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

2009 ◽  
Vol 21 (12) ◽  
pp. 3363-3407 ◽  
Author(s):  
Terry Elliott ◽  
Konstantinos Lagogiannis
Keyword(s):  
Stochastic Model ◽  
Neuronal Development ◽  
Synaptic Strength ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Large Numbers ◽  
Large Fluctuations ◽  
Low Pass ◽  
The Mean

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.

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

2010 ◽  
Vol 22 (5) ◽  
pp. 1180-1230 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Random Walk ◽  
Stochastic Model ◽  
Synaptic Strength ◽  
Spike Timing ◽  
Spatial Average ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Strength Change ◽  
Single Spike ◽  
Switch Mechanism

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.

Temporal Dynamics of Rate-Based Synaptic Plasticity Rules in a Stochastic Model of Spike-Timing-Dependent Plasticity

2008 ◽  
Vol 20 (9) ◽  
pp. 2253-2307 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Stochastic Model ◽  
Parameter Space ◽  
Synaptic Strength ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Firing Rates ◽  
Typical Sequence ◽  
Synaptic Dynamics

In a recently proposed, stochastic model of spike-timing-dependent plasticity, we derived general expressions for the expected change in synaptic strength, ΔSn, induced by a typical sequence of precisely n spikes. We found that the rules ΔSn, n ≥ 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 ΔSn, 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, ΔS(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 Δ 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.

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

2010 ◽  
Vol 22 (1) ◽  
pp. 244-272 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Stochastic Model ◽  
Transition Probabilities ◽  
Long Term Potentiation ◽  
Synaptic Strength ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Single Spike ◽  
The Impact

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.

Stable Competitive Dynamics Emerge from Multispike Interactions in a Stochastic Model of Spike-Timing-Dependent Plasticity

2006 ◽  
Vol 18 (10) ◽  
pp. 2414-2464 ◽  
Author(s):  
Peter A. Appleby ◽  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Stochastic Model ◽  
Higher Order ◽  
Spike Timing ◽  
Competitive Dynamics ◽  
Spike Timing Dependent Plasticity ◽  
Interaction Function ◽  
Dependent Plasticity ◽  
Order Interaction ◽  
Synaptic Dynamics

In earlier work we presented a stochastic model of spike-timing-dependent plasticity (STDP) in which STDP emerges only at the level of temporal or spatial synaptic ensembles. We derived the two-spike interaction function from this model and showed that it exhibits an STDP-like form. Here, we extend this work by examining the general n-spike interaction functions that may be derived from the model. A comparison between the two-spike interaction function and the higher-order interaction functions reveals profound differences. In particular, we show that the two-spike interaction function cannot support stable, competitive synaptic plasticity, such as that seen during neuronal development, without including modifications designed specifically to stabilize its behavior. In contrast, we show that all the higher-order interaction functions exhibit a fixed-point structure consistent with the presence of competitive synaptic dynamics. This difference originates in the unification of our proposed “switch” mechanism for synaptic plasticity, coupling synaptic depression and synaptic potentiation processes together. While three or more spikes are required to probe this coupling, two spikes can never do so. We conclude that this coupling is critical to the presence of competitive dynamics and that multispike interactions are therefore vital to understanding synaptic competition.

scholarly journals A spike-timing-dependent plasticity rule for single, clustered and distributed dendritic spines

2018 ◽  
Author(s):  
Sabrina Tazerart ◽  
Diana E. Mitchell ◽  
Soledad Miranda-Rottmann ◽  
Roberto Araya
Keyword(s):  
Dendritic Spines ◽  
Actin Polymerization ◽  
Pyramidal Neurons ◽  
Glutamate Release ◽  
Synaptic Strength ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Spine Shape ◽  
Stdp Rule

SUMMARYSpike-timing-dependent plasticity (STDP) has been extensively studied in cortical pyramidal neurons, however, the precise structural organization of excitatory inputs that supports STDP, as well as the structural, molecular and functional properties of dendritic spines during STDP remain unknown. Here we performed a spine STDP protocol using two-photon glutamate uncaging to mimic presynaptic glutamate release (pre) paired with somatically generated postsynaptic spikes (post). We found that the induction of STDP in single spines follows a classical Hebbian STDP rule, where pre-post pairings at timings that trigger LTP (t-LTP) produce shrinkage of the activated spine neck and a concomitant increase in its synaptic strength; and post-pre pairings that trigger LTD (t-LTD) decrease synaptic strength without affecting the activated spine shape. Furthermore, we tested whether the single spine-Hebbian STDP rule could be affected by the activation of neighboring (clustered) or distant (distributed) spines. Our results show that the induction of t-LTP in two clustered spines (<5 μm apart) enhances LTP through a mechanism dependent on local spine calcium accumulation and actin polymerization-dependent neck shrinkage, whereas t-LTD was disrupted by the activation of two clustered spines but recovered when spines were separated by >40 μm. These results indicate that synaptic cooperativity, induced by the co-activation of only two clustered spines, provides local dendritic depolarization and local calcium signals sufficient to disrupt t-LTD and extend the temporal window for the induction of t-LTP, leading to STDP only encompassing LTP.

Multispike Interactions in a Stochastic Model of Spike-Timing-Dependent Plasticity

2007 ◽  
Vol 19 (5) ◽  
pp. 1362-1399 ◽  
Author(s):  
Peter A. Appleby ◽  
Terry Elliott
Keyword(s):  
Stochastic Model ◽  
Ad Hoc ◽  
Detailed Examination ◽  
Spike Timing ◽  
Competitive Dynamics ◽  
Experimental Results ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Natural Way ◽  
Exact Timing

Recently we presented a stochastic, ensemble-based model of spike-timing-dependent plasticity. In this model, single synapses do not exhibit plasticity depending on the exact timing of pre- and postsynaptic spikes, but spike-timing-dependent plasticity emerges only at the temporal or synaptic ensemble level. We showed that such a model reproduces a variety of experimental results in a natural way, without the introduction of various, ad hoc nonlinearities characteristic of some alternative models. Our previous study was restricted to an examination, analytically, of two-spike interactions, while higher-order, multispike interactions were only briefly examined numerically. Here we derive exact, analytical results for the general n-spike interaction functions in our model. Our results form the basis for a detailed examination, performed elsewhere, of the significant differences between these functions and the implications these differences have for the presence, or otherwise, of stable, competitive dynamics in our model.

scholarly journals Optimality Model of Unsupervised Spike-Timing-Dependent Plasticity: Synaptic Memory and Weight Distribution

2007 ◽  
Vol 19 (3) ◽  
pp. 639-671 ◽  
Author(s):  
Taro Toyoizumi ◽  
Jean-Pascal Pfister ◽  
Kazuyuki Aihara ◽  
Wulfram Gerstner
Keyword(s):  
Optimality Criterion ◽  
Receptive Fields ◽  
Spike Timing ◽  
Postsynaptic Neuron ◽  
Spike Timing Dependent Plasticity ◽  
Basic Principles ◽  
Dependent Plasticity ◽  
The Mean ◽  
Synaptic Dynamics ◽  
The Stability

We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory.

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