Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light’s diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we’ve termed the interpretation problem

Statistical Design And Imaging Of Position-Encoded 3D Microarrays

We propose a three-dimensional microarray device with microspheres having controllable positions for error-free target identification. Here targets: such as mRNAs, proteins, antibodies, and cells) are captured by the microspheres on one side, and are tagged by nanospheres embedded with quantum-dots: QDs) on the other. We use the lights emitted by these QDs to quantify the target concentrations. The imaging is performed using a fluorescence microscope and a sensor. We conduct a statistical design analysis to select the optimal distance between the microspheres as well as the optimal temperature. Our design simplifies the imaging and ensures a desired statistical performance for a given sensor cost. Specifically, we compute the posterior Cram&eacuter-Rao bound on the errors in estimating the unknown target concentrations. We use this performance bound to compute the optimal design variables. We discuss both uniform and sparse concentration levels of targets. The uniform distributions correspond to cases where the target concentration is high or the time period of the sensing is sufficiently long. The sparse distributions correspond to low target concentrations or short sensing durations. We illustrate our design concept using numerical examples. We replace the photon-conversion factor of the image sensor and its background noise variance with their maximum likelihood: ML) estimates. We estimate these parameters using images of multiple target-free microspheres embedded with QDs and placed randomly on a substrate. We obtain the photon-conversion factor using a method-of-moments estimation, where we replace the QD light-intensity levels and locations of the imaged microspheres with their ML estimates. The proposed microarray has high sensitivity, efficient packing, and guaranteed imaging performance. It simplifies the imaging analysis significantly by identifying targets based on the known positions of the microspheres. Potential applications include molecular recognition, specificity of targeting molecules, protein-protein dimerization, high throughput screening assays for enzyme inhibitors, drug discovery, and gene sequencing

Single Particle Tracking: Analysis Techniques for Live Cell Nanoscopy.

Single molecule experiments are a set of experiments designed specifically to study the properties of individual molecules. It has only been in the last three decades where single molecule experiments have been applied to the life sciences; where they have been successfully implemented in systems biology for probing the behaviors of sub-cellular mechanisms. The advent and growth of super-resolution techniques in single molecule experiments has made the fundamental behaviors of light and the associated nano-probes a necessary concern among life scientists wishing to advance the state of human knowledge in biology. This dissertation disseminates some of the practices learned in experimental live cell microscopy. The topic of single particle tracking is addressed here in a format that is designed for the physicist who embarks upon single molecule studies. Specifically, the focus is on the necessary procedures to generate single particle tracking analysis techniques that can be implemented to answer biological questions. These analysis techniques range from designing and testing a particle tracking algorithm to inferring model parameters once an image has been processed. The intellectual contributions of the author include the techniques in diffusion estimation, localization filtering, and trajectory associations for tracking which will all be discussed in detail in later chapters. The author of this thesis has also contributed to the software development of automated gain calibration, live cell particle simulations, and various single particle tracking packages. Future work includes further evaluation of this laboratory\u27s single particle tracking software, entropy based approaches towards hypothesis validations, and the uncertainty quantification of gain calibration

Bayesian Inference Frameworks for Fluorescence Microscopy Data Analysis

abstract: In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates.Dissertation/ThesisMasters Thesis Applied Mathematics 201

Experimental Stochastics in High-Resolution Fluorescence Microscopy : Imaging Theory of PALMIRA Microscopy; Improved Models for FCS

This thesis presents a statistical imaging theory for photo-activation localization microscopy with independently running acquisition (PALMIRA). In this type of sub-resolution microscopy the switching of the fluorescence capability of macromolecules reduces imaging to the high-precision localization of individual fluorescent molecules. The point-spread function and the imaging equation of a PALMIRA imaging system are calculated and stochastic expressions for the measurement time and the confidence level of the image as a function of the spatial resolution are provided. Different localization schemes like astigmatic imaging, multi-channel defocus imaging, 4pi imaging and a multi-point setup using photo-diodes are analyzed. The theory for multi-color and polarization-resolved measurements is addressed and estimators for data evaluation procedures are provided. The role of background noise in producing artefacts is studied. Finally, it is assessed whether the quality of images can be augmented by a suitable deconvolution procedure. Furthermore, stochastic methods are applied to solve a couple of persistent problems in fluorescence correlation spectroscopy (FCS). The development of computational methods for the simulation of FCS experiments necessitates the analytical description of the architecture of a multiple-lag-time correlator that is used to estimate autocorrelations from intensity time traces. Recently, FCS has been combined with stimulated emission depletion (STED) focal volumes. The general phenomenology of STED-FCS correlation curves is studied as a function of the STED beam intensity. It is shown that the quality of a measurement is mainly determined by the fraction of signal originating from the focal plane. Then, an improved fit model taking into account the exact spatial dependency of intersystem crossing rates is presented and tested on synthetic data. Finally, the influence of second-order correlations among the points of the FCS curve on the determination of fit parameters is studied. Analytical results are provided wherever possible. Otherwise, Monte-Carlo computations are performed

