Pointwise error estimates in localization microscopy

Abstract

Pointwise localization of individual fluorophores is a critical step in super-resolution localization microscopy and single particle tracking. Although the methods are limited by the localization errors of individual fluorophores, the pointwise localization precision has so far been estimated using theoretical best case approximations that disregard, for example, motion blur, defocus effects and variations in fluorescence intensity. Here, we show that pointwise localization precision can be accurately estimated directly from imaging data using the Bayesian posterior density constrained by simple microscope properties. We further demonstrate that the estimated localization precision can be used to improve downstream quantitative analysis, such as estimation of diffusion constants and detection of changes in molecular motion patterns. Finally, the quality of actual point localizations in live cell super-resolution microscopy can be improved beyond the information theoretic lower bound for localization errors in individual images, by modelling the movement of fluorophores and accounting for their pointwise localization uncertainty.

Spot-On: robust model-based analysis of single-particle tracking experiments

“…Nevertheless, Figure Second, Spot-On models the localization error as the static mean localization error and this 410 feature can be used to infer the actual localization error from the data. However, the 411 localization error is affected both by the position of the particle with respect to the focal plane 412 (Lindén et al, 2017) and by motion blur (Deschout et al, 2012). Even though a high signal-413 to-background ratio and fast framerate/stroboscopic illumination help to mitigate these 414 disparities, it is likely that the localization error of fast moving particles will be higher than 415 the bound/slow-moving particles.…”

SMAUG: Analyzing single-molecule tracks with nonparametric Bayesian statistics

“…Two of the parameters we wish to find for our dataset are the diffusion coefficient values, D j , and the localization noise, . In a model derived by Berglund (16,24), we relate our dataset of step sizes from SPT experiments to these quantities of interest. By this model, the measured steps sizes, Δx, are zero-mean Gaussian variables whose covariances are related to D j and by:…”

Variational algorithms for analyzing noisy multi-state diffusion trajectories

“…Here, we extend our previous HMM analysis [7] by deriving and implementing variational algorithms that increase computational speed by more than an order of magnitude, allow statistical model selection using Bayesian or information-theoretic methods, and can be generalized to a wider class of localization error models. The new methods are available in a user-friendly open source software suite.…”

“…Accurate quantitative analysis of this type of data requires a faithful account of localization noise, which come in the form of localization errors and motion blur, sometimes referred to as "static" and "dynamic" errors, respectively [4,5]. In particular, live cell imaging often lead to heterogeneous and asymmetric localization errors, for example due to photobleaching, variability between and across cells, out-of-focus motion, or the dependence of localization errors on the diffusion constant [6,7]. Several emerging techniques for 3D localization also give different precision in the axial and lateral directions [8].…”

“…A fundamental unknown in many live cell SPT studies is the number of underlying molecular states, which may differ in, e.g., diffusion constant. Counting diffusive states in SPT data presents a statistical model selection problem that has so far only been solved with simplified noise models [2], which may be inappropriate in many live cell applications [7,9].…”