Light Scattering Techniques

Latex looks like milky white because the submicrometer particles scatter visible light. Developments in instrumentation have permitted the automatically full quantification of the immunological agglutination by light scattering, thus avoiding the subjectiveness of manual detection. These instrumental methods are far more sensitive than visual detection of the aggregates. Light scattering can be measured with rather inexpensive and simple instruments that are commercially available. The sensitivity, reproducibility, and detection limits of latex immunoagglutination tests depend on the technique used to detect the aggregated product.

Monitoring of the antigen-antibody reaction by measurement of light scattering has been known for the past 50 years, although the broader concept of agglutination had been explored in the 1920s for microbiological assays [101]. Light scattering methods can be divided into two major categories: methods that measure time-average scattering (static light scattering) and methods that observe the scattering fluctuation as a function of time (dynamic light scattering). Both methods can give information on the agglutination state of the protein-coated particles. During the immunoagglutination process particles aggregate with increasing diameter, resulting in the appearance of very large particles. The scattering particle size can vary from nanometers to millimeters. This change in the particle size of containing suspension provokes a dramatically increase in the scattered light. Light scattering studies applied to particle immunoassays have been published and reviewed [102-104]. Sensitivity, reproducibility, detection limit, reaction time, amount of particles needed, and availability of the required detection device are some characteristics that depend on the chosen technique [105]. There are different variables that must be optimized to obtain the best results. Some of them are specific for each technique, whereas others can be applied to all of them [106]. All of these techniques allow an increase in sensitivity and improve standardization, and the procedures involved may be automated. The difficulty for users, if they have not already purchased an instrument, is in how to choose the most appropriate system for their needs. In most cases this has probably been determined by the ease of use of the instrument itself.

1. Light Scattering Theory

When the light impinges on a particle, its electrons are subjected to a force in one direction and its nuclei to a force in the opposite direction, causing the electrons about the particle to oscillate in synchrony with the electric field of the incident light. Thus, an oscillating dipole is induced in the particle by the incident light. This oscillating dipole becomes a source of electromagnetic radiation, reradiating light at the same wavelength of the incident light and in all directions. This radiation from the particle is called scattered light. The theories of light scattering can be divided into three different regimes, depending on the relation between the particle size and the wavelength of the incident light (X). In 1871 Rayleigh developed a theory for light scattering by a very small dielectric sphere [107,108]. When the dimensions of the particle are much smaller than the wavelength of the incident light (diameter < 0.1X), then the entire parti cle is subjected to the same electric field strength at the same time. The intensity of the scattered light (I) at an angle 9 between the incident and the scattered beam is given by the expression:

where N is the number of nonabsorbing particles per unit volume, I0 is the intensity of the incident beam, r is the distance from the particle to the detector face, and a is the polarizability of the spherical particles given by:

where a is the radius of the particle, and n = np/nm is the ratio of refractive index of the particle, np, to that of the surrounding medium, nm. As can be seen, the intensity of scattered light is proportional to the square of the particle volume and to 1/A4. Hence, the scattering from larger particles may dominate the scattering from smaller particles, and a decrease in the wavelength will substantially increase the scattering intensity. The ratio of light scattered forward to light scattered backward at any pair of supplementary angles centered on 90° is known as the dissymmetry ratio. The scattering pattern for Rayleigh scatterer is symmetrical about the line corresponding to the 90° scattering angle.

When the particles are larger, the particle cannot be considered as a point source and some destructive interference between light originating from different sites within the particle will occur. The Rayleigh theory is no longer valid and must be modified. The physical basis of the modification, known as the Rayleigh-Gans-Debye theory, is that a particle of arbitrary shape is subdivided into volume elements [109,110]. Each element is treated as a Rayleigh scatterer excited by the incident beam, which is assumed to be unperturbed by the presence of the rest of the particle. The Rayleigh-Gans-Debye theory is valid in the region A/20 < 2a < A, where the radiation envelope will become asymmetrical with more light being scattered forward (9 < 90°) than backward (90° < 9 < 180°). The light scattering intensity at 90° is much less than the intensity at the forward (0°) angle due to destructive interferences. The relatively enhanced forward scattering with increasing particle size can be used as an index to predict the particle size. The evaluation of the dissymmetry ratio during the immunoagglutination process give valuable information, especially at various times after initiating the reaction.

