Simulated random walk on the cilium membrane recapitulates the patterns of axial GPCR movements. (A) Schematic of the cilium membrane. Green dot, a theoretical GPCR; θ, randomly generated angle that determines movement direction; arrows, a subset of possible trajectories; Circ, circumferential. (B–F) Simulation results with parameters found for the SSTR3 tracking shown in G: D_m = 0.15 µm²/s, l_ax = 8 µm, time step = 0.3 s (Video 6). (B) Axial position kymograph from a single simulation run. Red and black arrowheads indicate regions of low and high axial velocity, respectively. (C) 2D projection of the 3D circumferential positions from run in B show expected denser population of points at the edges. (D) Black symbols represent mean MSD(τ) of five runs; in each run, the MSD represents the mean of >1,000 squared displacements. Error bars = SEM. (E and F) Results from simulations including transient coupling to motors or stationary objects. In each plot, black circles represent the mean from five independent simulations with l_ax = 5 µm and D_m = 0.15 µm²/s. Straight lines connect the first two MSD(τ) points. Dashed lines are the Eq. 1 predictions. (E) Stochastic, transient coupling to an axial moving motor, where P_m = 0.2, v_m = 0.6 µm/s, and coupling duration, t_m, are indicated (Video 7). (F) Transient binding to immobile objects, where P_b = 0.2, t_b = 10 time steps (Video 6). Note that with transient motor transport, MSD(τ) consistently exceeds the Eq. 1 prediction, whereas transient binding leads to an overall reduced slope. (G–J) Comparison of GPCR motion and pure random walk simulation shows similar frequencies of apparent processive motion and absence of motion. (G) Kymograph segment of an SSTR3 tracking experiment (Video 3). Left, raw kymograph showing two Qdot-labeled SSTR3s. Right, Track 2 was masked for track 1 analysis. Overlaid markers plot detected positions; colors indicate instantaneous velocity categories: blue, v < 0.2 µm/s, green, v ≥ 0.2 µm/s. (H) Frequency of sequential low-velocity clusters (low v), high-velocity clusters, anterograde (high v ant) or retrograde (high v ret), pooled from 14 tracked Qdot-labeled GPCRs obtained in eight independent experiments (Table 1). Lines are exponential fittings. (I) Axial positions from 180 s of a pure random walk simulation. Clusters of sequential displacements are color coded: low v, red; high v anterograde, purple; high v retrograde, green. (J) Velocity cluster histograms from five simulation runs. Lines as in H.