Neural Correlates of the Time Marker for the Perception of Event Timing

Dissociation between two measures of timing perception. A, Stimulus configuration of the simple RT and SJ tasks. In both tasks, we used two types of temporal changes of the motion coherence: step (30%, 40%, and 90%) and ramp (80, 120, and 200%/s; for details, see Materials and Methods). B, Example data from the simultaneity judgment task with three levels of ramp stimuli. The horizontal axis shows the SOA between the coherent motion onset and a beep, while the vertical axis shows the percentage of simultaneous responses. The PSS was defined as the weighted average of SOA values based on the percentage of simultaneous responses. C, Averaged RTs for step and ramp stimuli. Error bars indicate SEs across participants. D, Averaged PSS for step and ramp stimuli. Error bars indicate SEs across participants. Both RT and PSS decrease with increasing stimulus amplitude, but the decrease is much larger for RT than for PSS. E, Comparison between the RT and PSS for both the step and ramp stimuli. Error bars indicate SEs across participants. The steeper slope for the ramp stimuli suggests that the amplitude of ramp stimuli has a larger effect on the PSS than the step stimuli. Please note that x- and y-axes are scaled differently. F, Correlation between the variance of RT across stimuli and that of PSS. Each dot represents the data of individual participants. A significant correlation supports the result that the same integrated signal could account for both RT and PSS variations (Fig. 3).

An example of MEG responses to step and ramp motion onsets and the extracted visual response time course. A, MEG response time courses averaged across trials for a typical participant. Data from 10 sensors that showed the greatest response for the 90% step stimulus at the peak latency are overlaid, and the gray region in each panel indicates the motion coherence time course. For the step stimuli, the MEG responses peaked at ∼230 ms, and the amplitude increased with motion coherence. For the ramp stimuli, the response peak was less clear and the peak latency was much longer. B, Normalized spatial pattern (topographic map) of the visual and auditory responses used in the SSP analysis, for the participant shown in A. The left image shows the peak MEG response evoked by the strongest visual stimulus (90% step), while the right image shows the largest peak MEG response averaged with respect to the timing of auditory stimuli. The auditory peak was either M100 or M200 (it was M100 for eight participants, and was M200 for three participants, including the participant shown here). C, The time course of visual responses for the 90% step stimulus, extracted by the SSP method (Tesche et al., 1995). The spatial pattern at each latency was decomposed into visual and auditory responses by calculating the best weight of the spatial pattern of visual and auditory responses (B), and the absolute value of the weight was defined as the response amplitude.

Neural correlates of RT and PSS. A, B, Schematic of the peak/level detector models (A) and the integrator model (B). C, The time course of visual responses for a typical participant. Solid and dotted lines represent the optimized threshold of the level detector model for RT and PSS, respectively (they were almost the same for this participant). Gray squares represent the latencies predicted by the peak detector model (common across the detection latencies for RT and time-marker latencies for PSS). Diamonds represent the latencies predicted by the level detector model (open and filled diamonds represent detection latencies for RT and time-marker latencies for PSS, respectively). D, The time course of integrated visual responses (τ = ∞) for the same participant as shown in A. Solid and dotted lines represent the optimized threshold of the integrator model for RT and PSS, respectively. Open and filled circles represent the detection latencies and time-marker latencies, respectively. The threshold for PSS was lower than that for RT. E, F, Relationship between RT and detection latency (E), or between PSS and time-marker latency (F), for the participant shown in A and B. Since we are interested in the model that quantitatively accounts for the RT or PSS variations, the model performance was evaluated by the MSE from the best-fitted line of unit slope, which takes into account not only poorly correlated data with a slope of 1 but also highly correlated data with a slope higher or lower than 1. G, Comparison of the threshold for the integrator model (τ = ∞) that best accounts for RT and PSS variations. Error bars indicate SEs across participants. The threshold was significantly lower for PSS than for RT, suggesting that the stimulus content information, which is necessary for manual response, was not available at the timing of the time marker, and the event timing is postdictively perceived (Nishida and Johnston, 2002).

Comparison of models that account for the changes in RT and PSS using the MEG response. A, B, The MSE from the best-fitted line of unit slope for the scatter plot between RT/PSS (x-axis) and the latency predicted by the model (y-axis), as shown in Figure 3, E and F . The MSE was summed across participants, and the error bars indicate SDs across 1000 bootstrap samples. C, D, While MSE is a biased estimator of the prediction error, bias-corrected MSE accounts for the difference in both susceptibility to noise and the number of parameters across models. The bias-corrected MSE was summed across participants, and the error bars indicate SDs across 1000 bootstrap samples. A and C, and B and D show the results for the RT and PSS data, respectively. The SH test (Shimodaira, 1998) performed on the bias-corrected MSE showed that the peak and level detector models were significantly worse than the best model for both RT and PSS (Table 1).

Effect of an auditory stimulus on the model latencies. A, B, Detection latency for RT (A) and time-marker latency for PSS (B) based on the full integrator model (τ = ∞), calculated separately for shorter and longer SOA trials. Similar latencies between shorter and longer SOA trials indicate that the auditory response was reasonably removed by the SSP analysis to extract the visual response time course, and had a negligible effect on the latencies predicted by the integrator model. C, Comparison of the threshold for the integrator model (τ = ∞) that best accounts for RT and PSS variations, calculated separately for shorter and longer SOA trials. Error bars indicate SEs across participants. The threshold was significantly lower for PSS than for RT for both shorter and longer SOA trials (p = 0.03 and p = 0.001, respectively), replicating the analysis that used all of the trials (Fig. 3G ).

Subjective delay of motor response. A, Stimulus configuration of the second experiment that measured the subjective delay of simple reactions. B, Stimulus detectability, expressed in terms of d', as a function of motion coherence. Error bars indicate SEs across participants. C, Representative histograms of RT and subjective delay of motor response for each motion coherence level. D, The RT, subjective delay of RT, and PSS, as a function of motion coherence. Error bars indicate SEs across participants. E, The slope of the fitted line for the plot between coherence level and RT/subjective delay for each individual participant. The subjective delay slope, on average, was shallower than the RT slope but was significantly <0 (p < 0.001). In addition, the RT and subjective delay slopes were similar for 4 of 11 participants (red lines).