Fast, single-molecule localization that achieves theoretically minimum uncertainty

Department of Imaging Science and Technology, Delft University of Technology, The Netherlands.
Nature Methods (Impact Factor: 32.07). 04/2010; 7(5):373-5. DOI: 10.1038/nmeth.1449
Source: PubMed


We describe an iterative algorithm that converges to the maximum likelihood estimate of the position and intensity of a single fluorophore. Our technique efficiently computes and achieves the Cramér-Rao lower bound, an essential tool for parameter estimation. An implementation of the algorithm on graphics processing unit hardware achieved more than 10(5) combined fits and Cramér-Rao lower bound calculations per second, enabling real-time data analysis for super-resolution imaging and other applications.

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    • "In [24] and [25] the fundamental limit of localization accuracy was introduced as the Cramér-Rao lower bound (CRLB) for the location estimation problem, in the context of ideal experimental conditions such as an infinite size photon detector without pixilation artefacts and without other extraneous noise sources. This measure has proved a reliable predictor for the best possible accuracy that can be achieved with a specific single molecule experiment [26], [27]. Due to the importance of registration in single molecule experiments the question therefore arises how the uncertainty introduced during the registration process influences the localization accuracy for a single molecule that has been registered. "
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    ABSTRACT: The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e.g. of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g. the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramer-Rao lower bound are given and under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data.
    IEEE Transactions on Medical Imaging 04/2015; DOI:10.1109/TMI.2015.2451513 · 3.39 Impact Factor
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    • "Calculating the CRLB thus provides insight into the amount of information about the bead position stored in any given image. In fluorescence microscopy, the CRLB has been computed to determine the theoretical limit for the localization of point spread functions modeled via 2D Gaussian functions (Smith et al., 2010). We have similarly applied the CRLB to the case of spherical bead localization by replacing the 2D Gaussian with a measured LUT that defines the probability distribution for each pixel in the image. "
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    ABSTRACT: Numerous biophysical techniques such as magnetic tweezers, flow stretching assays, or tethered particle motion assays rely on the tracking of spherical beads to obtain quantitative information about the individual biomolecules to which these beads are bound. The determination of these beads' coordinates from video-based images typically forms an essential component of these techniques. Recent advances in camera technology permit the simultaneous imaging of many beads, greatly increasing the information that can be captured in a single experiment. However, computational aspects such as frame capture rates or tracking algorithms often limit the rapid determination of such beads' coordinates. Here, we present a scalable and open source software framework to accelerate bead localization calculations based on the CUDA parallel computing framework. Within this framework, we implement the Quadrant Interpolation algorithm in order to accurately and simultaneously track hundreds of beads in real time using consumer hardware. In doing so, we show that the scatter derived from the bead tracking algorithms remains close to the theoretical optimum defined by the Cramer-Rao Lower Bound. We also explore the trade-offs between processing speed, size of the region-of-interests utilized, and tracking bias, highlighting in passing a bias in tracking along the optical axis that has previously gone unreported. To demonstrate the practical application of this software, we demonstrate how its implementation on magnetic tweezers can accurately track (with ∼1 nm standard deviation) 228 DNA-tethered beads at 58 Hz. These advances will facilitate the development and use of high-throughput single-molecule approaches.
    Review of Scientific Instruments 10/2014; 85(10):103712. DOI:10.1063/1.4898178 · 1.61 Impact Factor
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    • "A variety of algorithms for the precise and efficient localization of individual fluorescence spots have been proposed for the efficient reconstruction of a high quality SR image (Mortensen et al., 2010; Holden et al., 2011). These image processing algorithms allow the real-time reconstruction of SR images (Smith et al., 2010; Wolter et al., 2010, 2012). "
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    ABSTRACT: Super-resolution (SR) fluorescence microscopy has been revolutionizing the way in which we investigate the structures, dynamics, and functions of a wide range of nanoscale systems. In this review, I describe the current state of various SR fluorescence microscopy techniques along with the latest developments of fluorophores and labeling for the SR microscopy. I discuss the applications of SR microscopy in the fields of life science and materials science with a special emphasis on quantitative molecular imaging and nanoscale functional imaging. These studies open new opportunities for unraveling the physical, chemical, and optical properties of a wide range of nanoscale architectures together with their nanostructures and will enable the development of new (bio-)nanotechnology.
    Frontiers in Bioengineering and Biotechnology 06/2014; 2:20. DOI:10.3389/fbioe.2014.00020
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