Trajectory analysis of single molecules exhibiting non-Brownian motion

Abstract

Four techniques for analyzing single molecule tracking data--confinement level analysis, time series analysis and statistical analysis of lateral diffusion, multistate kinetics, and a newly developed method, radius of gyration evolution analysis--are compared using a set of sample fluorophore trajectories obtained from the lipophilic carbocyanine dye 1,1'-dioctadecyl-3,3,3'3'-tetramethylindocarbocyanine, DiIC(18), partitioned into surface tethered poly(n-isopropylacrylamide). The purpose here is two-fold: first to test that these techniques can be applied to single molecules trajectories, which typically contain a smaller total number of frames than those obtained from other particles, e.g. quantum dots or gold nanoparticles; and second to critically compare the information obtained from each method against the others. A set of five SMT trajectories, ranging in length from 41 to 273 steps with a 30 ms frame transfer exposure, were all successfully analyzed by all four techniques, provided two important criteria were met: enough steps to define the motion were acquired in the trajectory, generally on the order of 50 steps, and the fast and slow diffusion coefficients differ by at least a factor of 5. Beyond that the four trajectory analysis methods studied provide partially confirmatory and partially complementary information. SMT data resulting from more complex physical behavior may well benefit from using these techniques in succession to identify and sort populations.

Charge-Dependent Transport Switching of Single Molecular Ions in a Weak Polyelectrolyte Multilayer

“…Methods such as sliding time window mean squared displacement methods would be more appropriate for long trajectories. 57 …”

Molecule motion at polymer brush interfaces from single‐molecule experimental perspectives

“…Although the combination of FCS and single‐molecule polarization is useful in examining the diffusive and orientational dynamics of fluorescence probes in polymer brushes, it lacks spatial resolution and is incapable of detecting spatial heterogeneity in translational diffusions. Using SMT, Elliott et al investigated the diffusion of small fluorescent probes inside PNIPAM brushes of an estimated grafting density of ∼0.1 chains/nm 2 and a swollen brush thickness of 115 nm in deionized water, which is comparable to the excitation depth in a TIRF microscopic setup . Figure shows representative results.…”

Single-Molecule Investigations of Morphology and Mass Transport Dynamics in Nanostructured Materials

“…Detailed analyses of single-molecule step-size distributions have also been used to explore molecular confinement, as in representative work by Elliott et al (103). Diffusion in one dimension produces a distribution that is peaked at zero displacement, whereas isotropic diffusion yields a peak at nonzero step sizes.…”

“…By fitting the step-size distribution to Weibull or Chi functions, the dimensionality of molecular motion was obtained (103,104). Radius of gyration calculations were also explored as a means for quantifying the level of molecular confinement along short trajectory segments and, thus, to obtain a measure of diffusion anisotropy (103). Anisotropic diffusion can also be detected by measuring the diffusive step size as a function of step direction.…”

“…Diffusion in one dimension produces a distribution that is peaked at zero displacement, whereas isotropic diffusion yields a peak at nonzero step sizes. By fitting the step-size distribution to Weibull or Chi functions, the dimensionality of molecular motion was obtained (103,104). Radius of gyration calculations were also explored as a means for quantifying the level of molecular confinement along short trajectory segments and, thus, to obtain a measure of diffusion anisotropy (103).…”