2.1.

Sample Preparation

We used the ordinary immunofluorescence technique for cell extraction and staining with dye molecules adapted for flow cytometric analysis.¹⁶ Whole blood was taken from four donors by venopuncture into potassium salt of ethylenediamine tetraacetic acid. Lysing of red blood cells (RBCs) was performed adding $15\mathrm{mL}$ of lysing solution (BD Biosciences, FACS lysing solution) to $1.5\mathrm{ml}$ of blood and incubating it for $10\min$ in the dark. Two washing steps were performed to remove blood plasma and RBC debris, by centrifugation for $5\min$ at $450\times \mathrm{g}$ followed by supernatant removal. After the first step, the sediment was suspended in $15\mathrm{mL}$ of buffered saline and shaken. After the second washing step, the sediment, containing leukocytes, was shaken and added to $20\mathrm{mL}$ of antibodies (Immunotech, clone 3G8), which bind to CD16b, a receptor specific to neutrophils, and are labeled by fluorescein isothiocyanate (FITC).⁶ It is then incubated for $20\min$ in the dark, followed by a third washing step. Finally, the labeled leukocytes were suspended in buffered saline to a concentration $\sim {10}^7\text{cells}∕\mathrm{mL}$ . The analysis of a sample by SFC was performed for $3\mathrm{h}$ . All procedures were performed at room temperature $(23°\mathrm{C})$ .

2.2.

Scanning Flow Cytometer

The schematic layout of the SFC’s optical system is presented in Fig. 1 . A diode laser (Laser 1, LM-660-20-S, $660\mathrm{nm}$ , $40\mathrm{mW}$ ) was used for generation of the scattering pattern and the orthogonal laser (Laser 2, Uniphase 2214-12SLAB, $488\mathrm{nm}$ , $25\mathrm{mW}$ ) was used for excitation of fluorescence and for triggering the electronic unit. The beam of laser 1 was directed coaxially with the stream by a lens (lens 1, $f=45\mathrm{mm}$ ) through a hole in the mirror (mirror 3). The Polarizer and $\lambda ∕4$ plate provide a circular polarized incident beam. The hydrofocusing head (not shown) produces two concentric fluid streams: a sheath stream without particles and a probe stream that carries the analyzed particles. Two syringes controlled by step motors form the sample flow. The fluidics system directs a probe stream with a $12\mu \mathrm{m}$ diameter into the optical cell (Fig. 1). Operational function of the optical cell was previously described in detail.^{8, 17} The light scattered by a single cell is reflected by mirror 3 to the photomultiplier tube [(PMT), PMT 1, Hammamatsu H9 305-04]. The beam of laser 2 is focused by objective 2 $(\mathrm{NA}=0.2)$ into the capillary of the optical cell. The light scattered in the forward direction is collected by objective 1 $(\mathrm{NA}=0.2)$ and detected by PMT 3 (Hammamatsu H9 305-04). The beam stop prevents illumination of PMT 3 by the incoming laser beam. The fluorescence of specific dye molecules linked at the single cell is collected by objective 3 $(\mathrm{NA}=0.4)$ and detected by PMT 2 (Hammamatsu H9 305-04). The bandpass optical filter provides measurement of the specific fluorescence with an appropriate signal-to-noise ratio.

Fig. 1

Schematic layout of the optical system of the scanning flow cytometer.

The current optical setup of the SFC (PMT 1 in Fig. 1) measures the following combination of the scattering matrix elements:¹⁸

Neutrophils are CD16b-positive cells (i.e., those cells that have pronounced fluorescence signals). The cells that belong to the granulocyte cluster but lack fluorescence (CD16b-negative granulocytes) are either eosinophils or basophiles. However, they may also contain a small portion of monocytes because of small overlap of the corresponding clusters on the forward versus side-scattering map.¹⁰ We used the $488\text{-}\mathrm{nm}$ radiation to excite the FITC molecules (maximum of absorption of $490\mathrm{nm}$ ) and $660\mathrm{nm}$ radiation to observe light scattering. Spectral separation of light scattering and fluorescence reduce an effect of the dye molecules absorption on light-scattering profiles of cells. The legand-receptor complexes form the monomolecular layer on the cellular membrane with a thickness $<5\mathrm{nm}$ , which allows us to ignore an enlargement of a size of cells covered by dye molecules. In each sample, we collected from 120 to 1500 LSPs of those cells, which had pronounced fluorescence signals.

