Trajectory analysis is commonly based on the Brownian diffusion hypothesis and trajectories are usually characterized from the calculation of D_{inst}, the MSD, the confinement index, the size of the confinement domain and the dwell time along the trajectory (Saxton & Jacobson, 1997). Experience has shown that, within the sampling frequency limit, the diffusion of membrane proteins often differs from simple Brownian diffusion. This has been attributed to protein binding, crowding, constraints imposed by the cytoskeleton, active transport or even local membrane topology and composition. These factors plus statistical fluctuations lead to broad distribution of the diffusion coefficient, which typically extends over two to three orders of magnitude. Trajectories can be sorted on the basis of their compartment location and, by reference to the linear MSD obtained for regular diffusion, on the basis of the MSD curvature (Fig. 4B), which characterizes regular diffusion, oriented motion, confined diffusion and anomalous diffusion.

The MSD is obtained by averaging displacement over time intervals from single trajectories, error in the MSD calculation increasing when there are fewer points in the trajectory (Qian *et al.*, 1991; Saxton & Jacobson, 1997). D_{inst} can be calculated accurately using a linear fit of the short-term MSD (Fig. 4B) (Kusumi *et al.*, 1993). However, for longer time intervals, the number of data points decreases and, usually, only the first quarter of the MSD can be exploited. This defines the maximal time window accessible for the diffusion characterization and is commonly ∼ 10–20 s. This higher limit has direct implications for the analysis of confined diffusion, which results from the restriction, due to its environment, of the area that a particle can explore (Kusumi *et al.*, 1993; Simson *et al.*, 1995; Feder *et al.*, 1996; Dietrich *et al.*, 2002; Charrier *et al.*, 2006). For a confined particle, the MSD is linear over short times and eventually bends to reach a plateau when the particle has had enough time to reach the edges of the confinement domain. The ability to identify the plateau and to quantify the confinement domain size depends on the characteristic time to reach the plateau with regards to the exploitable time window. In other words, for small confinement areas, high time and space resolutions are needed. However, for larger confinement regions, longer acquisitions are needed to detect the confinement effect on the MSD. For the calculation of the MSD to be usable, the mean spot displacement must be higher than the pointing accuracy. This defines the lower threshold of diffusion coefficient below which the particle is considered to be immobile. At constant exposure time, spatial accuracy decreases with increasing diffusion coefficient (Schnapp *et al.*, 1988). Typically, in the experimental conditions described above, one may have access to diffusion coefficients ranging from 10^{−4} up to 10^{−1} μm^{2}/s and confinement areas ranging from tens to hundreds of nanometers. The range of accessible diffusion properties depends on the pointing accuracy, frequency and duration of acquisition, but also on the diffusion coefficient of the probed molecule itself (Schnapp *et al.*, 1988; Ritchie *et al.*, 2005). As a consequence, comparing distributions of diffusion coefficients for acquisitions made with different sets of parameters is not straightforward. This is of particular importance when comparing various organic dyes with QDs, which differ greatly in their photophysical properties. Careful analysis is also necessary when comparing proteins with significantly different dynamic properties, as in the case of receptors at inhibitory and excitatory synapses.