Static Light Scattering (SLS) is capable of measuring the average molecular weight of polydisperse materials, as well as of samples with discrete aggregation numbers, such as proteins. Synthetic polymers are intrinsically polydisperse and are well-suited to direct analysis using this technique, thus the meaning of an average molecular weight is more direct. In the case of Bovine Serum Albumin (BSA), a protein known to exhibit three isoforms (Mw = 66.5 kDa, 133 kDa, and 200 kDa), the meaning of this average molecular weight can be less obvious. The nature of this relationship is demonstrated by comparing the molecular weight measured on a goniometer using traditional static light scattering to the relative abundances from a size exclusion chromatography (SEC) experiment.
Bovine serum albumin (BSA) is an easy-to-source protein often used as a surrogate for more complex proteins or protein drugs. It is well established that at or near physiological pH and ionic strength, BSA is in equilibrium between 3 well-defined isoforms of increasing aggregation number: monomer, dimer, trimer (N agg =1,2,3). These can be difficult, although not impossible, to resolve by Dynamic Light Scattering (DLS). SLS, however, has no resolving power, and thus a single average molecular weight is obtained.
This representation (fig. 1) is known as a Zimm Plot, and requires both concentration and angle dependent intensity measurements. The Zimm Plot is a multiangle, multi-concentration extrapolation to zero angle and zero concentration, respectively. The concentrations measured are 10, 3, and 2 mg/mL, using scattering angles of θ = 60, 75, 90, 105, and 120o. The average molecular weight was determined to be on the order of 81 kDa, which is too large for BSA monomer (66.5 kDa), and substantially lower than either dimer or trimer (133 kDa and 200 kDa respectively). In order to understand this, it is necessary to consider the fact that BSA monomer is in constant equilibrium with higher aggregation number species.
Monomer ⇌ Dimer ⇌ Trimer
For a known material, in this case protein, the relationship between refractive index and concentration is known. If the differential refractive index increment (dn/dc) of the material is known, then an absolute concentration can be determined.
The dn/dc is the slope of ns vs. concentration extrapolated to zero concentration. Here ns is the refractive index of a solution. This slope is typically linear over a broad range of concentrations, and thus the limiting slope is often the same as the slope under dilution solution conditions.
This is similar to how concentration can be determined from a UV absorbance measurement at 280 nm, provided that the molar extinction coefficient is known. In the case of the chromatography experiment shown below (fig. 2) the initial concentration is known, and so even in the absence of any external calibration the relative abundances of each species can be determined.
The differential refractive index (fig. 2) is directly proportional to concentration, and thus allows for the relative size of the populations to be quantified on a number basis (monomer and dimer). Trimer is believed to be present but is too low in abundance to be identifiable solely from refractive index. Now that the relative concentrations of BSA monomer and dimer are known, it becomes possible to further evaluate the standalone SLS measurement reported above (fig. 1). By understanding the intrinsic intensity weighting inherent in light scattering, it is possible to estimate an average molecular weight from the relative size of these populations.
Note that while only dimer and monomer are identifiable by RI (fig. 2), the MALS trace clearly identifies trimer, dimer, and monomer (fig. 3). Here, the relative areas of the three peaks varies with scattering angle, with the largest species scattering the most at the lowest angles. This quantification is used to explore the effects of different weightings and compare those to the observed molecular weight obtained in Figure 1.
An average MW was calculated from the following expression:
Monomer N=1 = 66.5 kDa
Dimer N=2 = 2*66.5 kDa = 133 kDa
Trimer N=3 = 3*66.5 kDa = 200 kDa
MW average = ( X% Monomer * 66.5 kDa ) + ( Y% Dimer * 133 kDa ) + ( Z% Trimer * 200 kDa )
Table 1 – Expected average molecular weight based on relative abundances of each species (N = 1, 2, and 3).
|CALC MW Av||Monomer MW (kDa)||Monomer||Dimer||Trimer (kDa)||Av MW (kDa)|
|Intensity Weighting from MALS 130 degrees||66.5||80.8%||13.5%||5.7%||83.0|
|Intensity Weighting from MALS 105 degrees||66.5||80.0%||13.6%||6.5%||84.1|
|Intensity Weighting from MALS 90 degrees||66.5||78.7%||13.6%||7.7%||85.7|
|Number Weighting from RI||66.5||89.1%||10.9%||0.10%||74.0|
Refractive index is a direct probe of the concentration of a given material, while scattering intensity is a product of both molecular weight and concentration, thus the pure intensity weighted molecular weight overestimates the contribution of larger species, specifically dimer and trimer. Recall that the MW obtained from a standalone SLS measurement was around 81 kDa, which closely resembles the intensity weighted molecular weights represented in Table 1.
- Proteins often exist in equilibrium with multiple well-defined species of different aggregation numbers (in the case of BSA, N agg=1,2, 3).
- Any molecular weight obtained from a Zimm Plot will be an average of all three isoforms.
- Refractive index can be used to measure the relative abundance of different MW species when coupled with a chromatographic separations method (in this case GPC).
- It is relatively simple to calculate average molecular weights using i) intensity weighting and ii) number weighting
Static light scattering can be used to measure the molecular weight of polydisperse samples, including proteins. Biological samples often have well defined aggregation numbers (monomer, dimer, etc.). In the event of equilibrium controlled self-association, as is seen with protein dimerization, the components are extremely well-defined, and thus molecular weights will be whole number multiples of each other. The relationship between static intensity, molecular weight, and relative concentration for multi-component systems was explored.
- Zimm, Bruno H., “Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering”, J. Chem. Phys. 16, 1099 (1948)
- J. C. Moore, “Gel permeation chromatography. I. A new method for molecular weight distribution of high polymers”, J. Polym. Sci., A-2, 835 (1964).
- Weiner, Bruce B., “Let There Be Light: Characterizing Physical Properties of Colloids, Nanoparticles & Proteins Using Light Scattering”, Amazon, (2019).