2.3.

Theoretical Methods

3.1.

Neutrophil Optical Model

Neutrophils have a nonuniform structure and complex shape.^{2, 25} We use an optical model of a neutrophil consisting of a sphere filled by spheres of smaller diameter—the granules—and a nucleus in the form of four spheroids of the various sizes, which are randomly placed and oriented inside the cytoplasm (see Fig. 2 ). Then identical granules are randomly positioned inside the remaining cytoplasm. This model is an extension of a simpler model (without nucleus), which was recently used in theoretical study of light scattering by granulocytes.¹²

Fig. 2

Optical model of a neutrophil.

The numerical values of model parameters, given below, correspond to literature data on neutrophil morphology. However, these parameters have large biological variability, and we use only one or a few values for the current simulations. Nevertheless, as we show further these values do lead to meaningful results. Recently, distributions of diameters of granulocytes were determined microscopically for several donors.²⁵ Bacause neutrophils constitute $>90\%$ of granulocytes,²⁶ we can assume that distributions of neutrophil diameters are very similar. Therefore, we set the diameter of the cell to $d_{\mathrm{c}}=9.6\mu \mathrm{m}$ , which also agrees with our own results using spectral sizing (Fig. 3 and Table 1 ). Granule diameters are $d_{\mathrm{g}}=0.1$ , 0.15, and $0.2\mu \mathrm{m}$ ,^{27, 28} and their volume fraction is $f_{\mathrm{g}}=0.1$ .^{28, 29} The same as was used in the theoretical paper.¹² Volume fraction of nuclei is $f_{\mathrm{n}}=0.11$ ,^{25, 30} resulting in total volume fraction of noncytoplasm material, granules, and nucleus, equal to 0.2.

Fig. 3

Size distributions of neutrophils from four samples determined by spectral method.

Table 1

Parameters of size distribution of neutrophils for four individuals.

Dunn collected information on refractive indices of the cell cytoplasm and constituents from several sources.¹⁵ However, the ranges are broad, which makes it hard to select a particular value. We set the cytoplasm refractive indices to $m_{\mathrm{c}}=1.357$ , which corresponds to the values obtained by fitting experimental LSPs of lymphocytes by a multilayered sphere model.^{14, 31} Refractive indices of nuclei, reported in literature and used for theoretical simulations, are up to 1.50,^{15, 31, 32} while the upper limit for granule refractive index is equal to the refractive index of dried protein 1.58.¹⁵ We use a value in between those two, $m_{\mathrm{g}}=1.538$ , as refractive index of both nuclei and granules to eliminate one free parameter of the model. The refractive index of the medium (buffered saline) is $m_0=1.337$ . This optical model of neutrophil has been used for calculation of The differential light-scattering cross section using the DDA (Section 2.3.1).

3.2.

Differential Light-Scattering Cross Section of Neutrophils

The essential feature of the SFC is the ability to measure the absolute differential light-scattering cross section of single particles of any form and structure. This feature is realized by measurement of a mixture of unknown particles and polymer microspheres. The LSP of the polymer microsphere, measured with the SFC, gives a perfect agreement with the Mie theory.³³ This allows calibration in absolute light-scattering units. The differential cross section was calculated from the following equation:

In order to determine the differential cross section for neutrophils we simultaneously analyzed blood leukocytes and polystyrene microspheres (Duke Scientific Corporation, 269C) with a size of $5\mu \mathrm{m}$ . Sample preparation was carried out by the technique described above. The neutrophil LSPs were identified from specific fluorescent signal. Results of measurement of a sample from one individual are presented in Fig. 4 . Twenty LSPs of individual neutrophils and microspheres form two well-distinguishable sets of curves. We pulled out the LSP of a single microsphere to find the best-fit LSP calculated from the Mie theory. In order to take into account the experimental signal-to-noise ratio, the fitting procedure was applied for light-scattering traces. Actually, a LSP is a multiplication of a light-scattering trace with a normalizing coefficient of the SFC.⁸ The fitting result is shown in the inset in Fig. 4. Indeed, the experimental points are in a perfect agreement with the solid line that corresponds to a sphere with a size of $4.97\mu \mathrm{m}$ and a refractive index of 1.580. The best-fit pattern provided the absolute units for vertical scale in Fig. 4. Differences in differential cross-sections of individual neutrophils are apparently caused by inherent biological variability (i.e., variations in size of cells and their internal structures).

