SPT processing
In this section, we will further process the tracking results (i.e. the trajectories) from sptPALM to retrieve some basic parameters describing 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 an important parameter since, from inspection of the MSD plot, one can obtain information about the type of the motion of a particle. 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 from fitting the MSD vs. lag time plot. See the schematic on the right (Taken from Ruthardt, Mol Ther, 2011).
To calculate the mean square displacement, I am using a public Github repository, the MSDanalyzer. The MSDanalyzer repository is very worth going through. It provides the Matlab codes to analyze particle tracking data as well as some background information as well as a simulator function. The script calculate_MSD.m allows very simple interaction with MSDanalyzer and is the starting point of our further analysis. At the end you'll get something like this, which will appear in the matlab command window and informs about the calculated diffusion coefficients.
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)
You'll see an overlay of all MSD curves (for each individual track) 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.
At the end of calculate_MSD.m open the script tracks_post_processing.m without clearing the workspace.
This short script produces three outputs.
- A side-by-side view of mobile and immobile trajectories along with a rendered representation of the corresponding localizations.
- A histogram of the diffusion coefficients
- Two separate MSD plots for mobile and immobile trajectories.
Note that the script uses a threshold to discriminate mobile from immobile.
Particles or molecules often don't freely diffuse in a cellular environment. Due to the complexity and density of cellular organelles or the cytoplasm, molecules interact and bind frequently to other cellular components. This might lead to a transient immobilization and can be observed when inspecting the molecules trajectory or the MSD vs. time plot.
To identify such confined periods, I have used the so-called confinement index, which was described previously (Simson, Biophys J, 1995). The algorithm scans the trajectory searching for periods in which the molecule remains in a region considerably longer than expected for (free) Brownian motion. An input parameter is thus the diffusion coefficient as well as the radius of the confined region.
To get a better idea about transient confinement and calibrate the confinement index, simulating a few trajectories might be a good starting point. The simulation section allows to the generation of 2D trajectories with or without confinement.