Tolerance to aberration and misalignment in a two-point-resolving image inversion interferometer.

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.

Estimation of the diffusion constant from intermittent trajectories with variable position uncertainties.

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.

Publisher's Note: Estimation of the diffusion constant from intermittent trajectories with variable position uncertainties [Phys. Rev. E 93, 042401 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.042401.

Multi-color quantum dot tracking using a high-speed hyperspectral line-scanning microscope.

Many cellular signaling processes are initiated by dimerization or oligomerization of membrane proteins. However, since the spatial scale of these interactions is below the diffraction limit of the light microscope, the dynamics of these interactions have been difficult to study on living cells. We have developed a novel high-speed hyperspectral microscope (HSM) to perform single particle tracking of up to 8 spectrally distinct species of quantum dots (QDs) at 27 frames per second. The distinct emission spectra of the QDs allows localization with ∼10 nm precision even when the probes are clustered at spatial scales below the diffraction limit. The capabilities of the HSM are demonstrated here by application of multi-color single particle tracking to observe membrane protein behavior, including: 1) dynamic formation and dissociation of Epidermal Growth Factor Receptor dimers; 2) resolving antigen induced aggregation of the high affinity IgE receptor, FcεR1; 3) four color QD tracking while simultaneously visualizing GFP-actin; and 4) high-density tracking for fast diffusion mapping.

ErbB1 dimerization is promoted by domain co-confinement and stabilized by ligand binding.

The extent to which ligand occupancy and dimerization contribute to erbB1 signaling is controversial. To examine this, we used two-color quantum-dot tracking for visualization of the homodimerization of human erbB1 and quantification of the dimer off-rate (k(off)) on living cells. Kinetic parameters were extracted using a three-state hidden Markov model to identify transition rates between free, co-confined and dimerized states. We report that dimers composed of two ligand-bound receptors are long-lived and their k(off) is independent of kinase activity. By comparison, unliganded dimers have a more than four times faster k(off). Transient co-confinement of receptors promotes repeated encounters and enhances dimer formation. Mobility decreases more than six times 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.

Determining FcεRI diffusional dynamics via single quantum dot tracking.

Single-particle tracking (SPT) using fluorescent quantum dots (QDs) provides high-resolution spatial-temporal information on receptor dynamics that cannot be obtained through traditional biochemical techniques. In particular, the high brightness and photostability of QDs make them ideal probes for SPT on living cells. We have shown that QD-labeled IgE can be used to characterize the dynamics of the high-affinity IgE Receptor. Here, we describe protocols for (1) coupling QDs to IgE, (2) tracking individual QD-bound receptors, and (3) analyzing one- and two-color tracking data.

Time-resolved three-dimensional molecular tracking in live cells.

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.

Systematic method for the kinetic modeling of temporally resolved hyperspectral microscope images of fluorescently labeled cells.

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.

Methods for kinetic modeling of temporally resolved hyperspectral confocal fluorescence images.

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.