Quantitative Aspects of Single Molecule Microscopy.

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.

An information-theoretic approach to designing the plane spacing for multifocal plane microscopy.

Multifocal plane microscopy (MUM) is a 3D imaging modality which enables the localization and tracking of single molecules at high spatial and temporal resolution by simultaneously imaging distinct focal planes within the sample. MUM overcomes the depth discrimination problem of conventional microscopy and allows high accuracy localization of a single molecule in 3D along the z-axis. An important question in the design of MUM experiments concerns the appropriate number of focal planes and their spacings to achieve the best possible 3D localization accuracy along the z-axis. Ideally, it is desired to obtain a 3D localization accuracy that is uniform over a large depth and has small numerical values, which guarantee that the single molecule is continuously detectable. Here, we address this concern by developing a plane spacing design strategy based on the Fisher information. In particular, we analyze the Fisher information matrix for the 3D localization problem along the z-axis and propose spacing scenarios termed the strong coupling and the weak coupling spacings, which provide appropriate 3D localization accuracies. Using these spacing scenarios, we investigate the detectability of the single molecule along the z-axis and study the effect of changing the number of focal planes on the 3D localization accuracy. We further review a software module we recently introduced, the MUMDesignTool, that helps to design the plane spacings for a MUM setup.

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

Fluorescence microscopy is a photon-limited imaging modality that allows the study of subcellular objects and processes with high specificity. The best possible accuracy (standard deviation) with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramér-Rao lower bound, that is, the inverse of the Fisher information. However, the current approach for the calculation of the best possible localization accuracy relies on an analytical expression for the image of the object. This can pose practical challenges since it is often difficult to find appropriate analytical models for the images of general objects. In this study, we instead develop an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object. In this approach, we fit splines, i.e. smoothly connected piecewise polynomials, to the experimentally collected image set to provide a continuous model of the object, which can then be used for the calculation of the best possible localization accuracy. Due to its practical importance, we investigate in detail the application of the proposed approach in single molecule fluorescence microscopy. In this case, the object of interest is a point source and, therefore, the acquired image set pertains to an experimental point spread function.

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.

Use of Fc-Engineered Antibodies as Clearing Agents to Increase Contrast During PET.

UNLABELLED: Despite promise for the use of antibodies as molecular imaging agents in PET, their long in vivo half-lives result in poor contrast and radiation damage to normal tissue. This study describes an approach to overcome these limitations. METHODS: Mice bearing human epidermal growth factor receptor type 2 (HER2)-overexpressing tumors were injected with radiolabeled ((124)I, (125)I) HER2-specific antibody (pertuzumab). Pertuzumab injection was followed 8 h later by the delivery of an engineered, antibody-based inhibitor of the receptor, FcRn. Biodistribution analyses and PET were performed at 24 and 48 h after pertuzumab injection. RESULTS: The delivery of the engineered, antibody-based FcRn inhibitor (or Abdeg, for antibody that enhances IgG degradation) results in improved tumor-to-blood ratios, reduced systemic exposure to radiolabel, and increased contrast during PET. CONCLUSION: Abdegs have considerable potential as agents to stringently regulate antibody dynamics in vivo, resulting in increased contrast during molecular imaging with PET.

Fast opposite weight learning rules with application in breast cancer diagnosis.

Classification of breast abnormalities such as masses is a challenging task for radiologists. Computer-aided Diagnosis (CADx) technology may enhance the performance of radiologists by assisting them in classifying patterns into benign and malignant categories. Although Neural Networks (NN) such as Multilayer Perceptron (MLP) have drawbacks, namely long training times, a considerable number of CADx systems employ NN-based classifiers. The reason being that they provide high accuracy when they are appropriately trained. In this paper, we introduce three novel learning rules called Opposite Weight Back Propagation per Pattern (OWBPP), Opposite Weight Back Propagation per Epoch (OWBPE), and Opposite Weight Back Propagation per Pattern in Initialization (OWBPI) to accelerate the training procedure of an MLP classifier. We then develop CADx systems for the diagnosis of breast masses employing the traditional Back Propagation (BP), OWBPP, OWBPE and OWBPI algorithms on MLP classifiers. We quantitatively analyze the accuracy and convergence rate of each system. The results suggest that the convergence rate of the proposed OWBPE algorithm is more than 4 times faster than that of the traditional BP. Moreover, the CADx systems which use OWBPE classifier on average yield an area under Receiver Operating Characteristic (ROC), i.e. Az, of 0.928, a False Negative Rate (FNR) of 9.9% and a False Positive Rate (FPR) of 11.94%.

Classification of benign and malignant masses based on Zernike moments.

In mammography diagnosis systems, high False Negative Rate (FNR) has always been a significant problem since a false negative answer may lead to a patient's death. This paper is directed towards the development of a novel Computer-aided Diagnosis (CADx) system for the diagnosis of breast masses. It aims at intensifying the performance of CADx algorithms as well as reducing the FNR by utilizing Zernike moments as descriptors of shape and margin characteristics. The input Regions of Interest (ROIs) are segmented manually and further subjected to a number of preprocessing stages. The outcomes of preprocessing stage are two processed images containing co-scaled translated masses. Besides, one of these images represents the shape characteristics of the mass, while the other describes the margin characteristics. Two groups of Zernike moments have been extracted from the preprocessed images and applied to the feature selection stage. Each group includes 32 moments with different orders and iterations. Considering the performance of the overall CADx system, the most effective moments have been chosen and applied to a Multi-layer Perceptron (MLP) classifier, employing both generic Back Propagation (BP) and Opposition-based Learning (OBL) algorithms. The Receiver Operational Characteristics (ROC) curve and the performance of resulting CADx systems are analyzed for each group of features. The designed systems yield Az=0.976, representing fair sensitivity, and Az=0.975 demonstrating fair specificity. The best achieved FNR and FPR are 0.0% and 5.5%, respectively.