pH dependent isotherm parameter for Langmuir LDF

[rosario.cervellere]

Hello,

I am developing a protein capture model using the lumped rate model without pores and the Langmuir LDF isotherm.

I have K_eq at 5 different pH and want to vary K_eq based on the local pH with a model fit. The best fit is an exponential function based on local [H+] concentration something like ln(Keq) = 0.2*[H+]^(-0.25).

My question: how does one approach this? or is this even feasible with the Langmuir LDF isotherm? What other isotherms would be recommended?

[a.moser]

Hey Rosario,

According to the binding model feature matrix, the Langmuir LDF doesn’t have the mobile phase modifier option, but it sounds like you’re basically asking about a Mobile Phase Modulator Langmuir binding model. I am not sure if there’s a reason you’d want to use the Langmuir LDF specifically, but if it’s just to use Keq you can do that by setting K_d to 1 and use K_a as the K_eq. However, as it is implemented, the functional form for parameter dependence may not be what you need.

I’m not sure if there’s another way to do what you’re asking (maybe something with the Generalized Ion Exchange model?), and I can’t be of much help as I have just relied on the existing implementation of the colloidal isotherm for pH dependence so far, but I think the Mobile Phase Modulator Langmuir isotherm would be the most equivalent to that approach. However it might need to be modified to get the pH dependence right.

[alters]

I think you will need to use external functions if you want to use the pH-dependent Langmuir. Like @a.moser said, the colloidal model should also work. That one will not require external functions. I think the colloidal model is implemented using LDF. So the colloidal is probably the most sensible here.

[rosario.cervellere]

Thanks for the replies both. I believe we’ll move back toward the Colloidal Isotherm for pH dependence.

Thanks again!

[ronald.jaepel]

Hey Rosario,

can you get a good fit to your data with this equation: k_{eq} = a \frac{e^{\gamma*[H+]}}{[H+]^\beta} ? Because if you can, that equation can be used in CADET directly with the Mobile Phase Modulator as @a.moser mentioned.

[rosario.cervellere]

Hello @ronald.jaepel. Thanks for the suggestion. I was able to implement pH dependence with the above relationship by the binding model kinetics to false.

Thanks again!

-Rosario

[Flynn]

You could also try the ACT isotherm in this post:

An example to use ACT isotherm for protein A affinity chromatography

Introduction The ACT isotherm is a modified Langmuir isotherm tailored for mechanistic modeling in protein A chromatography. It is known that both binding capacity q_{max} and equilibrium constant (affinity) K_{eq} changes as a function of pH. ACT isotherm uses modification factors derived based on proA and mAb interaction stoichiometries. Details can be found in the paper. [ACT isotherm concept.] [ACT isotherm behaviors.] Example code from cadet import Cadet import numpy as np import matpl…

It will be available in the next release shortly.

One problem with mobile phase modulator Langmuir is that it cannot model q_{max} changes as a function of pH. ACT isotherm is capable of doing it.

[kautharmaalim]

Hi Ronald,

I am a bit confused here. How would I get Keq at different [H+] to fit the equation you stated? I have static binding capacity data, which did not change when I fitted with Langmuir Keq and q max.

[ronald.jaepel]

Hi Kauthar,

rosario had different kEq values, how he got them he did not specify.

@rosario.cervellere

I have K_eq at 5 different pH and want to vary K_eq based on the local pH with a model fit

I currently don’t know of an isotherm that varies qMax based on a mobile phase modulator.

[rosario.cervellere]

Hello Kauthar,

I used experimental data comprising of 100% breakthrough over a range of feed pH. With that data set I fit Keq at each loading pH with the Langmuir LDF isotherm. I then made the Langmuir MPM fit Keq for the pH range tested. I was able to get reasonably good agreement for total eluted mass for the range of pH I was interested in (pH > 5.5) and no binding at low pH (< 3.8 pH).

In this case q_max was assumed to be the maximum capacity at optimal binding conditions.

Let me know if this helps or if you require more details.

-Rosario