modeling compartments within compartments

From: rjames@rhoworld.com 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 compartments. Can I model the drug observations as the combined total drug from two compartments? 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) rjames@rhoworld.com

From: bachmanw@globomax.com 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.

From: n.holford@auckland.ac.nz Subject: RE: [NMusers] modeling compartments within compartments Date: 10/13/2003 2:08 PM Robert, 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 -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ ______________________________________________________