In this analysis, as throughout this work, we start with B8_total, the total frequency of B8 firing averaged over an entire single phase (for the purposes of this analysis always protraction) of a single feeding motor program. Examination of B20–B8 crosscorrelation histograms constructed from the protraction phases of programs pooled from each preparation or from the entire dataset (Fig. 4B) suggests that B8_total can be decomposed into two components: B8_background, the background frequency of B8 firing even in the absence of B20 firing, and B8_B20, an additional component of B8 firing induced by the excitatory synaptic input from B20. Thus,

B8_total = B8_background + B8_B20. [1]

We assume that the processes that give rise to B8_background (spontaneous firing of B8 or synaptic input from neurons other than B20) are completely independent of B20 firing, so that B8_background remains constant whether or not B20 is firing. In contrast, the peak in the crosscorrelation histogram in Fig. 4B implies that B8_B20 is concentrated preferentially after B20 spikes. Guided by the histogram, we take it to be concentrated into windows following each B20 spike of length 70 ms, but none of our main conclusions depend on this precise value. With these assumptions, B8_background and B8_B20 correspond, respectively, to the gray and black areas of the crosscorrelation histogram in Fig. 4B.

To decompose B8_total in any individual motor program, we partition the protraction phase into the set of 70-ms windows after the B20 spikes and the set of intervening segments (white and gray bars, respectively, in Fig. 4A). B8 firing frequency averaged over the set of intervening segments is B8_background. B8_B20 is then computed using Eq. 1.

Finally, B8_B20 is itself decomposed by using the relation

B8_B20 = B20 × FSE, [2]

where B20 is the firing frequency of B20 averaged over the entire protraction phase in the same way as B8_total. This defines FSE, the functional synaptic efficacy. The functional synaptic efficacy is thus the above-background number of B8 spikes expected to be induced by a B20 spike or, given that the dataset analyzed here has a functional synaptic efficacy always considerably <1, the approximate above-background probability that a B20 spike is followed by a B8 spike.

B8_total, B8_B20, and the functional synaptic efficacy are the quantities plotted respectively in Fig. 4 C and D, Top, Middle, and Bottom.

For accuracy, this analysis requires that the set of windows after the B20 spikes and the set of intervening segments both occupy a significant fraction of the protraction phase and that B8 fires a sufficient number of spikes to sample each of the two partitions. This was the case in the dataset analyzed here. In the 435 motor programs analyzed, the protraction phase lasted 14.2 ± 9.2 s (mean ± SD), of which the set of B20 windows occupied 4.5 ± 2.3 s, and the set of intervening segments occupied 9.7 ± 7.8 s. B8 fired 53.9 ± 32.8 spikes during the protraction phase. None of our major conclusions, however, depend on the precise choice of the window duration (Fig. 6).