Dynamic light scattering

Dynamic light scattering (DLS), also referred to as photon correlation spectroscopy or quasielastic light scattering, is used to determine the hydrodynamic size of native proteins, as well as aggregates and particles thereof from 1 nm to about 10 µm (size limit depending on sample properties and

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measurement conditions).73 _{The technique is based on intensity fluctuations of} laser light scattered by the analyte, which is moving in Brownian motion.74 Intensity fluctuations are quantified via an autocorrelation function which compares the initial scattering intensity to the intensity after specified time periods. A slow decay in the autocorrelation function is caused by slow fluctuations in intensity indicating the presence of slowly moving large particles; a fast decay is due to fast fluctuations indicating the presence of fast moving small particles. From the measured decay the diffusion coefficient D can be obtained, which is directly proportional to the inverse radius of the particles via the Stokes-Einstein equation.75,76 _{An important assumption for the validity of} Stokes-Einstein is that the analyzed molecules or particles are spherical and not interacting with each other. Provided that temperature and viscosity of the solution are known, the hydrodynamic diameter – usually reported as Z-average diameter, i.e. the mean diameter – is obtained from DLS measurements. Especially the viscosity, which affects the diffusion coefficient, plays an important role in the analysis of therapeutic protein formulations as many excipients, in particular sugars, increase the viscosity.32,71 _{Therefore, the viscosity needs to be} individually determined for the respective formulation. As protein aggregates and particles are mostly not spherical but of various shapes, the delivered hydrodynamic diameter for protein particles needs to be evaluated carefully. In addition, for polydisperse samples, indicated by a high polydispersity index (PdI), Z-average values do not necessarily reflect the different sizes present in the samples. Furthermore, DLS can only distinguish two populations in the sample if they theoretically differ in size at least by a factor of two77 _{or three.}78 _Particle populations with a lower difference in size appear as one broader population reflecting the average distribution.

DLS measurements provide intensity-based size distributions. However, this is not the best way for characterization of polydisperse samples as the scattering intensity I depends on the diameter d to the power of six in the Rayleigh approximation (Equation 1-1).

6 d I 

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The resulting size distribution by intensity is therefore biased to larger sizes. This can be an advantage if small amounts of larger aggregates shall be detected in the presence of monomeric protein. However, in most cases it is disturbing, as a few large aggregates/particles present in the sample can impede the measurement of many small molecules, e.g. protein monomer. Using volume, weight or number based size distributions may be a better estimation of the composition of the sample in some cases.79,80 _{Volume or weight based size} distributions are still biased to larger sizes, but less than intensity based size distributions.73,81 _{For a direct comparison of particle counts of different sizes, a} number based size distribution can be suitable. However, it should be noted that an inaccurate intensity distribution as obtained from DLS data will result in significant errors in the derived volume, weight or number distribution.

Another challenge lies in high particle concentrations in the sample which can lead to multiple scattering effects. A technical possibility to reduce confounding influences of very large particles or to deal with high sample concentrations is the use of laser light backscatter detection, which detects the scattered light not in the commonly used 90° angle, but at a higher angle, e.g 173° (Zetasizer Nano S and Nano ZS by Malvern Instruments Ltd, Worcestershire, UK)82 _{or 153°} (FOQELS by Brookhaven Instruments Corporation, Holtsville, NY).83 _{In this case,} the laser light does not need to pass far into the sample as the scattered light is detected close to the cuvette wall thereby circumventing multiple scattering effects.

Nevertheless, despite this improvement in the measurement of large particles, DLS is in particular suitable for the analysis of protein monomer and small aggregates in the nanometer range81,84-86 _{and less suitable for particles in the µm} size range. As an advantage of DLS, measurements in plate reader-based systems can save time and material.87 _{As a further benefit, the method is not} destructive and requires limited sample preparation. However, sufficient protein concentration is necessary for DLS to obtain reliable signals and the results are not quantitative as no absolute values for monomer content or aggregate concentration are provided.

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Taylor dispersion analysis (TDA) is a novel method for the analysis of protein aggregates and particles which also determines the hydrodynamic size based on the diffusion coefficient. In contrast to DLS, the diffusion coefficient is not based on light scattering fluctuations, but on band broadening of the UV signal of the sample analyzed in a cylindrical tube under laminar Poiseuille flow, which passes a detector twice. TDA was shown to accurately size monomers of BSA and IgG antibodies and should in principle also be applicable for protein particles.88