| Summary: | Observing biophysical phenomena at the nanometer scale with both high spatial and temporal resolution is a challenging feat. Although many techniques, including atomic force microscopy and scanning electron microscopy, have demonstrated subnanometer spatial resolution, most exhibit drawbacks which limit their temporal resolution. On the other hand, light microscopy exhibits poor spatial resolution (typically greater than 100 nm) due to diffraction. The desire to image features below the resolution of light has spawned the term super-resolution microscopy to which many powerful, albeit complicated, techniques may be associated; such techniques include Stimulated Emission-Depletion Microscopy (STED) and Stochastic Optical Reconstruction Microscopy (STORM). Within the field of super-resolution there exists a subset of methods which involve tagging features of interest (e.g., a virus or motor protein) with small, fluorescent molecules and measuring their emitted fluorescence over time. Although the emitted light is diffraction-limited, the precision of localizing the position of the molecule is proportional to the number of photons acquired. Thus, fluorescent particle tracking is a method which augments traditional light microscopy so that features may be localized to spatial resolutions below the diffraction limit while still maintaining useful temporal resolutions.
One common approach for tracking fluorescent particles involves passively observing the particle with a stationary detector; this approach, however, is limited by its inability to observe particles in three dimensions over a large field of view. Consequently, specialized techniques have been developed that actively track the particle, but the majority of these methods, unfortunately, utilize non-standard optical paths which complicate their use. Moreover, analysis methods pertaining to both paradigms, which infer both position locations and model-based parameter estimates, are often subjective or employ simplified and potentially inaccurate models. In widefield microscopy, for example, the common approach involves first localizing the particle within each image via a heuristic method, such as calculating the centroid, and then inferring diffusion coefficients by regressing to the mean squared displacement. This approach to localization disregards information involving the optical setup (e.g., the point spread function, aberrations, and noise) as well as information regarding the particle's motion. Although methods exist for optimally calculating diffusion coefficients, they are limited to the case of unconfined diffusion with measurements corrupted by additive, white noise.
The work in this thesis provides two specific contributions. The first presents an active approach to tracking a single fluorescent particle in three dimensions that requires no specialized hardware aside from a standard confocal microscope. Inspired by works involving the autonomous exploration of unknown potential fields, the algorithm operates by moving the microscope's focal volume toward the maximum of the field of light emitted by the particle. For a stationary particle and a radial field, an equilibrium trajectory is derived and its local stability is proven. In addition, the algorithm's ability to track both stationary and diffusive particles is numerically characterized. The second contribution presents the application of a numerical, iterative algorithm to the problem of simultaneously inferring both location and model parameters from particle tracking data of potentially nonlinear and non-Gaussian imaging modalities. The method, which is leveraged from the field of system identification, employs Sequential Monte Carlo methods in conjunction with the Expectation Maximization algorithm to provide approximate maximum likelihood estimates of model parameters (e.g., diffusion coefficients) as well as approximate posterior probability densities of the particle's location over time. The effectiveness of the method is demonstrated through numerical simulations of two- and three-dimensional motion (including free, confined, and tethered diffusion) imaged in a widefield context. Lastly, the effectiveness of both methods is demonstrated by tracking a quantum dot in a hydrogel with the proposed tracking method and by analyzing the resulting data using the aforementioned inference method.
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