Static light scattering (SLS) measures the average scattering intensity of a sample solution and can be used to generate a Debye plot. A Debye plot correlates the sample scattering intensity as a function of concentration to calculate the average sample molecular weight and extract the second virial coefficient or B₂₂.

B₂₂ is a self-interaction parameter that probes the interactions of protein molecules with the surrounding solvent and their propensity to aggregate at higher concentrations. Positive B₂₂ values indicate the protein favors solvation whereas negative B₂₂ values indicate the protein favors self-association and exhibits low solubility. Positive B₂₂ values are ideal as these conditions are less likely to lead to aggregation at high concentrations.

How to set up a B₂₂ and MW measurement

To calculate both B₂₂ and molecular weight, light scattering measurements are first acquired at multiple concentrations using the Size Analysis measurement mode in High Sensitivity set to On. These measurements are done with dilute sample solutions (0.5-20 mg/ml), which is ideal for predicting behaviors at higher concentrations without having to use large sample amounts in routine testing.

Once a Size Analysis measurement is completed, the option for B₂₂ and kD analysis will be enabled. These calculations can be performed in PR.PantaControl even if the instrument is not turned on or connected. For this, select B₂₂ and MW Analysis on the bottom right of a Size Analysis run in PR.PantaControl (Figure 1).

Figure 1. Size Analysis results window

Depending on sample and capillary slot availability a minimum linear dilution can be constructed with 1, 2.5, 5, 7.5, and 10 mg/ml. The antibody sample data in this guide uses 10 data point between 0.5-20 mg/ml in 2:1 dilution series.

A buffer blank is an optional inclusion to be measured and can be marked as such in the Software by selecting the check box in the Solvent Blank column (see Figure 2). 

An internal PEG-40 reference value for SLS intensity is saved as an instrument internal parameter after the initial instrument calibration and readjusted at each subsequent instrument service. However, as the laser output decreases with time and usage, usage of the Molecular Weight Reference Kit for each run is recommended. This external PEG-40 reference is denoted by selecting the corresponding check box in the Reference column.  

Generating a Debye plot requires information on sample concentration, solvent viscosity and refractive indices, scattering intensity and various instrument parameters.

Prior to measurement, the sample solvent must be specified for the Size Analysis measurement mode to proceed.  In order to calculate the radius from a DLS measurement, the viscosity and temperature of the solvent must be known; hence the software will not allow you to proceed with the measurement without the solvent information. 

The refractive index increment describes how the refractive index changes as a function of sample concentration. This value is generally the same for most proteins and is automatically populated in the RI Increment column by the software. Scattering intensity values are taken from the Size Analysis measurement.  The concentration is a required manual user input. 

In order to run a B₂₂ and molecular weight calculation, samples belonging to the same dilution series have to be grouped together by selecting the same series number in the Dilution Series column.

Once all the appropriate sample information has been applied, select Calculate to generate the Debye plot (Figure 2).

Figure 2. B₂₂ and MW Analysis sample annotation window.

Analyzing your B₂₂ and MW measurement results

B₂₂ and molecular weight calculation in PR.PantaControl is done with a non-linearized form of the Debye plot equation. This allows for an improved B₂₂ fit over the classical linear Debye plot, more robust to outliers at lower concentrations. Mathematical derivations and assumptions and are outlined in the Appendix section.

The non-linearized version of the Debye plot generated by the software is shown below in Figure 3. On the y-axis, the corrected Scattering Intensity is plotted against the sample concentration on the x-axis.  The software displays the calculated molecular weight and B₂₂ values below the Debye plot. Positive B₂₂ values indicate protein favors solvation while negative B₂₂ indicates protein favors self-association and an increased aggregation propensity. Visually a concave curvature equates to a positive B₂₂.

If multiple dilution series are being measured, individual curves can be viewed by clicking the Dilution Series drop down list above the chart. While one can only view the calculated parameters for one series at a time, multiple series can be overlaid and viewed at once by selecting ALL.

Figure 3. Debye plot for molecular weight and B₂₂ determination.

Appendix

The Debye plot formula is defined as:

where

The particle form factor P_Θ is derived the following way:

For particles with radii smaller than a twentieth of the DLS laser wavelength (<λ0/20), the form factor P(θ) can be approximated with 1, simplifying the Debye plot formula to:

This is the classical formula for the linear Debye plot, in which the slope corresponds to B22, the y-intercept to the molecular weight.

In PantaControl:

With

and 

the Debye plot is transformed to the following formula:

Further rearrangement then gives the non-linearized Debye plot used for the B₂₂ and MW calculations in PantaControl:

 

A description for used parameters and constants is listed below: