The scattering data collected with Prometheus Panta DLS optics yields additional output parameters that are not available for fluorescence and turbidity data. They provide quantitative information about particle sizes in the sample, and serve as a measure of homogeneity, aggregation, or weak particle interactions.

The hydrodynamic radius rH describes the observed size of particles in solution. It is calculated by entering measured translational diffusion coefficient into the Stokes-Einstein equation (viscosity and temperature need to be known). We distinguish between the intensity-weighted average radius obtained from cumulant fit and the intensity-weighted distribution of radii from the size distribution fit. In the tabulated results, the cumulant model reports a single hydrodynamic radius, while the size distribution model reports the hydrodynamic radii for up to three discreet peaks (the model can fit more than three peaks, but only the three largest will be summarized in the results table). 

Figure: Graphical representation of the hydrodynamic radius in a size analysis measurement. The violin plot is shown on the top, the size distribution plot on the bottom. The rH of the cumulant fit is displayed as purple dot or dotted line, while the results of the size distribution fit are output as blue lines. The violin plot is a size distribution mirrored on the radius axis, which contains an overlay of all acquisitions of a capillary, so each line/dot depicts a single DLS acquisition. These are particularly helpful for judging sample homogeneity and comparing samples.

Together with the hydrodynamic radius, PR.Panta Control outputs a polydispersity index, which is a measure of the heterogeneity of particle sizes in the sample and is derived from fitting the autocorrelation function. The PDI represents the broadness of the distribution and is a helpful parameter to judge if a sample is sufficiently homogeneous for subsequent characterization or serves as an early indicator for formation of oligomeric species.

For each DLS acquisition, PR.Panta Control reports additional parameters related to the DLS signal itself and the autocorrelation function, which can be used to assess signal quality: The average scattering intensity is the sum of the detected intensity fluctuations over time and proportional to the size and concentration of particles. According to scattering theory, large particles will scatter more light than small particles and the scattering intensity can thus be used in size analysis measurements to single out acquisitions containing dust or showing signs of sedimentation. Furthermore, the scattering intensity may indicate too low or too high particle concentrations. Parameters related to the quality of the autocorrelation function are the Signal/Noise ratio, the amplitude, and the baseline.

From the diffusion coefficients obtained from a size analysis measurement on a dilution series of particles, the diffusion interaction parameter kD can be calculated. It serves as a measure for weak attractive or repulsive interactions and is generally employed to understand and predict colloidal protein stability. Along with kD, PR.Panta Control outputs the diffusion coefficient and radius at infinite dilution, D₀ and R₀, which are independent of particle concentration and thus any concentration-related effects. Please note that in all calculations related to kD, PR.Panta Control uses an average diffusion coefficient from the size distribution model (calculated from the whole size range).

Figure: The diffusion interaction parameter kD is calculated from the concentration-dependence of the diffusion coefficient.

Prometheus Panta allows recording of DLS data in parallel to a thermal unfolding measurement from the same sample. From the resulting plots of the hydrodynamic radii and average scattering intensity over temperature, two onset parameters are derived. Tsize calculated from cumulant radius data denotes a change in the average particle size. Size changes can be caused by cooperative unfolding, oligomerization or formation of the first aggregates. Tscattering marks the increase in the average scattering intensity due to the formation of larger particles, which is typically related to aggregation. Note that Prometheus Panta software does not output an onset parameter for the corresponding size distribution data, however the plot will help to understand the underlying pathway of aggregation (see image below). 

Figure: Intensity size distribution over temperature from two proteins. The degree of color saturation reflects the magnitude of the corresponding peak in the size distribution plot of the DLS acquisition at a given temperature.