Field of the invention

The present invention relates to a flow cytometry method for determination of size and refractive index of substantially spherical single particles.

Background

Flow cyto meters measure light scattering of single particles, with the scattering signal in arbitrary units. Because data are in arbitrary units and light scattering is a complex process, interpretation of flow cytometry data requires optical expertise. Moreover, because data are in arbitrary units and flow cytometers differ in optical configuration, flow cytometry data cannot be compared between different instruments.

If the refractive index of substantially spherical particles is known, light scattering theory, such as Mie theory, can be used to describe the relation between the measured scattering parameter at one detector and the size of the single particles, wherein the size of a single particle is here defined as the diameter of the single particle. Furthermore, the relation between measured scattering parameter at one detector and the refractive index can be described if the size is known.

The method described above enables conversion of a single measured scattering parameter at one detector to either size or refractive index, if the respective other parameter is, at least approximately, known. A problem with the existing flow cytometry methods is that in most situations both the size and refractive index of the single particles will be unknown.

Furthermore, to find the relationship between the detected light scattering and the size and refractive index of a particle, it is essential to know the optical configuration of the flow cytometer.

In US 5.859.705 a method is described for using light scattering to measure the size of particles suspended in a fluid medium virtually independent of the particle refractive index. However, the method relates to a particle size of 1-2500 μιη and provides no information from single particles.

In US 7.999.936 Bl a method is described for using combined transmittance and angle selective scattering to measure the size, refractive index, extinction coefficient and density of particles suspended in a fluid medium. However, the method provides no information from single particles.

In US 2013/242.296 Al a method is described to calibrate a particle measuring and counting apparatus, as incorporated into flow cytometers, to determine either the size or the refractive index of particles in a sample. The first step of the method comprises analyzing the scattering parameters on two detectors of a mixture of particles of known refractive index X and a plurality of different sizes. The second step of the method comprises analyzing the scattering parameters on two detectors of a mixture of particles of known refractive index Y and a plurality of different sizes, of which also the size of at least one particle is known. The third step comprises the application of Mie theory to determine the size of a particle form its position on the flow cytometer histogram, or alternatively, if the size of the particles in a sample to be analyzed in a cytometer is known, the method could instead be used to infer the refractive index of particles in a sample. However, the method comprises the measurement and analysis of two calibration mixtures and the method provides either size or refractive index of particles.

Object of the invention

An object of the invention is to provide a method to determine size and refractive index of substantially spherical single particles without prior knowledge of either the size or the refractive index of the particles.

Summary of the invention

The object is achieved by a flow cytometry method for determination of size and/or refractive index of substantially spherical single particles, wherein the method comprises the following steps:

calibrating a flow cytometer based on light scattering signals;

performing a flow cytometry experiment, wherein the flow cytometer experiment comprises illuminating a flow cell of the flow cytometer by an illumination beam and subsequently detecting a first and a second light scattering signal of the single particles in the flow cell, wherein the first and second light scattering signal are differentiated by a scattering angle;

analyzing data resulting from the flow cytometry experiment for determination of size and/or refractive index of the single particles. Advantageously, neither the size nor the refractive index of the single particle needs to be determined, or obtained from literature, to perform the flow cytometry method. More advantageously, the arbitrary units of the scattering signal can be converted to physical units allowing users to compare measurement results and identify the single particles without fluorescently labeling them. Even more advantageously, the invention provides a method with improved data interpretation and higher handling speeds than dedicated sizing techniques, such as Nanoparticle Tracking Analysis (NTA) and Resistive Pulse Sensing (RPS).

An embodiment relates to the method as described above, wherein the analysis step further comprises determining the size of the single particles independently of the refractive index of the single particles from the first light scattering signal and the second light scattering signal, preferably using a lookup table, more preferably using an Optical Scattering Ratio (OSR) between the first light scattering signal and the second light scattering signal.

An embodiment relates to the method as described above, wherein the analysis step further comprises determining the refractive index of the single particles from the first light scattering signal and/or the second light scattering signal, preferably by using a lookup table, more preferably by solving an inverse light scattering problem using the size and the first or second light scattering signal.

An embodiment relates to the method as described above, wherein the size and/or the refractive index of the single particles is used for identification and differentiation of the single particles, for calculating a density, such as a number of antigens per surface area or a number of protein per volume of the single particles, or for comparison and standardization of measurement results on the single particles. Because the refractive index is related to the chemical composition of the particle, determination of the refractive index can also be utilized to differentiate between different components of samples.

