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

p.appleby{at}biologie.hu-berlin.de Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Invalidenstraße 43, D-10115 Berlin, Germany

Terry Elliott

te{at}ecs.soton.ac.uk Department of Electronics and Computer Science, University of Southampton, Highfield, Southampton, SO17 1BJ U.K.

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.