Ensemble models of bifurcation phenomenon in cortical synapses

Individual cortical synapses are known to exhibit a very complex short-time dynamic behaviour in response to simple “naturalistic” stimulation. Nonetheless, physiological models of synapses are unable to explain the observed behaviour. We describe a computational study of the experimentally obtained excitatory post-synaptic potential trains of individual cortical synapses. By adopting a new nonlinear modelling algorithm we construct robust and repeatable models of the underlying dynamics. These models imply that cortical synapses respond with a wide range of periodic or chaotic dynamics. In particular, for stimulus at a fixed rate, a single bifurcation parameter, our models predict that the response of the individual synapse will vary from a fixed point to periodic and chaotic, depending on the frequency of stimulus. Extending our method to a two dimensional bifurcation parameter space we observe a rich and characteristic dependence of synaptic response on the preceeding stimuli. Dynamics for individual synapses vary widely, suggesting that 17 the individual behaviour of synapses is highly tuned and that the dynamic behaviour of even a small network of synapse-coupled neurons can be highly varied.