Inhomogeneity Based Characterization of Distribution Patterns on the Plasma Membrane. Introduction. The function of cell surface proteins and lipids is tightly coupled to their spatial organization . Membrane constituents cluster in nano- and micro- domains originating from lipid affinity (e. Plasma membrane organization is also inherently asymmetric in polarized cells, such as migrating cells . The ability to detect this plasma membrane organization is crucial for unraveling the dependency of signaling events, and understanding membrane regulation in a disease- related context . Point processes can be classified as: (I) Homogeneous or random, characterized by a constant density of points; (II) Inhomogeneous, characterized by a non- constant density of points; (III) Regular, with points equally dispersed; and (IV) Clustered, where points are grouped . These measure the number from neighbors within a certain distance of a protein to determine the amount of clustering . Several modifications and extensions of Ripley’s K- function have been made, including a model- based Bayesian approach . The PC function has been applied to images acquired by Photoactivatable Localization Microscopy (PALM) to quantify the heterogeneity of protein distributions on the plasma membrane . In addition, the Density- Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, a density based tool, was used to identify clusters of varying shape against a background in super- resolution microscopy . Recently, the Ordering Points To Identify the Clustering Structure (OPTICS) algorithm was made available to the single molecule community to measure local density changes (overcoming some of the limitations of DBSCAN) . Moreover, the Getis- Ord G statistic . While the ability to detect specific clusters is of great importance, Sengupta et al. All these organizations should be accounted for when analyzing the overall distribution. Furthermore, current tools require knowledge of the precise localization of the proteins and are thus limited to super- resolution or electron microscopy images. Therefore, we aimed to create an analysis tool that investigates biomolecule distributions without upfront information about their organization, and that can be applied to a variety of microscopy methods, including super- resolution and widefield microscopy. The main principle of our approach is to investigate spatial patterns of proteins and lipids and to quantify any deviation from random towards clustered or polarized organization as a measure of increased inhomogeneity. We exploit a geometrical approach, called tessellation, to divide the image into tiles, and use the distribution of tile areas to characterize different patterns. The image analysis algorithm uses both the information of the neighbor relations of segmented objects and the intensity of the tiles in which they are confined. By using fluorescence intensity information for tile area correction, we have made the tool applicable to images acquired by a range of microscopy techniques. We have termed this analysis tool Quantitative Analysis of the Spatial- distributions in Images using Mosaic segmentation and Dual parameter Optimization in Histograms (Qu. ASIMo. DOH). Considering a number N of individual points p of the process placed on the support S, the distribution pattern P is defined as. P describes a homogenous, clustered, or inhomogeneous pattern. Considering the brightness f of the fluorescent emitters (represented by p) and assuming the emitters being equally bright, the distribution pattern can be defined as. When the point process P (S1. A Fig) is imaged by an optical system, each point of position r, p(r), will be diffracted by the Point Spread Function (PSF). The resulting microscope image g(r) is typically approximated by the convolution (. Due to the band limitation of the PSF, points of the pattern P placed at a distance shorter than the band limit will not be resolved as single points. In the blurred image, the intensity of the pixels depicting the diffraction pattern is directly related to the number of points contributing to this diffracted pattern. Aiding the development of Qu. ASIMo. DOH, we generated in silico images of points (shown as single pixels) dispersed on a surface (Fig 1. A, S1 Text). Blur and noise were then added into the image (Fig 1. B) to mimic the acquisition process of a fluorescence microscope (see S1 Fig and S1 Text for detailed description). The individual steps of Qu. ASIMo. DOH analysis are depicted in Fig 1 and described in detail below: Fig 1. Blur by a point spread function and noise are introduced in the image (A) as shown in S1 Fig. Thresholding. First, we apply a threshold to separate signal from background. The detected objects (o) are regions of connected pixels above the threshold (Fig 1. Nanofiltration Membrane Characterization using Mass Transfer Data with Emphasis on Temperature Effects Ramesh R. Sharma Trussell Technologies, Inc., Pasadena, CA. Author Summary Plasma membrane. Inhomogeneity Based Characterization of. C) in the image g. The pattern O of the threshold detected objects on the support S, with S representing the background of the image g, is. Preparation and characterization of a composite palladium-ceramic. Advanced Membrane Technology and Applications. Membrane Characterization by Ultrasonic Time-Domain Reflectometry. PDF(908K) References. O being a subset of P. For the thresholding step, the images are initially filtered to smooth the signal, preserving object boundaries and supporting image binarization (Materials and Methods). If more than the 2. An automated