Before revision:  We show by direct calculations that for sufficiently close vesicle-to-spine diameter ratios, there can only be unidirectional motion . The critical vesicle-to-spine diameter ratio predicted by our analysis , at which there is a transition from unidirectional to bidirectional motion, is consistent with experimental observations of vesicle trajectories in the literature.
After revision:  We show by direct calculations that for sufficiently close vesicle-to-spine diameter ratios, there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio predicted by our analysis , at which there is a transition from unidirectional to bidirectional motion, is consistent with experimental observations of vesicle trajectories in the literature.