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State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data
Figure 6
Analysis of experimental spike data using the state-space log-linear model.
(A) Experimental time table of delayed-response hand movement task. The experiments were designed and conducted by Riehle and her colleagues [8], [84]. During the preparatory period (PP, 1500 ms) that starts with the preparatory signal (PS), the presentation of the response signal (RS) was expected at three distinct moments at 600, 900, and 1200 ms (expected signals, ESs). Here the RS occurs finally after the longest possible delay of 1500 ms. After the RS, the requested movement was executed (reaction and movement time, RT-MT). See [8], [84] and the text for the detailed experimental protocol. (B) Dot displays of the spike sequences (duration: 2 s, sampling resolution 1 ms) of three neurons simultaneously recorded from the primary motor cortex (MI). The spike sequences are aligned at the onset of the PS (
trials). The synchronous spike events across the 3 neurons detected in individual trials (detection in bins of 
width) are marked by blue circles. (C) Observed rates of joint spike events, 
(
). All of the events are detected in bins with a width of 
. (Top) Observed rates of the spike occurrence of the individual neurons (
). (Middle) Observed rates of the synchronous spike events between two neurons specified by index 
(
). (Bottom) Observed rate of the synchronous spike events of all 3 neurons, 
. (D) Estimation of the time-varying log-linear parameters of 3 neurons, 
(
), from the binary data shown in C, according to the method summarized in Table 1. The panels depict the MAP estimates of the log-linear interaction parameters (solid lines; from top to bottom, the first and second order log-linear parameters and a triple-wise spike interaction, 
). The gray bands indicate the 95% credible interval. In this analysis, we used an identity matrix as an autoregressive parameter, i.e. 
, in the state model. The covariance matrix of the initial parameter was fixed to 
. (E) The smoothed estimate of a triple-wise spike interaction, 
, is computed from binary data constructed using a bin-width of 2 ms (Top) and a bin-width of 5 ms (Bottom). The top of each panel shows the timing of the synchronous spike events of all three neurons.
doi: https://doi.org/10.1371/journal.pcbi.1002385.g006