Vyacheslav M. Nekrasov

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.

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.

Kinetics of the initial stage of immunoagglutionation studied with the scanning flow cytometer

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.

Scanning flow cytometer modified to distinguish phytoplankton cells from their effective size, effective refractive index, depolarization, and fluorescence

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.

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.

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.

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.