potentiation (LTP) and long-term depression (LTD) protocols, these probabilities are unequal, skewing the distribution away from uniformity. If the number of states of strength is at least of order 10, then we find that three effective states of synaptic strength appear, consistent with some experimental data on ternary-strength synapses. On this view, LTP and LTD protocols may therefore be saturating protocols.

Taming Fluctuations in a Stochastic Model of Spike-Timing-Dependent Plasticity

A stochastic model of spike-timing-dependent plasticity proposes that single synapses express fixed-amplitude jumps in strength, the amplitudes being independent of the spike time difference. However, the probability that a jump in strength occurs does depend on spike timing. Although the model has a number of desirable features, the stochasticity of response of a synapse introduces potentially large fluctuations into changes in synaptic strength. These can destabilize the segregated patterns of afferent connectivity characteristic of neuronal development. Previously we have taken these jumps to be small relative to overall synaptic strengths to control fluctuations, but doing so increases developmental timescales unacceptably. Here, we explore three alternative ways of taming fluctuations. First, a calculation of the variance for the change in synaptic strength shows that the mean change eventually dominates fluctuations, but on timescales that are too long. Second, it is possible that fluctuations in strength may cancel between synapses, but we show that correlations between synapses emasculate the law of large numbers. Finally, by separating plasticity induction and expression, we introduce a temporal window during which induction signals are low-pass-filtered before expression. In this way, fluctuations in strength are tamed, stabilizing segregated states of afferent connectivity.

Synaptic plasticity in the subiculum

The subiculum is the principal target of CA1 pyramidal cells. It functions as a mediator of hippocampal-cortical interaction and has been proposed to play an important role in the encoding and retrieval of long-term memory. The cellular mechanisms of memory formation are thought to include long-term potentiation (LTP) and depression (LTD) of synaptic strength. This review summarizes the contemporary knowledge of LTP and LTD at CA1-subiculum synapses. The observation that the underlying mechanisms of LTP and LTD at CA1-subiculum synapses correlate with the discharge properties of subicular pyramidal cell reveals a novel and intriguing mechanism of cell-specific consolidation of hippocampal output.

Are binary synapses superior to graded weight representations in stochastic attractor networks?

Synaptic plasticity is an underlying mechanism of learning and memory in neural systems, but it is controversial whether synaptic efficacy is modulated in a graded or binary manner. It has been argued that binary synaptic weights would be less susceptible to noise than graded weights, which has impelled some theoretical neuroscientists to shift from the use of graded to binary weights in their models. We compare retrieval performance of models using both binary and graded weight representations through numerical simulations of stochastic attractor networks. We also investigate stochastic attractor models using multiple discrete levels of weight states, and then investigate the optimal threshold for dilution of binary weight representations. Our results show that a binary weight representation is not less susceptible to noise than a graded weight representation in stochastic attractor models, and we find that the load capacities with an increasing number of weight states rapidly reach the load capacity with graded weights. The optimal threshold for dilution of binary weight representations under stochastic conditions occurs when approximately 50% of the smallest weights are set to zero.

Tag-trigger-consolidation: a model of early and late long-term-potentiation and depression

Changes in synaptic efficacies need to be long-lasting in order to serve as a substrate for memory. Experimentally, synaptic plasticity exhibits phases covering the induction of long-term potentiation and depression (LTP/LTD) during the early phase of synaptic plasticity, the setting of synaptic tags, a trigger process for protein synthesis, and a slow transition leading to synaptic consolidation during the late phase of synaptic plasticity. We present a mathematical model that describes these different phases of synaptic plasticity. The model explains a large body of experimental data on synaptic tagging and capture, cross-tagging, and the late phases of LTP and LTD. Moreover, the model accounts for the dependence of LTP and LTD induction on voltage and presynaptic stimulation frequency. The stabilization of potentiated synapses during the transition from early to late LTP occurs by protein synthesis dynamics that are shared by groups of synapses. The functional consequence of this shared process is that previously stabilized patterns of strong or weak synapses onto the same postsynaptic neuron are well protected against later changes induced by LTP/LTD protocols at individual synapses.

