Multicomponent formulation of GIEX

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:

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and they argued it should be:

png-1

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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