Proteomics, Genomics & Microarrays
Optimising DLS Measurements for Protein Characterisation
Carlo Dessy1, Dr. Daniel Seeman2 1. Testa Analytical Solutions e.K., Sophienstraße 5, 12203 Berlin, Germany. 2. Brookhaven Instruments, 750 Blue Point Road, Holtsville, New York, 11742 USA
Many common globular proteins are very small in hydrodynamic size, with monomers rarely greater than 10 nm. Protein aggregates can easily reach large sizes, on the order of several hundred nm or larger, which complicate this already challenging measurement. In this scenario scattering from aggregated protein easily dominates the signal of free, or monomeric protein. This principle is demonstrated with a pharmaceutically relevant protein, monoclonal antibody, mAb, studied in both its monomeric and aggregated states.
Dynamic Light Scattering (DLS) has become a major asset in the lab toolbox for the characterisation of colloids. Ease of use, fast availability of results within minutes and a relatively low sample volume requirements, defi ne this technique as best and overcome any disadvantage we might want to consider. Best of all, DLS will supply, without the need of a calibration, not only size of the sample under investigation, but also, within certain limitations, size distribution information. This is achieved without need of prior separation of any kind, mechanical or chemical. As such, application of DLS is almost unlimited, ranging from polymer solutions, thus dissolved systems and sizes on the low nanometer range, up to particle dispersion with sizes ranging up to 10 µm.
However, in order to extract the information available from a DLS measurement, and most of all to assure the extracted values are representative for the given sample, we must take a step back and understand what DLS really measures and how, out of this primary information, fi nal results of size and size distributions are calculated.
The fundamental principle of DLS and all calculations following the measurement itself, is the determination of the translational diffusion coeffi cient of particles in suspension. The measurement is performed by directing a monochromatic beam of laser light through the sample in which the suspended particles undergo random thermal motion according to Brownian diffusion. The speed of this Brownian motion is function of size; large particles will show slow speed while smaller ones will move faster. Measurement of speed of movement, or translational diffusion, is achieved by determination of the autocorrelation function of the small fl uctuations in intensity of light scattered by the sample at a given detection angle.
DLS is a well know and powerful technique for the size determination of nanoparticles and proteins, its value has been demonstrated in innumerable publications. Proteins, however, still represent a challenge by themselves. Many common globular proteins are very small in hydrodynamic size, with monomers rarely greater than 10 nm, and many approaching 1 nm or smaller on the low end. Size determination of such small particles is by itself diffi cult as diffusion coeffi cient, which is the basis for the calculation of hydrodynamic size, is typically very high thus requiring a sophisticated high speed correlator with appropriately spaced delays for determination of the autocorrelation function for such rapidly diffusing particles. Protein aggregates can easily reach large sizes, on the order of several hundred nm or larger, which complicate this already challenging measurement. This is demonstrated clearly with monoclonal antibody (mAb). These results are contrasted with those obtained from serum albumin (BSA).
Methods.
Methods. Methods.
= π
For a known scattering angle, θ, and refractive index, n, the scattering vector q is calculated from the following expression:
DLS measurements were made on a continuous multi-angle goniometer, the BI200SM, using a red, λo = 640 nm, 40 mW solid state laser and an APDx detector, with a USB TurboCorr correlation card. A correlator layout was selected such that large diffusion coefficients, of the type see for small, rapidly diffusing, protein-sized particles, can be effectively resolved. These correspond to extremely small τ values, on the order of less than 100 ns.
For a known scattering angle, θ, and refractive index, n, the scattering vector q is calculated from the following expression:
A given correlation function C(τ) is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. The result of this deconvolution is a characteristic decay rate, Γ, and typically also a polydispersity index (PDI). Γ is related to the translational diffusion coeffi cient (Dt) as follows:
A given correlation function C(τ) is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. The result of this deconvolution is a characteristic decay rate, Г, and typically also a polydispersity index (PDI). Г is related to the translational diffusion coefficient (Dt) as follows:
The relationship between Dt, the primary quantity measured in DLS, and hydrodynamic particle size, dh, is inverse, and is given by the Stokes-Einstein Equation:
The relationship between Dt, the primary quantity measured in DLS, and hydrodynamic particle size, dh, is inverse, and is given by the Stokes-Einstein Equation:
Dt = Kb T / 3πηdh
Γ = Dt q⋅ Dt = Kb T / 3πηdh
Results & Discussion. 2
Where the Boltzmann constant (Kb), Temperature (T), and bulk viscosity () are all known values. Dt = Kb T / 3πηdh
Where the Boltzmann constant (Kb), Temperature (T), and bulk viscosity (η) are all known values.
Where the Boltzmann constant (Kb), Temperature (T), and bulk viscosity (η) are all known values.
The relationship between Dt, the primary quantity measured in DLS, and hydrodynamic particle size, dh, is inverse, and is given by the Stokes-Einstein Equation:
Results & Discussion.