An embodiment relates to the method as described above, wherein the analysis step further comprises using empirical determination or light scattering theory, such as Mie theory, Rayleigh theory, or diffraction theory.

An embodiment relates to the method as described above, wherein the analysis step further comprises using light scattering theory to determine physical properties of the single concentric particles other than size and refractive index, such as core diameter, core refractive index, shell or layer thickness and shell or layer refractive index.

An embodiment relates to the method as described above, wherein the size of the single particles is smaller than three times the wavelength of the illumination beam, preferably smaller than twice the wavelength of the illumination beam, more preferably smaller than the wavelength of the illumination beam.

An embodiment relates to the method as described above, wherein the wavelength of the illumination beam is in a wavelength range of 150 nm - 20 μιη, preferably in the visible spectrum, even more preferably around 405 or 488 nm.

An embodiment relates to the method as described above, wherein the single particles comprise bacteria, extracellular vesicles, such as exosomes and microparticles, lipoprotein particles, such as chylomicrons, very-low-density lipoproteins (VLDL), intermediate-density lipoproteins (IDL), low-density lipoproteins (LDL), and high- density lipoproteins (HDL), cells such as platelets, viruses, protein aggregates, synthetic nanoparticles, such as liposomes, soda lime, borosilicate, calcium carbonate, aluminum oxide, aluminum silicate, diamond, gold, nickel, poly(methyl methacrylate) (PMMA), and polytetrafluoroethylene (PTFE), or yeast.

Moreover, an embodiment relates to the method as described above, comprising a flow cytometer calibration method, suitable for use with the step of calibrating the flow cytometer based on light scattering signals, for determining optical parameters describing an optical configuration of a flow cytometer, wherein the flow cytometer calibration method comprises the following steps:

measuring a light scattering signal for at least three bead populations, wherein each bead population has a different mean light scattering signal, wherein size and refractive index of each bead population are known;

attributing a statistical parameter, such as a mean, a median or a mode, to a distribution of the light scattering signal of each bead population;

determining the optical parameters describing an optical configuration of a flow cytometer by fitting a light scattering theory or empirical relationship to the statistical parameters attributed to the light scattering signal of each bead population by varying optical parameters describing an optical configuration of a flow cytometer. An embodiment relates to the calibration method as described above, wherein at least one bead population of the at least three bead populations is marked, preferably fluorescently, and wherein the size and refractive index of the at least three bead populations are selected such that the at least three bead populations are identified relative to the at least one marked bead population.

An embodiment relates to the calibration method as described above, wherein the method further comprises the step of checking an alignment of the optical configuration of the flow cytometer and tracking a performance of the flow cytometer in time to identify a need to service the flow cytometer. Advantageously, a quality control step is included in the method.

An embodiment relates to the calibration method as described above, wherein the optical parameters comprise collection angles of a detector, such as the scattering angle and numerical aperture of a collection lens for a given wavelength and polarization of the illumination beam.

In the context of this patent application ' Substantially spherical' is to be understood as an aspect ratio between height, width and depth < 1.5.

In the context of this patent application 'Light Scattering Signal' is to be understood as a signal detected from at least one scattering angle using a light scattering detector. May also be referred to as light scattering channel or light scatter parameter.

In the context of this patent application 'Light Scattering Theory' is to be understood as a theory that relates the physical properties of a particle, such as size, refractive index, shape and composition, to its light scattering properties.

In the context of this patent application 'Mie theory' is to be understood as a theory that provides a solution to Maxwell's equations to relate the intensity of scattered radiation to particle size, refractive index and shape for substantially concentric and cylindrical particles. (Bohren and Huffman, 1983).

In the context of this patent application 'Second Light Scattering Signal' is to be understood as a light scattering signal distinguished from a first light scattering signal by the polarization state of the illumination beam, and/or the wavelength of the illumination beam, and/or the scattering angle, which may be realized using either a single detector which is measuring at different time points or by detection on multiple detectors. In the context of this patent application 'Size' is to be understood as any parameter that describes size of a particle, including but not limited to diameter, radius, volume, cross section, surface area.

