A non-transitory computer-readable medium storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform operations for determining an assumption-free radius of gyration (Rg) of particles in solution using a light scattering detector, the operations comprising:
- obtaining, by the computing system, light scattering intensities of the particles in the solution from the light scattering detector, wherein the light scattering intensities comprise a first scattering intensity (Iθ1), a second scattering intensity (Iθ2), and a third scattering intensity (Iθ3) of the particles in the solution at a first angle, a second angle, and a third angle, respectively, wherein the first angle, the second angle, and the third angle are determined relative to a beam of light of the light scattering detector;
- determining, by the computing system, a first weighting factor (FW1) based on a first form factor (FF1) and the light scattering intensities, wherein determining the first weighting factor (FW1) comprises:
- determining a ratio of observed light scattering of the particles at the first angle to observed light scattering of the particles at the third angle (R′θ1/θ3) based on the first scattering intensity (Iθ1) and the third scattering intensity (Iθ3);
- determining a ratio of observed light scattering of the particles at the second angle to observed light scattering of the particles at the third angle (R′θ2/θ3) based on the second scattering intensity (Iθ2), and the third scattering intensity (Iθ3);
- determining a ratio of calculated light scattering at the first angle to calculated light scattering at the third angle
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- based on the first form factor (FF1), the first angle, and the third angle;
- determining a ratio of calculated light scattering at the second angle to the calculated light scattering at the third angle
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- based on the first form factor (FF1), the second angle, and the third angle;
- determining a best fit of the ratio (R′θ1/θ3) to the ratio
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- and the ratio (R′θ2/θ3) to the ratio
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- based on the first form factor (FF1);
- and
- determining, by the computing system, the first weight factor (FW1) based on the best fit of the ratio (R′θ1/θ3) to the ratio
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- and the ratio (R′θ2/θ3) to the ratio
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 1
- ″
- )
- ;
- determining, by the computing system, a second weighting factor (FW2) based on a second form factor (FF2) and the light scattering intensities, wherein determining the second weighting factor (FW2) comprises:
- determining a ratio of calculated light scattering at the first angle to calculated light scattering at the third angle
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- based on the second form factor (FF2), the first angle, and the third angle;
- determining a ratio of calculated light scattering of the second angle to calculated light scattering at the third angle
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- based on the form factor (FF2), the second angle, and the third angle;
- determining a best fit of the ratio (R′θ1/θ3) to the ratio
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- and the ratio (R′θ2/θ3) to the ratio
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- based on the second form factor (FF2);
- and
- determining, by the computing system, the second weight factor (FW2) based on the best fit of the ratio (R′θ1/θ3) to the ratio
- (
- R
- θ1
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- and the ratio (R′θ2/θ2) to the ratio
- (
- R
- θ2
- θ3
-
- Calculated
-
- FF
-
- 2
- ″
- )
- determining, by the computing system, a first form factor contribution (FC1) for the first form factor (FF1) based on the first weighting factor (FW1) and the second weighting factor (FW2), wherein the first form factor contribution (FC1) is determined according to Equation (1):
- FC
- 1
- =
- FW
- 1
- ∑
- FW
- x
- ,
- (
- 1
- )
- wherein μFWx is the sum of each of the weighting factors;
- determining, by the computing system, a second form factor contribution (FC2) for the second form factor (FF2) based on the first weighting factor (FW1) and the second weighting factor
- FC
- 2
- =
- FW
- 2
- ∑
- FW
- x
- ;
- (
- 2
- )
- determining, by the computing system, the assumption-free radius of gyration (Rg) of the particles based on the first and second form factor contributions (FC1, FC2);
- and
- normalizing the light scattering detector based on the assumption-free radius of gyration (Rg).