For particles larger than the wavelength of incident light (2a > 10A) the Mie theory is used [111]. For this size particle region the scattered light progressively decreases with increasing 9, and eventually minima and maxima may appear in the radiation diagram (Fig 14). The number and position of minima

FIG. 14 Light scattering intensity distribution for two particle diameters: (top) 186 nm, (bottom) 665 nm.

and maxima which appear depend on the size parameter (nlafk) and the polariz-ability of the particle. For all previous theoretical considerations the dispersion is assumed dilute; light is scattered by single particles independent of other particles present.

There are a number of techniques based in light scattering phenomena to detect latex particles' immunoagglutination: turbidimetry, nephelometry, angular anisotropy, and photon correlation spectroscopy. Now we will discuss these techniques in regard to their relative merits for latex immunoagglutination assays.

2. Turbidimety

Turbidimetry involves measurement of the intensity of the incident beam as it passes through the sample. The light beam may pass through a suspension or be absorbed, reflected, or scattered by the particles. As a consequence, the intensity of light decreases as it is transmitted through the suspension. For nonab-sorbing particles the decrease in light intensity due to scattering is expressed as turbidity, t:

where I0 and I are the intensities of the initial and transmitted beams, respectively, and l is the length of the light path, usually the sample thickness. As can be seen, the turbidity is a measure of light attenuation caused by scattering. The spectrophotometer measures increased turbidity (i.e., the reduction in the intensity transmitted light), which is due to the increasing particle size resulting from the immunoagglutination reaction. This increased turbidity is a direct measure of the immunoagglutination caused by the analyte or an indirect measure of the immunoagglutination inhibition caused by the analyte. For dispersions with aggregating particles, turbidity measurements at two wavelengths may also be used to follow the aggregation process.

This technique is rapid and easy to use. With turbidity no special equipment is required other than a spectrophotometer, which is generally available in clinical laboratories. There are fully automatic spectrophotometers that not only measure transmitted light automatically at a desired time but also dilute, pipette, and transfer to the cuvette the convenient volumes of reagents buffers and samples, incubate at a programmed temperature and make the necessary calculations using the selected algorithms and calibration curves [112]. The possibility of running latex agglutination tests into these automatic analyzers allows the processing of hundreds of samples in a short time without investment in new instrumentation or personnel.

To optimize the turbitidy change, which occurs during immunoagglutination, it is important to select the appropriate particle size. The number of antigen-antibody bridges between pairs of particles during the immunoagglutination is about 2-10. With larger particles, the shear forces across these bridges may result in disruption of agglutinates when pumped at high speed in automatic machines. Thus, particles of smaller diameter may yield more robust assays. For particles to agglutinate they must first collide so that antigen-antibody bridges can form. For molecules and small particles diffusion is sufficiently rapid to produce the initial collisions necessary for aggregate formation. If the particles are larger diffusion is reduced (i.e., the agglutination kinetics) because the diffusion coefficient is inversely proportional to particle size. Small particles are desirable because of the requirement for increasing the collision frequency between particles or aggregates to enhance the rate of immunoaggregate production.

For the turbidimetric detection of the particle size change it is imperative that the particle size and the incident light wavelength be chosen with care since the turbidity reaches a maximum with time. This maximum occurs when the signal change exceeds the optical limits of the measuring system. It has been observed by photon correlation spectroscopy that changes in aggregates size continue beyond the plateau observed in turbidimetric assays [113]. The optimal performance may be a function of the ratio of the particle diameter to the illumination wavelength, and the refractive index of particle. Thus, the selection of particle material, particle size, and wavelength of detection of the immunoagglutination reaction are all important factors in optimizing assay sensitivity. For particles that are small in comparison with the wavelength of light, the scattering increases with the inverse fourth power of the wavelength. Shorter wavelengths, such as 340 nm, give larger signal differences during immunoagglutination than longer wavelengths, such as 450 nm. On the other hand, the higher the refractive index of the particles at the wavelength of choice, the higher the light scattering signal. In general, the refractive index of a material is greater at shorter wavelengths. Particles with a polyvinylnaphthalene core have been proposed to enhance sensitivity of latex immunoagglutination assays [114]. Galvin et al. claimed that for the lowest detection limits particles should be in the size range 40-70 nm, with a high refractive index but low absorbance at the wavelength of light used [115].

