Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.Comment: 13 pages, revtex4; uses packages: graphicx, subfigure; 9 figures, 16 subfigure

How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure

Long-term synaptic morphometry changes after induction of long-term potentiation and long-term depression in the dentate gyrus of awake rats are not simply mirror phenomena

Mechanisms of expression of long-term synaptic plasticity are believed to involve morphological changes of the activated synapses and remodelling of connectivity. Here, we investigated changes in synaptic and neuronal parameters in the dentate gyrus 24 h after induction of long-term potentiation (LTP) and long-term depression (LTD) in awake rats. In dentate granule cells, tetanization of the medial or lateral perforant paths induces LTP in specific synaptic bands along the dendrites in the middle and outer molecular layers, respectively, and tetanization of the lateral path induces robust LTD heterosynaptically in the middle molecular layer. This functional segregation allowed us to assess morphological changes associated with LTP and LTD in each pathway in the same population of neurons. Electron microscopy and unbiased counting methods were used to estimate neuronal density, axospinous, axodendritic and perforated synapse density, multiple synapse bouton density and postsynaptic density (PSD) area. Whereas there was no change in neuronal density, PSD area and multiple synapse boutons 24 h after either LTP or LTD, there was a noninput-specific increase in unperforated axospinous synapses after both LTP and LTD. However, we found that LTP of the medial, but not lateral, perforant path is associated with a specific increase in perforated axospinous synapses in the potentiated area. We also show that heterosynaptic LTD is associated with an input-specific increase in axodendritic synapse density. These results suggest that each perforant pathway may differ with respect to the nature of LTP-induced long-term changes and show that morphologically LTD is not simply the converse of LTP