Figure 1.
Schematic of extracting spike timing networks. Neuronal spiking time series can contain consistent spike timing between neurons, forming spike sequences. A, Schematic of two spike timing networks, with their neurons (circles) and sequence spikes (vertical lines) colored blue and green. The dashed lines reflect the between-neuron consistent spike time relationships resulting from the spike sequences. The blue network’s sequence goes from neuron 3–4–5 (dark dashed lines), with 1 ms time delays, resulting in a 2 ms delay from 3 to 5 (light dashed line). The green network’s sequence is the same but from neuron 5–6 to 7. B, The spike time consistencies in A can also be visualized as cross-correlograms between all neuron pairs, at lags ranging from -10 to 10 ms with 1 ms bins. C, The networks in A, B but shown as spike trains per trial of two experimental conditions. The blue network trials’ have one sequence in condition A and two sequences in condition B, vice versa for the green network. To extract these two networks, we arrange spike trains of all neurons in a neuron-by-time binary matrix. These spike trains are then convolved with complex exponentials (or wavelets) of equal length at different frequencies, resulting in a complex-valued neuron-by-time matrix per frequency per trial. D, The cross products are then computed along the time dimension, resulting in a neuron-by-neuron cross-product matrix per frequency per trial: the cross spectrum. The between-neuron phase differences of the cross spectra over frequencies, reflect the consistent between-neuron spike time delays. E, Using a recent technique denoted as SPACE, the structure in the cross spectra over frequencies can be extracted, and described as separate spike timing networks. The blue and green networks are each described by a neuron profile, describing network membership by a single weight per neuron, a time profile, describing the spike sequence by a time coefficient per neuron, and a trial profile, having a single weight per trial, indicating how strongly the network was present. For details, see Materials and Methods, sections Extracting spiking timing networks from neuronal spike recordings, SPACE describes time consistency-induced phase coupling in cross spectra, and Obtaining cross spectra that are optimal for extracting spike timing networks.