threshold, implemented in Image. UNESCO – EOLSS SAMPLE CHAPTERS WATER AND WASTEWATER TREATMENT TECHNOLOGIES - Membrane Characterization - Khulbe KC, Feng CY and Matsuura T Membrane characterization by microscopic methods: Multiscale structure. Download PDF Opens in. Fouling on ion-exchange membranes: Classification, characterization and strategies of. Membrane electrical resistance and conductivity. Title: Characterization of Reverse Osmosis Membrane Foulants in Seawater Desalination Author: David A. Ladner Created Date: 2/10/2015 1:54:42 PM. Characterization of the Cell Membrane During Cancer Transformation 243 A-+ Na+ ANa (2) B+ + OH- BOH (3) B+ + Cl- BCl (4) -4,5-3-1,5. This book describes the human amniotic membrane from its origin, characterization and medical applications, summarizing all the latest developments and. J/Fiji, was chosen to compare sets of images (see Materials and Methods; for recommendations on threshold selection, see S1 Text). Tessellation. Next, tessellation is used to divide up the space occupied by the threshold- detected objects (o) into polygons, or tiles, based on the relationship of each object with its neighbors (Fig 1. D). We implemented a procedure to take the extension of the objects into account. Given two neighboring objects (U and V), we measure the half way Euclidean distance () between U and V starting from their borders (u and v). To this aim, we used the skeletonization function first described by Lantu. This function removes pixels surrounding the threshold- detected objects until the tile boundaries between the objects remain (Fig 1. D). This will lead to a number of tiles T that are similar to the number of objects (or watershed separated objects). Creating the tiles from object borders (u and v) is better suited than the common Voronoi tessellation . For separated point sets, like in super- resolution images, the different strategies however converge. Tile area intensity measurement. As indicated in eq (3), the imaging process of the microscope leads to the generation of a blurred image. Therefore, depending on the resolution of the microscope, the threshold- detected object, o (eq (4)), in a tile may consist of multiple, spatially indistinguishable fluorescent emitters (in the context of eq (2), a number of pf). In Fig 1, for instance, the threshold- detected objects in tiles 2 and 5 are the result of blurring two emitters (simulated as single points), while the object in tile 4 is the result of blurring three emitters (see Fig 1. A and 1. D). We assume that the pixels of a tile T contain on average the intensity of the imaged fluorophores. IT represents the intensity of the tile T, containing a number PT of single emitters, that are equally fluorescent, with brightness f. To determine the intensity of single tiles, the full set of tiles, obtained by skeletonization of the thresholded image (Fig 1. D), is applied as regions of interest (ROIs) to the original smoothed grayscale image (Fig 1. E). The intensity of each tile is then measured together with its area. Tile area correction. Since the tile intensity IT varies with the number of fluorophores contained per tile, we aim to correct the area of brighter tiles based on their intensity by introducing a correction factor C. This correction factor represents the intensity of a fluorescent entity in the image (e. The correction is carried out by symmetrically dividing the tiles into multiple areas using the correction factor. Considering a tile of area AT and intensity IT and the correction factor C, with C being . With this, the total area remains the same, as. If IT < C, then A = AT, meaning no correction is applied (Fig 1. F). Using this correction and if the correction factor equals the intensity of a single emitter (C = f), the number of tile areas obtained after correction would approximate the number of points pi of the process P. For C larger than f, the analysis holds a relative distribution measure of multiples of p. As such the brightness information of a fluorescent component (i. Number and Brightness (N& B) approaches . Alternatively, we implemented an estimation for the correction factor from the image itself. This is based on the distribution of tile intensities and yields a correction with the detectable intensity of a fluorescent entity from the image, as determined by the sensitivity of the microscope. A comprehensive description of correction factor determination can be found in S1 Text. An advantage of using the correction factor is the enrichment of tile area datasets with information otherwise ignored regarding the density of fluorophores contained within each tile. Incorporating intensity information into the distribution analysis makes Qu. ASIMo. DOH a powerful tool and a specific case in the analysis of marked point processes (processes characterized by a certain distribution and by a mark, which is, in this case, the intensity) . Tile area distribution analysis. The distribution of the obtained (corrected) tile areas is then modeled by the Inverse Gamma PDF . The Inverse Gamma was chosen based on literature . The Inverse Gamma is a continuous two- parameter PDF, defined over a support x > 0, as. We used the Maximum Likelihood Estimation (MLE) of the Inverse Gamma parameters to identify values for the shape and scale parameters, which are descriptive of the point pattern. Once estimated, the parameters are used to fit tile area histograms for quality control of the MLE by calculation of the coefficient of determination r. Fits with a quality less than r. We next validated Qu.
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