(A) One of the PMSI neurons (glutamatergic neurons involved in the speed regulation; [Kohsaka et al., 2014]), named A02j, relates GDLs to each other across abdominal segments. In particular, A02j synapses onto the GDLs of the two segments anterior to its own segment, potentially starting the excitatory drive over GDLs to promote the relaxation of segments anterior to the muscle contraction wave. Additionally, A02j synapses directly onto some motor neurons of the segments anterior to its own segment (not shown), with potentially an inhibitory effect as shown in (Kohsaka et al., 2014). Interestingly, A02j in one segment might promote the disinhibition of its anterior homologs, given than GDL, a GABAergic neuron, synapses onto a segment-local putatively GABAergic neuron (A31d; similar morphology and belonging to the same lineage as the GABAergic neurons A31b and A31k [Schneider-Mizell et al., in press]). (B) The GDL-A27h circuit interacts with neurons known to affect the speed of locomotion (PMSIs and GVLIs). A02d is a PMSI neuron (Kohsaka et al., 2014) that receives inputs from GDL and in turn synapses onto the A08a neuron (a GVLI; [Itakura et al., 2015]). A08a, in turn, synapses onto two putatively GABAergic neurons (A31d and A31x). This circuit suggests that GDL prevents A02d from driving A08a, which could potentially underlie the observed activation pattern of A08a, which is active two segments posterior to the forward-moving peristaltic wave (Itakura et al., 2015). We did not observe synapses between A08a and motor neurons. Furthermore, GDL might provide inhibition ipsilaterally to the contralaterally projecting, Eve-Skipped+ neuron A08e3, which is necessary for maintaining bilaterally symmetric muscle contraction amplitude (Heckscher et al., 2015). This suggests a role for GDL in the regulation of posture adjustment, and therefore a close relationship between the circuits for wave propagation and the circuits for ensuring symmetrical muscle contractions in forward locomotion. (C) The connectivity matrix between proprioceptive sensory neurons and A02d (one of the PMSIs), A08a (GVLIs), and A08e3 (one of the Even-Skipped+ neurons).