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The Poisson process is an often employed model for the activity of neuronal populations. It is known, though, that superpositions of realistic, non- Poisson spike trains are not in general Poisson processes, not even for large numbers of superimposed processes. Here we construct superimposed spike trains from intracellular in vivo recordings from rat neocortex neurons and compare their statistics to specific point process models. The constructed superimposed spike trains reveal strong deviations from the Poisson model. We find that superpositions of model spike trains that take the effective refractoriness of the neurons into account yield a much better description. A minimal model of this kind is the Poisson process with dead-time (PPD). For this process, and for superpositions thereof, we obtain analytical expressions for some second-order statistical quantities-like the count variability, inter-spike interval (ISI) variability and ISI correlations-and demonstrate the match with the in vivo data. We conclude that effective refractoriness is the key property that shapes the statistical properties of the superposition spike trains. We present new, efficient algorithms to generate superpositions of PPDs and of gamma processes that can be used to provide more realistic background input in simulations of networks of spiking neurons. Using these generators, we show in simulations that neurons which receive superimposed spike trains as input are highly sensitive for the statistical effects induced by neuronal refractoriness.
Pubmed ID: 21964584
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NEURON is a simulation environment for modeling individual neurons and networks of neurons. It provides tools for conveniently building, managing, and using models in a way that is numerically sound and computationally efficient. It is particularly well-suited to problems that are closely linked to experimental data, especially those that involve cells with complex anatomical and biophysical properties. NEURON has benefited from judicious revision and selective enhancement, guided by feedback from the growing number of neuroscientists who have used it to incorporate empirically-based modeling into their research strategies. NEURON's computational engine employs special algorithms that achieve high efficiency by exploiting the structure of the equations that describe neuronal properties. It has functions that are tailored for conveniently controlling simulations, and presenting the results of real neurophysiological problems graphically in ways that are quickly and intuitively grasped. Instead of forcing users to reformulate their conceptual models to fit the requirements of a general purpose simulator, NEURON is designed to let them deal directly with familiar neuroscience concepts. Consequently, users can think in terms of the biophysical properties of membrane and cytoplasm, the branched architecture of neurons, and the effects of synaptic communication between cells. * helps users focus on important biological issues rather than purely computational concerns * has a convenient user interface * has a user-extendable library of biophysical mechanisms * has many enhancements for efficient network modeling * offers customizable initialization and simulation flow control * is widely used in neuroscience research by experimentalists and theoreticians * is well-documented and actively supported * is free, open source, and runs on (almost) everything
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