In the context of this patent application 'Inverse Light Scattering Problem' is to be understood as a problem describing that the size and/or refractive index of a single spherical particle cannot be derived from a single light scattering signal because these parameters are interrelated.

In the context of this patent application 'Solution to the Inverse Light Scattering Problem' is to be understood as the solution for some optical configurations and particle sizes and refractive indices, wherein the particle size can be derived from a light scattering signal if the particle refractive index is known, and the particle refractive index can be derived from a light scattering signal if the particle size is known.

Brief description of drawings

The invention will be explained in more detail below with reference to drawings in which illustrative embodiments thereof are shown. They are intended exclusively for illustrative purposes and not to restrict the inventive concept, which is defined by the appended claims.

Fig. 1 shows a schematic view of a particle measuring and counting apparatus, as incorporated in flow cytometers, to perform a flow cytometry experiment according to a step of a flow cytometry method according to an embodiment to the invention;

Fig. 2a shows a graphical representation of a side scattering parameter versus a forward scattering parameter of a mixture of single particles following the flow cytometry experiment according to figure 1 ;

Fig. 2b shows a graphical representation of a refractive index versus a size of the mixture of single particles after analyzing the gathered data in figure 2a according to a step of a flow cytometry method according to an embodiment to the invention;

Fig. 3 shows a graphical representation of the relationship between scattering and size for three bead populations with similar refractive index R but different sizes. The solid line shows the relation between scattering and size for particles with refractive index R. The dashed line shows the relation between scattering and size for particles with a refractive index lower than R. Fig. 4 shows a graphical representation of the relationship between the optical scattering ratio (OSR), which is the ratio between a first light scatter signal (e.g. SSC) to a second scatter light signal (e.g. FSC), and the particle size. In the regime where the solid and the dashed line overlap, the OSR is independent of the refractive index and provides a unique solution for particle size.

Detailed description of embodiments

Figure 1 shows a schematic view of a particle measuring and counting apparatus, as incorporated in flow cytometers, to perform a flow cytometry experiment according to a step of a flow cytometry method according to an embodiment of the invention. It is noted that the angles in the figure are indicative and in no way limiting to the invention.

The flow cytometer 1 comprises a flow cell 6, along the x-axis, arranged for guiding particles in a hydrodynamically focused fluid stream through an illumination beam L in a hydrodynamically focused fluid stream. The flow cytometer further comprises two scattering detectors 3, 4, along the y- and z-axis. The first detector 3 is located in substantially the longitudinal direction of the illumination beam L. Substantially orthogonal to this longitudinal direction of the illumination beam L, with the center of a substantially spherical single particle 2 as the point of origin, the second detector 4 is located.

In a flow cytometry experiment using an illumination beam L light scattered from the single particle is measured in two directions y;z, a narrow angle scattering detector 3 detects the forward scattered light (FSC) and the wide angle scattering detector 4 detects the side scattered light (SSC). These scattering detectors 3;4 are arranged for measuring a forward scattering signal and a side scattering signal of a single particle.

Figure 2a shows a parameter of a scattering signal on a wide angle scattering detector 4 versus a parameter of a scattering signal on a narrow angle scattering detector 3 of a mixture of single particles 7, 8, 9, 10 resulting from a flow cytometry experiment according to a step of a flow cytometry method according to an embodiment of the invention. Because the data is represented in arbitrary units, physical properties, such as the particle size and refractive index, of the particles cannot be quantified. According to the invention a method is presented to obtain the optical configuration of the flow cytometer 1 and to derive the size and refractive index of single particles from the light scattering signal of the flow cytometry experiment, thus enabling characterization of the size and refractive index of single particles from light scattering by flow cytometry.

Figure 2b shows the refractive index versus the size of the mixture of single particles 7, 8, 9, 10 after analyzing the gathered data in figure 2a. Since size and refractive index are physical quantities, they facilitate data interpretation and can be compared to other measurement results. Moreover, derivation of the size is essential to compare the concentration of polydisperse particle populations, such as extracellular vesicles, between flow cytometers. Furthermore, derivation of the size and refractive index can be used to identify particles, such as viruses, which are monodisperse and have a typical size and refractive index.

