Abstract
It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.
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Bannister NJ, Nelson JC, Jack JJB (2002) Excitatory inputs to spiny cells in layers 4 and 6 of cat striate cortex. Philos Trans Biol Sci 357(1428):1793–1808
Branco T, Staras K, Darcy KJ, Goda Y (2008) Local dendritic activity sets release probability at hippocampal synapses. Neuron 59(3):475–485
Bugmann G, Christodoulou C, Taylor JG (1997) Role of temporal integration and fluctuation detection in the highly irregular firing of a leaky integrator neuron model with partial reset. Neural Comput 9(5):985–1000
Christodoulou C, Bugmann G (2000) Near Poisson-type firing produced by concurrent excitation and inhibition. Biosystems 58(1–3):41–48
Christodoulou C, Bugmann G (2001) Coefficient of variation vs. mean interspike interval curves: What do they tell us about the brain? Neurocomputing 38:1141–1149
Destexhe A, Contreras D, Steriade M (1999) Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states. J Neurosci 19(11):4595–4608
Feldmeyer D, Sakmann B (2000) Synaptic efficacy and reliability of excitatory connections between the principal neurones of the input (layer 4) and output layer (layer 5) of the neocortex. J Physiol 525(1):31–39
Feller W (1968) An introduction to probability theory and its applications, vol 1, 3rd edn. Wiley, New York
Feng JFJ, Brown DD (1999) Coefficient of variation of interspike intervals greater than 0.5. How and when? Biol Cybern 80(5):291–297
Feng JJ, Brown DD (1998) Impact of temporal variation and the balance between excitation and inhibition on the output of the perfect integrate-and-fire model. Biol Cybern 78(5):369–376
Fusi S, Mattia M (1999) Collective behavior of networks with linear (vlsi) integrate-and-fire neurons. Neural Comput 11(3):633–652
Gabbiani F, Koch C (1998) Principles of spike train analysis. Methods Neuronal Model 12:313–360
Gerstein G, Mandelbrot B (1964) Random walk models for the spike activity of a single neuron. Biophys J 4:41–68
Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics. Neural Comput 10(5):1047–1065
Holden AV (1976) Models of the stochastic activity of neurones. Springer, Berlin
Kara P, Reinagel P, Reid R (2000) Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27:635–646
Lengler J, Jug F, Steger A (2013) Reliable neuronal systems: the importance of heterogeneity. PLoS One 8(12):e80694
Markram H, Lübke J, Frotscher M, Roth A, Sakmann B (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol (Lond) 500(Pt 2):409–440
Moreno-Bote R (2014) Poisson-like spiking in circuits with probabilistic synapses. PLoS Comput Biol 10:1–13
Salinas E, Sejnowski TJ (2000) Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. J Neurosci 20(16):6193–6209
Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci 18(10):3870–3896
Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random epsps. J Neurosci 13(1):334–350
Stiefel KM, Englitz B, Sejnowski TJ (2013) Origin of intrinsic irregular firing in cortical interneurons. PNAS 110:78867891
Terman D, Rubin J, Diekman C (2013) Irregular activity arises as a natural consequence of synaptic inhibition. Chaos Interdiscip J Nonlinear Sci 23(4):046110
Troyer T, Miller K (1997) Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Comput 9:971–983
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Lengler, J., Steger, A. Note on the coefficient of variations of neuronal spike trains. Biol Cybern 111, 229–235 (2017). https://doi.org/10.1007/s00422-017-0717-y
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DOI: https://doi.org/10.1007/s00422-017-0717-y