E.S. Ward

Quantitative study of single molecule location estimation techniques

Estimating the location of single molecules from microscopy images is a key step in many quantitative single molecule data analysis techniques. Different algorithms have been advocated for the fitting of single molecule data, particularly the nonlinear least squares and maximum likelihood estimators. Comparisons were carried out to assess the performance of these two algorithms in different scenarios. Our results show that both estimators, on average, are able to recover the true location of the single molecule in all scenarios we examined. However, in the absence of modeling inaccuracies and low noise levels, the maximum likelihood estimator is more accurate than the nonlinear least squares estimator, as measured by the standard deviations of its estimates, and attains the best possible accuracy achievable for the sets of imaging and experimental conditions that were tested. Although neither algorithm is consistently superior to the other in the presence of modeling inaccuracies or misspecifications, the maximum likelihood algorithm emerges as a robust estimator producing results with consistent accuracy across various model mismatches and misspecifications. At high noise levels, relative to the signal from the point source, neither algorithm has a clear accuracy advantage over the other. Comparisons were also carried out for two localization accuracy measures derived previously. Software packages with user-friendly graphical interfaces developed for single molecule location estimation (EstimationTool) and limit of the localization accuracy calculations (FandPLimitTool) are also discussed.

Noise suppression of point spread functions and its influence on deconvolution of three‐dimensional fluorescence microscopy image sets

The point spread function (PSF) is of central importance in the image restoration of three‐dimensional image sets acquired by an epifluorescent microscope. Even though it is well known that an experimental PSF is typically more accurate than a theoretical one, the noise content of the experimental PSF is often an obstacle to its use in deconvolution algorithms. In this paper we apply a recently introduced noise suppression method to achieve an effective noise reduction in experimental PSFs. We show with both simulated and experimental three‐dimensional image sets that a PSF that is smoothed with this method leads to a significant improvement in the performance of deconvolution algorithms, such as the regularized least‐squares algorithm and the accelerated Richardson–Lucy algorithm.

Quantitative Aspects of Single-Molecule Microscopy: Information-theoretic analysis of single-molecule data

Single-molecule microscopy is a relatively new optical microscopy technique that allows the detection of individual molecules such as proteins in a cellular context. This technique has generated significant interest among biologists, biophysicists, and biochemists, as it holds the promise to provide novel insights into subcellular processes and structures that otherwise cannot be gained through traditional experimental approaches. Single-molecule experiments place stringent demands on experimental and algorithmic tools due to the low signal levels and the presence of significant extraneous noise sources. Consequently, this has necessitated the use of advanced statistical signal- and image-processing techniques for the design and analysis of single-molecule experiments. In this tutorial article, we provide an overview of single-molecule microscopy from early works to current applications and challenges. Specific emphasis will be on the quantitative aspects of this imaging modality, in particular single-molecule localization and resolvability, which will be discussed from an information-theoretic perspective. We review the stochastic framework for image formation, different types of estimation techniques, and expressions for the Fisher information matrix. We also discuss several open problems in the field that demand highly nontrivial signal processing algorithms.

Anti‐Vβ8 antibodies induce and maintain staphylococcal enterotoxin B‐triggered Vβ8+ T cell anergy

The mechanism involved in the maintenance of staphylococcal enterotoxin B (SEB)‐induced T cell anergy is poorly understood. We demonstrated earlier that B cells play an important role in the maintenance of SEB‐induced T cell anergy in vivo and in vitro. Here, we demonstrate that B cells are not essential in SEB‐induced T cell activation, but are important for the maintenance of T cell memory phenotype and anergy in vivo. Studying the activated B cell repertoire, we observe that SEB treatment increases serum anti‐Vβ8 antibody titer as detected by enzyme‐linked immunosorbent assay using soluble Vβ8 chains as antigens, and by staining of a Vβ8‐expressing thymoma. These antibodies disappear gradually after immunization with SEB, whereas the capacity of the T cells to respond to SEB in vitro is restored. Anti‐Vβ8 monoclonal antibody treatment causes Vβ8+ T cell unresponsiveness to SEB in vitro (anergy), without affecting CD4Vβ8+ T cell frequency. Together, these results suggest a new mechanism to explain the maintenance of SEB‐induced T cell anergy, which is dependent on B cells and on anti‐Vβ8 antibody that specifically interacts with Vβ8+ T cells.