Before a flow cytometry experiment, as described in figure 1, is performed, the system is calibrated. Calibration means that the measured scattering parameter on a detector of particles with known size and refractive index is related to the theoretical scattering cross section. This theoretical scattering cross section is based on the size and refractive of the particles being analyzed, refractive index of the medium, and the optical configuration of the flow cyto meter. The optical configuration of the flow cyto meter encompasses the wavelength, polarization state, and power of the illumination beam, and the collection angles and transmission efficiency of the optics that guide the light to the detector. The calibration is performed using calibration beads of different bead sizes, preferably at least three within a dynamic range of the flow cytometer 1 , wherein each calibration bead has known size and refractive index. During calibration, optical parameters describing the optical configuration of the flow cytometer are determined by light scattering theory, such as Mie theory, and numerical optimization. These optical parameters include the numerical aperture of the collection lens, the angle theta with regards to the longitudinal direction of the illumination beam L, and optionally the size and orientation of an obscuration bar. The derivation of these optical parameters requires supplementary knowledge on the wavelength and polarization state of the illumination beam L, which are typically known for a flow cytometer.

Figure 3 shows a graphical representation of the relationship between scattering and size for three bead populations with similar refractive index R but different sizes. The optical parameters describing an optical configuration of a flow cytometer are determined by fitting a light scattering theory or empirical relationship to the statistical parameters attributed to the light scattering signal 3,4 of each bead population with refractive index R by varying optical parameters describing an optical configuration of a flow cytometer (solid line). The dashed line shows the calculated relationship between scattering and size for particles with a refractive index lower than R. Figure 3 also shows that the particle refractive index can be determined for particles of known size. Furthermore, the light scattering signal to size relationship can be extrapolated to particles with a different refractive index or particles with a more complicated structure. Figure 4 shows an optical scattering ratio (OSR) versus single particle size for two beads of different refractive index. The solid lines in figure 3 enable conversion of a scattering parameter to either size or refractive index of the single particle 2 if the other parameter is approximately known. To derive the size of single particles 2 independent of the refractive index of the particle, the OSR is used, which is in this embodiment the ratio of a first light scatter signal (e.g. SSC) to a second light scatter signal (e.g. FSC). Derivation of the OSR versus size relationship can be done theoretically (lines), e.g. using light scattering theory and design specifications of the flow cytometer, or experimentally, e.g. using beads measurements and empirical fitting (symbols), or both. The OSR as function of the particle size is independent of the refractive index and has a unique solution below approximately three times the illumination wavelength. The OSR can be used to derive the size of particles up to approximately three times the illumination wavelength without foreknowledge of their refractive index.

If the size of a particle is known from OSR and a light scattering signal of the particle is measured on a calibrated flow cytometer, the particle refractive index can be derived by solving the inverse light scattering problem. For example, a lookup table of a scattering signal versus particle size for several particle refractive indices can calculated by light scattering theory using the calibrated parameters of the flow cytometer, as shown in Figure 3. Then, using the OSR derived size as input, the refractive index of each particle is obtained from the lookup table.

The skilled person will furthermore understand that the above-described flow cytometry method in principle can also be used with other types of particle analysis systems (i.e. can be used with particle systems in the broad sense). Working example

The relationship between the detected light scattering signal on a flow cytometer (1) and the size and refractive index of a single particle (2) depends on the optical configuration of the flow cytometer. The illumination beam (L) of the flow cytometer in this example (A50-Micro, Apogee, Hemel Hempstead, UK) has a wavelength of 405 nm and has an electric field that is polarized in the x direction. Forward scattering (FSC) and side scattering (SSC) signals are collected with one lens, which has a numerical aperture (NA) of approximately 1.3 and which is placed under an angle θ ~ 45° with regards to the propagation direction of the illumination beam (L). FSC and SSC are separated at an angle θ ~ 25° using a mirror. The illumination beam (L) is blocked by an obscuration bar (6) which blocks light with an angle Θ smaller than approximately 10°.

To obtain the exact optical configuration of the flow cytometer, FSC and SSC signals of 8 polystyrene bead populations with known size and refractive index are measured (Fig. 3, symbols). To derive the mean FSC and SSC, the histograms are fitted by a Gaussian function. Next, a least square fit procedure is applied to the Mie theory in MATLAB (v7.9.0.529) (Fig. 3, lines). The model calculates the detected scattering intensity as a function of particle size and refractive index, refractive index of the medium, wavelength, polarization state, and power of the illumination beam, and the collection angles and transmission efficiency of the optics that guide the light to the detector. The laser power and transmission efficiency are combined into a scaling factor. Table 1 lists the initial fit parameters describing the approximate optical configuration of the flow cytometer. Table 1 also lists the optical parameters derived from the model after calibration.

