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\}.

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.

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

Thank you all for your interest in this topic and apologies for the delayed response. I can confidently say that there are indeed necessary improvements needed in the CADET implementation of the multi-component GIEX model, specifically stemming from Mollerup activity model.

To provide clarity and contribute to the CADET project, I have rederived Mollerup activity model for multi-component systems and published it as a short communication in JCA (https://authors.elsevier.com/c/1jTn-4-ggYqEs).

I look forward to the CADET team updating the multi-component GIEX model to facilitate its use by more researchers. I suggest naming the updated version the nGIEX model. It must be emphasized that due to the change in the number of model parameters, transitioning from the old GIEX model to the new nGIEX model might not be straightforward. Table 3 of our communication provides several alternative solutions.

Below is the abstract from our communication:

“The single-component Mollerup model, with over 40 direct applications and 442 citations, is the most widely used activity model for chromatographic mechanistic modeling. Many researchers have extended this formula to multi-component systems by directly adding subscripts, a modification deemed thermodynamically inconsistent (referred to as the reference model). In this work, we rederived the asymmetric activity model for multi-component systems, using the van der Waals equation of state, and termed it the multi-component Mollerup model. In contrast to the reference model, our proposed model accounts for the contributions of all components to the activity. Three numerical experiments were performed to investigate the impact of the three different activity models on the chromatographic modeling. The results indicate that our proposed model represents a thermodynamically consistent generalization of the single-component Mollerup model to multi-component systems. This communication advocates adopting of the multi-component Mollerup model for activity modeling in multi-component chromatographic separation to enhance thermodynamic consistency.”

I read your new short communication and found it very interesting. I agree with the derivation and would like to test it in CADET. Unfortunately, I don’t have the expertise to implement this myself - @Flynn maybe this is something we can work on?