Stochastic Perturbation Methods for Spike-Timing-Dependent Plasticity

2012 ◽  
Vol 24 (5) ◽  
pp. 1109-1146 ◽  
Author(s):  
Todd K. Leen ◽  
Robert Friel
Keyword(s):  
Perturbation Expansion ◽  
Stochastic Perturbation ◽  
Planck Equation ◽  
Jump Process ◽  
System Size ◽  
Spike Timing ◽  
Equilibrium Solutions ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Learning Rules

Online machine learning rules and many biological spike-timing-dependent plasticity (STDP) learning rules generate jump process Markov chains for the synaptic weights. We give a perturbation expansion for the dynamics that, unlike the usual approximation by a Fokker-Planck equation (FPE), is well justified. Our approach extends the related system size expansion by giving an expansion for the probability density as well as its moments. We apply the approach to two observed STDP learning rules and show that in regimes where the FPE breaks down, the new perturbation expansion agrees well with Monte Carlo simulations. The methods are also applicable to the dynamics of stochastic neural activity. Like previous ensemble analyses of STDP, we focus on equilibrium solutions, although the methods can in principle be applied to transients as well.

A Stochastic Method to Predict the Consequence of Arbitrary Forms of Spike-Timing-Dependent Plasticity

2003 ◽  
Vol 15 (3) ◽  
pp. 597-620 ◽  
Author(s):  
Hideyuki Câteau ◽  
Tomoki Fukai
Keyword(s):  
Planck Equation ◽  
Bimodal Distribution ◽  
Spike Timing ◽  
Window Function ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Ca1 Region ◽  
Window Functions ◽  
Conductance Distribution ◽  
Synaptic Conductances

Synapses in various neural preparations exhibit spike-timing-dependent plasticity (STDP) with a variety of learning window functions. The window functions determine the magnitude and the polarity of synaptic change according to the time difference of pre- and postsynaptic spikes. Numerical experiments revealed that STDP learning with a single-expo nential window function resulted in a bimodal distribution of synaptic conductances as a consequence of competition between synapses. A slightly modified window function, however, resulted in a unimodal distribution rather than a bimodal distribution. Since various window functions have been observed in neural preparations, we develop a rigorous mathematical method to calculate the conductance distribution for any given window function. Our method is based on the Fokker-Planck equation to determine the conductance distribution and on the Ornstein-Uhlenbeck process to characterize the membrane potential fluctuations. Demonstrating that our method reproduces the known quantitative results of STDP learning, we apply the method to the type of STDP learning found recently in the CA1 region of the rat hippocampus. We find that this learning can result in nearly optimized competition between synapses. Meanwhile, we find that the type of STDP learning found in the cerebellum-like structure of electric fish can result in all-or-none synapses: either all the synaptic conductances are maximized, or none of them becomes significantly large. Our method also determines the window function that optimizes synaptic competition.

scholarly journals Long vs short-term synaptic learning rules after optogenetic spike-timing-dependent plasticity

2019 ◽  
Author(s):  
Margarita Anisimova ◽  
Bas van Bommel ◽  
Marina Mikhaylova ◽  
J. Simon Wiegert ◽  
Thomas G. Oertner ◽  
...  
Keyword(s):  
Spike Timing ◽  
Information Storage ◽  
Spike Timing Dependent Plasticity ◽  
Dependent Plasticity ◽  
Neuronal Populations ◽  
Learning Rules ◽  
Blocking Activity ◽  
Synaptic Learning ◽  
The Brain

AbstractSpike-timing-dependent plasticity (STDP) is a candidate mechanism for information storage in the brain. However, it has been practically impossible to assess the long-term consequences of STDP because recordings from postsynaptic neurons last at most one hour. Here we introduce an optogenetic method to, with millisecond precision, independently control action potentials in two neuronal populations with light. We apply this method to study spike-timing-dependent plasticity (oSTDP) in the hippocampus and reproduce previous findings that depression or potentiation depend on the sequence of pre- and postsynaptic spiking. However, 3 days after induction, oSTDP results in potentiation regardless of the exact temporal sequence, frequency or number of pairings. Blocking activity between induction and readout prevented the synaptic potentiation, indicating that strengthened synapses have to be used to get strong. Our findings indicate that STDP potentiates synapses and that the change in synaptic strength persist to behaviorally relevant timescales.

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