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Molecular/cell level of gas exchange function assumes the accurate measurement of erythrocyte characteristics and rate constants concerning to molecules involved into the CO

Analysis of blood platelets encounters a number of different preanalytical issues, which greatly decrease the reliability and accuracy of routine clinical analysis. Modern hematology analyzers determine only four parameters relating to platelets. Platelet shape and dose-dependent activation parameters are outside the scope of commercial instruments. We used the original scanning flow cytometer for measurement of angle-resolved light scattering and the discrete dipole approximation for simulation of light scattering from a platelet optical model, as an oblate spheroid, and global optimization with two algorithms: the DATABASE algorithm to retrieve platelet characteristics from light scattering and the DIRECT algorithm to retrieve dose-dependent activation parameters. We developed the original sampling protocol to decrease spontaneous platelet activation. The new protocol allows us to keep most of the platelets in resting and partially activated states before analysis. The analysis delivers 13 content and morphological parameters of the platelets. To analyze platelet shape change during ADP activation we developed a phenomenological model. This model was applied to the analysis of ADP activation of platelets to give 8 dose-dependent activation parameters. To demonstrate the applicability of the developed protocol and analytical method, we analyzed platelets from five donors. This novel approach to the analysis of platelets allows the determination of 21 parameters relating to their content, morphology and dose-dependent activation.

Pulse dipolar spectroscopy (PDS) in Electron Paramagnetic Resonance (EPR) is the method of choice for determining the distance distribution function for mono-, bi- or multi- spin-labeled macromolecules and nanostructures. PDS acquisition schemes conventionally use uniform sampling of the dipolar trace, but non-uniform sampling (NUS) schemes can decrease the total measurement time or increase the accuracy of the resulting distance distributions. NUS requires optimization of the data acquisition scheme, as well as changes in data processing algorithms to accommodate the non-uniformly sampled data. We investigate in silico the applicability of the NUS approach in PDS, considering its effect on random, truncation and sampling noise in the experimental data. Each type of noise in the time-domain data propagates differently and non-uniformly into the distance spectrum as errors in the distance distribution. NUS schemes seem to be a valid approach for increasing sensitivity and/or throughput in PDS by decreasing and redistributing noise in the distance spectrum so that it has less impact on the distance spectrum.

Most of known light-scattering technologies, which allow one to separate spherical from non-spherical single particles, utilize either analysis of 2D light-scattering pattern or depolarization of light scattered. Both approaches force one to use high-sensitive detectors to provide a suitable signal to noise ratio for two-dimensionless photo matrix or for optical system with crossed polarizers. In this study, we introduce the method for discrimination of spherical and non-spherical single particles. The approach is based on measurement of leading, most intensive, element S11 of light-scattering matrix. To provide maximal signal to noise ratio we specified the light-scattering profile (LSP) in terms of integrated over azimuthal angle S11 as a function of polar scattering angle. The shape-sensitive vector-invariant for individual spherical particles was constructed from the parameters of LSP spectrum. The vector-invariant plays a role of the numerical criterion to identify spherical particles from LSPs. It can be applied to find a sphere with characteristics ranging from 16.5 to 70 and from 0.5 to 7.0 for size and phase-shift parameters respectively (size parameter α = πdn0/λ, where d – sphere diameter, λ – wavelength of the incident light, and n0 – medium refractive index, RI, phase-shift parameter ρ = 2α(m − 1), where relative RI m = n/n0 and n is the sphere RI). These ranges cover all possible characteristics of blood cells within the visible region of wavelengths. The ability of the vector-invariant to recognize spherical cells among non-spherical ones was tested theoretically by LSP databases of optical models of platelets and mature red blood cells. Moreover, experimentally the vector-invariant demonstrated good performance in searching of near-perfect spheres among milk fat globules, isolated nuclei of mononuclear cells, and completely spherized cells in a course of red blood cell lysis.

Whereas commercially available hematological analyzers measure volume of individual platelets, angle-resolved light-scattering provides unique ability to additionally measure their shape index. We utilized the scanning flow cytometer to measure light-scattering profiles (LSPs) of individual platelets taken from 16 healthy donors and the solution of the inverse light-scattering problem to retrieve the volume and shape index of each platelet. In normal conditions, the platelet shape index distribution (PSID) demonstrates three peaks, which relate to resting, partially activated, and fully activated platelets. We developed an algorithm, based on fitting PSID by a sum of three peak functions, to determine the percentage, mean platelet shape index, and distribution width of each platelet fraction. In total, this method gives eight additional parameters of platelet morphology and function to be used in clinical hematological analysis. We also stimulated the platelets with adenosine diphosphate (ADP) and measured the dependence of equilibrium PSID, including the total percentage of activated platelets, on ADP concentration. © 2016 International Society for Advancement of Cytometry.

