I started an issue in GitHub, but I think this is the better place for this discussion:

During a SOCSS presentation, a presenter argued that the GIEX multicomponent formulation is incorrect.

This is the current state:

and they argued it should be:

The suggestion was made to name the second version the `nGIEX`

model and leave the `GIEX`

as is.

(with “n” refering to the number of components (except salt)).

You could unify both models by specifying an index set over which the sum is taken. The default would be j \in \{i\}, the general form j \in \{1,...,n\}.

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Very interesting… What was the individual’s reasoning for his/her claim? I am not sure I agree. The k_{a, i, prot} and k_{salt, i, prot} come from Mollerup’s thermodynamic framework (see his few papers from 2006-2008). These terms provide an approximation to the activity coefficient of protein i in solution. The purpose of NOT having a sum concentration term is so that each protein provides a distinct contribution to the deviation from ideal behavior. By using a sum concentration, we would be overcounting these contributions.

The above is my understanding of Mollerup’s thermodynamic framework. There is another way to think about this which I think is more correct. Protein-protein interactions can be practically described via pairwise interaction terms. The colloidal isotherm does this using the B_{pp, i} which is conceptually similar to the second virial coefficient B_{22} (see Yuan, Oberholzer, Lenhoff 2000), which describes the energetics of protein-protein interaction. The sum concentration terms in this equation, iirc, are the sum of only the considered protein pair.

In any case, I don’t see why we would sum over all protein concentration.

BTW what was this conference, I have not heard of it.

Hey Scott,

I’ve since confirmed with the speaker if it’s okay to share his name and he agreed: It was Yu-Cheng Chen. He also said he’d be willing to share his reasoning in the forum when he gets a chance.

The conference is the SOCSS, the “International PhD Seminar on Chromatographic Separation Science”. This year it was in Lund: announcement and photos

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