Why do my SAXS fit chi2 correlate with concentration?

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sammahdi
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Why do my SAXS fit chi2 correlate with concentration?

#1 Post by sammahdi » 2023.05.02 04:06

Hello,

I have found an interesting observation I'm a bit confused about.

I have run SAXS on a sample at 3 concentrations. All 3 concentrations should be a single species of which I have a crystal structure for. I fit the 3 concentrations with the single species using crysol. Ideally, I would expect to get relatively similar fits, but instead I notice a trend where the chi2 increases proportional to the increase in concentration.

So let's say the 3 concentrations are 10, 5, 2.5. The chi2 for these would be 4,2,1 (approximately). Why does the chi2 increase or decrease with concentration? Is this normal? I'm attempting to understand why for the highest concentration I am getting a chi2 of 4 (which from what I've seen in many papers is not ideal), and why I can get almost perfect fits chi2=1 at the lowest concentration?

Any help would greatly be appreciated!

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AL
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Re: Why do my SAXS fit chi2 correlate with concentration?

#2 Post by AL » 2023.05.03 10:41

Keep in mind that the Chi2 value depends on the experimental errors. You can verify the correctness of your experimental error estimates following these instructions (slide 33).

I'll assume that your experimental errors are correct and the exposure times for the three concentrations were the same (i.e. the low-concentration data are noisier than the high-concentration data).

Check the Guinier Rg estimates. (Ideally, they all should be close to the Rg from the slope of net intensity calculated by CRYSOL from the structure.)
If the higher concentration data appears to have a smaller Rg, your sample is affected by repulsive interactions ("structure factor").
If the higher concentration data appears to have a larger Rg, your sample is affected by unspecific aggregation or oligomerization.

If there are no differences between the data from different concentrations (apart from the amount of noise) then it could be that CRYSOL just managed to vary the fitting parameters to get a Chi2=1 on noisy low concentration data but on the less noisy data CRYSOL is more restricted and your crystal structure just doesn't fit the SAXS data.

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Re: Why do my SAXS fit chi2 correlate with concentration?

#3 Post by sammahdi » 2023.05.12 16:00

When you say smaller/larger, by how much?

For example the theoretical Rg is 34.15 and the highest concentration Rg is 34.8. Therefore it appears the higher concentration data does have a larger Rg, but how big of a difference is big? Is the 0.7 difference here significant enough that this deviation could be attributed to unspecific aggregation?

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Re: data does have a larger Rg, but how big of a difference is big?

#4 Post by AL » 2023.05.15 19:16

0.7 Å is 2% of your theoretical Rg.

A Guinier Rg estimate may come with a standard deviation, e.g. on this nice glucose isomerase data AUTORG estimates an Rg of 32.3 Å with a standard deviation of 0.3 Å (just 1% - which is normal for low-noise data). But if we calculate the Rg from the slope of net intensity from the 1OAD model we get 33.0 Å. Most probably this SAXS data set is affected by repulsive interparticle interference.
(Indeed, other glucose isomerase data have a Guinier Rg of 33 Å.)

Assuming that your data are of similar quality I'd say that a 2% difference in Rg is significant. If you see an uprise before the first Guiner point, it means unspecific aggregation.

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Re: Why do my SAXS fit chi2 correlate with concentration?

#5 Post by sammahdi » 2023.06.03 04:10

I do see exactly that type of uprise in my data. Thank you for your help!

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