Mean square displacement (MSD) analysis is a technique commonly used in colloidal studies and biophysics to determine what is the mode of displacement of particles followed over time. In particular, it can help determine whether the particle is:
- freely diffusing;
- transported;
- bound and limited in its movement.
On top of this, it can also derive an estimate of the parameters of the movement, such as the diffusion coefficient.

@msdanalyzer is a MATLAB per-value class that helps performing this kind of analysis. The user provides several trajectories he measured, and the class can derive meaningful quantities for the determination of the movement modality.

@msdanalyzer can deal with tracks (particle trajectories) that do not start all at the same time, have different lengths, have missing detections (gaps: a particle fails to be detected in one or several frame then reappear), and do not have the same time sampling. As soon as you added your tracks to the class, everything is transparent. It offers facilities to plot and inspect the data, whether for individual particles, or on ensemble average quantities. It has several methods for correcting for drift, which is the main source of error in the analysis. Once corrected, the data can analyzed via the MSD curves or via the velocity autocorrelation. Automated fits of the MSD curves are included (but they require you have the curve fitting toolbox), allowing to derive the type of motion and its characteristics.

Included is a rather long tutorial with references, that will introduce you to the problem using numerical simulations, make you reproduce published results, and detail how the class work. Some basis of physics are required.

http://tinevez.github.io/msdanalyzer/

If you use this tool for your work, we kindly ask you to cite the following article for which it was created:

Nadine Tarantino, Jean-Yves Tinevez, Elizabeth Faris Crowell, Bertrand Boisson, Ricardo Henriques, Musa Mhlanga, Fabrice Agou, Alain Israël, and Emmanuel Laplantine. TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO-IKK supramolecular structures. J Cell Biol (2014) vol. 204 (2) pp. 231-45

http://jcb.rupress.org/content/204/2/231