Alexander E. Moskalensky

Accurate measurement of volume and shape of resting and activated blood platelets from light scattering

Abstract. 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.

Light-scattering flow cytometry for identification and characterization of blood microparticles

We describe a novel approach to study blood microparticles using the scanning flow cytometer, which measures light scattering patterns (LSPs) of individual particles. Starting from platelet-rich plasma, we separated spherical microparticles from non-spherical plasma constituents, such as platelets and cell debris, based on similarity of their LSP to that of sphere. This provides a label-free method for identification (detection) of microparticles, including those larger than 1 μm. Next, we rigorously characterized each measured particle, determining its size and refractive index including errors of these estimates. Finally, we employed a deconvolution algorithm to determine size and refractive index distributions of the whole population of microparticles, accounting for largely different reliability of individual measurements. Developed methods were tested on a blood sample of a healthy donor, resulting in good agreement with literature data. The only limitation of this approach is size detection limit, which is currently about 0.5 μm due to used laser wavelength of 0.66 μm.

Polarized light-scattering profile—advanced characterization of nonspherical particles with scanning flow cytometry

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.

Super‐resolved calibration‐free flow cytometric characterization of platelets and cell‐derived microparticles in platelet‐rich plasma

Importance of microparticles (MPs), also regarded as extracellular vesicles, in many physiological processes and clinical conditions motivates one to use the most informative and precise methods for their characterization. Methods based on individual particle analysis provide statistically reliable distributions of MP population over characteristics. Although flow cytometry is one of the most powerful technologies of this type, the standard forward‐versus‐side‐scattering plots of MPs and platelets (PLTs) overlap considerably because of similarity of their morphological characteristics. Moreover, ordinary flow cytometry is not capable of measurement of size and refractive index (RI) of MPs. In this study, we 1) employed the potential of the scanning flow cytometer (SFC) for identification and characterization of MPs from light scattering; 2) suggested the reference method to characterize MP morphology (size and RI) with high precision; and 3) determined the lowest size of a MP that can be characterized from light scattering with the SFC. We equipped the SFC with 405 and 488 nm lasers to measure the light‐scattering profiles and side scattering from MPs, respectively. The developed two‐stage method allowed accurate separation of PLTs and MPs in platelet‐rich plasma. We used two optical models for MPs, a sphere and a bisphere, in the solution of the inverse light‐scattering problem. This solution provides unprecedented precision in determination of size and RI of individual spherical MPs—median uncertainties (standard deviations) were 6 nm and 0.003, respectively. The developed method provides instrument‐independent quantitative information on MPs, which can be used in studies of various factors affecting MP population.

Fluorescence-free flow cytometry for measurement of shape index distribution of resting, partially activated, and fully activated platelets

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.

Dynamic quantification of antigen molecules with flow cytometry

Traditional methods for estimating the number of expressed molecules, based on the detection of target antigens bound with fluorescently labeled antibodies, assume that the antigen-antibody reaction reaches equilibrium. A calibration procedure is used to convert the intensity of the fluorescence signal to the number of target molecules. Along with the different limitations of every calibration system, this substantially limits the applicability of the traditional approaches especially in the case of low affinity antibodies. We address this problem here with studies in which we demonstrate a new approach to the antigen molecule quantification problem. Instead of using a static calibration system, we analyzed mean fluorescence values over time by flow cytometry during antibody-antigen binding. Experimental data obtained with an LSRII cytometer were fitted by a diffusion-reaction mathematical model using the Levenberg-Marquardt nonlinear least squares curve-fitting algorithm in order to obtain the number of target antigen molecules per cell. Results were compared with the Quanti-BRITE calibration system. We conclude that, instead of using experiment-specific calibration, the value of the binding rate constant for each particular antibody-antigen reaction can be used to quantify antigen molecules with flow cytometry. The radius of CD8 antibody molecule binding site was found, that allows recalculating the binding rate constant for other conditions (different sizes of reagent molecules, fluorescent label, medium viscosity and temperature). This approach is independent of specially prepared calibration beads, antibody reagents and the specific dye and can be applied to both low and high affinity antibodies, under both saturating and non-saturating binding conditions. The method was demonstrated on a human blood sample dataset investigating CD8α antigen on T cells in stable binding conditions.

Additivity of light-scattering patterns of aggregated biological particles

Abstract. The paper is focused on light scattering by aggregates of optically soft particles with a size larger than the wavelength, in particular, blood platelets. We conducted a systematic simulation of light scattering by dimers and larger aggregates of blood platelets, each modeled as oblate spheroids, using the discrete dipole approximation. Two-dimensional (2-D) light scattering patterns (LSPs) and internal fields showed that the multiple scattering between constituent particles can be neglected. Additionally, we derived conditions of the scattering angle and orientation of the dimer, under which the averaging of the 2-D LSPs over the azimuthal scattering angle washes out interference in the far field, resulting in averaged LSPs of the aggregate being equal to the sum of that for its constituents. We verified theoretical conclusions using the averaged LSPs of blood platelets measured with the scanning flow cytometer (SFC). Moreover, we obtained similar results for a model system of aggregates of polystyrene beads, studied both experimentally and theoretically. Finally, we discussed the potential of discriminating platelet aggregates from monomers using the SFC.

Method for the simulation of blood platelet shape and its evolution during activation

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.

Calibration-free quantitative immunoassay by flow cytometry: Theoretical consideration and practical implementation for IgG antibody binding to CD14 receptors on human leukocytes: Calibration-Free Quantitative Immunoassay by Flow Cytometry

We propose a calibration‐free method to determine the number of receptors per cell, as well as the direct and the reverse reaction rate constants for a single receptor. The method is based on the analysis of the temporal evolution of the cells mean fluorescent intensity measured by a flow cytometer during the ligand–receptor (antigen–antibody) binding under the conditions of their comparable concentrations. We developed the kinetic approach accounting both for the delay between the dilution and the measurement and for the practical duration of the measurement itself. The method was applied to determine thenumber of CD14 receptors on human blood mononuclear (granulocytes, monocytes, lymphocytes) cells of several donors. We also obtained the direct ( k+= (5.6 ± 0.2) × 107 M−1 min−1) and reverse ( k−= (1.3 ± 0.2) × 10−2 min−1) rate constants of ligand–receptor interaction, and estimated the size of the binding site as b = 0.5 nm. The latter allows one to recalculate the rate constants for a different ligand, fluorescent label, medium viscosity, and/or temperature. The knowledge of the rate constants is essential for the calibration‐free determination of the number of receptors per cell from a single kinetic curve of the cells mean fluorescence intensity.

A physical model of blood platelets shape and its effect on light scattering

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.