Fig. 4

Differential light-scattering cross sections of neutrophils and polymer microspheres. The inset shows the experimental (points) and best-fit (solid) light-scattering traces of one polymer microsphere. The best-fit pattern corresponds to a sphere with a size of $4.97\mu \mathrm{m}$ and refractive index of 1.580.

3.3.

Different Samples and Comparison to Numerical Simulations

DDA simulations were performed for six sets of the parameters presented in Table 2 . We varied both the diameter of granules $d_{\mathrm{g}}$ and the angle $\beta$ , rotating the cell relative to the direction of the incident laser beam. Rotation is only one of the possible ways to vary internal composition of the model. Evidently, we do need a much larger set of simulated LSPs to develop a more exact optical model of neutrophils, but we leave this for future study. Here we limit ourselves to six simulated LSPs, presented in Fig. 5 . They have different intensities for different granule sizes, but the differences are significant only for $\theta >30\mathrm{deg}$ , which agree with our previous results using the model without a nucleus.¹²

Fig. 5

LSPs calculated from DDA for the optical model of a neutrophil.

Table 2

Parameters of the neutrophil optical model used for DDA simulations.

Next, we compared experimental LSPs of neutrophils to the simulated ones. Twenty-five randomly chosen experimental LSPs and one theoretical LSP simulated for the set N6 (Table 2) are shown in Fig. 6 . In general, the absolute cross section of the LSP calculated from our optical model coincides with experimental LSPs, which demonstrate a relatively large variability in their intensities and shapes.

Fig. 6

Experimental LSPs of single neutrophils (gray) and LSP calculated by DDA (black) from the optical model of the cell.

We measured LSPs of neutrophils of four donors to estimate their intersample variability. The result of the measurement is shown in Fig. 7 as LSPs averaged over all neutrophils in each sample. LSPs of individual neutrophils (gray lines in Fig. 6) have a random oscillating structure, while averaged LSP is almost featureless except a minimum and maximum between 7 and $10\mathrm{deg}$ . These extrema are present in all individual LSPs as well as in the averaged LSP. The position of extrema of individual LSPs for small scattering angles is mostly determined by neutrophil diameter (i.e., it can be described by diffraction). The simulated LSPs (Fig. 5) also have these two extrema at similar angles, which proves that we used more or less correct size for the neutrophil model. It is important to note that simulated LSPs do not agree with experimental LSPs of the other three individuals as well, as they do with the individual 1. Variation of model parameters, especially refractive indices and nuclei sizes, is definitely required to produce better agreement for other individuals, and that is left for future research. However, we believe that Fig. 6 clearly supports the adequacy of our optical model.

Fig. 7

Experimental LSPs of neutrophils of four donors averaged over sample.

Averaged LSPs of neutrophils of different individuals are essentially different (e.g., they have different overall magnitudes and decay rates for larger scattering angles). These differences are caused by morphological differences of neutrophils (size, internal composition, refractive indices of the constituents, etc.). Hence, we put forward the hypothesis that averaged LSPs may serve as a diagnostic parameter. However, an extensive clinical study of both normal and abnormal samples is required to clarify its diagnostic value.

3.4.

Size Distributions

Size distributions obtained by the spectral decomposition method (Section 2.3.2) for four samples are shown in Fig. 3. Mean sizes of neutrophils with an error of the mean size and width of distribution (two standard deviations) are presented in Table 1. Mean values agrees well with recent microscopic data,²⁵ but standard deviations are on average 50% larger. This shows that spectral sizing method produces meaningful results for neutrophils, but it produces significant errors for each individual cell, leading to widening of distributions. As was mentioned in Section 2.3.2, the spectral decomposition method plays a role of an indicator for a neutrophil size because of unknown systematical error of this method for granular cells. The developed optical model of a neutrophil given a good agreement with experimental results should help us to determine this error from future theoretical study.

One can see that there is only a small difference in neutrophil sizes between the samples, $<10\%$ for sample-averaged values. Therefore, significant changes in neutrophil internal structure (granularity, size of nucleus, refractive indices, etc.) must be involved to explain the fivefold intersample variation of LSP magnitude. Further study is required to make any definite conclusions.