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Schodt DJ, Cutler PJ, Becerra FE, Lidke KA. Tolerance to aberration and misalignment in a two-point-resolving image inversion interferometer. Opt Express 2023; 31:16393-16405. [PMID: 37157718 PMCID: PMC10316753 DOI: 10.1364/oe.487808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Revised: 04/19/2023] [Accepted: 04/19/2023] [Indexed: 05/10/2023]
Abstract
Image inversion interferometry can measure the separation of two incoherent point sources at or near the quantum limit. This technique has the potential to improve upon current state-of-the-art imaging technologies, with applications ranging from microbiology to astronomy. However, unavoidable aberrations and imperfections in real systems may prevent inversion interferometry from providing an advantage for real-world applications. Here, we numerically study the effects of realistic imaging system imperfections on the performance of image inversion interferometry, including common phase aberrations, interferometer misalignment, and imperfect energy splitting within the interferometer. Our results suggest that image inversion interferometry retains its superiority to direct detection imaging for a wide range of aberrations, so long as pixelated detection is used at the interferometer outputs. This study serves as a guide for the system requirements needed to achieve sensitivities beyond the limits of direct imaging, and further elucidates the robustness of image inversion interferometry to imperfections. These results are critical for the design, construction, and use of future imaging technologies performing at or near the quantum limit of source separation measurements.
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Affiliation(s)
- David J. Schodt
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA
- Teledyne Scientific & Imaging, LLC, USA
| | | | - Francisco E. Becerra
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico, USA
| | - Keith A. Lidke
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA
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Relich PK, Olah MJ, Cutler PJ, Lidke KA. Estimation of the diffusion constant from intermittent trajectories with variable position uncertainties. Phys Rev E 2016; 93:042401. [PMID: 27176323 DOI: 10.1103/physreve.93.042401] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2015] [Indexed: 11/07/2022]
Abstract
The movement of a particle described by Brownian motion is quantified by a single parameter, D, the diffusion constant. The estimation of D from a discrete sequence of noisy observations is a fundamental problem in biological single-particle tracking experiments since it can provide information on the environment and/or the state of the particle itself via the hydrodynamic radius. Here, we present a method to estimate D that takes into account several effects that occur in practice, important for the correct estimation of D, and that have hitherto not been combined together for an estimation of D. These effects are motion blur from the finite integration time of the camera, intermittent trajectories, and time-dependent localization uncertainty. Our estimation procedure, a maximum-likelihood estimation with an information-based confidence interval, follows directly from the likelihood expression for a discretely observed Brownian trajectory that explicitly includes these effects. We begin with the formulation of the likelihood expression and then present three methods to find the exact solution. Each method has its own advantages in either computational robustness, theoretical insight, or the estimation of hidden variables. The Fisher information for this likelihood distribution is calculated and analyzed to show that localization uncertainties impose a lower bound on the estimation of D. Confidence intervals are established and then used to evaluate our estimator on simulated data with experimentally relevant camera effects to demonstrate the benefit of incorporating variable localization errors.
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Affiliation(s)
- Peter K Relich
- Department of Physics and Astronomy, University of New Mexico, Mexico
| | - Mark J Olah
- Department of Physics and Astronomy, University of New Mexico, Mexico
| | | | - Keith A Lidke
- Department of Physics and Astronomy, University of New Mexico, Mexico
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Relich PK, Olah MJ, Cutler PJ, Lidke KA. Publisher's Note: Estimation of the diffusion constant from intermittent trajectories with variable position uncertainties [Phys. Rev. E 93, 042401 (2016)]. Phys Rev E 2016; 93:049906. [PMID: 27176448 DOI: 10.1103/physreve.93.049906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Indexed: 06/05/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevE.93.042401.
