Analysis and interpretation of two-dimensional single-particle tracking microscopy measurements: effect of local surface roughness.

Methodological advances in light microscopy have made it possible to record the motions of individual lipid and protein molecules resident in the membrane of living cells down to the nanometer level of precision in the x, y plane. Such measurement of a single molecule's trajectory for a sufficiently long period of time or the measurement of multiple molecules' trajectories for a shorter period of time can in principle provide the necessary information to derive the particle's macroscopic two-dimensional-diffusion coefficient-a quantity of vital biological interest. However, one drawback of the light microscopy procedures used in such experiments is their relatively poor discriminatory capability for determining spatial differences along the z axis in comparison to those in the x, y plane. In this study we used computer simulation to examine the likely effect of local surface roughness over the nanometer to micrometer scale on the determination of diffusion constants in the membrane bilayer by the use of such optical-microscope-based single-particle tracking (SPT) procedures. We specifically examined motion of a single molecule along (i) a locally planar and (ii) a locally rough surface. Our results indicate a need for caution in applying overly simplistic analytical strategies to the analysis of data from SPT measurements and provide upper and lower bounds for the likely degree of error introduced on the basis of surface roughness effects alone. Additionally we present an empirical method based on an autocorrelation function approach that may prove useful in identifying the existence of surface roughness and give some idea of its extent.