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Challenges, solutions, and biological applications of three-dimensional nanoscale spatial localization of single molecules [electronic resource]

Single fluorescent molecules and particles can be localized in space with precision on the order of tens of nanometers (i.e. "super localized") using state-of-the-art microscopy techniques. The ability to probe complex environments at the sub-diffraction size scale has proven invaluable in revealing fundamental heterogeneity and improving overall understanding across the applied physical sciences. Super-localization microscopy is at the heart of both single-molecule super-resolution microscopy and single-particle tracking. The work presented in this dissertation concerns the application of super-localization microscopy to problems of biophysical interest, as well as theoretical and experimental advances in the methodology of this class of techniques. While the most common methods of super-localized position estimation ensure high localization precision, they might not always ensure high accuracy. In particular, the anisotropy of single-molecule dipole emission can result in mislocalizations of hundreds of nanometers, depending on the orientation of the molecule and its distance from the focal plane. In this dissertation I discuss different ways to correct this potential source of error. On the one hand, a theory based on a wobbling-in-a-cone model is presented that shows how this error is mitigated by molecular rotational mobility. On the other hand, for the worst-case scenario of a rotationally fixed emitter, an experimental approach based on Fourier optics is also discussed that allows for estimation of molecular orientation and enables active correction of mislocalization effects. The last third of this dissertation discusses applications of super-localization microscopy to three-dimensional tracking of fluorescently labeled genetic loci in budding yeast. In order to localize loci in the axial dimension, I used a Fourier optics approach to engineer the point spread function of the microscope into a Double-Helix Point Spread Function (DH-PSF). With this method, many single copies of a specific locus were analyzed, each with 3D spatial precision on the order of 10 nm at a rate of 10 Hz. A two-color implementation of the microscope allowed measurement of the correlations of 3D motion between pairs of loci under variable transcriptional pressure. I also discuss the importance of properly accounting for the inescapable effects of static and dynamic tracking errors caused by finite photon statistics and motion blur, respectively. These errors affect the statistics of the estimated motion and distort common metrics for characterizing stochastic motion such as the mean-squared displacement (MSD) and velocity autocorrelation (VAC). Analytical expressions for the MSD and VAC in the presence of these errors are given, along with applications to chromosomal locus tracking.