A novel resolution measure for optical microscopes: stochastic analysis of the performance limits

In the recent past, the increased use of optical microscopes in quantitative studies, such as single molecule microscopy, has generated significant interest in quantifying its performance limit. Here, by adopting an information-theoretic stochastic framework, we present expressions to calculate performance limits that quantify the capabilities of optical microscopes. We revisit the resolution problem from the stochastic framework and derive a new resolution measure. Our result, unlike Rayleighs resolution criterion, predicts that the resolution of an optical microscope is not limited, but that the resolvability depends on the detected photon count. Analytical expressions are also given that take into account the effect of deteriorating experimental factors such as pixelation and noise sources. We also consider the location estimation problem, which is of relevance for particle tracking applications

3D resolution measure for multifocal plane microscopy

The distance separating two biomolecules in close proximity is an important determinant of the nature of their interaction. While much focus has been given to resolving distances in 2D, the 3D cell in which biological interactions occur necessitates the evaluation of resolution in 3D. Recently, we introduced an information-theoretic 3D resolution measure which predicts that the resolution of an optical microscope is unlimited, and that it improves as more photons are detected from the imaged molecules. Here, we investigate the 3D resolution measure for a multifocal plane microscope. Used for the simultaneous imaging of distinct focal planes within a specimen, multifocal plane microscopy has important applications in the tracking of microscopic objects in 3D. By comparing their 3D resolution measures, we determine the circumstances under which a two-plane microscope setup offers better re- solvability than a comparable conventional microscope.

Localizing single molecules in three dimensions - A brief review

Single molecule tracking in three dimensions (3D) in a live cell environment holds the promise of revealing important new biological insights. However, conventional microscopy based imaging techniques are not well suited for fast 3D tracking of single molecules in cells. Previously we developed an imaging modality multifocal plane microscopy (MUM) to image fast intracellular dynamics in 3D in live cells. Recently, we have reported an algorithm, the MUM localization algorithm (MUMLA), for the 3D localization of point sources that are imaged using MUM. Here, we present a review of our results on MUM and MUMLA. We have validated MUMLA through simulated and experimental data and have shown that the 3D-position of quantum dots (QDs) can be determined with high spatial accuracy over a wide spatial range. We have calculated the Cramer-Rao lower bound for the problem of determining the 3D location of point sources from MUM and from conventional microscopes. Our analyses shows that MUM overcomes the poor depth discrimination of the conventional microscope, and thereby paves the way for high accuracy tracking of nanoparticles in a live cell environment. We have also shown that the performance of MUMLA comes consistently close to the Cramer-Rao lower bound.

BREAKING THE RESOLUTION BARRIER IN OPTICAL MICROSCOPY: A NEW RESOLUTION MEASURE WITH APPLICATIONS TO SINGLE MOLECULE IMAGING

Rayleighs resolution criterion, although extensively used in optical microscopy, is well known to be based on heuristic notions. In fact, recent single molecule experiments have shown that this criterion can be surpassed in a regular optical microscope. The inadequacy of Rayleighs criterion has necessitated a reassessment of the resolution limits of optical microscopes. Recently, we proposed a new resolution measure that overcomes the limitations of Rayleighs criterion. Known as the fundamental resolution measure FREM, our new result predicts that distances well below Rayleighs limit can be resolved in an optical microscope. The effect of deteriorating experimental factors on the new resolution measure is also investigated. Further, it is experimentally verified that distances well below Rayleighs limit can be measured from images of closely spaced single molecules with an accuracy as predicted by the new resolution measure. We have also addressed an important problem in single molecule microscopy that concerns the accuracy with which the location of a single molecule can be determined. In particular, we have derived analytical expressions for the limit to the 2D/3D localization accuracy of a single molecule.

Breaking resolution limits: advances and challenges in single molecule microscopy

The resolution of an optical system is a measure of its ability to distinguish two closely spaced point sources. In optical microscopy, Rayleighs criterion has been extensively used to determine the resolution of microscopes. Despite its widespread use, it is well known that this criterion is based on heuristic notions that are not suited to modern imaging approaches. Formulated within a deterministic framework, this criterion neglects the stochastic nature of photon emission and therefore does not take into account the total number of detected photons. In fact, single molecule experiments have shown that this criterion can be surpassed in a regular optical microscope thereby illustrating that Rayleighs criterion is inadequate for current microscopy techniques. This inadequacy of Rayleighs criterion has, in turn, necessitated a reassessment of the resolution limits of optical microscopes. By adopting an information-theoretic framework and using the theory concerning the Fisher information matrix, we proposed a new resolution measure that overcomes the limitations of Rayleighs criterion. Here, we provide a review of this and other related results. The new resolution measure predicts that distances well below Rayleighs limit can be resolved in an optical microscope. The effect of deteriorating experimental factors on the new resolution measure is also investigated. Further, it is experimentally verified that distances well below Rayleighs limit can be measured from images of closely spaced fluorescent single molecules with an accuracy as predicted by the new resolution measure. We have also addressed an important problem in single molecule microscopy that concerns the accuracy with which the location of a single molecule can be determined. In particular, by using the theory concerning the Fisher information matrix we have derived analytical expressions for the limit to the 2D/3D localization accuracy of a single molecule.

How accurately can a single molecule be localized when imaged through an optical microscope

We present a simple analytical expression for the fundamental limit to the accuracy with which the location of a single molecule can be determined that is imaged through an optical microscope. This expression depends on the optical properties of the microscope and the photophysical properties of the single molecule. We also show how the fundamental limit is deteriorated by factors like pixelation of the detector and noise sources in the detection system. The present results gives an experimenter insight into what is achievable in an optical microscope and provide guidelines for experimental design.