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• W2750661811 abstract "Recently we complemented the raster image correlation spectroscopy (RICS) method of analysing raster images via estimation of the image correlation function with the method single particle raster image analysis (SPRIA). In SPRIA, individual particles are identified and the diffusion coefficient of each particle is estimated by a maximum likelihood method. In this paper, we extend the SPRIA method to analyse mixtures of particles with a finite set of diffusion coefficients in a homogeneous medium. In examples with simulated and experimental data with two and three different diffusion coefficients, we show that SPRIA gives accurate estimates of the diffusion coefficients and their proportions. A simple technique for finding the number of different diffusion coefficients is also suggested. Further, we study the use of RICS for mixtures with two different diffusion coefficents and investigate, by plotting level curves of the correlation function, how large the quotient between diffusion coefficients needs to be in order to allow discrimination between models with one and two diffusion coefficients. We also describe a minor correction (compared to published papers) of the RICS autocorrelation function. Diffusion is a key mass transport mechanism for small particles. Efficient methods for estimating diffusion coefficients are crucial for analysis of microstructures, for example in soft biomaterials. The sample of interest may consist of a mixture of particles with different diffusion coefficients. Here, we extend a method called Single Particle Raster Image Analysis (SPRIA) to account for particle mixtures and estimation of the diffusion coefficients of the mixture components. SPRIA combines elements of classical single particle tracking methods with utilizing the raster scan with which images obtained by using a confocal laser scanning microscope. In particular, single particles are identified and their motion estimated by following their center of mass. Thus, an estimate of the diffusion coefficient will be obtained for each particle. Then, we analyse the distribution of the estimated diffusion coefficients of the population of particles, which allows us to extract information about the diffusion coefficients of the underlying components in the mixture. On both simulated and experimental data with mixtures consisting of two and three components with different diffusion coefficients, SPRIA provides accurate estimates and, with a simple criterion, the correct number of mixture components is selected in most cases. Table S8: N is the observed number of particles, D is the expected diffusion coefficient, is the estimated diffusion coefficient as presented in (Longfils et al., 2017), and is the estimated diffusion coefficient with the method suggested herein. The values after the ± signs are standard errors computed by bootstrapping. Table S9: Results for a mixtures of 175 nm, 500 nm, and 1000 nm beads with different proportions. Sizes indicates which beads have been mixed in each row and in parentheses we report the expected diffusion coefficients according to Stokes-Einstein relation. is the expected proportion of the larger bead species in the mixture (=). and are the two estimated diffusion coefficients for the mixture model, and is the diffusion estimated for the single diffusion coefficient model. is the estimated proportion β1. Table S10: Results for single populations of beads. Sizes indicates which beads have been considered in each row and in parentheses we report the expected diffusion coefficients according to Stokes-Einstein. is the estimated diffusion coefficient by SPRIA with one component, while and are the two estimates for a mixture with two diffusing species. is the estimated proportion of particles with diffusion coefficient . Comp15 is the selected number of components with a 15% threshold on the minimum proportion and finally, is the estimated diffusion coefficient by RICS. The values after the ± signs are standard errors computed by bootstrap. Table S11: Results for simulated non-mixed beads. is the true diffusion coefficient used for the simulation, is the estimated diffusion coefficient by SPRIA with one component, while and are the two estimates for a mixture with two diffusing species, and is the estimated proportion of particles with diffusion coefficient . Comp15 is the selected number of components with a 15% threshold on the minimum proportion and finally is the estimated diffusion coefficient by RICS. The values after the ± signs are standard errors computed by bootstrapping. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article." @default.
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• W2750661811 date "2017-09-01" @default.
• W2750661811 modified "2023-09-23" @default.
• W2750661811 title "Single particle raster image analysis of diffusion for particle mixtures" @default.
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• W2750661811 doi "https://doi.org/10.1111/jmi.12625" @default.
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