Schematic of one possible model of the BF-ERP interaction that is consistent with our findings. This model consists of 10 BF bursting neurons (green to red traces show the PSTHs), where the ones with stronger bursting also have earlier onset latencies. Specifically, we set the peak bursting amplitudes to range from 100 to 20 spikes per second, and the onset latency to stagger by 5 msec. The population average is shown in black. In this model, we assume that all BF bursting neurons contribute to the generation of the frontal ERP with a fixed delay of 5 msec. The contribution of individual BF bursting neurons to the frontal ERP, indicated by dashed traces, cannot be directly observed and only the summed ERP response (black) can be experimentally observed. Two example trials are shown to illustrate how the BF bursting amplitude linearly scales with the frontal ERP (Figure 2): one with bursting amplitude set at 100% (left) to resemble a hit trial, and the other with bursting amplitude set at 50% (right) to resemble a miss or standard trial. The relative amplitude and relative timing between BF bursting neurons, and also between BF and the frontal ERP, are unaffected by the amplitude scaling. Raster plots for neuron#1 and #10 are shown below the two example trials (30 repeats each). Baseline tonic activity of BF bursting neurons is omitted for clarity. In this model, the bursting amplitudes of all BF neurons are linearly scaled with the frontal ERP amplitude. The subset of BF neurons with stronger bursting responses temporally leads the frontal ERP, while the activity of the majority of BF neurons trails the frontal ERP, even though all BF neurons causally contribute to ERP generation. This model further predicts higher magnitudes of BF-ERP cross correlation coefficient in BF neurons with stronger bursting responses, even though each of the smoothed PSTHs should be perfectly and equally correlated with the frontal ERP. This prediction arises because the higher firing rate in strongly bursting BF neurons allows the underlying spike trains to better approximate the smoothed PSTH function in single trials (e.g., neuron #1), while the stochastic spike trains provide a poor approximation of the smoothed PSTH especially when the BF bursting rate is low (e.g., neuron #10), partly because no spike was generated in a significant proportion of trials. Clearly, this model is only one of many possible models compatible with our findings. The purpose of this model is to show that our results are fully compatible with the scenario that all BF neurons causally contributes to the frontal ERP, even for the BF bursting neurons whose activity trails the frontal ERP in the cross correlation analysis. Alternatively, our results are compatible with the model that the subset of BF neurons trailing the frontal ERP may instead be driven by inputs from the frontal cortex.