Temporal dynamics of rate-based synaptic plasticity rules in a stochastic model of spike-timing-dependent plasticity

In a recently proposed, stochastic model of spike-timing-dependent plasticity, we derived general expressions for the expected change in synaptic strength, DeltaS n, induced by a typical sequence of precisely n spikes. We found that the rules DeltaS n, n >or= 3, exhibit regions of parameter space in which stable, competitive interactions between afferents are present, leading to the activity-dependent segregation of afferents on their targets. The rules DeltaS n, however, allow an indefinite period of time to elapse for the occurrence of precisely n spikes, while most measurements of changes in synaptic strength are conducted over definite periods of time during which a potentially unknown number of spikes may occur. Here, therefore, we derive an expression, DeltaS(t), for the expected change in synaptic strength of a synapse experiencing an average sequence of spikes of typical length occurring during a fixed period of time, t. We find that the resulting synaptic plasticity rule Delta S(t) exhibits a number of remarkable properties. It is an entirely self-stabilizing learning rule in all regions of parameter space. Further, its parameter space is carved up into three distinct, contiguous regions in which the exhibited synaptic interactions undergo different transitions as the time t is increased. In one region, the synaptic dynamics change from noncompetitive to competitive to entirely depressing. In a second region, the dynamics change from noncompetitive to competitive without the second transition to entirely depressing dynamics. In a third region, the dynamics are always noncompetitive. The locations of these regions are not fixed in parameter space but may be modified by changing the mean presynaptic firing rates. Thus, neurons may be moved among these three different regions and so exhibit different sets of synaptic dynamics depending on their mean firing rates.

Dendritic excitability and synaptic plasticity

Most synaptic inputs are made onto the dendritic tree. Recent work has shown that dendrites play an active role in transforming synaptic input into neuronal output and in defining the relationships between active synapses. In this review, we discuss how these dendritic properties influence the rules governing the induction of synaptic plasticity. We argue that the location of synapses in the dendritic tree, and the type of dendritic excitability associated with each synapse, play decisive roles in determining the plastic properties of that synapse. Furthermore, since the electrical properties of the dendritic tree are not static, but can be altered by neuromodulators and by synaptic activity itself, we discuss how learning rules may be dynamically shaped by tuning dendritic function. We conclude by describing how this reciprocal relationship between plasticity of dendritic excitability and synaptic plasticity has changed our view of information processing and memory storage in neuronal networks.

Metaplasticity: tuning synapses and networks for plasticity

Synaptic plasticity is a key component of the learning machinery in the brain. It is vital that such plasticity be tightly regulated so that it occurs to the proper extent at the proper time. Activity-dependent mechanisms that have been collectively termed metaplasticity have evolved to help implement these essential computational constraints. Various intercellular signalling molecules can trigger lasting changes in the ability of synapses to express plasticity; their mechanisms of action are reviewed here, along with a consideration of how metaplasticity might affect learning and clinical conditions.

Target-cell-specific bidirectional synaptic plasticity at hippocampal output synapses

