Computational protocol: Bridging the Gap between Single Molecule and Ensemble Methods for Measuring Lateral Dynamics in the Plasma Membrane

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Protocol publication

[…] Similarly to the kICS analysis, the SPT analysis was performed separately for each color channel using the Particle Tracker plug-in in ImageJ as has been described previously . This analysis generates a text file containing the positions of the detected QD particle positions in each image frame as well as linked trajectories describing the motion of individual QDs in time. In this analysis, a major limitation to the use of QDs in SPT is apparent by the generation of a large number of short trajectories rather than a more desirable few very long continuous particle trajectories. In order to minimize the number of inaccurate particle linking events, this analysis was done with very conservative particle linking criteria, corresponding to a particle link range of 5 image frames and a maximum allowed particle displacement of one pixel per image frame. The detected particle motion data was post-processed using custom written Mathematica routines. This post-processing included further linking of particle trajectories by a coincidence search routine in time and space of all trajectories, with a minimal length greater than a cut-off value (here n = 10 to 20 frames) with other trajectories that coincided within space, δr (here set to 8 pixels) but not time. We next calculated the mean squared displacements for each single trajectory, m, that contained n>20 displacements, and for all possible time intervals, nτ, (4)where τ is the acquisition time interval and N is the total number of displacements in a trajectory. The average diffusion coefficient, , of all trajectories for a given molecule and label was then determined by calculating the average mean squared displacements at each time interval, n τ, for each individual trajectory, m(5)The average diffusion coefficient was then determined by curve fitting the initial five time points, with fit weights equal to the inverse variance (1/σ2), to the expression for free diffusion plus a constant, c,(6)where is the average diffusion coefficient.Furthermore, the mean squared displacement for all single trajectories that contained n>50 frames were analyzed at time intervals, 1≤n≤5, corresponding to a maximum time displacement of approximately 0.2 s respectively, by curve fitting to three simple motion models,Free diffusion,(7)Confined diffusion,(8)andMixed transient diffusion(9)where DConfined is the confined diffusion coefficient, τConfined is the confinement time, and where the area of the confinement region, L2, is given by(10)Having thus fitted each of the experimentally determined single molecule trajectories to all three theoretical models (–) for the time interval, 1≤n≤5, we then used F-statistics in order to identify the simplest model (i. e. the model with the least number of free fitting parameters) that described the data. Specifically, this was done by use of the F-test, where we calculated the F-statistic(11)where n is the number of data points, RSSi is the residual sum of squares of model i, and pi is the number of free fitting parameters of model i, and where p2>p1. We next compared the calculated F-statistics for the individual trajectories to the critical F distribution with (p2-p1,n-p2) degrees of freedom and a significance level of p = 0.05. Fitted values for all trajectories best described as free diffusion are shown as Box- and- Whisker plots ( and ). In these plots, the box ranges from the first to the third quartiles, and where the statistical median is the center line in the box, while the whiskers extend to the farthest point that are within 3/2 of the interquartile range, and where remaining points are plotted individually as outliers, indicating the presence of heterogeneity among single trajectories. […]

Pipeline specifications

Software tools Particle Tracker, ImageJ
Applications Laser scanning microscopy, Microscopic phenotype analysis
Organisms Homo sapiens