A mathematical estimation of membrane expansion. (A) Hierarchical diagram of the Bayesian linear model of neuronal surface area increases. Probability distributions (blue) of surface areas at 24 and 48 h represent priors imposed, with mean μ and SD σ for the normal distributions, and a uniform distribution for the model error. (B) Posterior predictions of surface area expansion by the model (orange lines) were compared with actual data (black line) to check for model fit. (C) Credible regression lines (orange) and mean (blue line) regression line of predicted plasma membrane expansion (n = 400 credible regression lines, n = 62 cells). (D) Estimates of membrane addition between 24 and 48 h. The black line is the measured surface area at 24 h in vitro. The blue line and blue shaded area represent predicted amount of plasma membrane expansion using a Bayesian linear model (A–C). Green lines represent predicted membrane added by VAMP2-mediated exocytosis. Orange lines represent predicted net membrane addition from VAMP2-mediated exocytosis after accounting for clathrin-mediated membrane removal. (E) Example transmission electron micrograph and histogram of measured diameters of non–clathrin-coated vesicles with density line overlaid (black solid line), 25th percentile (red dotted line), and 75th percentile (black dotted line) of the interquartile range (n = 88). (F) Box and whisker plots of frequency of clathrin-mediated endocytosis (n = 7 cells at 24 h and n = 8 cells at 24 h; box represents median ± IQR and whiskers reach minimum and maximum values within 1.5 times the IQR). (G) Example transmission electron micrograph and histogram of measured diameters of clathrin-coated vesicles with a density line overlaid (black solid line). The 25th percentile of the interquartile range (red dotted line, 30 nm) and 75th percentile of the interquartile range (black dotted vertical line, 40 nm; n = 13).