It is commonly accepted that the hippocampus is critically involved in the explicit memory formation of mammals. The subiculum is the principal target of CA1 pyramidal cells and thus serves as the major relay station for the outgoing hippocampal information. Pyramidal cells in the subiculum can be classified according to their firing properties into burst-spiking and regular-spiking cells. In the present study we demonstrate that burst-spiking and regular-spiking cells show fundamentally different forms of low frequency-induced synaptic plasticity in rats. In burst-spiking cells, low-frequency stimulation (at 0.5-5 Hz) induces frequency-dependent long-term depression (LTD) with a maximum at 1 Hz. This LTD is dependent on the activation of NMDAR and masks an mGluR-dependent long-term potentiation (LTP). In contrast, in regular-spiking cells low-frequency stimulation induces an mGluR-dependent LTP that masks an NMDAR-dependent LTD. Both processes depend on postsynaptic Ca(2+)-signaling as BAPTA prevents the induction of synaptic plasticity in both cell types. Thus, mGluR-dependent LTP and NMDAR-dependent LTD occur simultaneously at CA1-subiculum synapses and the predominant direction of synaptic plasticity relies on the cell type investigated. Our data indicate a novel mechanism for the sliding-threshold model of synaptic plasticity, in which induction of LTP and LTD seems to be driven by the relative activation state of NMDAR and mGluR. Our observation that the direction of synaptic plasticity correlates with the discharge properties of the postsynaptic cell reveals a novel and intriguing mechanism of target specificity that may serve in tuning the significance of neuronal information by trafficking hippocampal output onto either subicular burst-spiking or regular-spiking cells.

Co-induction of long-term potentiation and long-term depression at a central synapse in the leech

Most studies of long-term potentiation (LTP) have focused on potentiation induced by the activation of postsynaptic NMDA receptors (NMDARs). However, it is now apparent that NMDAR-dependent signaling processes are not the only form of LTP operating in the brain [Malenka, R. C., & Bear, M. F. (2004). LTP and LTD: An embarrassment of riches. Neuron, 44, 5-21]. Previously, we have observed that LTP in leech central synapses made by the touch mechanosensory neurons onto the S interneuron was NMDAR-independent [Burrell, B. D., & Sahley, C. L. (2004). Multiple forms of long-term potentiation and long-term depression converge on a single interneuron in the leech CNS. Journal of Neuroscience, 24, 4011-4019]. Here we examine the cellular mechanisms mediating T-to-S (T-->S) LTP and find that its induction requires activation of metabotropic glutamate receptors (mGluRs), voltage-dependent Ca(2+) channels (VDCCs) and protein kinase C (PKC). Surprisingly, whenever LTP was pharmacologically inhibited, long-term depression (LTD) was observed at the tetanized synapse, indicating that LTP and LTD were activated at the same time in the same synaptic pathway. This co-induction of LTP and LTD likely plays an important role in activity-dependent regulation of synaptic transmission.

What can we learn from synaptic weight distributions?

Much research effort into synaptic plasticity has been motivated by the idea that modifications of synaptic weights (or strengths or efficacies) underlie learning and memory. Here, we examine the possibility of exploiting the statistics of experimentally measured synaptic weights to deduce information about the learning process. Analysing distributions of synaptic weights requires a theoretical framework to interpret the experimental measurements, but the results can be unexpectedly powerful, yielding strong constraints on possible learning theories as well as information that is difficult to obtain by other means, such as the information storage capacity of a cell. We review the available experimental and theoretical techniques as well as important open issues.

STDP in a bistable synapse model based on CaMKII and associated signaling pathways

The calcium/calmodulin-dependent protein kinase II (CaMKII) plays a key role in the induction of long-term postsynaptic modifications following calcium entry. Experiments suggest that these long-term synaptic changes are all-or-none switch-like events between discrete states. The biochemical network involving CaMKII and its regulating protein signaling cascade has been hypothesized to durably maintain the evoked synaptic state in the form of a bistable switch. However, it is still unclear whether experimental LTP/LTD protocols lead to corresponding transitions between the two states in realistic models of such a network. We present a detailed biochemical model of the CaMKII autophosphorylation and the protein signaling cascade governing the CaMKII dephosphorylation. As previously shown, two stable states of the CaMKII phosphorylation level exist at resting intracellular calcium concentration, and high calcium transients can switch the system from the weakly phosphorylated (DOWN) to the highly phosphorylated (UP) state of the CaMKII (similar to a LTP event). We show here that increased CaMKII dephosphorylation activity at intermediate Ca(2+) concentrations can lead to switching from the UP to the DOWN state (similar to a LTD event). This can be achieved if protein phosphatase activity promoting CaMKII dephosphorylation activates at lower Ca(2+) levels than kinase activity. Finally, it is shown that the CaMKII system can qualitatively reproduce results of plasticity outcomes in response to spike-timing dependent plasticity (STDP) and presynaptic stimulation protocols. This shows that the CaMKII protein network can account for both induction, through LTP/LTD-like transitions, and storage, due to its bistability, of synaptic changes.

