I was wondering if anyone has used CADET, or CADET in conjunction with other routines, to model induced pH transitions in salt steps and/or salt gradients due to ligand titration. I remember that some work had been done in CADET to thermodynamically model pH gradients, so I am curious how this could be extended towards titration of the stationary phase itself. I have attached a paper (Pabst and Carta 2006 JChromA) describing the phenomena and how it was modeled.
The problem we are looking to model is prediction of the pH profile (inside column and at outlet) for a multimodal ligand (Capto MMC) with a carboxylic acid group and its impact on the protein elution profile. I have a strange result here that we would like to predict. Here, there are multiple peaks in a single elution step for a pure protein species. The buffer was acetate 20 mM acetate pH 5.5. We theorize that the double peak behavior is seen here because of the protein acting as a buffering species in the thermodynamic equilibria and thus slowing the return of pH to its nominal value. So, we would also like to include the protein species in the reaction kinetics if possible.
Sam and Johannes have substantially improved the code since then, and we are currently preparing a publication. Maybe Johannes can give you a preview after the Easter break.
Since I made this post, I wrote a MATLAB routine (using ode15s) that follows the approach outlined by Pabst and Carta 2007 to simulate pH transients in columns with weakly charged ionogenic groups (e.g., carboxylic acid). Not sure if it would be helpful, but I can provide this if you are interested.
I recommend that you read the Pabst and Carta 2007 paper (see below attachment), since the script directly uses the key equations and approach described in the publication.
Here is an example of predictions (taken from my thesis) of induced pH gradients for the Capto MMC resin using blank salt steps (protein-free) with different sodium acetate buffer concentrations. Here, the dots are the experimental pH traces recorded by the pH meter and the solid lines are model predictions.
In the Pabst and Carta 2007 paper, they describe two solution approaches—method of characteristics and numerical. I tested both of these to compare their predictive accuracy and found that the numerical approach was more accurate. It is also much more flexible because it can be used for linear gradient elution which is not possible using the method of characteristics described in the publication. However, if you would like to see the script for the method of characteristics, I can share that too.
