Research ReportEffectiveness of systematic spike dithering depends on the precision of cortical synchronization
Introduction
Current experimental protocols for the study of brain function result in highly non-stationary spike trains. In this context, experimental data typically contain a number of statistical features that do not allow an analytical treatment or parametric testing in particular in the context of the analysis of precise spike correlation of simultaneous spike trains. Therefore, surrogate methods are used to either implement the null-hypothesis for statistical tests or for additional controls. The idea behind such surrogate data sets is to destroy a particular feature, which we are interested to test for, while other features are preserved. In the context of spike correlation analysis, one aims to destroy spike correlation across the neurons while keeping features like the firing rate of the neurons, in time and across trials, and the internal spike train structure (i.e. to first order the inter-spike interval distribution) as similar as possible to the original data. Then these data are analyzed as the original data and compared to the latter. For this purpose a number of techniques for generating surrogates are used, like e.g. spike time randomization, trial shuffling, or modeling. However, each of them has some drawbacks in the sense that they involuntarily also destroy other features of the data that may lead to an uncontrolled perturbation of the data and may cause false positive results (Grün, submitted for publication).
In this context, spike dithering (Date et al., 1998) is currently considered as one of the best methods and widely used in correlation analysis (Abeles and Gat, 2001, Hatsopoulus et al., 2003, Gerstein, 2004, Shmiel et al., 2006, Maldonado et al., submitted for publication). For doing so, each original individual spike is displaced randomly by a small amount to destroy the exact timing of the spikes but to conserve the trial by trial firing rates and the interval statistics of the data. Typically the randomization is undertaken homogeneously within a window around the spikes, but also other methods are in use that make the dithering dependent on the interval distributions to the foregoing and the following spike (Gerstein, 2004). In any case, the exact spike timing across the neurons is destroyed. However, depending on the allowed temporal scale of spike correlation, the dither range needs to be properly adjusted to reliably destroy the correlation features under evaluation. Pazienti et al. (2007) presented results on the destruction ability of dithering in a comparison of different coincidence detection methods. The limitation of the former study is that it only considers exact coincident events. The goal of this paper is to provide a theoretical understanding of the decay rate we have to expect if synchronous spike events of a given temporal jitter are present. Here we focus on (1) the usage of the multiple shift detection method for coincidence detection.We allow for (2) imprecise, “jittered” coincidences, which enables us to (3) explain effects of dithering observed in experimental data by relating them to underlying parameters. This is explored by simulations of stochastic point processes and confirmed by analytical derivations.
Section snippets
Detection of excess synchrony in experimental data
In Maldonado et al. (submitted for publication) we investigated the neuronal activity in the visual cortex of monkeys while they freely view natural scenes (see Experimental procedures for details). The spike activity from small numbers of neurons and the eye movements were recorded simultaneously. The aim of the study was to not only investigate changes of discharge rate in individual neurons related to saccadic eye movements and the following fixation periods, but to examine correlations
Discussion
The study of Maldonado et al. (submitted for publication) revealed the presence of spike synchrony in early visual processing of freely viewing monkeys. The authors demonstrated that the significance deteriorates if the experimental spike data are intentionally dithered and that the dependence on dither width is consistent with simulations of jittered coincidences embedded in uncorrelated background spikes. The slowness of the decay, however, remained a puzzle. As large dithers have undesired
Neurophysiological data
Spike trains of simultaneously recorded neurons were obtained from the primary visual cortex of two adult capuchin monkeys (Cebus apella). Full details of these recordings can be found in Maldonado et al. (submitted for publication). All experiments followed institutional and NIH guidelines for the care and use of laboratory animals. Briefly, animals seated in a dimly lit chamber were allowed to freely explore 15 different natural images presented on a 21-in. computer monitor located 57 cm in
Acknowledgments
Partly funded by Stifterverband für die deutsche Wissenschaft, the Bernstein Center for Computational Neuroscience Berlin (BMBF grant 01GQ014123), the Iniciativa Cientifica Milenio P04-068F, and DIP F1.2.
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