Kim I. Mortensen

Optimized localization-analysis for single-molecule tracking and super-resolution microscopy

We optimally localized isolated fluorescent beads and molecules imaged as diffraction-limited spots, determined the orientation of molecules and present reliable formulas for the precision of various localization methods. Both theory and experimental data showed that unweighted least-squares fitting of a Gaussian squanders one-third of the available information, a popular formula for its precision exaggerates beyond Fishers information limit, and weighted least-squares may do worse, whereas maximum-likelihood fitting is practically optimal.

Caulobacter chromosome in vivo configuration matches model predictions for a supercoiled polymer in a cell-like confinement

We measured the distance between fluorescent-labeled DNA loci of various interloci contour lengths in Caulobacter crescentus swarmer cells to determine the in vivo configuration of the chromosome. For DNA segments less than about 300 kb, the mean interloci distances, 〈r〉, scale as n0.22, where n is the contour length, and cell-to-cell distribution of the interloci distance r is a universal function of r/n0.22 with broad cell-to-cell variability. For DNA segments greater than about 300 kb, the mean interloci distances scale as n, in agreement with previous observations. The 0.22 value of the scaling exponent for short DNA segments is consistent with theoretical predictions for a branched DNA polymer structure. Predictions from Brownian dynamics simulations of the packing of supercoiled DNA polymers in an elongated cell-like confinement are also consistent with a branched DNA structure, and simulated interloci distance distributions predict that confinement leads to “freezing” of the supercoiled configuration. Lateral positions of labeled loci at comparable positions along the length of the cell are strongly correlated when the longitudinal locus positions differ by <0.16 μm. We conclude that the chromosome structure is supercoiled locally and elongated at large length scales and that substantial cell-to-cell variability in the interloci distances indicates that in vivo crowding prevents the chromosome from reaching an equilibrium arrangement. We suggest that the force causing rapid transport of loci remote from the parS centromere to the distal cell pole may arise from the release at the polar region of potential energy within the supercoiled DNA.

Optimized measurements of separations and angles between intra-molecular fluorescent markers

We demonstrate a novel, yet simple tool for the study of structure and function of biomolecules by extending two-colour co-localization microscopy to fluorescent molecules with fixed orientations and in intra-molecular proximity. From each colour-separated microscope image in a time-lapse movie and using only simple means, we simultaneously determine both the relative (x,y)-separation of the fluorophores and their individual orientations in space with accuracy and precision. The positions and orientations of two domains of the same molecule are thus time-resolved. Using short double-stranded DNA molecules internally labelled with two fixed fluorophores, we demonstrate the accuracy and precision of our method using the known structure of double-stranded DNA as a benchmark, resolve 10-base-pair differences in fluorophore separations, and determine the unique 3D orientation of each DNA molecule, thereby establishing short, double-labelled DNA molecules as probes of 3D orientation of anything to which one can attach them firmly.

“Calibration-on-the-spot”: How to calibrate an EMCCD camera from its images

In order to count photons with a camera, the camera must be calibrated. Photon counting is necessary, e.g., to determine the precision of localization-based super-resolution microscopy. Here we present a protocol that calibrates an EMCCD camera from information contained in isolated, diffraction-limited spots in any image taken by the camera, thus making dedicated calibration procedures redundant by enabling calibration post festum, from images filed without calibration information.

How To Characterize Individual Nanosize Liposomes with Simple Self-Calibrating Fluorescence Microscopy

Nanosize lipid vesicles are used extensively at the interface between nanotechnology and biology, e.g., as containers for chemical reactions at minute concentrations and vehicles for targeted delivery of pharmaceuticals. Typically, vesicle samples are heterogeneous as regards vesicle size and structural properties. Consequently, vesicles must be characterized individually to ensure correct interpretation of experimental results. Here we do that using dual-color fluorescence labeling of vesicles-of their lipid bilayers and lumens, separately. A vesicle then images as two spots, one in each color channel. A simple image analysis determines the total intensity and width of each spot. These four data all depend on the vesicle radius in a simple manner for vesicles that are spherical, unilamellar, and optimal encapsulators of molecular cargo. This permits identification of such ideal vesicles. They in turn enable calibration of the dual-color fluorescence microscopy images they appear in. Since this calibration is not a separate experiment but an analysis of images of vesicles to be characterized, it eliminates the potential source of error that a separate calibration experiment would have been. Nonideal vesicles in the same images were characterized by how their four data violate the calibrated relationship established for ideal vesicles. In this way, our method yields size, shape, lamellarity, and encapsulation efficiency of each imaged vesicle. Applying this procedure to extruded samples of vesicles, we found that, contrary to common assumptions, only a fraction of vesicles are ideal.

