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.

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.

Spike Timing-Dependent Plasticity: From Synapse to Perception

2006 ◽  
Vol 86 (3) ◽  
pp. 1033-1048 ◽  
Author(s):  
Yang Dan ◽  
Mu-Ming Poo
Keyword(s):  
Neuronal Excitability ◽  
Human Perception ◽  
Long Term Potentiation ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Functional Changes

Information in the nervous system may be carried by both the rate and timing of neuronal spikes. Recent findings of spike timing-dependent plasticity (STDP) have fueled the interest in the potential roles of spike timing in processing and storage of information in neural circuits. Induction of long-term potentiation (LTP) and long-term depression (LTD) in a variety of in vitro and in vivo systems has been shown to depend on the temporal order of pre- and postsynaptic spiking. Spike timing-dependent modification of neuronal excitability and dendritic integration was also observed. Such STDP at the synaptic and cellular level is likely to play important roles in activity-induced functional changes in neuronal receptive fields and human perception.

scholarly journals Long-term population spike-timing-dependent plasticity promotes synaptic tagging but not cross-tagging in rat hippocampal area CA1

2019 ◽  
Vol 116 (12) ◽  
pp. 5737-5746 ◽  
Author(s):  
Karen Ka Lam Pang ◽  
Mahima Sharma ◽  
Kumar Krishna-K. ◽  
Thomas Behnisch ◽  
Sreedharan Sajikumar
Keyword(s):  
Synaptic Plasticity ◽  
Long Term Potentiation ◽  
Neuronal Population ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Adult Rat ◽  
Term Potentiation ◽  
Hippocampal Ca3

In spike-timing-dependent plasticity (STDP), the direction and degree of synaptic modification are determined by the coherence of pre- and postsynaptic activities within a neuron. However, in the adult rat hippocampus, it remains unclear whether STDP-like mechanisms in a neuronal population induce synaptic potentiation of a long duration. Thus, we asked whether the magnitude and maintenance of synaptic plasticity in a population of CA1 neurons differ as a function of the temporal order and interval between pre- and postsynaptic activities. Modulation of the relative timing of Schaffer collateral fibers (presynaptic component) and CA1 axons (postsynaptic component) stimulations resulted in an asymmetric population STDP (pSTDP). The resulting potentiation in response to 20 pairings at 1 Hz was largest in magnitude and most persistent (4 h) when presynaptic activity coincided with or preceded postsynaptic activity. Interestingly, when postsynaptic activation preceded presynaptic stimulation by 20 ms, an immediate increase in field excitatory postsynaptic potentials was observed, but it eventually transformed into a synaptic depression. Furthermore, pSTDP engaged in selective forms of late-associative activity: It facilitated the maintenance of tetanization-induced early long-term potentiation (LTP) in neighboring synapses but not early long-term depression, reflecting possible mechanistic differences with classical tetanization-induced LTP. The data demonstrate that a pairing of pre- and postsynaptic activities in a neuronal population can greatly reduce the required number of synaptic plasticity-evoking events and induce a potentiation of a degree and duration similar to that with repeated tetanization. Thus, pSTDP determines synaptic efficacy in the hippocampal CA3–CA1 circuit and could bias the CA1 neuronal population toward potentiation in future events.

scholarly journals Learning complex temporal patterns with resource-dependent spike timing-dependent plasticity

2012 ◽  
Vol 108 (2) ◽  
pp. 551-566 ◽  
Author(s):  
Jason F. Hunzinger ◽  
Victor H. Chan ◽  
Robert C. Froemke
Keyword(s):  
Long Term Potentiation ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Rate Dependent ◽  
Temporal Relationships ◽  
Term Potentiation ◽  
Functional Mechanisms

Studies of spike timing-dependent plasticity (STDP) have revealed that long-term changes in the strength of a synapse may be modulated substantially by temporal relationships between multiple presynaptic and postsynaptic spikes. Whereas long-term potentiation (LTP) and long-term depression (LTD) of synaptic strength have been modeled as distinct or separate functional mechanisms, here, we propose a new shared resource model. A functional consequence of our model is fast, stable, and diverse unsupervised learning of temporal multispike patterns with a biologically consistent spiking neural network. Due to interdependencies between LTP and LTD, dendritic delays, and proactive homeostatic aspects of the model, neurons are equipped to learn to decode temporally coded information within spike bursts. Moreover, neurons learn spike timing with few exposures in substantial noise and jitter. Surprisingly, despite having only one parameter, the model also accurately predicts in vitro observations of STDP in more complex multispike trains, as well as rate-dependent effects. We discuss candidate commonalities in natural long-term plasticity mechanisms.