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Cutler PJ, Relich P, Lidke KA. Bayesian Estimation of Diffusion Constants from Single Particle Tracking Data. Biophys J 2013. [DOI: 10.1016/j.bpj.2012.11.3691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022] Open
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Cutler PJ, Malik MD, Wilson BS, Lidke KA, Lidke DS. Multi-Color Single Particle Tracking of QD-IgE-FcεRI: Directly Correlating Oligomer Size with Receptor Mobility and Signaling. Biophys J 2013. [DOI: 10.1016/j.bpj.2012.11.681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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Relich PK, Cutler PJ, Lidke KA. A Likelihood based Approach for Building Trajectories from Intermittent Observations. Biophys J 2013. [DOI: 10.1016/j.bpj.2012.11.2759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022] Open
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Low-Nam ST, Lidke KA, Cutler PJ, Roovers RC, van Bergen en Henegouwen PMP, Wilson BS, Lidke DS. ErbB1 dimerization is promoted by domain co-confinement and stabilized by ligand binding. Nat Struct Mol Biol 2011; 18:1244-9. [PMID: 22020299 PMCID: PMC3210321 DOI: 10.1038/nsmb.2135] [Citation(s) in RCA: 197] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2011] [Accepted: 08/09/2011] [Indexed: 12/11/2022]
Abstract
The extent to which ligand occupancy and dimerization contribute to erbB1 signaling is controversial. To examine this, we utilized two-color Quantum Dot tracking for visualization of erbB1 homodimerization and quantification of the dimer off rate (koff) on living cells. Kinetic parameters were extracted using a 3-state Hidden Markov Model to identify transition rates between free, co-confined, and dimerized states. We report that dimers composed of 2 ligand-bound receptors are long-lived and their koff is independent of kinase activity. By comparison, unliganded dimers have >4-fold faster koff. Transient co-confinement of receptors promotes repeated encounters and enhances dimer formation. Mobility decreases >6-fold when ligand-bound receptors dimerize. Blockade of erbB1 kinase activity or disruption of actin networks results in faster diffusion of receptor dimers. These results implicate both signal propagation and the cortical cytoskeleton in reduced mobility of signaling-competent erbB1 dimers.
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Affiliation(s)
- Shalini T Low-Nam
- Department of Pathology, University of New Mexico School of Medicine, Albuquerque, New Mexico, USA
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Malik M, Cutler PJ, Liu S, Byars J, Lidke D, Lidke K. Hyperspectral Line Scanning Microscopy for High-Speed Multicolor Quantum Dot Tracking. Biophys J 2011. [DOI: 10.1016/j.bpj.2010.12.1052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
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Low-Nam ST, Lidke KA, Cutler PJ, Roovers RC, van Bergen PM, Henegouwen E, Wilson BS, Lidke DS. Single Quantum Dot Tracking Coupled to a Three-State HMM Provides New Mechanistic Insight Into erbB1 Homodimerization. Biophys J 2011. [DOI: 10.1016/j.bpj.2010.12.1595] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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Cutler PJ, Malik M, Liu S, Huang F, Byars J, Lidke D, Lidke K. Single Particle Tracking of QD-IgE in Hyperspectral Fluorescent Images. Biophys J 2011. [DOI: 10.1016/j.bpj.2010.12.2794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022] Open
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Wells NP, Lessard GA, Goodwin PM, Phipps ME, Cutler PJ, Lidke DS, Wilson BS, Werner JH. Time-resolved three-dimensional molecular tracking in live cells. Nano Lett 2010; 10:4732-7. [PMID: 20957984 PMCID: PMC3061257 DOI: 10.1021/nl103247v] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We report a method for tracking individual quantum dot (QD) labeled proteins inside of live cells that uses four overlapping confocal volume elements and active feedback once every 5 ms to follow three-dimensional molecular motion. This method has substantial advantages over three-dimensional molecular tracking methods based upon charge-coupled device cameras, including increased Z-tracking range (10 μm demonstrated here), substantially lower excitation powers (15 μW used here), and the ability to perform time-resolved spectroscopy (such as fluorescence lifetime measurements or fluorescence correlation spectroscopy) on the molecules being tracked. In particular, we show for the first time fluorescence photon antibunching of individual QD labeled proteins in live cells and demonstrate the ability to track individual dye-labeled nucleotides (Cy5-dUTP) at biologically relevant transport rates. To demonstrate the power of these methods for exploring the spatiotemporal dynamics of live cells, we follow individual QD-labeled IgE-FcεRI receptors both on and inside rat mast cells. Trajectories of receptors on the plasma membrane reveal three-dimensional, nanoscale features of the cell surface topology. During later stages of the signal transduction cascade, clusters of QD labeled IgE-FcεRI were captured in the act of ligand-mediated endocytosis and tracked during rapid (~950 nm/s) vesicular transit through the cell.
