After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

Super-resolution microscopy with phase masks is a promising technique for 3D imaging and tracking. Due to the complexity of the resultant point spread functions, generalized recovery algorithms are still missing. We introduce a 3D super-resolution recovery algorithm that works for a variety of phase masks generating 3D point spread functions. A fast deconvolution process generates initial guesses, which are further refined by least squares fitting. Overfitting is suppressed using a machine learning determined threshold. Preliminary results on experimental data show that our algorithm can be used to super-localize 3D adsorption events within a porous polymer film and is useful for evaluating potential phase masks. Finally, we demonstrate that parallel computation on graphics processing units can reduce the processing time required for 3D recovery. Simulations reveal that, through desktop parallelization, the ultimate limit of real-time processing is possible. Our program is the first open source recovery program for generalized 3D recovery using rotating point spread functions.

Super-resolution microscopy typically achieves high spatial resolution, but the temporal resolution remains low. We report super temporal-resolved microscopy (STReM) to improve the temporal resolution of 2D super-resolution microscopy by a factor of 20 compared to that of the traditional camera-limited frame rate. This is achieved by rotating a phase mask in the Fourier plane during data acquisition and then recovering the temporal information by fitting the point spread function (PSF) orientations. The feasibility of this technique is verified with both simulated and experimental 2D adsorption/desorption and 2D emitter transport. When STReM is applied to measure protein adsorption at a glass surface, previously unseen dynamics are revealed.

We report a single particle investigation of the polarized scattering spectra of individual Au nanotriangles (NTs) of the truncated bifrustrum type. We unexpectedly observed a wide diversity in the scattering spectra from a population of NTs with low shape polydispersity. Correlation of the optical measurements with electron microscopy revealed that the different optical responses were not due to distinct NT shapes. Rather, finite element simulations revealed that distinct polarized spectra originated from minute changes in the inclination of the NTs on the substrate. NT inclination resulted in asymmetric image charge formation in the substrate, thus, breaking the degeneracy of the modes supported by the NTs. The degeneracy of the NT modes was extremely sensitive to such symmetry breaking, with inclination angles as small as 2°, producing clearly resolved, nondegenerate, and orthogonally polarized plasmon modes.

Developing a mechanistic understanding of protein dynamics and conformational changes at polymer interfaces is critical for a range of processes including industrial protein separations. Salting out is one example of a procedure that is ubiquitous in protein separations yet is optimized empirically because there is no mechanistic description of the underlying interactions that would allow predictive modeling. Here, we investigate peak narrowing in a model transferrin–nylon system under salting out conditions using a combination of single-molecule tracking and ensemble separations. Distinct surface transport modes and protein conformational changes at the negatively charged nylon interface are quantified as a function of salt concentration. Single-molecule kinetics relate macroscale improvements in chromatographic peak broadening with microscale distributions of surface interaction mechanisms such as continuous-time random walks and simple adsorption–desorption. Monte Carlo simulations underpinned by the stochastic theory of chromatography are performed using kinetic data extracted from single-molecule observations. Simulations agree with experiment, revealing a decrease in peak broadening as the salt concentration increases. The results suggest that chemical modifications to membranes that decrease the probability of surface random walks could reduce peak broadening in full-scale protein separations. More broadly, this work represents a proof of concept for combining single-molecule experiments and a mechanistic theory to improve costly and time-consuming empirical methods of optimization.