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.

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.

scholarly journals Interaction between theta-phase and spike-timing dependent plasticity simulates theta induced memory effects

2021 ◽  
Author(s):  
Danying Wang ◽  
George Michael Parish ◽  
Kimron L Shapiro ◽  
Simon Hanslmayr
Keyword(s):  
Episodic Memory ◽  
Theta Rhythm ◽  
Long Term Potentiation ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Cell Culture Study ◽  
Dependent Plasticity ◽  
Hippocampal Cell Culture ◽  
Theta Phase

Rodent studies suggest that spike timing relative to hippocampal theta activity determines whether potentiation or depression of synapses arise. Such changes also depend on spike timing between pre- and post-synaptic neurons, known as spike-timing-dependent plasticity (STDP). STDP, together with theta-phase-dependent learning, has inspired several computational models of learning and memory. However, evidence to elucidate how these mechanisms directly link to human episodic memory is lacking. In a computational model, we modulate long-term potentiation (LTP) and long-term depression (LTD) of STDP, by opposing phases of a simulated theta rhythm. We fit parameters to a hippocampal cell culture study in which LTP and LTD were observed to occur in opposing phases of a theta rhythm. Further, we modulated two inputs by cosine waves with synchronous and asynchronous phase offsets and replicate key findings in human episodic memory. Learning advantage was found for the synchronous condition, as compared to the asynchronous conditions, and was specific to theta modulated inputs. Importantly, simulations with and without each mechanism suggest that both STDP and theta-phase-dependent plasticity are necessary to replicate the findings. Together, the results indicate a role for circuit-level mechanisms, which bridges the gap between slice preparation studies and human memory.

Inhibition of the slow afterhyperpolarization restores the classical spike timing-dependent plasticity rule obeyed in layer 2/3 pyramidal cells of the prefrontal cortex

2012 ◽  
Vol 107 (1) ◽  
pp. 205-215 ◽  
Author(s):  
Aleksey V. Zaitsev ◽  
Roger Anwyl
Keyword(s):  
Prefrontal Cortex ◽  
Pyramidal Cells ◽  
Long Term Potentiation ◽  
Spike Timing ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Layer 2 ◽  
Stdp Rule ◽  
Stimulation Of

The induction of long-term potentiation (LTP) and long-term depression (LTD) of excitatory postsynaptic currents was investigated in proximal synapses of layer 2/3 pyramidal cells of the rat medial prefrontal cortex. The spike timing-dependent plasticity (STDP) induction protocol of negative timing, with postsynaptic leading presynaptic stimulation of action potentials (APs), induced LTD as expected from the classical STDP rule. However, the positive STDP protocol of presynaptic leading postsynaptic stimulation of APs predominantly induced a presynaptically expressed LTD rather than the expected postsynaptically expressed LTP. Thus the induction of plasticity in layer 2/3 pyramidal cells does not obey the classical STDP rule for positive timing. This unusual STDP switched to a classical timing rule if the slow Ca2+-dependent, K+-mediated afterhyperpolarization (sAHP) was inhibited by the selective blocker N-trityl-3-pyridinemethanamine (UCL2077), by the β-adrenergic receptor agonist isoproterenol, or by the cholinergic agonist carbachol. Thus we demonstrate that neuromodulators can affect synaptic plasticity by inhibition of the sAHP. These findings shed light on a fundamental question in the field of memory research regarding how environmental and behavioral stimuli influence LTP, thereby contributing to the modulation of memory.

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