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

Abstract

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 paper, 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 non-trivial signal processing algorithms.

A Guided Tour of Selected Image Processing and Analysis Methods for Fluorescence and Electron Microscopy

“…The next initiatives "Particle Tracking" (ISBI 2012 [1]), "Cell Tracking" (ISBI 2013(ISBI , 2014(ISBI , 2015), "3D Deconvolution Microscopy" (ISBI 2013(ISBI , 2014, "Single Molecule Localization Microscopy" (ISBI 2013), "3D segmentation of Neurites in Electron Microscopy" (ISBI 2013), are particularly useful to define the state-of-the-art algorithms to be included into analysis workflows, to compare standard and recent cutting-edge algorithms and to specify future progress and advances for specific topics. Moreover, related books [4], [5] and special issues [6]- [9] include a few tutorial-style overview articles covering progress in recent years for a large variety of topics (e.g., tracking in fluorescence bioimaging [10]- [12], sub-diffraction limited imaging and single molecule localization [13], [14], parametric active contour-based image segmentation [15] ). Finally, several authors presented independently state of the art methods for specific and important topics including cell-shape analysis [16], neuron tracing [17], co-localization (percentage of co-detection of interacting protein types at the same location) [18], [19], 3D image deconvolution [20], spot detection [21] in fluorescence microscopy Even if it is generally a difficult task to present a broad view of activities in bio-image processing and analysis [2], several authors [22]- [25] already explained successfully how computer vision, image analysis and visualization algorithms combined in workflows, will play a significant role in image-based studies of cell biology.…”

Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy

“…R 2 ) due to the object, M is the lateral magnification of the objective lens and q z 0 is the image function [5,10]. The image function is a bivariate probability density function (pdf) that describes the image of a stationary object on the detector plane at unit lateral magnification when it is located on the optical axis at position z 0 ∈ R [4,10]. The image function for a 2D localization problem is simply given by setting z 0 = 0.…”

“…Fluorescence microscopy, a light microscopy technique that enables the detection of specifically-labeled objects, is extensively used to study subcellular structures, proteins and dynamics [1][2][3][4]. An important question in fluorescence microscopy concerns the best possible accuracy, in terms of standard deviation, with which an object of interest can be localized.…”

“…An important question in fluorescence microscopy concerns the best possible accuracy, in terms of standard deviation, with which an object of interest can be localized. This is particularly important for applications such as localization-based superresolution microscopy in which the spatial resolution is closely related to the localization accuracy [2,4]. This problem has been addressed by introducing the practical localization accuracy measure (PLAM) [5][6][7].…”

“…Lower bounds on the accuracy of estimates are useful in assessing the quantitative performance of systems as they can predict how well a system can perform an estimation task without specifying a particular estimator [5,8,10]. This feature has turned the PLAM into a reliable measure of accuracy that helps to optimize the design of fluorescence microscopy experiments [4,[10][11][12][13][14][15].…”