Probabilistic modeling and inference for sequential space-varying blur identification

International audienceThe identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric model of the blur and introduce an 1D state-space model to describe the statistical dependence among the neighboring kernels. We apply a Bayesian approach to estimate the posterior distribution of the kernel parameters given the available data. Since this posterior is intractable for most realistic models, we propose to approximate it through a sequential Monte Carlo approach by processing all data in a sequential and efficient manner. Additionally, we propose a new sampling method to alleviate the particle degeneracy problem, which is present in approximate Bayesian filtering, particularly in challenging concentrated posterior distributions. The considered method allows us to process sequentially image patches at a reasonable computational and memory costs. Moreover, the probabilistic approach we adopt in this paper provides uncertainty quantification which is useful for image restoration. The practical experimental results illustrate the improved estimation performance of our novel approach, demonstrating also the benefits of exploiting the spatial structure the parametric blurs in the considered models

Transient absorption imaging of hemeprotein in fresh muscle fibers

2022 Summer.Includes bibliographical references.Mitochondrial diseases affect 1 in 4000 individuals in the U.S. among adults and children of all races and genders. Nevertheless, these diseases are hard to diagnose because they affect each person differently. Meanwhile the gold standard diagnosis methods are usually invasive and time- consuming. Therefore, a non-invasive and in-vivo diagnosis method is highly demanded in this area. Our goal is to develop a non-invasive diagnosis method based on the endogenous nonlinear optical effect of the live tissues. Mitochondrial disease is frequently the result of a defective electron transport chain (ETC). Our goal is to develop a non-invasive way to measure redox within the ETC, specifically, of cytochromes. Cytochromes are iron porphyrins that are essential to the ETC. Their redox states can indicate cellular oxygen consumption and mitochondrial ATP production. So being able to differentiate the redox states of cytochromes will offer us a method to characterize mitochondrial function. Meanwhile, Chergui's group found out that the two redox states of cytochrome c have different pump-probe spectroscopic responses, meaning that the transient absorption (TA) decay lifetime can be a potential molecular contrast for cytochrome redox state discrimination. Their research leads us to utilize the pump-probe spectroscopic idea to develop a time-resolved optical microscopic method to differentiate not only cytochromes from other chemical compounds but also reduced cytochromes from oxidized ones. This dissertation describes groundbreaking experiments where transient absorption is used to reveal excited-state lifetime differences between healthy controls and an animal model of mitochondrial disease, in addition to differences between reduced and oxidized ETC in isolated mitochondria and fresh preparations of muscle fibers. For our initial experiments, we built a pump-probe microscopic system with a fiber laser source, producing 530nm pump and 490nm probe using a 3.5kHz laser scanning rate. The pulse durations of pump and probe are both 800fs. For the preliminary results, we have successfully achieved TA decay contrast between reduced and oxidized cytochromes in solution form. Then we have achieved SNR enhanced pump-probe image of BGO crystal particles with the help of the software- based adaptive filter noise canceling method. We also have installed a FPGA-based adaptive filter to enhance the pump-probe signals of the electrophoresis gels that contain different mitochondrial respiratory chain supercomplexes. However, because the noise floor was still 30 dB higher than shot noise limit, cytochrome imaging in live tissues was still problematic. We then built another pump-probe microscope with a solid- state ultrafast laser source. In that way, we do not need to worry about laser relative intensity noise (RIN) anymore, since the noise floor of the solid-state laser source can reach the shot noise limit at MHz region. One other advantage of the new laser source is that it can provide one tunable laser output that can be directly converted to the probe pulse with tunable center wavelength. Its tunability can cover the entire visible spectrum. We realized a pump-probe microscopy with a 520nm pump pulse and a tunable probe pulse. The tunability on the probe arm allows us to explore better pump-probe contrast between two redox states. What's more, I will introduce my preliminary results of utilizing supercontinuum generation in a photonic crystal fiber (PCF) to realize tunability on pump wavelength. In that way, more possibilities will be unlocked. And the hyperspectral pump-probe microscope will be able to distinguish more molecules