Effects of correlated and synchronized stochastic inputs to leaky integrator neuronal model

We present an analysis of neuronal model behaviour with correlated synaptic inputs including the cases that correlated inputs are equivalent to exactly synchronized inputs and correlated inputs are not equivalent to exactly synchronized inputs. For the former case, it is found that the fully (synaptically) correlated inputs assumption (see Section 1 for definition), which is used in most, if not all, theoretical and experimental work in the past few years, results in a waste of resources and might be an unrealistic assumption; with an exactly balanced excitatory and inhibitory, and synaptically correlated input, the integrate-and-fire model simply behaves as a synchrony detector in certain parameter regions; the well-known diffusion model, upon which most theoretical work is based, fails to approximate the model with synaptically correlated Poisson inputs. A novel way to approximate synaptically correlated Poisson inputs is then presented;an optimization principle on neuronal models with partially (synaptically) correlated inputs is proposed, which enables us to predict microscopic structures in neuronal systems. For the latter case,with tightly synchronized inputs (see Section 1 for definition), the model behaviour depends on its integration time of input signals and could exhibit bursting discharge.for loosely synchronized inputs, we found that correlated inputs are equivalent to the post-spike voltage reset mechanism proposed in the literature.