Heller and Pangonis gave some information about how to optimize the particle size to wavelength ratio in turbidimetric assays [116]. Sharp absorbance changes during the agglutination process can be obtained if the value of the term 2nal\ is in the range 1-2. This theoretical prediction, obtained from Mie's theory, has often been corroborated experimentally. Different authors provided some evidence that minimal detection limits are achieved if the light wavelength used was in the order of 340 nm for particles in the size range 40-70 nm [117-119]. This recommendation has been frequently followed by Price et al. [120-123]. These authors even claimed that minimal detection limits are achieved using a wavelength of 340 nm independent of the particle size [101], which is a questionable statement. If latex particles are bigger (i.e., diameters from 100 to 400 nm) the optimal wavelength would be in the 450- to 700-nm range [124-127], as shown in Fig. 15. If larger particles are used instead, the infrared region on the spectrum should be employed [128]. Finally, small particles of high refractive index with short wavelength detection are preferred for high sensitivity in the turbidimetric assays. There is a practical limit in the ultraviolet region for measurement of sample in serum because of light absorption by proteins and other components. Thus, convenient wavelengths are those in excess of approximately 320 nm. Turbidimetry measurements require a higher particle number than the other light scattering techniques.

FIG. 15 Turbidity change for agglutination of latex-F(ab')2-aCRP in presence of a constant concentration of CRP as a function of wavelength: (■) particle with 180 nm diameter; (▲) particle with 340 nm diameter.

3. Nephelometry

Nephelometry refers to the measurement of the light scattered at an angle 9 from the incident beam when the incident beam is passed through the sample. The scattering theories show the importance of choosing a forward scattering angle for the study of particles with size approaching the wavelength of the incident light (Fig. 14). Common nephelometers measure scattered light at right angles to the incident light. The ideal nephelometric instrument would be free of stray light; neither light scatter nor any other signal would be seen by the detector when no particles are present in solution in front of the detector. However, due to stray light-generating components in the optics path as well as in the sample cuvette or sample itself, a truly dark-field situation is difficult to obtain when making nephelometric measurements. The sensitivity of nephelo-metric measurements clearly depends on this background signal [129,130]. On the other hand, the sensitivity of this technique also depends on the intensity of the light source with the highest sensitivity being achieved with a laser light source [131]. Some nephelometers are designed to measure scattered light at an angle lower than 90° in order to take advantage of the increased forward scatter intensity caused by light scattering from larger particles (immunoaggregates). Unfortunately, forward scattering optical systems are harder to construct but several manufacturers now have forward scattering nephelometers [132]. A good example of nephelometers that have been specially designed to operate with latex immunoagglutination is the Behring Nephelometer Analyzer with the following main features: (1) the light source is a red diode with a wavelength of 850 nm; (2) the detector is a photodiode that measure the scattered light in the forward direction at small angles (13-24°); (3) the detection limit is as low as 10 ng/mL for some measuring systems. Dedicated instrumentation is thus required for nephelometry, whereas turbidimetry is more broadly applicable [102].

In nephelometry the change in the intensity of the scattered light after a time is measured because the scattering species rapidly increase size. The scattered light is proportional to the initial antigen concentrations when measured in the presence of a fixed antibody-latex complex. Calibration curves can therefore be generated by plotting the intensity increment values against antigen concentrations. The concentration of the same antigen in an unknown sample can then be determined by measuring the intensity increment value under identical conditions and extrapolating on the calibration curve. Figure 16a and b show the importance of the angle in nephelometric observations. These figures correspond to the agglutination kinetics of latex particles sensitized with two different F(ab')2 anti-CRP coverages for various low angles of measurement of the light scattering intensity (5°, 10°, and 20°). The intensity of light scattered by small clusters is weak and linear (low antibody coverage or beginning of the process), and is better monitored at higher angles (Rayleigh's scattering). Nevertheless, in the case of high coverage, after some time aggregates grow and light scattering amplification increases, preferably at lower angles (Mie's scattering).

Figure 17a and b show the immunoreactivity (scattered light intensity increment) as a function of CRP concentration at three different angles after 10 min of reaction for two latex-F(ab')2 anti-CRP complexes. As can be seen, the main response features (intensity increments, detection limit, and sensitivity) are dependent on the scattering angle and antibody coverage. For the lowest coverage (Fig. 17a) the intensity increments increase with increasing the light scattering angle, and the shape of these curves coincides with that of the precipitin curve proposed by Heidelberger and Kendall [133]. Such response can be explained considering that an antigen molecule acts as a bridge to coagulate two sensitized particles. It is easy to understand why before reaching the maximum the immu-nological response increases as CRP concentration does. At higher antigen concentrations the system seems to lose reactivity. It may be due to the blocking of the antibody active sites by antigens; thus, the bridging process is unfavored. Nevertheless, in the case of a higher protein coverage (Fig. 17b) the change in the scattered intensity for the 20° angle does not show the typical bell curve of