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Affiliation(s)
- Nathan P Wells
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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Low-Nam ST, Lidke KA, Cutler PJ, Roovers RC, van Bergen en Henegouwen PM, Wilson BS, Lidke DS. Determination of Single Molecule erbB1 Homodimer Lifetimes Using Single Quantum Dot Tracking and a Diffusive Hidden Markov Model. Biophys J 2010. [DOI: 10.1016/j.bpj.2009.12.2710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022] Open
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Cutler PJ, Wilson BS, Oliver JM, Lidke KA, Lidke D. Multi-Color Quantum Dot Tracking to Correlate FcɛR1 Aggregate Size with Mobility. Biophys J 2010. [DOI: 10.1016/j.bpj.2009.12.2687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022] Open
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Werner JH, Wells NP, Lessard GA, Phipps M, Cutler PJ, Lidke DS, Wilson BS. Confocal, 3D Tracking of Single Quantum Dots: Following Receptor Traffic and Membrane Topology. Biophys J 2010. [DOI: 10.1016/j.bpj.2009.12.1083] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022] Open
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Cutler PJ, Haaland DM, Gemperline PJ. Systematic method for the kinetic modeling of temporally resolved hyperspectral microscope images of fluorescently labeled cells. Appl Spectrosc 2009; 63:261-270. [PMID: 19281641 DOI: 10.1366/000370209787598825] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
In this paper we report the application of a novel method for fitting kinetic models to temporally resolved hyperspectral images of fluorescently labeled cells to mathematically resolve pure-component spatial images, pure-component spectra, and pure-component reaction profiles. The method is demonstrated on one simulated image and two experimental cell images, including human embryonic kidney cells (HEK 293) and human A549 pulmonary type II epithelial cells. In both cell images, inhibitor kappa B kinase alpha (IKK(alpha)) and mitochondrial antiviral signaling protein (MAVS) were labeled with green and yellow fluorescent protein, respectively. Kinetic modeling was performed on the compressed images by using a separable least squares method. A combination of several first-order decays were needed to adequately model the photobleaching processes for each fluorophore observed in these images, consistent with the hypothesis that each fluorophore was found in several different environments within the cells. Numerous plausible mechanisms for kinetic modeling of the photobleaching processes in these images were tested and a method for selecting the most parsimonious and statistically sufficient model was used to prepare spatial maps of each fluorophore.
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Affiliation(s)
- Patrick J Cutler
- Department of Chemistry, East Carolina University, Greenville, North Carolina 27858, USA
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Cutler PJ, Haaland DM, Andries E, Gemperline PJ. Methods for kinetic modeling of temporally resolved hyperspectral confocal fluorescence images. Appl Spectrosc 2009; 63:153-163. [PMID: 19215644 DOI: 10.1366/000370209787391950] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Elucidating kinetic information (rate constants) from temporally resolved hyperspectral confocal fluorescence images offers some very important opportunities for the interpretation of spatially resolved hyperspectral confocal fluorescence images but also presents significant challenges, these being (1) the massive amount of data contained in a series of time-resolved spectral images (one time course of spectral data for each pixel) and (2) unknown concentrations of the reactants and products at time = 0, a necessary precondition normally required by traditional kinetic fitting approaches. This paper describes two methods for solving these problems: direct nonlinear (DNL) estimation of all parameters and separable least squares (SLS). The DNL method can be applied to reactions of any rate law, while the SLS method is restricted to first-order reactions. In SLS, the inherently linear and nonlinear parameters of first-order reactions are solved in separate linear and nonlinear steps, respectively. The new methods are demonstrated using simulated data sets and an experimental data set involving photobleaching of several fluorophores. This work demonstrates that both DNL and SLS hard-modeling methods applied to the kinetic modeling of temporally resolved hyperspectral images can outperform traditional soft-modeling and hard/soft-modeling methods which use multivariate curve resolution-alternating least squares (MCRALS) methods. In addition, the SLS method is much faster and is able to analyze much larger data sets than the DNL method.
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Affiliation(s)
- Patrick J Cutler
- Department of Chemistry, East Carolina University, Greenville, North Carolina 27858, USA
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Abstract
The extent of disease as detected by magnetic resonance imaging was compared between 32 patients with benign multiple sclerosis (MS) and 32 patients with the chronic progressive form matched for age, sex, and disease duration. Computer-assisted quantitation of magnetic resonance images revealed a higher mean lesion load in chronic progressive multiple sclerosis (CPMS); however, in approximately 20% of benign MS patients the lesion load was higher than that in the CPMS patients. CPMS patients had a higher number of infratentorial lesions, yet similar numbers of supratentorial lesions, when compared with benign MS patients. The degree of confluency of lesions and the clinical expression of infratentorial lesions were typically higher in the CPMS patients. Benign MS was characterized by a lower degree of confluency and a higher number of asymptomatic infratentorial lesions. Thus, magnetic resonance imaging shows characteristic differences in magnetic resonance-detected changes between MS patients with different clinical courses.
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Affiliation(s)
- R A Koopmans
- Department of Medicine, University of British Columbia, Vancouver, Canada
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