Fig. 3.

Spine shape transition studied by SIM-based geometrical analysis. a Trajectories of shape transition for three examples of spines mapped into the feature space. The right images of reconstructed spine shapes are from three spines at multiple time points (0–60 min). The values of mean curvatures are mapped onto the surface. Bar: 500 nm. b Projection and 3D maps of trajectories created from a population of spines (46 spines from eight neurons in five independent culture preparations). c The direction and length of trajectories in spine shape changes, mapped into the feature space. Total lengths of trajectories are shown as the radii of yellow circles, and trajectories projected onto four orthogonal directions are shown as black arrows. The PC1–2 plane is shown. The positions of spines at different time points were also mapped after SVM-based shape classification into mushroom and non-mushroom spines (magenta and green dots). d A scheme of three types of spine behavior in the feature space. Orange, magenta, and green dots indicate spines classified in groups 1, 2, and 3, respectively. e Mapping of the most concave surface on spine heads classified in groups 1, 2, and 3. Group 2 spines maintained the concave surface, whereas the concave surface was less stable in group 1, and did not exist in group 3. f The fraction of time points when the concave surfaces can be mapped to spine heads (concave surface ratio), and the fraction of time points when the concave surfaces located in the same direction within the spine heads (concave surface stability) were measured for three groups of spines [n = 16, 10, and 7 spines for groups 1, 2, and 3, respectively; one-way ANOVA followed by Tukey–Kramer procedures for multiple comparison tests; concave surface ratio: F(2,30) = 41.57, p = 2.25 × 10⁻⁹; concave surface stability: F(2,30) = 33.78, p = 2.08 × 10⁻⁸; *p < 0.05, ***p < 0.001. Data are presented as the mean ± SEM]