Stochastic Models of Neural Synaptic Plasticity

Pierpoint, Robert; Vignoud, Gaëtan

doi:10.1137/20m138288x

Cited by 9 publications

(22 citation statements)

References 26 publications

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“…In Robert and Vignoud [37] we have introduced a general class of mathematical models to represent and study synaptic plasticity mechanisms. Their purpose is to investigate the synaptic weight dynamics, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…These kernels have a representation in terms of finite dimensional vectors whose coordinates are shot-noise processes. See Section 3 of [37].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, after a pre-synaptic spike and the associated rise in membrane potential X, the probability that a post-synaptic spike occurs is increased. As seen in [37], STDP synaptic mechanisms depend, in a complex way, on past spiking times of both adjacent neurons.…”

Section: Introductionmentioning

confidence: 99%

“…A Spike-Timing Dependent Plasticity (STDP) rule is a biologically-based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. A general mathematical framework has been introduced in [37].In this paper we develop and investigate a scaling approach of these models based on several biological assumptions. Experiments show that long-term synaptic plasticity evolves on a much slower timescale than the cellular mechanisms driving the activity of neuronal cells, like their spiking activity or the concentration of various chemical components created/suppressed by this spiking activity.…”

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confidence: 99%

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confidence: 99%

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Stochastic Models of Neural Plasticity: A Scaling Approach

Robert,

Vignoud

2021

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In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP) rule is a biologically-based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. A general mathematical framework has been introduced in [37].In this paper we develop and investigate a scaling approach of these models based on several biological assumptions. Experiments show that long-term synaptic plasticity evolves on a much slower timescale than the cellular mechanisms driving the activity of neuronal cells, like their spiking activity or the concentration of various chemical components created/suppressed by this spiking activity. For this reason, a scaled version of the stochastic model of [37] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [36] is entirely devoted to the tightness properties used to prove these convergence results.These averaging principles are used to study two important STDP models: pair-based rules and calcium-based rules. Our results are compared with the approximations of neuroscience STDP models. A class of discrete models of STDP rules is also investigated for the analytical tractability of its limiting dynamical system.

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Section: Introductionmentioning

confidence: 99%

“…These kernels have a representation in terms of finite dimensional vectors whose coordinates are shot-noise processes. See Section 3 of [37].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Stochastic Models of Neural Plasticity: A Scaling Approach

Robert,

Vignoud

2021

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Stochastic analysis of frequency bandwidth and noise attenuation in neurotransmission

Vahdat

Singh

2022

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Action potential (AP)-triggered neurotransmitter release forms the key basis of inter-neuronal communication. We present a stochastic hybrid system model that captures the release of neurotransmitter-filled vesicles from a presynaptic neuron. More specifically, vesicles arrive as a Poisson process to attach at a given number of docking sites, and each docked vesicle has a certain probability of release when an AP is generated in the presynaptic neuron. The released neurotransmitters enhance the membrane potential of the postsynaptic neuron, and this increase is coupled to the continuous exponential decay of the membrane potential. The buildup of potential to a critical threshold level results in an AP firing in the postsynaptic neuron, with the potential subsequently resetting back to its resting level. Our model analysis develops formulas that quantify the fluctuations in the number of released vesicles and mechanistically connects them to fluctuations in both the postsynaptic membrane potential and the AP firing times. Increasing the frequency of APs in the presynaptic neuron leads to saturation effects on the postsynaptic side, resulting in a limiting frequency range of neurotransmission. Interestingly, AP firing in the postsynaptic neuron becomes more precise with increasing AP frequency in the presynaptic neuron. We also investigate how noise in AP timing varies with different parameters, such as the probability of releases, the number of docking sites, the voltage threshold for AP firing, and the timescale of voltage decay. In summary, our results provide a systematic understanding of how stochastic mechanisms in neurotransmission enhance or impinge the precision of AP fringing times.

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Characterizing the role of autaptic feedback in enhancing precision of neuronal firing times

Vahdat,

Gambrell,

Singh

2023

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In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an Action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. Interestingly, we find regimes for noise amplification that specifically occur when the inhibitory synapse has a low probability of release for synaptic vesicles. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.

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Stochastic Models of Neural Synaptic Plasticity

Cited by 9 publications

References 26 publications

Stochastic Models of Neural Plasticity: A Scaling Approach

Stochastic Models of Neural Plasticity: A Scaling Approach

Stochastic analysis of frequency bandwidth and noise attenuation in neurotransmission

Characterizing the role of autaptic feedback in enhancing precision of neuronal firing times

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