Jerry Chao

High Accuracy 3D Quantum Dot Tracking with Multifocal Plane Microscopy for the Study of Fast Intracellular Dynamics in Live Cells

Single particle tracking in three dimensions 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 three-dimensional (3D) tracking of single particles in cells. Previously we developed an imaging modality multifocal plane microscopy (MUM) to image fast intracellular dynamics in three dimensions in live cells. Here, we introduce an algorithm, the MUM localization algorithm (MUMLA), to determine the 3D position of a point source that is imaged using MUM. We validate MUMLA through simulated and experimental data and show that the 3D position of quantum dots can be determined over a wide spatial range. We demonstrate that MUMLA indeed provides the best possible accuracy with which the 3D position can be determined. Our analysis 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. Here, using MUM and MUMLA we report for the first time the full 3D trajectories of QD-labeled antibody molecules undergoing endocytosis in live cells from the plasma membrane to the sorting endosome deep inside the cell.

Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy.

The intracellular events on the recycling pathway that lead from sorting endosomes to exocytosis at the plasma membrane are central to cellular function. However, despite intensive study, these processes are poorly characterized in spatial and dynamic terms. The primary reason for this is that, to date, it has not been possible to visualize rapidly moving intracellular compartments in three dimensions in cells. Here, we use a recently developed imaging setup in which multiple planes can be simultaneously imaged within the cell in conjunction with visualization of the plasma membrane plane by using total internal reflection fluorescence microscopy. This has allowed us to track and characterize intracellular events on the recycling pathway that lead to exocytosis of the MHC Class I-related receptor, FcRn. We observe both direct delivery of tubular and vesicular transport containers (TCs) from sorting endosomes to exocytic sites at the plasma membrane, and indirect pathways in which TCs that are not in proximity to sorting endosomes undergo exocytosis. TCs can also interact with different sorting endosomes before exocytosis. Our data provide insight into the intracellular events that precede exocytic fusion.

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.

Ultrahigh accuracy imaging modality for super-localization microscopy

Super-localization microscopy encompasses techniques that depend on the accurate localization of individual molecules from generally low-light images. The obtainable localization accuracies, however, are ultimately limited by the image detectors pixelation and noise. We present the ultrahigh accuracy imaging modality (UAIM), which allows users to obtain accuracies approaching the accuracy that is achievable only in the absence of detector pixelation and noise, and which we found can experimentally provide a >200% accuracy improvement over conventional low-light imaging.

A comparative study of high resolution microscopy imaging modalities using a three-dimensional resolution measure

From an acquired image, single molecule microscopy makes possible the determination of the distance separating two closely spaced biomolecules in three-dimensional (3D) space. Such distance information can be an important indicator of the nature of the biomolecular interaction. Distance determination, however, is especially difficult when, for example, the imaged point sources are very close to each other or are located near the focal plane of the imaging setup. In the context of such challenges, we compare the limits of the distance estimation accuracy for several high resolution 3D imaging modalities. The comparisons are made using a Cramer-Rao lower bound-based 3D resolution measure which predicts the best possible accuracy with which a given distance can be estimated. Modalities which separate the detection of individual point sources (e.g., using photoactivatable fluorophores) are shown to provide the best accuracy limits when the two point sources are very close to each other and/or are oriented near parallel to the optical axis. Meanwhile, modalities which implement the simultaneous imaging of the point sources from multiple focal planes perform best when given a near-focus point source pair. We also demonstrate that the maximum likelihood estimator is capable of attaining the limit of the accuracy predicted for each modality.

Designing the focal plane spacing for multifocal plane microscopy.

Multifocal plane microscopy (MUM) has made it possible to study subcellular dynamics in 3D at high temporal and spatial resolution by simultaneously imaging distinct planes within the specimen. MUM allows high accuracy localization of a point source along the z-axis since it overcomes the depth discrimination problem of conventional single plane microscopy. An important question in MUM experiments is how the number of focal planes and their spacings should be chosen to achieve the best possible localization accuracy along the z-axis. Here, we propose approaches based on the Fisher information matrix and report spacing scenarios called strong coupling and weak coupling which yield an appropriate 3D localization accuracy. We examine the effect of numerical aperture, magnification, photon count, emission wavelength and extraneous noise on the spacing scenarios. In addition, we investigate the effect of changing the number of focal planes on the 3D localization accuracy. We also introduce a new software package that provides a user-friendly framework to find appropriate plane spacings for a MUM setup. These developments should assist in optimizing MUM experiments.

Fisher information theory for parameter estimation in single molecule microscopy: tutorial

Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based super-resolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramér-Rao lower bound. The Cramér-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation and, more generally, to demonstrate the flexibility of the mathematical framework.

A Software Framework for the Analysis of Complex Microscopy Image Data

Technological advances in both hardware and software have made possible the realization of sophisticated biological imaging experiments using the optical microscope. As a result, modern microscopy experiments are capable of producing complex image datasets. For a given data analysis task, the images in a set are arranged, based on the requirements of the task, by attributes such as the time and focus levels at which they were acquired. Importantly, different tasks performed over the course of an analysis are often facilitated by the use of different arrangements of the images. We present a software framework that supports the use of different logical image arrangements to analyze a physical set of images. This framework, called the Microscopy Image Analysis Tool (MIATool), realizes the logical arrangements using arrays of pointers to the images, thereby removing the need to replicate and manipulate the actual images in their storage medium. In order that they may be tailored to the specific requirements of disparate analysis tasks, these logical arrangements may differ in size and dimensionality, with no restrictions placed on the number of dimensions and the meaning of each dimension. MIATool additionally supports processing flexibility, extensible image processing capabilities, and data storage management.

Investigation of the numerics of point spread function integration in single molecule localization

The computation of point spread functions, which are typically used to model the image profile of a single molecule, represents a central task in the analysis of single molecule microscopy data. To determine how the accuracy of the computation affects how well a single molecule can be localized, we investigate how the fineness with which the point spread function is integrated over an image pixel impacts the performance of the maximum likelihood location estimator. We consider both the Airy and the two-dimensional Gaussian point spread functions. Our results show that the point spread function needs to be adequately integrated over a pixel to ensure that the estimator closely recovers the true location of the single molecule with an accuracy that is comparable to the best possible accuracy as determined using the Fisher information formalism. Importantly, if integration with an insufficiently fine step size is carried out, the resulting estimates can be significantly different from the true location, particularly when the image data is acquired at relatively low magnifications. We also present a methodology for determining an adequate step size for integrating the point spread function.

Design and application of the Microscopy Image Analysis Tool

Advancements in microscopy instrumentation have resulted in larger volumes of acquired image data and, consequently, increased memory and space requirements for the processing and storage of the data. To address the issue in software, the Microscopy Image Analysis Tool (MIATool) was created to support processing of large image sets that makes efficient use of available resources. Implemented in MATLAB using object-oriented design, MIATool works with image pointer arrays to utilize RAM effectively and to support the analysis of different interpretations of data. Furthermore, the software provides image editing tools which operate on parameter objects that are saved in lieu of processed images to exploit the available disk space. A detailed image analysis example is given to illustrate the design and features of MIATool.