How to measure separations and angles between intra-molecular fluorescent markers

Structure and function of an individual biomolecule can be explored with minimum two fluorescent markers of different colors. Since the light of such markers can be spectrally separated and imaged simultaneously, the markers can be colocalized. Here, we describe the method used for such two-color colocalization microscopy. Then we extend it to fluorescent markers with fixed orientations and in intramolecular proximity. Our benchmarking of this extension produced two extra results: (a) we established short double-labeled DNA molecules as probes of 3D orientation of anything to which one can attach them firmly; (b) we established how to map with super-resolution between color-separated channels, which should be useful for all dual-color colocalization measurements with either fixed or freely rotating fluorescent molecules. Throughout, we use only simple means: from each color-separated microscope image in a time-lapse movie, we simultaneously determine both the relative (x,y)-separation of the fluorophores and their individual orientations in space, both with accuracy and precision. The relative positions and orientations of two domains of the same molecule are thus time-resolved. Using short double-stranded DNA (dsDNA) molecules internally labeled with two fixed fluorophores, we (i) demonstrate the accuracy and precision of our localization- and mapping-methods, using the known structure of dsDNA as benchmark; (ii) resolve 10 base pair differences in fluorophore separations; (iii) determine the unique 3D orientation of each DNA molecule.

Chapter Six – How to Measure Separations and Angles Between Intramolecular Fluorescent Markers

Structure and function of an individual biomolecule can be explored with minimum two fluorescent markers of different colors. Since the light of such markers can be spectrally separated and imaged simultaneously, the markers can be colocalized. Here, we describe the method used for such two-color colocalization microscopy. Then we extend it to fluorescent markers with fixed orientations and in intramolecular proximity. Our benchmarking of this extension produced two extra results: (a) we established short double-labeled DNA molecules as probes of 3D orientation of anything to which one can attach them firmly; (b) we established how to map with super-resolution between color-separated channels, which should be useful for all dual-color colocalization measurements with either fixed or freely rotating fluorescent molecules. Throughout, we use only simple means: from each color-separated microscope image in a time-lapse movie, we simultaneously determine both the relative (x,y)-separation of the fluorophores and their individual orientations in space, both with accuracy and precision. The relative positions and orientations of two domains of the same molecule are thus time-resolved. Using short double-stranded DNA (dsDNA) molecules internally labeled with two fixed fluorophores, we (i) demonstrate the accuracy and precision of our localization- and mapping-methods, using the known structure of dsDNA as benchmark; (ii) resolve 10 base pair differences in fluorophore separations; (iii) determine the unique 3D orientation of each DNA molecule.

Optimal Estimation of Location and Orientation of Myosin V Lever Arm from Focused Diffraction-Limited Images of Single, Double-Bound Fluorophore

In “... the most complete theoretical description of localization microscopy to date ...” (1,2), we showed how to estimate location and orientation of fixed, fluorescent probes from focused images. We demonstrated the superiority of the theoretical point spread function over a 2D Gaussian and of maximum likelihood estimation over least squares fitting. Here we compare our approach to popular methods that use de-focused imaging and/or 2D Gaussians (3). Experimentally, we verify theoretical expectations using internally labeled dsDNA as benchmark. Then we show from motility assays that our method provides high-resolution angular and positional information about myosin V dynamics. Specifically, bifunctional rhodamine-labeled calmodulin is exchanged to the lever arm of myosin V. The orientation of the dye shows two angular states during stepping, which very stably are separated by ∼70 deg. This result is consistent with the 70 deg rotation of the lever arm between pre- and post-stroke states.References:1. Kim I. Mortensen, L. Stirling Churchman, James A. Spudich, and Henrik Flyvbjerg: Optimized localization-analysis for single-molecule tracking and super-resolution microscopy. Nature Methods 7, 377-381 (2010).2. Characterization by Daniel R. Larson: The economy of photons. News and Views, Nature Methods 7, 357-359 (2010).3. Erdal Toprak, Joerg Enderlein, Sheyum Syed, Sean A. McKinney, Rolfe G. Petschek, Taekjip Ha, Yale E. Goldman, and Paul R. Selvin: Defocused orientation and position imaging (DOPI) of myosin V. PNAS 103, 6495-6499 (2006).