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

Abstract

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.

Population approach to a neural discrimination task

“…This simplification is commonly used, e.g. by Feng (2003). Then, using the diffusion approximation, as is common in the literature (Tuckwell 1988;Ricciardi and Sato 1990) and assuming that a = b, we reach the simplified following description of the dynamics of our discriminating neuron:…”

“…It has been shown by Feng et al (2003) that measuring the FR over only ten spikes significantly reduces the discrimination accuracy of the neuronal system. However, especially in the case of a ratio r close to one, the FR becomes very small, because the generation of a spike becomes an exceptional event, entirely dependent on the random variable N .…”

“…In order to overcome this daunting flaw, instead of discriminating with the measured FR of one neuron (Feng and Liu 2002;Feng et al 2003), we can discriminate with the measured FR of a population of neurons. The basic advantage is that each neuron only needs to fire a few spikes, which allows us to work with biologically realistic times.…”

“…Feng and Liu (2002) and Feng et al (2003) have analytically proved the simple fact that for r = 1 the discrimination is better than for r = 0. Here we have a more detailed description of how the probability of error of the single neuron is not monotonically decreasing, but reaches a peak around a ratio equal to 0.7, as we can see in Fig.…”

Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators

“…The LIF model is more than a century old (Lapicque, 1907), and was first proposed by an experimenter to formulate accumulation of charge on the cell membrane in response to an applied current. Despite the dynamics of only the leakage current in the model, it nevertheless became a test bed for studies on synchrony and activity of neurons (Brunel & Sergi, 1998; Kuhlmann, Burkitt, Paolini, & Clark, 2002; Feng, 2003; Brette & Gerstner, 2005). With the realization of the importance of the PRC or phase response function in determining the synchrony of a network of oscillating neurons (Winfree, 1977; Tsubo, Teramae, & Fukai, 2007; Perez Velazquez et al, 2007; Tateno & Robinson, 2007; Achuthan & Canavier, 2009; Cui, Canavier Carmen, & Butera Robert, 2009; Smeal et al, 2010) the LIF model became more useful in constructing theories that may be extended or generalized to other more complex models (Chow & Kopell, 2000; Pfeuty, Mato, Golomb, & Hansel, 2003).…”