Implementing SANS Analysis Models for 

Concentrated Protein Solutions

Author: Alex Zheng - Urbana High School, Frederick // 

UCLA

Mentor: Dr. Yun Liu 

Collaborators: Paul Kienzle, Paul Butler, Jeffrey Krzywon
Background:

❖ My project develops software to supplement and improve Sasview, 

particularly in investigating the properties of proteins

➢ There are many different focuses and parts to the project

➢ Main goal is to develop fit models for Sasview

❖ By comparing SANS data to these models, size and interactions between 

proteins are revealed

❖ Important in cases such as pharmaceuticals

➢ Protein-protein structure and interactions are essential to their 

applications.

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NIST MAB Protein

Special thanks to Dr. Christina Bergonzo 

for providing the MD Simulation files
Brief Overview: 

Radius of Gyration (RG) // Scattering Pattern (I(Q)) // Beta Q 

(β(Q))
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Radius of Gyration: RG

❖ Size of the molecule (unit: Angstrom (Å), 0.1 nanometer or 10-10 meters)

❖ Used for calculating other properties as well

❖ RGis the average distance of all the atoms in the molecule from the center of mass.

➢ A smaller RG means a more compact protein

❖ We can calculate it with Mass or Scattering Length Density (SLD)

Trajectory A: Protein change over time

Frame 170:

RG: 51.9 Å

Frame 1000:

RG: 48.2 Å

Frame 1:

RG: 57.7 Å
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Scattering Pattern: I(Q)

❖ I(Q) is the 1D scattering pattern obtained from averaging 2D scattering data

➢ Essential to understanding interactions between proteins through SANS

➢ Dependent on Q (Angle)

➢ We can find I(Q) either experimentally through physical scattering in real 

space (see below) or theoretically through calculations (next slide) 
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Scattering Pattern: I(Q)

❖ I(Q) can be also be calculated (see equation)

❖ This allows us to compare the experimental and calculated I(Q) to ascertain 

various properties of the sample. 

➢ More details later

φ - Scale

ρ - Scattering Length Density; effective size of 

interaction field, related to probability of 

scattering

v - Volume

P

~

(Q) - Normalized Form Factor; Particle Shape 

Seff(Q) - Effective Structure Factor; Protein 

Location & Interaction

B - Background
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Beta Q: β(Q)

❖ Beta Q is a correction factor that accounts for the orientation and 

interaction between proteins in solution

❖ I(Q) (SANS Scattering pattern) is calculated with Seff(Q)

■ Results from the experiments is Seff(Q) rather than S(Q)

■ S(Q) assumes a spherical shape (β(Q) of 1)

■ β(Q) is used to transform S(Q) to Seff(Q)

❖ It is important to calculate the Effective Structure factor to 

accurately obtain the Scattering patterns

The effect of the static beta 

approximation

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NIST MAB Protein
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Project 1: RG and β(Q)

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❖ Calculate RGand β(Q) from Nuclear data (PDB Files)

❖ Integration into the Generic Scattering Calculator of Sasview to make it more accessible

❖ Involves revamping the GUI as well as working in the backend to properly integrate 

features.

Before After

PDB file example
Generated β(Q) 

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Program Beta(Q) Visualization: 

Sample Size: 200

Separate Program Visualization Post-Sasview Integration

Notice how the separate program visualization has a linear spacing between the points and is plotted 

on a linear scale. In contrast, the Sasview program has linear spacing, but is plotted on a log scale.

NIST MAB Protein
Project 2: Adjusting Q Spacing

❖ Sasview utilizes linear spacing between points, but is plotted on a log scale.

❖ At times, log spacing is more useful than linear spacing

❖ Adjust the program to allow the user to choose between linear and log spacing.

❖ Allow User to set a QMinimum as well

➢ Default set to .001 * QMax in the past
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Linear vs Log Spacing

Linear Spacing, Log Scale Log Spacing, Log Scale
Project 3: Adding Custom Fit Models in the GSC

❖ Adding Custom Fit Models into the Generic Scattering Calculator of Sasview

❖ Takes the protein that has been imported and builds a custom plugin model to calculate 

and interpolate I(Q).

❖ Simulates the scattering pattern the protein would produce.

❖ Now able to fit data to obtain interaction information from PDB files in Sasview
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❖ Simulate the scattering pattern of the protein 

with our calculated plugin model

❖ Work backwards by adjusting parameters of the 

protein minimize the differences (residuals) 

between the experimental and simulated data.

❖ Derive meaningful structural information 

and gain insights into the properties 
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All Changes:
THANKS!

Any questions?

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