Quantifying spike train synchrony and directionality: Measures and Applications

TL;DR

The paper addresses how to quantify spike train synchrony and directional propagation across $N$ spike trains over time, introducing time-scale independent ($D_I$) and time-resolved ($D_S$) measures along with SPIKE-Synchronization, SPIKE-Order, and Spike Train Order to reveal leader-follower dynamics and potential synfire patterns. It develops adaptive coincidence detection to pair spikes across trains and defines instantaneous dissimilarity profiles $I(t)$ and $S(t)$, together with multivariate extensions and latency-correction algorithms that operate on the spike time difference matrix (STDM). The work provides a cohesive framework for analyzing both reliability and discrimination in neural responses, enables latency-corrected alignment of sparse spike trains, and demonstrates applicability to artificial data and real neural recordings, with broad potential across neuroscience and other domains. Fully implemented tools (SPIKY, PySpike, cSPIKE) support these measures and algorithms, enabling researchers to quantify synchrony, directionality, and precise temporal structure in complex spike-train data and to explore extensions such as event-weighted analyses and cross-domain applications.

Abstract

By introducing the twin concepts of reliability and precision along with the corresponding measures, Mainen and Sejnowski's seminal 1995 paper "Reliability of spike timing in neocortical neurons" (Mainen and Sejnowski, 1995) paved the way for a new kind of quantitative spike train analysis. In subsequent years a host of new methods was introduced that measured both the synchrony among neuronal spike trains and the directional component, e.g. how activity propogates between neurons. This development culminated with a new class of measures that are both time scale independent and time resolved. These include the two spike train distances ISI- and SPIKE-Distance as well as the coincidence detector SPIKE-Synchronization and its directional companion SPIKE-Order. This article will not only review all of these measures but also include two recently proposed algorithms for latency correction which build on SPIKE-order and aim to optimize the spike time alignment of sparse spike trains with well-defined global spiking events. For the sake of clarity, all these methods will be illustrated on artificially generated data but in each case exemplary applications to real neuronal data will be described as well.

Figures (9)

• Figure 1: Schematic illustration of how the ISI-Distance $D_I$ and the SPIKE-Distance $D_S$ are derived from local quantities around an arbitrary time instant $t$. A. The ISI dissimilarity profile $I (t)$ is calculated from the instantaneous interspike intervals. B. Additional spike-based variables make the SPIKE dissimilarity profile $S (t)$ sensitive to spike timing. Modified from Kreuz15.
• Figure 2: Artificial example dataset of $50$ spike trains (A) and the corresponding profiles for the ISI-Distance (B), the SPIKE-Distance (C), and SPIKE-Synchronization (D), as well as their average values. In the first half within the noisy background there are $4$ regularly spaced global events with increasing jitter. The second half consists of $10$ global events with decreasing jitter but without any noisy background. Modified from Satuvuori17b.
• Figure 3: Instantaneous clustering for artificially generated spike trains (A, C) whose clustering behavior changes every $500$ ms: from four different variants of two clusters via three, four and eight clusters to random spiking. B, D. Matrices of pairwise instantaneous SPIKE-dissimilarity values for the time instants marked by the green lines in A and C, respectively. Modified from Kreuz13.
• Figure 4: A. Motivation for adaptive coincidence detection. Depending on local context the same two spikes (left) can appear as coincident (right, top) or as non-coincident (right, bottom). B/C. Illustration of adaptive coincidence detection. The first step (B) assigns to each spike $t_i^{(n)}$ of spike train $n$ a potential coincidence window that does not overlap with any other coincidence window: $\tau_i^{(n)} = \min \{t_{i+1}^{(n)} - t_i^{(n)}, t_i^{(n)} - t_{i-1}^{(n)}\}/2$. Thus any spike from spike train $m$ can at most be coincident with one spike from spike train $n$. Short vertical lines mark the times right in the middle between two spikes. For better visibility spikes and their coincidence windows are shown in alternating bright and dark color. In the same way (C) a coincidence window $\tau_j^{(m)} = \min \{t_{j+1}^{(m)} - t_j^{(m)}, t_j^{(m)} - t_{j-1}^{(m)}\}/2$ is defined for spike $t_j^{(m)}$ from spike train $m$. For two spikes to be coincident they have to be in each other's coincidence window which means that their absolute time difference has to be smaller than $\tau_{ij}=\min \{\tau_i^{(n)}, \tau_j^{(m)}\}$ (which is equivalent to Eq. \ref{['Eq:Coincidence-MaxDist']}). In this example the two spikes on the left are coincident, whereas the two spikes on the right are not. Modified from Kreuz17.
• Figure 5: Using the Spike Train Order framework to sort spike trains from leader to follower. A. Perfect Synfire pattern. B. Unsorted set of spike trains. C. The same spike trains as in B but now sorted. Modified from Kreuz17.