Parameter Initial specified value Value from calibration

Illumination wavelength (nm) 405 405

Electric field polarization x direction x direction

Numerical aperture lens 1.30 1.30

Scaling factor 1.000 1.055

Qoptical axis lens ( ) 45.0 47.6

Θ separation (°) 25.0 28.5

Qobscuration bar ( ) 10.0 16.0 Table 1. Specified and calibrated parameters describing the optical parameters of the flow cytometer . To validate the calibration, the mean FSC and SSC intensity versus particle size for silica beads with a refractive index of 1.445 were measured and calculated (Fig. 3, lines). Theory describes the data well for both detectors, which confirms that the optical configuration of the flow cytometers is correctly derived by numerical optimization. To derive the size of particles independent of their refractive index, the optical scatter ratio (OSR) is used, which is the ratio of SSC to FSC. The OSR needs to be calibrated because it depends on the optical configuration of the flow cytometer. The data of the beads are used to find the OSR to particle size relationship for the flow cytometer (Fig. 4). The OSR as function of the particle size is independent of the refractive index and has a unique solution below ~1.1 times the illumination wavelength (405 nm) for this flow cytometer. Please note that derivation of the OSR versus size relationship can be done theoretically, e.g. using light scattering theory and design specifications of the flow cytometer, or experimentally, e.g. using beads measurements and empirical fitting, or both.

Using the calibrated OSR and/or application of light scattering theory to a calibrated flow cytometer, a lookup table can be created to relate SSC and FSC to particle size. Using application of light scattering theory to a calibrated flow cytometer, also a lookup table can be created to relate FSC and SSC to particle refractive index. Such a lookup table can be visually presented by a plot depicting the side scatter versus forward scatter relationship for particles in a diameter range. The slope uniquely defines the particle diameter. Such a lookup table can be visually presented by a plot depicting the side scatter versus forward scatter relationship for particles in a refractive index range. To validate the OSR approach, a mixture of particles as listed in Table 2 was prepared.

The refractive index of the particles is obtained by solving the inverse light scattering problem. Therefore, a lookup table of SSC versus particle size for several particle refractive indices is calculated by light scattering theory using the calibrated parameters of the flow cytometer (Table 1). Then, using the OSR derived size as input, the refractive index of each particle is obtained from the lookup table. Instead, another approach to derive the refractive index would be to perform a 2-dimensional interpolation on the SSC to FCS lookup table for refractive indices.

All beads populations could be clearly resolved except the 125 nm polystyrene beads. The determined mode refractive index of the bead populations falls within the expectation value. However, for smaller particles the refractive index distribution broadens. Table 2 lists the mean diameter and standard deviation of each sub population of beads as measured by the flow cytometer. For all bead populations that were resolved, the measurement error on the mean diameter is <8%. This accuracy outperforms nanoparticle tracking analysis and is comparable to resistive pulse sensing, two advanced techniques which are dedicated to sizing of single particles. Additionally, flow cytometry is ideally suited to perform multiplex immuno fluorescence measurements on individual particles. For some applications, the density of certain proteins, antibodies, etc. is more important than the total number. With the described method to determine size independent of refractive index, this density of proteins or antigens can now be determined on a flow cytometer.

Label Manufacturer Catalog number Material Specified Measured diameter (nm) diameter

(nm) a Thermo Fisher Scientific PS 380 ± 10 382 ± 26 b Microparticles GmbH PS-F-0.3 PS 313 ± 8 309 ± 10 c Microparticles GmbH M-PS-F-0.25 PS 248 ± 8 234 ± 25 d Microparticles GmbH SiO2-F-0.25 Si0 ₂ 254 ± 10 255 ± 24 e Thermo Fisher Scientific 3125A PS 125 ± 5

f Kisker Biotech GmbH PSi-0.4 Si0 ₂ 391 ± 20 424 ± 34

Table 2. Label, manufacturer, catalog number, material, specified diameter, and measured diameter of the mixture of particles. PS: polystyrene. Si0 ₂ : silica. Diameter as mean ± standard deviation.