I(Q) curve generated by real-world 

SANS experiment

Creating Small Angle Neutron Scattering (SANS) Analysis 

Models for Concentrated Protein Solutions

Alex Zheng - NIST Center for Neutron Research

1. Background

What is Neutron Scattering?

The NIST Center for Neutron Research (NCNR) utilizes a small 20 MW nuclear reactor to produce neutrons 

for the numerous instruments and enable neutron scattering experiments, which improves our 

understanding of various materials and samples. My project focuses on one of the methods of neutron 

scattering- Small Angle Neutron Scattering, or SANS.

Why Neutron Scattering?

As neutrons only interact with the nucleus of atoms rather than their much larger electron cloud, we can 

determine various properties of materials. A real world example of this is that the NTSB (National 

Transportation Safety Board) has come to the NCNR to investigate and analyze material stresses to 

determine the cause of airliner accidents and crashes.

Background to SANS

In SANS, unknown samples are put into the instrument and bombarded with neutrons to obtain scattering 

patterns from the detector. From this scattering pattern, we can use a lot of math implemented in analysis 

software such as Sasview in order to work backwards and discover various properties of the sample.

My work focuses on developing software in Sasview to create fit models to analyze scattering patterns for 

SANS, particularly for proteins. This reveals properties such as the size and interactions of the proteins. 

This is especially important in cases such as pharmaceuticals, where these properties define the results of 

the products, such as toothpaste or shampoos.

NCNR Guide Hall

3. Theory and Modelling

Calculated ValuesMy project requires a deeper mathematical understanding of SANS to calculate three properties- Radius of 

Gyration (RG), Scattering Pattern (I(Q)) and Beta Q (β(Q)). This section will dive into these three properties and 

how we use them.

4. GUI Changes

Change 1: RG and β(Q)

❖ Calculate RG(Mass & SLD) and β(Q) from atomic coordinates (PDB Files)

➢ PDB files are the atomic position of every atom in a protein

❖ Integration into the Generic Scattering Calculator to make it more 

accessible

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

properly integrate features.

❖ Rather than opening a seperate software to calculate β(Q) and RG, 

scientists can do it within the Sasview program now.

2. Overview Sasview

❖ Sasview is an open source, collaboratively developed software for the analysis of any small angle 

scattering data

❖ Compare Small Angle Scattering data to existing shapes such as cylinders or ellipsoids to determine 

properties such as size

❖ Various tools:

➢ Data Operation

➢ SLD calculator

➢ Density/Volume calculator

➢ Slit Size Calculator

➢ Kiessig Thickness Calculator

My Project:

❖ Project primarily contributes to the Generic Scattering Calculator

❖ Generic Scattering Calculator simulates scattering data for different types of sample structures and 

compare these simulated patterns to their experimental data

➢ Understand how parameters, such as size, shape, and distribution, affect the scattering pattern

❖ Project calculates various properties and builds a custom plugin model with these values

➢ Q Resolution Estimator

➢ Generic Scattering Calculator

➢ Orientation Viewer

➢ Python Shell/Editor

➢ Image Viewer

Radius of Gyration (RG)

❖ In simplest terms, Radius of Gyration is the size of the 

molecule (unit: Angstrom (Å), 0.1 nanometer or 10

-10

 meters)

❖ Used for calculating other properties as well

❖ Mathematically, RG is the average distance of all the atoms 

in the molecule from the center of mass.

➢ A smaller RG means a more compact protein

❖ Calculated with Mass (mi) or Scattering Length Density (bi); 

in the latter case, it is called the Guinier Radius

Scattering Pattern I(Q)

❖ Scattering Pattern (I(Q)) is the 1D scattering pattern 

obtained from averaging 2D scattering data

❖ Essential to understanding interactions between proteins 

through SANS

❖ Dependent on Q (Related to angle)

❖ We can obtain I(Q) either experimentally through physical 

scattering in real space (see right) or theoretically through 

calculations (see equation below) 

❖ By comparing the experimental and calculated I(Q)

curve, we can ascertain various properties of the sample.

Theoretical Calculated I(Q) curve

Beta Q (β(Q))

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

of anisotropic proteins to extract interactions between 

proteins in solution

❖ I(Q) is calculated with Seff(Q) for anisotropic particles

■ 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

β(Q) Graph

Before After

2

1 3

Change 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 Q Minimum as well

❖ Default set to .001 * QMax in the past

Change 3: Adding Custom Fit Models in the GSC

❖ 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

5. Summation

❖ Simulate the scattering pattern of the 

protein with our calculated plugin model

❖ Work backwards by adjusting parameters 

of the protein to minimize the differences 

(residuals) between the experimental and 

simulated data.

❖ Derive meaningful structural information 

and gain insights into the properties 

Special Thanks

Mentor: Dr. Yun Liu CHRNS for sponsoring this program

Collaborators: Paul Kienzle, Paul Butler, Jeff Krzywon

 SHIP Directors: Julie Borchers and Leland Harriger