Subject:[NMusers] modeling compartments within compartments
Date: 10/13/2003 10:17 AM

Dear all,

I am trying to fit a model where a compund is cleared in both a
protein-bound and free-state from the central compartment by different
processes at different rates.  The drug assay concentration data does not
distinguish between the protein-bound and free drug states and thus
measures only total drug concentration.  So, the protein-bound state is
like another compartment with its own clearance rate but with the drug
concentration observations being the combined total drug in both

Can I model the drug observations as the combined total drug from two

Robert James
Robert L. James, M.S., M.Stat.
Senior Biostatistician
Rho, Inc.
100 Eastowne Drive
Chapel Hill, NC 27514

(919) 408-8000 x 468
(919) 408-0999 (fax)


Subject: RE: [NMusers] modeling compartments within compartments
Date: 10/13/2003 11:33 AM

You can model the two species but because you do not have free and bound
concentrations, you won't be able to identify the different rate constants.
The best you can do is model a hybrid combined rate representing the sum of
both processes.

Subject: RE: [NMusers] modeling compartments within compartments
Date: 10/13/2003 2:08 PM


The answer to your question is yes. You *can* model the total drug concentration
as the sum of predicted concentrations from 2 compartments. However, the data you
describe is not sufficient by itself to identify uniquely the structure of the 2
compartment model and its parameters. 

You seem to have some have prior knowledge to support your assertions about the
clearance processes of protein bound and unbound drug. You can use this information
and other assumptions based on your prior knowledge to help model the data you have now. 

For example, if you know from in vitro experiments the Bmax for the binding protein
and Kd for the unbound drug then you can predict both the bound and the unbound
concentrations from total drug concentration. With this assumption about the binding
model and its parameters then you have enough information to model the time course
of the total drug concentration and estimate the model parameters for bound and unbound drug. 

Note that with this assumption your model is a priori identifiable but the a posteriori
identifiability and imprecision and bias of the parameter estimates will depend on the
design of your experiment and the error properties of your assay. 

It is quite possible (indeed certain) that the biology is more complex than the simple
binding model I have described. However, my suggestion to you is not to ignore work
that has preceded your study but to use whatever knowledge you can find to learn more
about the system.

Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand tel:+64(9)373-7599x86730 fax:373-7556