SPT processing
In this section, we will process the tracking results (i.e. the trajectories) from sptPALM to retrieve some basic parameters on the particle dynamics.
A common, if not the most common analysis starts with calculating the so-called mean square displacement (MSD).
The MSD <r^2> describes the average of the squared distances between a trajectory's start and end position for all time lags (delta t). It is important because from inspection of the MSD plot, you can obtain information about the mode of motion. This type of movement can then be used for data interpretation in a biological context. The following types of movement can be identified from the MSD plot and/or fitting the MSD vs. lag time plot. See the schematic on the right.
To calculate the mean square displacement, I am using a public Github repository, which can be found here MSDanalyzer. The MSDanalyzer repository is very worth going through. It provides the Matlab code to analyze particle tracking data as well as some background information and also a simulator function. The script calculate_MSD.m allows very simple interaction with MSDanalyzer and is the starting point of further analysis. At the end you'll get something like this, which in the matlab prompt informs about the calculated diffusion coefficient.
Estimating D through linear weighted fit of the mean MSD curve. D = 4.620e-03 with 95% confidence interval [ 4.115e-03 - 5.126e-03 ]. Goodness of fit: R² = 0.968. Fitting 91 curves of MSD = f(t), taking only the first 25% of each curve... Done. Estimation of the diffusion coefficient from linear fit of the MSD curves: D = 0.0256 +/- 0.0359 (mean +/- std, N = 6)
Without clearing the workspace, open the script tracks_post_processing.m
The first cell produces an overlay of all MSD curves together with the average curve on the right. Note that with increasing lag time, fewer data points are available which leads to increased uncertainty of the MSD values. The diffusion coefficient is thus measured by performing a linear fit of only the first part of the MSD curve.
