How to build indirect response model?

Hi,

I want to bulid a population PK/PD model, in the PD part, I used the indirect response(IDR) model to illustrates my response data. The equation of the IDR model is below.

I have a question, each individual has their own baseling protein (Protein0), the protein is change from their baselline, how shoud I build the model and how to set protein0 ?

Protein = Kin - Kout*(1+Imax*Conc/(Conc+IC50))*Protein

Answer 1

[Fulden Buyukozturk]

Hi,

If I understand your question correctly, your indirect response model is in derivative form as: dProtein/dt = kin - kout*(1+Imax*Conc/(Conc+IC50))*Protein, is that right? If not, can you elaborate on your question?

If so and if Protein is defined in units of mass, amount, or concentration, in other words if Protein can be described using a Species, you can use reactions to define input/production (kin) and loss (kout) processes. See the screenshot below.

If you'd like to define Protein as a measured dimensionless quantitiy or with units other than mass, amount, or concentration (that cannot be descibed by a Species) you can use a Rate Rule instead to define it as

Protein = kin - kout*(1+Imax*Conc/(Conc+IC50))*Protein

where Protein is a Parameter.

To address your question about different Protein baseline/initial values: I assume you're interested in applying different initial values to Protein for each individual during parameter estimation. Is that right? If that's the case, you can store these initial values in different Variants and apply these variants in a Fit Data program using Variants and Dose Setup table. Please see the screenshot below.

Fulden

[voZnW]

Thank you very much for your detailed answers.

The protein in my data was expressed as percentages (%), so I think it was a dimensionless value. I tred to use a Rate Rule and set Protein as s Parameter. The model structure was shown in the screenshot below.

But how to set the value of parameter "Protein"? Each individual was different, in the parameter input box, only one value can be entered.

And in the Fit Data program, how to store these initial values in different Variants? Please see my data and the Fit Data program in the below screenshot.

Thank you very much!

[Fulden Buyukozturk]

Hi, I believe Protein0 in your data is the column that stores different baseline values for Protein. If so, in "variant from data" setup in Data Map, you should set Protein0 as the Column.

However, if you're only interested in setting the initial value of Protein per group, then you can just specifiy this value in the Protein column in the row corresponding to time = 0, as I see you already did. No need to capture this info in a variant. I initially thought that you're interested using baseline Protein/Protein0 in an expression in the model but that doesn't seem to be the case.

As a side note, as you probably already figured out, you can either create and use variants that are in the model or you can create variants from a column in dataset (as you do). In my example/screenshot, I created variants in the model and named them individually as Protein0_ID1, *ID2, *ID3. You are creating variant from data and therefore Variant2 in Variant and Dose Setup will display the name of the column.

I notice from other threads that you have multiple questions. If it's easier, I'm happy to have a call and go through any other questions. If you prefer that, please feel free to reach out via my community profile.

Fulden