Computational consequences of experimentally derived spike-time and weight dependent plasticity rules

We present two weight- and spike-time dependent synaptic plasticity rules consistent with the physiological data of Bi and Poo (J Neurosci 18:10464-10472, 1998). One rule assumes synaptic saturation, while the other is scale free. We extend previous analyses of the asymptotic consequences of weight-dependent STDP to the case of strongly correlated pre- and post-synaptic spiking, more closely resembling associative learning. We further provide a general formula for the contribution of any number of spikes to synaptic drift. Asymptotic weights are shown to principally depend on the correlation and rate of pre- and post-synaptic activity, decreasing with increasing rate under correlated activity, and increasing with rate under uncorrelated activity. Spike train statistics reveal a quantitative effect only in the pre-asymptotic regime, and we provide a new interpretation of the relation between BCM and STDP data.

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

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

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

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

Limits on the memory storage capacity of bounded synapses

Memories maintained in patterns of synaptic connectivity are rapidly overwritten and destroyed by ongoing plasticity related to the storage of new memories. Short memory lifetimes arise from the bounds that must be imposed on synaptic efficacy in any realistic model. We explored whether memory performance can be improved by allowing synapses to traverse a large number of states before reaching their bounds, or by changing the way these bounds are imposed. In the case of hard bounds, memory lifetimes grow proportional to the square of the number of synaptic states, but only if potentiation and depression are precisely balanced. Improved performance can be obtained without fine tuning by imposing soft bounds, but this improvement is only linear with respect to the number of synaptic states. We explored several other possibilities and conclude that improving memory performance requires a more radical modification of the standard model of memory storage.

Spine Ca2+ signaling in spike-timing-dependent plasticity

Calcium is a second messenger, which can trigger the modification of synaptic efficacy. We investigated the question of whether a differential rise in postsynaptic Ca2+ ([Ca2+]i) alone is sufficient to account for the induction of long-term potentiation (LTP) and long-term depression (LTD) of EPSPs in the basal dendrites of layer 2/3 pyramidal neurons of the somatosensory cortex. Volume-averaged [Ca2+]i transients were measured in spines of the basal dendritic arbor for spike-timing-dependent plasticity induction protocols. The rise in [Ca2+]i was uncorrelated to the direction of the change in synaptic efficacy, because several pairing protocols evoked similar spine [Ca2+]i transients but resulted in either LTP or LTD. The sequence dependence of near-coincident presynaptic and postsynaptic activity on the direction of changes in synaptic strength suggested that LTP and LTD were induced by two processes, which were controlled separately by postsynaptic [Ca2+]i levels. Activation of voltage-dependent Ca2+ channels before metabotropic glutamate receptors (mGluRs) resulted in the phospholipase C-dependent (PLC-dependent) synthesis of endocannabinoids, which acted as a retrograde messenger to induce LTD. LTP required a large [Ca2+]i transient evoked by NMDA receptor activation. Blocking mGluRs abolished the induction of LTD and uncovered the Ca2+-dependent induction of LTP. We conclude that the volume-averaged peak elevation of [Ca2+]i in spines of layer 2/3 pyramids determines the magnitude of long-term changes in synaptic efficacy. The direction of the change is controlled, however, via a mGluR-coupled signaling cascade. mGluRs act in conjunction with PLC as sequence-sensitive coincidence detectors when postsynaptic precede presynaptic action potentials to induce LTD. Thus presumably two different Ca2+ sensors in spines control the induction of spike-timing-dependent synaptic plasticity.