Dedicated high-speed correlator channels make it viable to measure such rapidly diffusing, small proteins. For a typical medium-sized protein, decay rates (Г), of as -1
Dedicated high-speed correlator channels make it viable to measure such rapidly diffusing, small proteins. For a typical medium-sized protein, decay rates (Г), of as low as several hundred s-1, and as high as 50,000 s-1 may be observed, depending on scattering angle. As shown for serum albumin (Figure 1), Г depends linearly on q2, for a particle of a given size. When measurements are made at a series of appropriately spaced scattering angles, commonly between about (θ = 10, 155 o), the slope of this Г vs q2 plot is used to determine an average Dt. So long as this dependence is linear, it is only necessary to measure at a single-angle, and particle
-1
Results & Discussion. Dedicated high-speed correlator channels make it viable to measure such rapidly
Where the Boltzmann constant (Kb), Temperature (T), and bulk viscosity (η) are all known values.
The relationship between Dt, the primary quantity measured in DLS, and hydrodynamic particle size, dh, is inverse, and is given by the Stokes-Einstein Equation:
A given correlation function C(τ) is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. The result of this deconvolution is a characteristic decay rate, Г, and typically also a polydispersity index (PDI). Г is related to the translational diffusion coefficient (Dt) as follows:
Γ = Dt q⋅ Γ = Dt q⋅
2 2
A given correlation function C(τ) is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. The result of this deconvolution is a characteristic decay rate, Г, and typically also a polydispersity index (PDI). Г is related to the translational diffusion coefficient (Dt) as follows:
q 4 ns 2in⎛ θ
= π= π λoλo
q 4 ns 2in⎛ θ
⎜ ⎞ ⎝
⎟ ⎠
⎜ ⎞ ⎝
⎟ ⎠
For a known scattering angle, θ, and refractive index, n, the scattering vector q is calculated from the following expression:
λo
⎜ ⎞ ⎝
⎟ ⎠
Figure 1. DLS results for serum albumin monomer as a function of θ. Effective dh = 7.5 nm. For this Γ vs q2 dependence to be useful, a minimum of 4-5 scattering angles is required.
Common DLS confi gurations, as seen on discrete-angle benchtop instruments, tend to use backscatter, right-angle, and forward-scatter (θ = 173, 90, and 15 o). Generally, backscatter is useful for measuring samples in which there is a mixture of large and small particles, since larger angles minimise the d6 bias towards larger particles, which would otherwise obscure scattering from smaller particles. In contrast, very low-angles, typically θ << 30o, are highly sensitive to large particles, especially those >> 1000 nm. While forward-scatter is highly sensitive to presence of aggregates, backscatter is more useful for accurately determining the size of any small particles that may coexist with aggregated material. As shown in Figure 2, the scattering of BSA could easily be mistaken for that of pure monomer, when only examining angles of 90o or higher. The existence of second mode only becomes obvious at the lowest angle. This also accounts for the deviation from linearity at low angles, or small q2, as seen in Figure 1. As we recall, a shift towards slower diffusion, or smaller Γ, indicates that larger, slow moving particles must coexist with monomeric protein.
DLS measurements were made on a continuous multi-angle goniometer, the BI200SM, using a red, λo = 640 nm, 40 mW solid state laser and an APDx detector, with a USB TurboCorr correlation card. A correlator layout was selected such that large diffusion coefficients, of the type see for small, rapidly diffusing, protein-sized particles, can be effectively resolved. These correspond to extremely small τ values, on the order of less than 100 ns.
Methods.
DLS measurements were made on a continuous multi-angle goniometer, the BI200SM, using a red, λο = 640 nm, 40 mW solid state laser and an APDx detector, with a USB TurboCorr correlation card. A correlator layout was selected such that large diffusion coeffi cients, of the type see for small, rapidly diffusing, protein-sized particles, can be effectively resolved. These correspond to extremely small values, on the order of less than 100 ns. q 4 ns 2in⎛ θ
For a known scattering angle, θ, and refractive index, n, the scattering vector q is calculated from the following expression:
DLS measurements were made on a continuous multi-angle goniometer, the BI200SM, using a red, λo = 640 nm, 40 mW solid state laser and an APDx detector, with a USB TurboCorr correlation card. A correlator layout was selected such that large diffusion coefficients, of the type see for small, rapidly diffusing, protein-sized particles, can be effectively resolved. These correspond to extremely small τ values, on the order of less than 100 ns.
Results & Discussion.
Dedicated high-speed correlator channels make it viable to measure such rapidly diffusing, small proteins. For a typical medium-sized protein, decay rates (), of as low as several hundred s-1, and as high as 50,000 s-1 may be observed, depending on scattering angle. As shown for serum albumin (Figure 1), Γ depends linearly on q2, for a particle of a given size. When measurements are made at a series of appropriately spaced scattering angles, commonly between about (θ = 10, 155 o), the slope of this Γ vs q2 plot is used
to determine an average Dt. So long as this dependence is linear, it is only necessary to measure at a single-angle, and particle size can be determined from an arithmetic rearrangement of the basic scattering equation, where the average decay rate, Γ, or a distribution of Γ’s, can be obtained from direct processing of a correlation function.
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