The effects of subdiffusion on the NTA size measurements of extracellular vesicles in biological samples

The interest in the extracellular vesicles (EVs) is rapidly growing as they became reliable biomarkers for many diseases. For this reason, fast and accurate techniques of EVs size characterization are the matter of utmost importance. One increasingly popular technique is the Nanoparticle Tracking Analysis (NTA), in which the diameters of EVs are calculated from their diffusion constants. The crucial assumption here is that the diffusion in NTA follows the Stokes-Einstein relation, i.e. that the Mean Square Displacement (MSD) of a particle grows linearly in time (MSD $\propto t$). However, we show that NTA violates this assumption in both artificial and biological samples, i.e. a large population of particles show a strongly sub-diffusive behaviour (MSD $\propto t^\alpha$, $0<\alpha<1$). To support this observation we present a range of experimental results for both polystyrene beads and EVs. This is also related to another problem: for the same samples there exists a huge discrepancy (by the factor of 2-4) between the sizes measured with NTA and with the direct imaging methods, such as AFM. This can be remedied by e.g. the Finite Track Length Adjustment (FTLA) method in NTA, but its applicability is limited in the biological and poly-disperse samples. On the other hand, the models of sub-diffusion rarely provide the direct relation between the size of a particle and the generalized diffusion constant. However, we solve this last problem by introducing the logarithmic model of sub-diffusion, aimed at retrieving the size data. In result, we propose a novel protocol of NTA data analysis. The accuracy of our method is on par with FTLA for small ($\simeq$200nm) particles. We apply our method to study the EVs samples and corroborate the results with AFM.