Statistical Assessment and Neuronal Composition of Active Synfire Chains

The synfire chain (SFC) model has been suggested as a network model for cortical cell assemblies. It is composed of consecutive groups of neurons, where each group is connected to the next in a feedforward fashion by a large number of convergent and divergent inputs. This connectivity structure enables stable propagation of packets of synchronous spiking activity through the network after stimulation of the first group. Recent advances in electrophysiological recording techniques allow for a hundred or more individual neurons to be recorded simultaneously, increasing the chance to detect active cell assemblies. A method that uses an intersection matrix to display repeated consecutive activations of identical groups of synchronously active neurons was suggested in Schrader (2008) and Gerstein (2012). Each entry in the matrix contains the degree of overlap of identical neurons being active at two different time bins. If a particular SFC is activated twice, a diagonal structure appears in the matrix, composed of consecutive time bins of high intersection values. Further convolution of the matrix with a diagonal linear filter enhances diagonal structures compared to isolated high intersection values, allowing to distinguish among the two. Several features of the data are expected to interfere with the analysis. First, the contrast between diagonal structures and the rest of the matrix can be severely diminished by higher firing rates of the neurons, thereby increasing the intersection values of individual pixels. Second, undersampling of the system and/or stochastic participation in assembly activation may lead to diagonal structures that fluctuate in intensity or even become discontinuous. Third, diagonal structures may become wiggly due to interference of the analysis bin width and the propagation speed of the SFC.Here we introduce a quantitative statistical evaluation of the presence of SFCs which enables for an automatic identification of the neurons participating in the SFC. This approach performs additional steps on the intersection matrix. Diagonal structures are enhanced by convolving the intersection matrix with a rectangular filter, which enables to cope with wiggly structures. Then, we test if there are significant sequences of high intersection values by generating multiple realizations of surrogate matrices where the positions of the original entries are randomized before filtering, thereby implementing the null hypothesis of repeated synchronous activations of specific neuronal groups but not in a consecutive manner in time. The entries of all surrogate matrices form the distribution of matrix entries under the stated null hypothesis. By choosing an upper quantile (e.g. 0.1%) we define a threshold to identify statistically significant entries that exceed this threshold. Using a clustering algorithm on those entries we label the diagonal structures as active synfire chains. The IDs of the neurons participating in the chain(s) are then extracted to identify the neurons composing the SFC and their group membership.We calibrated the method using stochastic simulations consisting of repeating consecutive synchronous spike patterns embedded in otherwise independent data. Our calibrations show that in most realistic scenarios with realistic spike rates and downsampled networks we are able to successfully identify large portions (> 90%) of the embedded SFCs while having low false positive and false negative levels. We discuss future improvements and possible applications to electrophysiological data