k_D is known as the self-interaction or diffusion-interaction parameter and can predict behaviors at higher concentrations that could lead to protein aggregation. Avoiding self-interactions is critical to selecting the best candidate molecule and successfully delivering a therapeutic to patients.

k_D values are calculated by measuring how the protein’s diffusion coefficient changes with its concentration, since the interaction between particles will affect how they move through solution. Attraction between molecules slows down their diffusion, leading to negative k_D values where the protein favors self-association, whereas repulsion between molecules increases their diffusion through solution and results in positive k_D values. Positive k_D values are considered ideal as these conditions are less likely to lead to increased viscosity or aggregation at high protein concentrations.

How to set up a k_D measurement

To calculate the k_D, we first need to perform DLS measurements at multiple concentrations using the Size Analysis measurement mode. These measurements are done using dilute concentrations (1-20 mg/ml), which is ideal for predicting behaviors at higher concentrations without having to use large sample amounts in routine testing.

At least 5 sample dilutions should be prepared, spanning the entire concentration range with enough sample volume available for replicate measurements to get a linear and reproducible fit. For example, you could prepare samples at 1, 5, 10, 15, and 20 mg/ml. Size Analysis measurements are made using the High Sensitivity mode to acquire more acquistions and increase the signal-to-noise.

The sample solvent must also be specified since the function of the Size Analysis measurement mode is to determine a sample’s size and polydispersity. In order to calculate the radius from DLS measurements, the viscosity and temperature of the solvent must be known. The solvent can be selected from the drop down list in the Solvent column. The software will not allow you to proceed with the measurement without this information. Once ready, select the Start Size Analysis button.

Figure 1. Size Analysis measurement parameters and sample annotation window.

Once the DLS measurements are completed, the additional measurement buttons will be toggled on. Select k_D Analysis.  

Figure 2. Size Analysis results window.

The k_D is determined by plotting the diffusion coefficient as a function of concentration so the Concentration as well as the Diultion Series must be defined in their respective columns in the Dilutions Series and Annotations window.

Figure 3. k_D Analysis sample annotation window.

Analyzing your kD measurement results

Underneath the plot in Figure 4 are the k_D and goodness of fit values, along with the radius and diffusion coefficients at zero concentration. If you have multiple sample dilution series, you can select the one you want to view by clicking the Dilution Series drop down list above the chart. While you 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 4. Plot of concentration vs diffusion coefficient for k_D determination under different solvent conditions.