We describe a new model-free approach to solve the inverse problem in pulsed double electron–electron resonance (PELDOR, also known as DEER) spectroscopy and obtain the distance distribution function between two radicals from time-domain PELDOR data. The approach is based on analytical solutions of the Fredholm integral equations of the first kind using integral Mellin transforms to provide the distance distribution function directly. The approach appears to confine the noise in the computed distance distribution to short distances and does not introduce systematic distortions. Thus, the proposed analysis method can be a useful supplement to current methods to determine complicated distance distributions.

Quantitative description of blood platelet shape and its dramatic change during activation is necessary for the correct interpretation of light-scattering data, routinely measured in diagnostic laboratories. We propose the model of platelet shape, based on the known information on the cell cytoskeleton. The model geometry is characterized by two parameters: the cell volume and the overcurvature of the internal microtubule bundle, which changes during platelet activation. We describe the procedure for the construction of a cell shape given the volume and overcurvature, and also the way for simulation of light scattering by such objects.

We instrumentally, theoretically, and experimentally demonstrate a new approach for characterization of nonspherical individual particles from light scattering. Unlike the original optical scheme of the scanning flow cytometer that measures an angle-resolved scattering corresponding in general to S11 element of the light-scattering matrix, the modernized instrument allows us to measure the polarized light-scattering profile of individual particles simultaneously. Theoretically, the polarized profile is expressed by the combination of a few light-scattering matrix elements. This approach supports us with additional independent data to characterize a particle with a complex shape and an internal structure. Applicability of the new method was demonstrated from analysis of polymer bispheres. The bisphere characteristics, sizes, and refractive indices of each sphere composing the bisphere were successfully retrieved from the solution of the inverse light-scattering problem. The solution provides determination of the Eulerian angles, which describe the orientation of the bispheres relative to the direction of the incident laser beam and detecting polarizer of the optical system. Both the ordinary and polarized profiles show a perfect agreement with T-matrix simulation resulting to 50-nm precision for sizing of bispheres. © 2011 International Society for Advancement of Cytometry.

We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem., Author summary Blood platelets are the second most numerous component of blood after red blood cells. Their main function is to stop bleeding upon vessel wall injury. Contact with foreign substances, normally absent inside the bloodstream, leads to platelet activation. After this, platelets adhere to the damaged surface and to each other, finally forming a mechanical plug. Activation is very fast and complex process, and is accompanied by dramatic change of cell shape. This morphological alteration may be vital for the prevention of blood loss. However, there is no complete understanding of its significance, maybe because the quantitative description of the platelet shape during activation is absent. Here, we describe the shape change based on the physical consideration of the platelet cytoskeleton. We propose the formulation of mathematical problem and its solution, which allows one to easily simulate a wide class of shapes for both resting and activated cells. These models are in a good agreement with platelet images observed in numerous experiments published elsewere. They may be used to simulate the shape change and hence the influence of activation on hydrodynamic, mechanical and optical properties of platelets. As a result, novel diagnostic and therapeuthic strategies and clinical implications may be obtained.

A mathematical model of erythrocyte lysis in isotonic solution of ammonium chloride is presented in frames of a statistical approach. The model is used to evaluate several parameters of mature erythrocytes (volume, surface area, hemoglobin concentration, number of anionic exchangers on membrane, elasticity and critical tension of membrane) through their sphering and lysis measured by a scanning flow cytometer (SFC). SFC allows measuring the light-scattering pattern (indicatrix) of an individual cell over the angular range from 10 degrees to 60 degrees . Comparison of the experimentally measured and theoretically calculated light scattering patterns allows discrimination of spherical from non-spherical erythrocytes and evaluation of volume and hemoglobin concentration for individual spherical cells. Three different processes were applied for erythrocytes sphering: (1) colloid osmotic lysis in isotonic solution of ammonium chloride, (2) isovolumetric sphering in the presence of sodium dodecyl sulphate and albumin in neutrally buffered isotonic saline, and (3) osmotic fragility test in hypotonic media. For the hemolysis in ammonium chloride, the evolution of distributions of sphered erythrocytes on volume and hemoglobin content was monitored in real-time experiments. The analysis of experimental data was performed in the context of a statistical approach, taking into account that parameters of erythrocytes vary from cell to cell.

The use of a scanning flow cytometer (SFC) to study the evolution of monomers, dimers and higher multimers of latex particles at the initial stage of the immunoagglutination is described. The SFC can measure the light-scattering pattern (indicatrix) of an individual particle over an angular range of 10-60 deg. A comparison of the experimentally measured and theoretically calculated indicatrices allows one to discriminate different types of latex particles (i.e. monomers, dimers, etc.) and, therefore, to study the evolution of immunoagglutination process. Validity of the approach was verified by simultaneous measurements of light-scattering patterns and fluorescence from individual polymer particles. Immunoagglutination was initiated by mixing bovine serum albumin (BSA)-covered latex particles (of 1.8 um in diameter) with anti-BSA IgG. The analysis of experimental data was performed on the basis of a mathematical model of diffusion-limited immunoagglutination aggregation with a steric factor. The steric factor was determined by the size and the number of binding sites on the surface of a latex particle. The obtained data are in good agreement with the proposed mathematical modeling., 12 pages, 6 figures

A statistical approach is presented to model the kinetics of cell distribution in the process of ligand–receptor binding on cell surfaces. The approach takes into account the variation of the amount of receptors on cells assuming the homogeneity of monovalent binding sites and ligand molecules. The analytical expressions for the kinetics of cell distribution have been derived in the reaction-limited approximation. In order to demonstrate the applicability of the mathematical model, the kinetics of binding the rabbit, anti-mouse IgG with Ig-receptors of the murine hybridoma cells has been measured. Anti-mouse IgG was labeled with fluorescein isothiocyanate (FITC). The kinetics of cell distribution on ligand–receptor complexes was observed during the reaction process by real-time measuring of the fluorescence and light-scattering traces of individual cells with the scanning flow cytometer. The experimental data were fitted by the mathematical model in order to obtain the binding rate constant and the initial cell distribution on the amount of receptors.

We theoretically analyze the aggregation kinetics of colloid particles with several active sites. Such particles (so-called "patchy particles") are well known as chemically anisotropic reactants, but the corresponding rate constant of their aggregation has not yet been established in a convenient analytical form. Using kinematic approximation for the diffusion problem, we derived an analytical formula for the diffusion-controlled reaction rate constant between two colloid particles (or clusters) with several small active sites under the following assumptions: the relative translational motion is Brownian diffusion, and the isotropic stochastic reorientation of each particle is Markovian and arbitrarily correlated. This formula was shown to produce accurate results in comparison with more sophisticated approaches. Also, to account for the case of a low number of active sites per particle we used Monte Carlo stochastic algorithm based on Gillespie method. Simulations showed that such discrete model is required when this number is less than 10. Finally, we applied the developed approach to the simulation of immunoagglutination, assuming that the formed clusters have fractal structure.

We introduce a novel approach for determination of volume and shape of individual blood platelets modeled as an oblate spheroid from angle-resolved light scattering with flow-cytometric technique. The light-scattering profiles (LSPs) of individual platelets were measured with the scanning flow cytometer and the platelet characteristics were determined from the solution of the inverse light-scattering problem using the precomputed database of theoretical LSPs. We revealed a phenomenon of parameter compensation, which is partly explained in the framework of anomalous diffraction approximation. To overcome this problem, additional a priori information on the platelet refractive index was used. It allowed us to determine the size of each platelet with subdiffraction precision and independent of the particular value of the platelet aspect ratio. The shape (spheroidal aspect ratio) distributions of platelets showed substantial differences between native and activated by 10 μM adenosine diphosphate samples. We expect that the new approach may find use in hematological analyzers for accurate measurement of platelet volume distribution and for determination of the platelet activation efficiency.

A laser flow cytometer based on scanning flow cytometry has been assembled. The unpolarized and linearly polarized light-scattering profiles, as well as the side emitted light in different spectral bands, were measured, allowing the simultaneous and real-time determination of the effective size and the effective refractive index of each spherelike particle. Additionally, each particle could be identified from depolarization and fluorescence measured simultaneously. The tests with aqueous samples of polystyrene spheres, fluorescent or nonfluorescent, and phytoplankton cells demonstrate that the system is able to retrieve size and refractive index with an accuracy of 1% and that the depolarization and fluorescence measurements allow the classification of particles otherwise indistinguishable.