Understanding a Measure for Synchrony: Spike Time Tiling Coefficient Method

Synchrony is an important feature of brain activities for the coordination of neural information and is also related to some neuronal disorders. Around 40 different measures have been proposed in literature for quantifying the synchrony of spike trains and the list is still growing. The main issue is that it is not clear to users which one to use and how measurements correspond to different features of synchrony. In this work, instead of looking at all methods at once, we focus on investigating one of the popular measures in the field of neuroscience: Spike Time Tiling Coefficient (STTC) proposed by Cutts and Eglen in 2014. We simulate three scenarios of neural spike trains and study how STTC values depend on distributions and phase shifts of spike trains. Firstly, we study pairs of simple periodic binary time series. We derive an analytical formula showing that the dependence of the STTC value on the phase shift is symmetric and has a general trend where the maximum value of STTC occurs when the phase shift is zero and the minimum value occurs when the phase shift is half of the period. Secondly, we investigate pairs of “periodic” normally distributed spike trains. While we observe the similar trends shown in the first scenario, we notice an exception. We also observe a general trend where the STTC value decreases as the standard deviation of the normal distribution increases. Thirdly, we study pairs of Poisson distributed spike trains. Using properties of the Poisson distribution, we generate pairs of Poisson distributed spike trains with certain overlap ratios and study the relationship between STTC and the overlap ratio. In general, this relationship is nonlinear. We observe that as the synchronicity window decreases towards zero, this nonlinear relationship tends toward a linear relationship. We derive analytical formulas to describe this nonlinear relationship and quantitatively evaluate its closeness to a linear relationship as the syn-chronicity window decreases towards zero. Through studying STTC, we notice that when the synchronicity window is too large, the problem of dividing by zero occurs in the calculation of STTC. To avoid such a problem, we derive an upper bound for the synchronicity window. We also argue that STTC can only approach − 1, and show a case to demonstrate this argument