FIG. 16 Scattered light intensity at various angles for the immunoagglutination of particles covered with F(ab')2 anti-CRP. (▲) 5°; (■) 10°; (•) 20°: (a) 0.9 mg/m2; (b) 2.1

FIG. 16 Scattered light intensity at various angles for the immunoagglutination of particles covered with F(ab')2 anti-CRP. (▲) 5°; (■) 10°; (•) 20°: (a) 0.9 mg/m2; (b) 2.1

FIG. 17 Immunoreactivity as a function of CRP concentration at three different angles (▲) 5°; (■) 10°; (•) 20° for two latex-F(ab')2 anti-CRP complexes: (a) 0.9 mg/m2; (b) 2.1 mg/m2.

the immunoprecipitin reaction, and gives an apparent plateau when the CRP concentration is above 50 ng/mL. This plateau represents a limitation of the nephelometric technique for high concentrations of antigen at 20°. It is important to emphasize that equilibrium and equivalence points in these assays are illusory. They are produced not only by the classical Heidelberger-Kendall immune aggregation phenomena but also optically [102]. When monitoring the light scattered by an immunoaggregate, further optical considerations may influence the apparent kinetics.

The preceding figures demonstrate that it is advisable to choose a 20° angle for agglutination processes of short-duration, low-antigen concentration or complexes with low antibody coverage. In these cases, the measurements made at 20° are more sensitive than at 10° or 5° angles because the size of the aggregates is small enough. Nevertheless, if the size of the aggregates (or the initial single particles) is high, a smaller angle is preferred. Montagne et al. has followed the immunoagglutination of latex particles at different scattering angles (from 9.8° to 40.2°), concluding that the best light scattering amplification is obtained at small angles (9.8° and 12.2°) [134].

Although some authors have claimed that turbidimetric responses are more reproducible and much simpler to reach than those obtained by nephelometry [135,136], the latter has been successfully employed by many over the last 20 years [128,137-139]. Ortega et al. has demonstrated that both techniques provide similar detection limit, although turbidimetry is slightly more reproducible [105]. No longer reaction times are used with turbidimetric and nephelometric detection systems. On the other hand, nephelometry is best performed in dilute dispersion (in which background signal is reduced).

4. Angular Anisotropy

Angular anisotropy is a technique in which the ratio of the intensity of light scattering at two different angles is measured (dissymmetry ratio), usually one above and one below 90°. If the nephelometer measures the angular distribution of the scattered intensity a calibration curve can be obtained where the dissymmetry ratio is shown as a function of antigen concentration. The intensity of the light scattered at small angles is directly proportional to the square volume of the aggregates, whereas for higher angles this dependence on volume is drastically reduced. This feature was studied by Von Schulthess et al. who proposed a new strategy to analyze latex agglutination immunoassays [140]. These authors applied angular anisotropy to the detection of human chorionic gonadotropin (HCG), measuring the scattered light at 10° and 90° to maximize sensitivity and to skip source light fluctuations. This method yields high sensitivity, at least theoretically [140], provided that the two angles and the carrier particle size are properly chosen. The above authors demonstrated that the particles acting as antibody carriers should have a radius (a) in the range X/4 < a < X. They also showed that the angular anisotropy technique could be very useful if one angle is lower than or equal to 15°, and the other is in the 60-100° range. Ortega et al. has shown that angular anisotropy is a very sensitive technique detecting 1 ng/mL of CRP, after longer reaction time [105].

5. Photon Correlation Spectroscopy

Photon correlation spectroscopy (PCS) is based on the fact that the intensity of light scattered from a latex suspension, when it is illuminated with a coherent light, fluctuates with time, depending on Brownian movement and therefore on the average diffusion coefficient, which could be correlated to the particle size [112]. A photon correlation spectroscopy instrument is essentially a multiangle laser nephelometer. The PCS-based immunoassays generally have greater sensitivity than nephelometric and turbidimetric detection systems, although to achieve this longer reaction times are used due to the reduced particle numbers present in the dispersion. The device for PCS experiments is relatively expensive, as it is necessary to use a correlator. Furthermore it is difficult to find clinical laboratories with the sophisticated and extremely delicate equipment for carrying out dynamic light scattering measurements. This technique was first applied to latex immunoagglutination test for the detection of anti-bovine serum albumin by Cohen and Benedek in 1975 [141] and they claimed a sensitivity of 20 ng/ ml in a highly reproducible way. Different authors have indicated that photon correlation spectroscopy offers lower detection limits, and use little reagent, but have longer assay times than the classical optical techniques of turbidimetry and nephelometry [105,142].

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