Figure 2. Novel prediction and experimental confirmation of PDB involvement in locomotion.

(a) According to control theory, nodes 2 and 3 (pink) cannot be controlled by a single signal u₁(t). By Eq. (2), the time evolution of x₂(t) of and x₃(t) follows a₃₁ẋ₂(t) = a₃₁ẋ₃(t), hence no signal u₁(t) is able to control x₂(t) and x₃(t) independently of each other. To independently control nodes 2 and 3, we need two input signals, as shown in (b). Similarly, when m independent signals aim to control k nodes connected to them, as shown in (c), the pink nodes are not controllable unless m ≥ k, which is the case shown in (d). (e) To explore the control role of PDB, we show the paths through which control signals can pass from receptor neurons (blue) to downstream muscles (pink). Control analysis finds that the five motor neurons, {VB11, VD13, PDB, VA12, VD12}, receive independent signals from {ALML, ALMR, AVM} (see SI Sec. II B). According to the principle illustrated in (c), in the intact worm, five of the seven muscles are independently controllable. When PDB is ablated, control signals can still reach all seven muscles, but the ablation of PDB forces the signal through only four neurons, reducing the number of independently controllable muscles from five to four. (f) Experimental validation of the involvement of PDB in locomotion. N = 43 PDB ablations were tested in the same experiment together with n = 35 mock-ablated controls. Error bars indicate mean ± standard deviation. Ablation of PDB resulted in significant abnormalities in Eigen Projection 1 features and a loss of ventral bias to deep body bends (SI Table III). Statistical test: multiple t-tests, significance level = 0.05, n.s. = not significant. See SI Sec. III B for experimental details of laser ablations, subsequent data analysis and exact p-values.