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Tutotial: Contrast Variation

Tutorial contributors: Andreas Haahr Larsen

Before you start

• Download and install SasView (needed for Part 2 and 3)

Learning outcomes

• Understand contrast variation in small-angle neutron scattering (SANS)
• Design a contrast match experiment

Part 1: Monodisperse spheres with various contrasts

Go to: Shape2SAS, and simulate a spheres with a radius of 50 Å and contrast (ΔSLD) of 1 as Model 1, and a sphere with contrast -1 as Model 2 (set parameters and press Submit):

Comment on the resulting scattering. Why is the scattering the same despite that the ΔSLD have opposite sign? (Hint)

Try to vary the contrast. How does a numerically larger ΔSLD affect the simulated scattering, and why? (Hint)

Part 2: Core-shell spheres

Go to: Shape2SAS, and simulate a spherical core-shell particle with inner radius of 30 Å and core ΔSLD of -1, and outer radius of 50 Å and shell ΔSLD of 1. This can be done by combining two spheres as Model 1, where the smaller should be above the larger in the list:

Comments on the results. Try to compare with a sphere with radius 30 Å or 50 Å (as Model 2). What should the radii of the cores-shell (Model 1) be to get an I(0) of 0? (Hint). Try to simulate this. Due to the stochastic nature of Shape2SAS, I(0) may not be exactly 0.

Download the simulated data for the core-shell particle (Model 1): Isim.dat (example data).

Load into SasView and fit a core-shell sphere form factor. The result may look like this:

Are the fitted values the same as the input values? Can you fit with different combinations of sld_core, sld_shell and sld_solvent? why (not)? (Hint)

What happens if you fit both sld_core, sld_shell and sld_solvent? why? (Hint)

Part 3: Virtual design of a contrast-variation experiment

This part is inspired by Midtgaard et al 2018, where the detergent DDM is matched-out in SANS to get the scattering from a membrane protein, which is solubilized in DDM, without getting the detergent signal.

Go to: Shape2SAS, and simulate a cylinder with radius 30 Å and length 90 Å and ΔSLD of 2. This cylinder is our highly simplistic model of an integral membrane protein. The transmembrane part of the protein is hydrophobic, and would therefore needs to be solubilized in an actual experiment.

In Shape2SAS, make as Model 2 a cylinder as before, but this time surrounded by a ellipsoidal core-shell particle, which is a model for protein in a detergent micelle. To make this model in Shape2SAS, use these input parameters. Overlapping regions are excluded (by default), so if two shapes are overlapping, e.g. the cylinder and the first ellipsoid, then the top shape is prioritized, and all overlapping points from the second models are not part of the Model:

The following is a schematic cross section of the simplified model of a membrane protein solubilized in a DDM micelle:

The output should look more or less like the below. There is some random variation when building the models, so there will be small differences in the output:

We consider the situation, where the scientist is interested in finding the shape of the protein (here: the cylinder), and not the detergent micelle (here: the core-shell ellipsoid). The whole system (protein+micelle) can be fitted simultaneously (see, eg., Perez and Koutsioubas, 2015), but the shape can be determined more precisely, if the scattering signal from the micelle is removed.

This can be achieved in SANS, by deuteration. First step is to partly deuterate the detergents, so head and tailgroups have the same scattering, i.e. replace some H's by D's. Make a naive simulation of this by changing the ΔSLD of the ellipsoid to the same value, e.g. 3.

Next step is to match the ΔSLD to the detergent, by mixing H₂O and D₂O. Simulate this by decreasing the ΔSLD of all elements by 3, so the ΔSLD of the ellipsoid is 0 and ΔSLD of the cylinder is -1. Now compare with Model 1 (protein without detergent).

Download the simulated data for Model 2 (cylinder "membrane protein" with contrast-matched DDM micelle): Isim_2.dat (example data). Load into SASView and fit with a cylinder form factor. The result may look like this:

OBS: the simulated data is made with a finite number of points and placed at random in the user-defined volume, so the the fits may not be perfect (not unlike a fit to experimental data).

Part 4: Match-out DDM in 100% D₂O

The goal here is to calculate how much to deuterate a DDM detergent in order to match it out in a SANS experiment at 100% D₂O. First, use the chemical formulas to calculate the neutron coherent scattering lenghts for heavy water (D₂O), DDM headgroups (C₁₂H₂₁O₁₁) and DDM tailgroups (C₁₂H₂₅), using NIST tabular values.. Secod, use experimentally determined molecular volumes to calculate SLD and ΔSLD = SLD-SLD_D2O for heavy water (30.0 ų), DDM headgroups (350.4 ų) and DDM tailgroup (350.2 ų). Put the results into a spreadsheet:

7 Hs from the DDM headgroup are exchangable, i.e, when DDM is dissolved in D₂O, these Hs spontaneously exchange with Ds from the solvent. There are no exchangable Hs in the tailgroup (i.e. they are tightly bound). Calculate the SLD and dSLD of the DDM headgroup after exchange (C₁₂H₁₄D₇O₁₁).

OBS: find the average values - no need to reach an integer number. Why is this ok, experimentally?

Why is it better to match in D₂O rather than H₂O as solvent? (Hint)

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